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Project No. UNB01 Value to Wood Project Research Report 2009

Development of Advanced System Design Procedures for the Canadian Wood Design Standard

by

Andi Asiz, Ying Hei Chui, Ian Smith and Lina Zhou

Wood Science and Technology Centre Faculty of Forestry and Environmental Management

University of New Brunswick, Fredericton

This report was produced as part of the Value to Wood Program, funded by Natural Resources Canada

June 2009

UNB01 Development of Advanced System Design Procedures ii

Executive Summary The current design of light-frame wood structures (LFWS) is largely performed on an element-by-element basis, neglecting the overall behaviour of the structural system. Forces on the components and substructures are calculated by simplified analysis methods, ignoring the fact that most structures are three-dimensional systems comprising a number of interacting parts. It is generally assumed that existing simple approaches are conservative and lead to over-designed elements and connections, and in turn stifle innovations in design practice and the introduction of innovative structural products to the marketplace. The goal of this project is to develop a system design methodology for engineered light-frame wood construction that can be incorporated into the Canadian design standard, CSA O86-01 ‘Engineering design in wood’. The expected benefit of the system design method over the traditional single-element design method is more economical design solutions that will improve the competitive position of wood as a structural material, and increase wood’s market share in non-residential construction. The focus of this project was on engineered LFWS consisting of wood diaphragms, wood shear walls and wood roof trusses, inter-connected through nail or metal connector to perform as a 3-dimensional structural system. The main vehicle in this study was an extensive 3-D numerical modeling of LFWS. A few typical structural forms of LFWS were identified as studied structures in this project. The models were used to analyse the responses of these structures subjected to wind and earthquake loads. Specific activities included: (1) review of technical literatures on 3-D numerical models of LFWS subjected to wind and earthquake loads; (2) development of 3-D numerical models of LFWS; (3) testing of connection components in LFWS; (4) full-scale testing of simple LFWS subjected under real wind load; and (4) development of system reliability analysis. From the 3-D numerical modeling of one- and two-storey LFWS subjected to high wind load, the critical component is in the roof-to-wall connections fastened using toe-nails. Load redistribution in the toe-nail connections was also observed when one or more toe-nails have already reached their peak load, while the applied wind load is increased. Based on the structures analysed in this project, it was found that the critical wind speed causing failure in the roof-to-wall connections was 125 mph. This corresponds to Category 4 (131-155mph) of commonly used Saffir-Simpson Hurricane Scale. Strengthening the roof-to-wall connection using hurricane metal connector led to an increase in the critical wind speed and a shift in failure mechanism from roof-wall connection to other parts of LFWS. Current analytical methods to calculate lateral force distribution to the walls could lead to either conservative or unconservative results depending on structural details. Based on the reliability analysis of one-storey LFWS under seismic load, the reliability of the whole structural system is higher than that of an isolated wall component, indicating system effect. Practical design implication and impacts/benefits to the wood industry resulting from findings of this project include: identification of major technical issues that need to be addressed if system design factors for shear walls and diaphragms are to be developed for CSAO86; and creation of technical databases for 3-D numerical model of LFWS and for connection properties. Future work should be developed based on these databases to answer what if scenarios in engineering design of LFWS.

UNB01 Development of Advanced System Design Procedures iii

Acknowledgements

The University of New Brunswick acknowledges the financial support of this project by Natural Resources Canada under the Value-to-Wood Program. Thanks are due to Kenneth Koo (formerly of Jager Building Systems), Dominique Janssens (formerly of the Structural Board Association), and industry liaison Peggy Lepper (Canadian Wood Council) for their support and technical advice.

Research Staff

• Dr. Y.H. Chui, Project Leader • Dr. Andi Asiz, Research Associate • Dr. Ian Smith, Technical Research Advisor • Dr. Frank Lam (UBC), Research Partner • Dr. Mike Bartlett (UWO), Research Partner • Lina Zhou, Graduate Student Research Assistant • Nannan Zhou (Tongji University), Visiting Graduate Student • Tshering Wangmo, Graduate Student Research Assistant (part-time) • Donny Johnston, Technician • Andrew Sutherland, Technician

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List of Tables

Table 2.1: Classification of members, subsystems, and systems......................................................... 10 Table 5.1: Mechanical properties used in the analysis (Mi 2004; Winkel 2006) ......................... 23 Table 5.2: Link element properties used in the analysis............................................................... 24 Table 5.3: Wind pressure distribution (v=100 mph)..................................................................... 26 Table 5.4: Critical wind speed ...................................................................................................... 32 Table 5.5: Critical wind speed for structures strengthened with hurricane tie ............................. 33 Table 5.6: Lateral force distribution to the walls.......................................................................... 36 Table 5.7: Lateral force distribution (tributary area method/simple beam method vs 3-d

numerical model) .................................................................................................................. 40 Table 5.8: Lateral force distribution (continuous beam method vs 3-d numerical model)........... 40 Table 5.9: Lateral force distribution to the walls (relative stiffness method without torsion vs 3-d

numerical model) .................................................................................................................. 41 Table 5.10: Lateral force distribution to the walls (rigid beam on elastic foundation vs 3-d

numerical methods)............................................................................................................... 41 Table 6.1: Roof-to-wall toe nail connection ................................................................................. 46 Table 6.2: Data points used as input for numerical modeling ...................................................... 48 Table 6.3: Test result..................................................................................................................... 50 Table 6.4: Data points as input for numerical modeling............................................................... 51 Table 6.5: Test result..................................................................................................................... 53 Table 6.6: Data points as input for numerical modeling............................................................... 54 Table 7.1: Average of the airbag pressure (kPa) taken over 0.9 second prior to observed

peak/failure load.................................................................................................................... 62 Table 7.2: Testing stages............................................................................................................... 64 Table 7.3:Wind speed vs reaction (R1)......................................................................................... 71

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List of Figures

Figure 2.1: Wood structural system.............................................................................................. 10 Figure 4.1: 2-D frame model of the FPS test house (Nateghi, 1988) ........................................... 13 Figure 4.2: Rigid floor diaphragm model of a single story LFWB (Folz and Filiatrault, 2004) .. 14 Figure 4.3: Degrees of freedom for LFWB model by Gupta and Kuo (1987) ............................. 15 Figure 4.4: Modeled test building developed by Tarabia (1994).................................................. 16 Figure 4.5: 3-D model from Kasal (1992) .................................................................................... 17 Figure 4.6: Wall model and inter-component connection model (Kasal, 1992; Kasal et al, 1994)

............................................................................................................................................... 17 Figure 5.1: One-storey structure ................................................................................................... 21 Figure 5.2: Two-storey structure................................................................................................... 22 Figure 5.3: 3-D FE model of the one-storey building................................................................... 23 Figure 5.4: 3-D FE model of two-storey building ........................................................................ 24 Figure 5.5: Wind load distribution based on ASCE 7-05 ................................................................... 25 Figure 5.6: Load-deformation response for selected wall-to-roof toe-nail connections............... 27 Figure 5.7: Axial force in toe-nail connections of one-storey structure with internal partitions. 28 Figure 5.8: Resultant displacement contours for one-storey with partitions (a) and without

partitions (b).......................................................................................................................... 29 Figure 5.9: Axial force distribution in the toe-nail connections for Model B. ............................. 29 Figure 5.10: Displacement responses ........................................................................................... 30 Figure 5.11: 3-D roof structure ..................................................................................................... 30 Figure 5.12: 2-d roof truss analysis............................................................................................... 31 Figure 5.13: wind speed vs uplift load based on the simple 2-d roof truss analysis..................... 31 Figure 5.14: Example of hurricane metal connector (Simpson Strong Tie) ................................. 33 Figure 5.15: Assigned hurricane ties stiffness (uplift direction) {Did you use uplift data to scale

the lateral data. } ................................................................................................................... 33 Figure 5.16: Force distribution in the wall components due to wind load .................................. 35 Figure 5.17: Layout of the structures with varying wall partitions locations ............................... 38 Figure.5.18: Various analytical methods to obtain lateral load distribution to walls .................. 39 Figure 6.1: Connection modeling process .................................................................................... 44 Figure 6.2: Roof-to-wall toe-nail connection test ......................................................................... 45 Figure 6.3: Average load-slip curve for roof-to-wall connection. ................................................ 47 Figure 6.4: Interior-to-exterior walls connection.......................................................................... 49 Figure 6.5: Average load-slip curve for interior-to-exterior walls connection............................. 50 Figure 6.6: Testing of wall-to-floor connection............................................................................ 52 Figure 6.7: Average load-slip curve of wall-to-floor connection. ................................................ 53 Figure 6.8: Failure observed in wall-floor connection.................................................................. 54 Figure 6.9: 3-D finite element analysis......................................................................................... 55 Figure 6.10: Selected connection response................................................................................... 56 Figure 7.1: Test concept................................................................................................................ 58 Figure 7.2: Test structure .............................................................................................................. 60 Figure 7.3: Loading system using pressure loading actuator (PLA) ............................................ 61 Figure 7.4: Wind pressure time history used ................................................................................ 61 Figure 7.5: Airbags distribution.................................................................................................... 62

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Figure 7.6: Placement and numbering of the LVDTs and load cells............................................ 63 Figure 7.7: Hurricane ties used in the test..................................................................................... 64 Figure 7.8: Failure mechanism for Test #1................................................................................... 66 Figure 7.9: Wind speed vs deformation at toe-nail connection .................................................... 66 Figure 7.10: Failure mechanism for Test #2................................................................................. 67 Figure 7.11: Failure mechanism for Test #3................................................................................. 67 Figure 7.12: 3-d FE model of the test structure ............................................................................ 68 Figure 7.13: Total base reaction forces......................................................................................... 69 Figure 7.14: Deformation at the corners ....................................................................................... 69 Figure 7.15: Toe-nail connection responses ................................................................................. 70 Figure 7.16: Simply supported roof-joist under wind load and corresponding estimated axial load

’test’ value (R1, maximum uplift reaction force) ................................................................. 71

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Table of Contents Executive Summary ........................................................................................................................ ii Acknowledgements........................................................................................................................ iii Research Staffs............................................................................................................................... iii List of Tables ................................................................................................................................. iv List of Figures ................................................................................................................................. v Table of Contents.......................................................................................................................... vii 1 Objectives ............................................................................................................................... 9 2 Introduction............................................................................................................................. 9 3 Methodology......................................................................................................................... 11 4 Literature review of 3-d numerical modeling of LFWS ....................................................... 12

4.1 Background................................................................................................................... 12 4.2 Degeneration of 3-D structure into 2-D model ............................................................. 12

4.2.1 Simple 2-D frame (under wind load) .................................................................... 12 4.2.2 Rigid horizontal diaphragm (under earthquake load) ........................................... 13

4.3 3-D diaphragm elements assembly ............................................................................... 14 4.4 Full 3-D model representation ...................................................................................... 16 4.5 Failure modes................................................................................................................ 18 4.6 Concluding remarks ...................................................................................................... 19

5 3-D numerical model of LFWS ............................................................................................ 20 5.1 Background................................................................................................................... 20 5.2 LFWS to analyse........................................................................................................... 20 5.3 Detail structural model.................................................................................................. 22 5.4 Wind load...................................................................................................................... 25 5.5 Post-yielding and failure analysis ................................................................................. 26 5.6 Investigation of system effects...................................................................................... 28

5.1.1 Critical wind speeds for various structural system configuration......................... 30 5.1.2 Effect of strengthening using hurricane metal connectors.................................... 32 5.1.3 Effect of varying internal wall locations............................................................... 34

5.4 Concluding remarks ...................................................................................................... 41 6 Test of connection components in LFWS............................................................................. 43

6.1 Background................................................................................................................... 43 6.2 Roof-to-wall connection ............................................................................................... 44

6.2.1 Test description..................................................................................................... 44 6.2.2 Test results ............................................................................................................ 46

6.3 Interior-to-exterior walls connection ............................................................................ 48 6.3.1 Test description..................................................................................................... 48 6.3.2 Test result.............................................................................................................. 49

6.4 Wall-to-floor connection............................................................................................... 51 6.4.1 Test description..................................................................................................... 51 6.4.2 Test result.............................................................................................................. 52

6.5 Numerical modeling implication .................................................................................. 55 6.5.1 3-D structural model ............................................................................................. 55 6.5.2 Connection response ............................................................................................. 56

UNB01 Development of Advanced System Design Procedures viii

6.6 Concluding remarks ...................................................................................................... 57 7 Full-scale test of LFWS ........................................................................................................ 58

7.1 Background................................................................................................................... 58 7.2 Overview of test program ............................................................................................. 59

7.2.1 Test specimen description..................................................................................... 59 7.2.2 Loading and instrumentation ................................................................................ 60 7.2.3 Test sequences ...................................................................................................... 64 7.2.4 Test results ............................................................................................................ 65

7.3 3-d numerical model ..................................................................................................... 67 7.3.1 Model description ................................................................................................. 67 7.3.2 Test results vs model............................................................................................. 68 7.3.3 Load-deformation at the toe-nail connections ...................................................... 69

7.4 Discussion..................................................................................................................... 71 7.5 Concluding remarks ...................................................................................................... 71

8 3-d numerical model of LFWS under earthquake (dynamic) load ....................................... 72 9 System reliability analysis .................................................................................................... 73

9.1 Design procedure in steel structure............................................................................... 73 9.2 Design of LFWS ........................................................................................................... 75 9.3 Concluding remarks ...................................................................................................... 76

10 Conclusions....................................................................................................................... 78 References..................................................................................................................................... 80 Appendix A: Critical wind speeds and toe-nail force distributions of the LFWS studied ........... 83 Appendix B: Detail calculation using analytical method of the lateral force distribution due to wind load....................................................................................................................................... 86 Appendix C: Test results of the toe-nail connection..................................................................... 99 Appendix D: Test of roof-to-wall connection with hurricane metal connector.......................... 103 Appendix E: 3-d numerical model of LFWS under earthquake load ......................................... 108

UNB01 Development of Advanced System Design Procedures 9

1 Objectives The goal of this project is to develop a system design methodology for engineered light-frame wood construction that can be incorporated into the Canadian design standard, CSA O86-01 ‘Engineering design in wood’. The expected benefit of the system design method over the traditional single-element design method is more economical design solutions that will improve the competitive position of wood as a structural material, and increase wood’s market share in non-residential construction. The planned specific objectives of this project were:

1. To develop potential design provisions for engineered light-frame wood buildings that recognize that these structures behave as 3-dimensional systems, and not as an assembly of structural elements.

2. To provide a framework for future system design provisions for other types of structural wood systems, like heavy frames.

3. To help substantiate that the performance of non-engineered wood frame buildings covered by Part 9 of the National Building Code of Canada is acceptable.

2 Introduction The current design of light-frame wood structures is largely performed on an element-by-element basis. This in essence ignores the fact that most structures are three-dimensional systems comprising a number of structural elements connected together to resist the applied load. Engineers generally design a structure by distributing the design loads using relatively simple, and yet conservative rules, to an individual element or connection. The element or connection is then ‘sized’ to resist the distributed load using engineering mechanics principles, and on the assumption that the structure as a whole fail if a single element or connection reaches one of its limiting states. This is generally thought to lead to conservative design solutions and stifles innovation in design solutions and structural products. It is expected that timber design codes will gradually move towards recognizing system effects. For light-frame wood structures (LFWS), which is the focus of this project, system effects arise from the following:

1. Load combination effect – loads act simultaneously in different directions, some of these have a counteracting whereas others have cumulative effect.

2. Numerous load paths – loads from one element are often transferred to other elements through a few load paths resulting in load sharing.

3. Redistribution of applied load – when certain elements or connections yield or fail, there is a redistribution of loads within a structure through various load paths (note: to account for this effect, there is a need to define system failure and for code committee to accept that yielding of some elements does not constitute system failure).

4. Statistical variations in resistive capabilities of systems versus isolated components. 5. Size of system effects on the energy required to fail components embedded within

systems. An issue that is coupled to execution of this project is that the basis on which the resistance side of LRFD equations in the current Canadian timber design code (CSA Standard 086-01) were


calibrated does not match the basis of the loading side of the same LRFD equations as given in the 2005 edition of the National Building Code (NBC) of Canada. The present project should adopt approaches that harmonize with the NBC methodology. Definition of structural systems depends on the idealization of how the physical system behaves and the loading conditions involved. Complete (whole) structural systems are three-dimensional forms created by assembling structural elements (components) and structural subsystems (subassemblies). Table 2.1 illustrates the classifications for members, subsystems, and systems commonly used in steel structures (Kulak et al, 1995; Salmon, 1996).

Table 2.1: Classification of members, subsystems, and systems

element subsystem system

columns floors 2D/3D frames (braced/unbraced) beams walls space trusses beams-columns roofs shells/folded plates connections grids tensile/compressive systems

cables foundation combination systems Achieving consistency in design solutions, and in how buildings will perform, depends on a clear definition of the levels of classification and how design practices at each level fit together. Figure 2.1 illustrates the definition of system, subsystem, and member/component in light-frame wood structure.

Figure 2.1: Wood structural system Design at the element level normally involves choices of the material and its arrangement. Design at the subsystem level requires decisions to be made regarding the types and arrangement of elements, and connection concepts for attachment to the rest of the system. Design at the system level involves choice between viable structural forms and between an infinite number of possible combinations of subsystems and elements. It is usually oriented towards optimum total system performance. System based design contrasts with element-by-element design wherein

Member/component

Sub-structure/sub-system

SystemMember/component

Sub-structure/sub-system

System


sufficiency of all elements is presumed to ensure that performance of a completed system built with those elements will be adequate. It is not expected that design engineers will embrace the use of 3D structural analysis program to account for system effects, beyond performing standard 3D elastic analyses to estimate the factored internal design forces in various components of systems. Rather, it is felt that the initial attempt to include system effect should focus on the development of a system factor, analogous to the system factor for repetitive member designs, that can be added to the current design equations for structural elements such as shear walls. Therefore the deliverable of this project will be the derivation of a system factor that can be applied to element designs that accounts for the 3 factors listed above. To be efficient this will require the creation of categories of systems, because taking the lowest common denominator approach will undoubtedly be grossly conservative. 3 Methodology The main vehicle in this study was an extensive 3-d numerical modeling of LFWS. A few typical structural forms of LFWS were identified as studied structures in this project. The models were used to analyse the responses of these structures subjected to wind and earthquake loads. Through this project the project team expected to achieve a better understanding of the following:

1. Load paths through typical light-frame wood structures, and how these load paths are affected by construction details.

2. Load paths when redistribution of loads occurs after yielding of selected elements. 3. Definition of failure in light-frame systems, with recognition that critical failure states

will differ between types of loadings (e.g. wind, seismic design). Specific activities included:

• Review of technical literatures on 3-D numerical model of LFWS subjected to lateral loads (wind and earthquake).

• 3-d numerical models of LFWS using finite element analysis to investigate structural system response under various structural configurations.

• Testing of connection components for creation of technical database and for 3-D numerical modeling input.

• Full-scale testing of simple LFWS subjected under real wind load to understand failure processes and to improve and validate the 3-D numerical models.

• Development of system reliability analysis


4 Literature review of 3-D numerical modeling of LFWS 4.1 Background Development of 3-D numerical models of light-frame wood structures (LFWS) is one of the important steps in this project. An ideal numerical model should be capable of predicting structural performance indicators of a building at multi-scale level (members, subsystems, and complete system) including strength, deformation, ductility, mode of failure(s), and load redistribution (in case of failure of one or more members). The main objectives of this activity are:

• to collect information from technical literature regarding development of 3D numerical models of LFWS.

• to identify numerical modeling strategy that can be applied in this project. • to study possible modes of failure in LFWS under wind loading

During the last few decades there have been many numerical models of LFWS developed. Most of these models are based on the finite element (FE) method. Early LFWS models were usually over-simplified and limited to static and linear elastic analyses and implemented into specially developed (in-house) FE programs. Efforts have been made recently to develop LFWS models capable of predicting nonlinear and dynamic behaviours using either extensive FE programming (coding) or application of advanced commercial FE software or combination of both (via user-defined elements). In general, the modeling efforts of LFWS can be categorized as follows:

• degeneration of 3-D structure into 2-D model • development of 3-D structure from diaphragm element assembly • development of full 3-D representation (via commercial FE software)

Discussion for each modeling feature is described below using examples of existing models. This includes reviewing modeling principle assumptions, verification results, limitations, and extended applicability. Also, possible failure mode of LFWS is briefly discussed. 4.2 Degeneration of 3-D structure into 2-D model

4.2.1 Simple 2-D frame (under wind load) One of the earlier work of modeling simple LFWS subjected to static and lateral (wind) load was conducted at the University of Missouri at Columbia (Nateghi, 1988). The work involved modeling actual LFWS tested at the US Forest Product Laboratory (Tuomi and McCutcheon, 1974). The model was a degeneration of 3-D structure into 2D frame structure (Figure 4.1). Each member of the structure was modeled as a beam element with a rotational spring at each end. The stiffness of the rotational springs was determined from the moment-rotation curve obtained from joint tests taking into account only linear part of the load-deformation response curve (linear-elastic behaviour). The diaphragm action was incorporated into the model by a set of cross bars with elastic properties determined from the full-scale test. These bars are modeled as tension element or spring-like element with pin connections at the ends. The main loading types


considered in that study were static and wind loads calculated based on the applicable building code at that time (ANSI A58.1). No extended model verification was conducted. The model was used mainly to identify weak link element in a building under wind load. It was concluded that connections were the weakest parts of the structure. Attempts were made to compare the model with other models developed elsewhere during that time (e.g. WSU model, NCSU model). Since the procedure for determining connection properties and the loads applied were different amongst the researchers, no definitive conclusions were made with respect to the detailed numerical results (e.g. deformations, forces). It is clear that the model developed by Nateghi (1984) can only be applied to 2-D cases with gravity and wind as major loads. To be applicable for earthquake load, non-linear behaviour of joints and diaphragm actions are needed in addition to new modeling strategy to account for the effect of unsymmetrical (torsional) response of the building.

Figure 4.1: 2-D frame model of the FPS test house (Nateghi, 1988)

4.2.2 Rigid horizontal diaphragm (under earthquake load) Folz and Filiatrault (2004a) developed a simple numerical model for LFWS as part of a CUREE (Consortium of Universities for Research in Earthquake Engineering) wood frame project. In that model, the actual 3D building structure is degenerated into a 2-D planar structure composed of non-linear lateral load resisting shear wall spring elements that connect the rigid floor and roof diaphragms together or to the foundation (Figure 4.2). In modeling of the building, the diaphragms were assumed to have sufficiently high in-plane stiffness to be considered as rigid elements. To maintain this assumption, the planar aspect ratio should be in the order of 2:1. By this approach the global response of the building can be represented by only three degrees of freedom. Each of the shear wall spring element properties (strength, stiffness degrading hysteretic behaviour) was determined from a detail numerical analysis of shear wall subsystem or from shear wall test data. A specific FE program was written to solve the global degrees of freedom and dynamic response of a building. The model developed in that study was verified using experimental results


obtained from shake table test performed on a full-scale two-storey wood frame house (Foltz and Filiatrault, 2004b). It was shown that the model predictions were in good agreement with the test results in terms of the dynamic characteristics and seismic response of the building. The numerical model developed was efficient and can be a fast numerical tool to analyze global response of LFWS subjected to earthquake load. This is because a minimum number of input parameters (three degrees of freedom for each storey, limited number of wall spring properties) are required in the FE program making it quicker to solve non-linear equation and dynamic equations. However, the major limitation of this model is that it cannot handle analysis of important construction details such as connections, making it difficult to identify weakest members or components in the building structure.

Figure 4.2: Rigid floor diaphragm model of a single story LFWB (Folz and Filiatrault, 2004) 4.3 3-D diaphragm elements assembly LFWS is usually an assembly of several wood diaphragms such as vertical shear wall diaphragms, horizontal floor and ceiling diaphragms, and inclined roof diaphragms connected together along their edges. Accurate modeling of diaphragm and inter-diaphragm (inter-component) connections is crucial to obtaining accurate 3-D structural response. In this type of modeling, ‘super-elements’ (macro-elements) are formulated based on the basic behaviour of diaphragm subjected to various possible loads. One of the early models on 3-D LFWS assembled using diaphragm elements was developed by Gupta and Kuo (1987), Figure 4.3. They used the test data obtained by Tuomi and McCutcheon (1974) to verify the models. The super-element developed was based on the laterally loaded shear wall model that included the shear deformation, uplift, and rotation of the sheathing as local degrees of freedom. This super-element was used to represent the shear walls, flange walls, floor, roof, and ceiling. A limited number of global degrees of freedom (vertical and horizontal displacements) were identified and used in the analysis (Figure 4.3). To solve for these displacements, a simple matrix structural analysis was performed after applying appropriate boundary and compatibility conditions along the edges and corner nodes of each diaphragm. The verification results showed that the models generate results that were in good agreement with test measurements. However, the model was applicable only to small deformation within the linear elastic range under static lateral load and could not predict the entire load-displacement response.


Tarabia (1994) extended diaphragm elements application to include non-linear and dynamic analyses. In that study, the building was modeled as an assembly of diaphragm elements that are connected by inter-component connection elements (Figure 4.4a). The diaphragm elements were used to represent shear walls, floor, and roof and consist of several framing, sheathing, fasteners, framing connector, and sheathing interface elements (Figure 4.4b). A general assumption used in the modeling of diaphragm elements was that fasteners were the only source of non-linearity and that the sheathing and framing materials were linear elastic. The fastener element was modeled as decoupled spring system joining the sheathing and the framing elements. To accommodate building openings, different displacement field was derived in the FE formulation. An in-house FE program was written specifically for theat study. An extensive model verification was conducted using other FE models and available experimental data. The verification result showed that the models provide reasonable predictions of responses of shear wall subjected to dynamic load and LFWS subjected to quasi-static load (Tarabia and Itani, 1997).

Figure 4.3: Degrees of freedom for LFWB model by Gupta and Kuo (1987)

v1

v2

u3

u4u5u2

u1

Load

v1

v2

u3

u4u5u2

u1

Load

u = global horizontal displacementv = global vertical displacement


(a) 3-D diaphragm assembly (b) components of a diaphragm element

Figure 4.4: Modeled test building developed by Tarabia (1994)

4.4 Full 3-D model representation Development of commercial FE software has made complex 3-D modeling of LFWS easier to implement. There has been concern though about utilizing software package because of limited necessary elements in the package to efficiently and accurately model the materials and connections in LFWS, which behave differently from those in structures built with other common structural materials such as reinforced concrete and steel. However, advanced FE package usually offers a special user-defined routine (algorithm) to accommodate this deficiency. Recent FE packages have even incorporated more routines (e.g. connection behaviour, dynamic response, nonlinear response), which were previously developed using in-house FE program or user-defined subroutine elements. Kasal (1992) developed a 3-D model using FE package ANSYS to analyze a one-storey LFWS tested at Washington State University by Phillips (1990), Figure 4.5a. In the model, the structure was assembled using linear super elements (floor and roofs) and quasi-shear wall super-elements, Figure 4.5b. The quasi-super-elements comprised of beam, truss (bar), and shell elements, as well as a hypothetical nonlinear diagonal spring element whose characteristic was determined from experimental shear wall test data and detailed numerical modeling of shear wall (Figure 4.6a). The inter-component connections connecting various super-elements and quasi super-elements were modeled as non-linear one-dimensional spring elements with the properties determined from small-scale joint tests. The model was verified using data from actual test building loaded under monotonic load applied to the top corner of each shear wall. In general, the model showed that the overall response of the system is non-linear with some of the substructures retaining a linear response and others responding nonlinearly. This was in accordance with the test observation. However, a major model limitation was that the model could not accommodate the strength degradation when the structure was reloaded, which is important in dynamic analysis. Also, the model was limited to decoupled behaviour of the shear


wall diagonal spring between in-plane and out-of-plane deformation. From a practical point of view, using the developed model requires a large number of shear wall tests to be conducted, since the nonlinear characteristic of the diagonal spring element was needed for each wall component in the building. Recently, the model developed by Kasal’s group in the early 1990’s was updated to overcome the issue in dealing with dynamic analysis (Collins et al, 2005a). The model developed was experimentally validated based on local and global response, energy dissipation in connections, and load path distribution using data from a test building constructed in Australia (Collins et al, 2005b). It was noted that the model predicts higher order response parameters such as energy dissipation more accurately than load or displacement.

(a) tested building (Phillips, 1990) (b) 3D FE mesh of the building

Figure 4.5: 3-D model from Kasal (1992)

(a) wall model (b) intercomponent connections Figure 4.6: Wall model and inter-component connection model (Kasal, 1992; Kasal et al, 1994)

Beam/frame elements

Plate element

Nonlinear spring

Beam/frame elements

Plate element

Nonlinear spring


4.5 Failure modes As mentioned earlier, a good numerical model of LFWS should be equipped with an algorithm that can predict failure modes and associated failure load. Understanding failure behavior is also important for system reliability analyses, which will be need to be addressed before system design provisions are implemented in Canadian timber design code. Many observations of the failure modes of light-frame wood buildings have been made using historical performance and various laboratory and experimental studies of the actual damage. In general, the failure modes generated are dependent on the types of external load applied. For example, lateral loads produced from wind and earthquake would produce different failure mechanisms in that wind load is proportionally applied to the exposed surface of the building; whereas earthquake load is inertial forces resulted from the deformation produced by the earthquake motion and lateral resistance of the structures. However, in general the typical failure mode in LFWS subjected to lateral load can be categorized as follows: wall nailed connection failure, hold-down anchorage and roof connection failures, and buckling of sheathing, Figure 4.7. Figure 4.7: Wall model and inter-component connection model (Kasal, 1992; Kasal et al, 1994) The failure of the wall nailed connections is the most common type of failure of LFWS and probably the most dominant mode of failure. Generally, nails are pulled out of sheathing and framing or the sheathing is punched out by the nails. In conjunction with numerical model, actual force and deformation in the nails due to external load can be used as numerical indicator to determine whether nail design capacity is exceeded (Yoon, 1991). However, one failed nail member does not necessarily lead to system failure because of possible load redistribution to adjacent members. Some failure definition could be used to identify system failure (e.g. failure of three adjacent nail members). Both wind and earthquake loads can cause hold-down anchorage and roof connection failures. Typical failure is usually excessive shear or axial load developed on the connector or anchorage causing total separation or disintegration between substructures (wall-roof or wall-foundation). Severe damage to hold-down anchorage can be resulted from a building subjected to earthquake accompanied by a strong vertical motion (Liska and Bohannan, 1973). Again this anchorage failure could be used to define system failure.

Roof connections

Hold down anchorage

Wall connection nails

Buckling sheathing panels

Roof connections

Hold down anchorage

Wall connection nails

Buckling sheathing panels


Buckling of sheathing panel is a possible for LFWS with thin sheathing and large opening. This is mainly caused by large stress concentration around the corner of opening leading to loosening of nail withdrawal resistance around that area after several reversed cycle of loading. Fracture of plasterboard around opening can also be used as indication that there is buckling of sheathing failure (Patton-Mallory, 1985). The numerical parameters that can be used to indicate this type of failure is stress distribution around the corners in addition to load-deformation behaviour of nails. 4.6 Concluding remarks From the review of numerical models of 3-D LFWS it can be concluded that:

• Degeneration of 3-D structure into 2-D model would not be suitable to implement in this project. This is because many structural details (connections, members) would be missed in the analysis making it difficult to predict failure of structural system.

• Development of 3-D LFWS model assembled using super-elements (macro-elements) can be performed in this project. However, since this work will involve extensive computer programming (coding), developing the numerical FE procedure from ‘scratch’ would not be practical, since the project time frame is limited.

Application of commercial FE software package to construct 3-D LFWS would be an efficient way to achieve the project objectives provided that the package is equipped with necessary element library or facility to incorporate user-defined subroutines.


5 3-D numerical models of LFWS 5.1 Background Light-frame wood structures (LFWS) represent the most commonly constructed residential buildings in North America. LFWS are normally assembled from several substructures such as walls, floors and roofs. The substructures consist of simple framing members of dimension lumber sheathed with nailed-on wood-based panels such as Oriented Strand Board (OSB) and plywood. This type of structure is well known to have excellent ability to withstand short-term extreme loads, such as those caused by earthquakes and strong wind. This is due to its highly redundant structural form and the use of slender fasteners in connecting components together. Structural redundancy offers alternative load paths and redistributes applied loads when one member or connection fails. Slender fasteners such as nails fail by plastic yielding and therefore are a major source of energy absorption under extreme loads. These factors allow LFWS to exhibit some level of damage and undergo large deformation without collapse. The current design procedure sizes components and substructures on an element-by-element basis, neglecting the overall behaviour of the structural system. Forces on the components and substructures are calculated by simplified analysis methods, ignoring that most structures are three-dimensional systems comprising a number of interacting parts (CWC 2004). It is generally assumed that this simplified approach is conservative and leads to over-designed elements and connections, and that in turn stifles innovations in design practice and the introduction of innovative structural products to the marketplace. To understand load distributions, internal force flows and failure mechanisms of LFWS it is necessary to study complete three-dimensional (3-D) building systems. This project used finite element models to help us achieve this understanding, with a particular emphasis on wind loads. A parallel study on response under seismic load is presented in Appendix E. As failure in LFWS is likely to occur in connections between sub-systems, such as wall, roof and floor, modelling appropriate connection behaviour in the numerical models is a crucial step in this exercise to obtain appropriate structural system response. To achieve this goal, a connection test program (which will be reported in Chapter 6 of this report) was conducted to obtain the complete load-deformation response, including strength and stiffness degradation, of these connections, which was used as input into the finite element program. The failure analysis is normally started with identification of the location of first failure in these structures and how the applied loads would be re-distributed to adjacent components after progressive failure of structural elements or connections. 5.2 Analysis of LFWS In this project, typical one and two storey LFWS’s were selected to be studied. Selection of the structural members and other components was based on construction guidelines from the Canada Mortgage and Housing Corporation (CMHC 2003). Layouts and elevations of the structures are shown in Figures 5.1 and 5.2. The arrangement followed the so-called platform frame


construction method wherein a floor platform is constructed to extend fully beneath all walls and above a perimeter supporting foundation wall.

(a) floor layout (b) side view elevation

(c) elevation

Figure 5.1: One-storey structure

28’

8’

4’-8”

28’

8’

4’-8”

28’

8’

4’-8”

8’

28’

8’

4’-8”

8’

42’

8’

3’-8”

42’

8’

3’-8”


(b) layout –second storey (b) side view

(c) elevation

Figure 5.2: Two-storey structure 5.3 Detailed structural models Commercial finite element (FE) software SAP2000 version 11 (CSI 2007) was used to model the structures shown in Figures 5.1 and 5.2. In this section, the modelling technique is described using the one-storey structure as an illustration. The same modelling technique applies to the two-storey structure. Linear-elastic orthotropic shell elements were used to model the sheathing panels in the walls, roof and floor plate. Those elements had four nodes with six degrees of freedom at each node. Wall studs, floor joists, and roof truss framing members were modelled using two-node linear frame elements with six degrees of freedom at each node. Roof rafter and tie members were made continuous within their length with hinge joints at apex and heel connections. Interior truss members were hinge-connected to rafters and the tie. Internal wall partitions were connected to the floor framing and exterior wall framing, but they were not connected to the roof framing. Mechanical properties and element types used are given in Table 5.1, with mechanical properties taken from previous thesis projects at the University of New Brunswick (Mi 2004; Winkel 2006). All nailed sheathing-to-framing and framing-to-framing connections were modelled using non-linear link elements composed of internal springs with axial, shear and rotational degrees of freedom. Figure 5.3c shows typical modelling of connections at a corner junction where walls and the roof meet. A 3mm gap was maintained between wall sheathing panels to simulate practice in construction, Figure 5.3d. Properties of the link elements for each degree of freedom were derived from experimental load-deformation responses and are summarised in Table 5.2. Boundary conditions at the base of exterior walls were modelled using non-linear contact-link elements with zero lengths in combination with spring elements, spaced at 2.44 m (8 ft), to


represent anchor bolts connecting to the foundation. Only the outside face of exterior walls was sheathed with OSB. Modelling of door and window openings included framing modifications that are typical of building practice (CMHC 2003), but no attempt was made to model doors, windows, or their frames and glazing. No plasterboard wall was incorporated into the model, but incorporating plasterboard ceiling would be conducted to investigate additional rigidity of the roof system. In total the finite element mesh generated to analyse the one-storey building comprises 11,539 nodes, 5,348 frame elements, 6,218 shell elements, and 4,294 link elements. Figure 5.4 shows the mesh for the two-storey building.

(a) whole building (b) external and internal walls

(c) corner details (d) wall panel-to-wall panel and wall-to-roof model

Figure 5.3: 3-D FE model of the one-storey building

Table 5.1: Mechanical properties used in the analysis (Mi 2004; Winkel 2006)

Modulus of elasticity (MPa)

Poisson’s ratio Shear modulus (MPa)

Element (mm)

Element type & thickness (mm)

Ex (Dir 1)

Ey (Dir 2)

Ez (Dir 3)

Dir 1-2

Dir 1-3

Dir 2-3

Dir 1-2

Dir 1-3

Dir 2-3

38x140 wall studs

Frame (38)

12000 900 500 0.3 0.3 0.3 900 700 50

OSB wall sheathing

Shell (11.1)

3000 5000 3000 0.3 0.3 0.15 1200 1700 1200

OSB roof Shell 3000 5000 3000 0.3 0.3 0.15 1200 1700 1200

Roof sheathing

Exterior walls

Link elements for nail joints model

Roof sheathing

Exterior walls

Link elements for nail joints model

Roof sheathing Link element for roof-to-wall joint model

Gap between wall panels

Top plate

Roof sheathing Link element for roof-to-wall joint model

Gap between wall panels

Top plate


sheathing (11.1) OSB floor sheathing

Shell (15.9)

3000 5000 3000 0.3 0.3 0.15 1200 1700 1200

38x235 floor joists

Frame (38)

12000 900 500 0.3 0.3 0.3 900 700 50

38X89 truss framing

Frame (38)

12000 900 500 0.3 0.3 0.3 900 700 50

Table 5.2: Link element properties used in the analysis Link element Direction Assigned stiffness

(load-deformation response) Horizontal Non-linear shear stiffness from connection tests by Mi (2004) Sheathing-to-

framing nails Vertical Non-linear shear stiffness from connection tests by Mi (2004) Horizontal Non-linear shear stiffness from connection tests by Mi (2004) Vertical

Compressive mode, linear stiffness = 106.8 kN/mm (Winkel 2006)

Framing-to-framing nails

Rotation Non-linear moment-rotation stiffness from connection tests by Mi (2004)

Horizontal Linear stiffness = 2.292 kN/mm (Winkel 2006) Anchor bolts Vertical Linear stiffness, tensile mode= 53,590 N/mm

Linear stiffness, compressive mode = 1 GN/mm Horizontal Non-linear shear stiffness from connection tests, see chapter 6 in

this report Roof truss-to- external wall

Vertical Non-linear withdrawal stiffness from connection tests (chapter 6 in this report) Compressive mode, Linear stiffness = 106.8 kN/mm (Winkel 2006)

(a) whole building (b) external and internal walls in the 2nd storey Figure 5.4: 3-D FE model of two-storey building


5.4 Wind load The wind load applied was based on ASCE 7-05 with the assumed wind direction being perpendicular to the plane of the windward wall of the building, Figure 5.5. It should be noted here that in design practice all other wind directions must be specified to find critical load acting on the structure. Self-weight of the structure was not included in the analysis. The wind velocity pressure (qz) at height z above the ground is determined according to the following equation:

qz = 0.002619 KzKztKdV2I , (psf)

where Kz is the velocity exposure coefficient evaluated at building height z. The following selections are made for “design parameters” related to defining of wind pressures:

• Exposure B, corresponding to urban locations with numerous closely spaced obstructions. • Basic wind speed V (mph) • Importance factor I = 1.0, corresponding to “normal” importance. • Topographic factor Kzt = 1.0, corresponding to level topography. • Wind directionality factor Kd = 0.85, corresponding to “constant” wind direction during

loading. The design pressure p distributed to the main-wind force resisting system is then calculated using:

p = qzGCp - qh(GCpi) , (psf)

where qh is qz value at the roof height, and Cp is the external pressure coefficient determined based on the building surfaces considered, Cpi is the internal pressure coefficient for a partially enclosed building, and G is the gust factor (=0.85).

Figure 5.5: Wind load distribution based on ASCE 7-05 Table 5.3 shows an example of the wind pressure distribution based on 100 mph wind and the direction as well as distribution shown in Figure 5.5, and using roof angle 18.40 (the roof angles of the structures being analyzed, Figures 5.3 and 5.4).

1

23

4

1E

2E3E

4E

a

1

23

4

1E

2E3E

4E

1

23

4

1E

2E3E

4E

aa = width of edge strip = 3 feet, in this study

Wind direction


Table 5.3: Wind pressure distribution (v=100 mph)

Net pressure (psf) Surface GCp +GCpi -GCpi 1 0.51 5.06 10.57 2 -0.69 -13.33 -7.81 3 -0.46 -9.80 -4.29 4 -0.42 -9.19 -3.68

1E 0.78 9.19 14.71 2E -1.07 -19.15 -13.63 3E -0.67 -13.02 -7.51 4E -0.62 -12.26 -6.74

Note: negative denotes suction force 5.5 Post-yielding and failure analysis To analyze post-yielding (overload) behaviour of structures subject to wind loads, non-linear static analysis must be performed using load or displacement control to define the failure mechanism. The load control method was used because that is most appropriate for wind effects. All loads on elements were applied incrementally from zero to a user-specified target value. Zero initial damage conditions were assumed, i.e. no pre-stressed elements, no prior loading beyond the elastic range at the beginning of incremental analysis. Ten increments of wind speed were used with 10 iterations per step to ensure equilibrium of forces and convergence (0.01 % of the actual force acting on the structural element at the end of each load increment). The non-linear scheme in the FE software adopts the ‘implicit method’ to define the failure mechanisms in the structural elements. The analysis for each increment of load checks all elements that already have reached post-linear (post-yield) response. However, since only nailed connections were defined as having non-linear load-deformation response, attention was focused on checking link elements such as those in the walls and roof-to-wall anchorage. When individual elements yielded, load re-distributions to adjacent elements were automatically applied within the solution algorithm. This was accomplished by applying a localized self-equilibrating condition near any element that sustained loading beyond its peak force capacity. The solution algorithm became unstable when more than one element became overloaded in a particular region where the self-equilibrating condition had previously been applied. It was assumed that progressive failure of the complete LFWS building would ensue. This may not necessarily reflect actual behaviour but as yet alternative assumptions have not been investigated. The one-storey structure was analyzed first using applied wind pressures. After running the models using various wind speeds, it was found that at 125 mph wind the numerical solution became unstable indicating that more than one connection (link) elements have already reached their capacity. This wind speed corresponds to Category 4 (131-155mph) of commonly used Saffir-Simpson Hurricane Scale. After checking the load-deformation response for all link elements, the critical elements were found to be the roof-to-wall roof truss connections where the trusses were toe-nailed to the top plates of the windward and leeward walls. Figure 5.6 shows the


load-deformation response at wind speed 128 mph along the axial direction of selected link elements superimposed on the uplift response for the toe-nail connection to the top wall plate. It can be seen that the link element of the middle roof trusses has reached the peak resistance of the connection, which is around 2.41 kN (see the connection test program in chapter 6 of this report), while other link elements shown are still below this load (on the linear range).

Figure 5.6: Load-deformation response for selected wall-to-roof toe-nail connections Figure 5.7b shows the plot between the wind speed and the axial forces developed at the toe-nail connections located at the windward side shown in Figure 5.7a. The 128 mph wind speed was not plotted in the graph because the numerical solution obtained was unstable (non-convergence), therefore it is not the true representation of the forces distribution developed in the toe-nail connections. It can be seen that at 125 mph wind, few of the toe-nails closely reached their capacity altogether indicating that there was load redistribution process when one two-nail reached its capacity.

(a) layout of the bottom cord of roof truss and toe-nail connection (windward)

Notes:

• tnail-A=heel joint (toe-nail) at building corner, between gable frame (bottom chord) and exterior wall

• tnail-B=heel joint (toe-nail) at between the mid roof truss (bottom chord) and the top wall plate

• tnail-C= heel joint (toe-nail) at the mid roof truss

• test data = signifies resistance of an isolated connection tested in the laboratory

0

0.5

1

1.5

2

2.5

0 5 10 15

deformation (mm)

load

(kN

)

test datatnail-Atnail-Btnail-C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 38 40 41 42 43

Wall partitions

Bottom chord of trusses

Wall partitions


Wall partitions


windward wall 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

gabl

e en

d w

all

gabl

e en

d w

all

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 38 40 41 42 43

Wall partitions


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 38 40 41 42 4323 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 38 40 41 42 43

Wall partitions


Wall partitions


Wall partitions


windward wall 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

gabl

e en

d w

all

gabl

e en

d w

all


(b) Axial force at toe-nailed connections

Figure 5.7: Axial force in toe-nail connections of one-storey structure with internal partitions. An attempt was made to investigate whether progressive failure was initiated at 125 mph wind. One toe-nail connection that has already reached the capacity was removed from the model, and the wind load was re-applied from the previous increment level. It was found that the numerical solution obtained was unstable; despite refinement of the load increment was tried. This could indicate that progressive failure has been initiated. In term of computer running time, the unstable solution needed more time to run compared to the stable solution. Using 4 GB-computer-memory, the run time needed to perform stable solution was approximately 10 minutes, while the unstable solution took more than 2 hours to run. 5.6 Investigation of system effects System effects were investigated first by comparing the effects of the presence of internal wall partitions to the overall structural response of the one-storey structure shown in Figure 5.3. It was found that the numerical solutions for the structures with full wall partition (Model A) and without any internal wall partitions (Model B) were unstable when 128mph-wind pressure was applied. However, the number of the toe-nail connections that have reached ultimate capacity in Model A was more than in Model B. Figure 5.8 shows contours of resultant displacement at the final increment for each model loaded under 125-mph wind. By comparing the contour patterns, it is clear that in Model A a significant force concentration developed around the intersection of one internal wall and the external wall. The tendency towards force concentration at roof-to-wall link elements (i.e., the toe-nailed connections) was suppressed by the elimination of the internal partition walls as shown in Model B. Force concentration in Model A led to more forces developed in the toe-nail connections. In general it can be concluded that openings in walls and wall junctions cause irregularities in force transfers between roofs and walls. Although it is probably premature to draw broad conclusions from the single situation analysed, the results do suggest that it is highly feasible to create quite simple construction practice ‘rules’ for placement

0.000

0.500

1.000

1.500

2.000

2.500

1 3 5 7 9 11 13 15 17 19 21

toe-nail joint number

axia

l for

ce (k

N) 90 mph100 mph110 mph120 mph125 mph


of reinforcements in roof anchoring systems. However, as is often the case, reinforcement introduced at one location of a structure will shift failure location and change failure mode.

(a) Model A (b) Model B Figure 5.8: Resultant displacement contours for one-storey with partitions (a) and without

partitions (b) Figure 5.9 shows the axial force developed at the toe-nail connections located at the windward side shown in Figure 5.7a at various wind speeds. By comparing Figure 5.7 with Figure 5.9, it can be seen that the axial force distribution in the toe-nail connections in Model A is more uniform because of presence of internal wall partitions.

Figure 5.9: Axial force distribution in the toe-nail connections for Model B. Figure 5.10 shows the displacement responses at point X (as illustrated in Figure 5.8a) as a function of the loading step. In both cases the displacement responded linearly as the load was increased until close to the failure load. The structure with partition (Model A) was about twice as stiff as the structure without internal partitions ((Model B). This is due to the sharing of the applied force by a larger number of elements i.e. a higher system effect in the Model A.

Force concentration

X

0.000

0.500

1.000

1.500

2.000

2.500

1 3 5 7 9 11 13 15 17 19 21


axia

l for

ce (k

N) 90 mph

100 mph110 mph120 mph125 mph


Figure 5.10: Displacement responses

5.6.1 Critical wind speeds for various structural system configurations To investigate the system effect further, several structural configurations were analysed and the wind speed that caused failure to each configuration was determined. These include the two-storey structure shown in Figure 5.4 (with and without internal wall partitions), 3-d roof structure (Figure 5.11), and 2-d roof truss (Figure 5.12). For the analysis of the 3-d roof structure, no wall and floor sub-systems were included in the model. The toe-nail connections between the roof and exterior walls were connected to a rigid system, as shown in Figure 5.11. But, the non-linear connection properties were the same as those in the structures with all walls included (Models A, B). The results for the roof-only structure (Figure 5.11) indicated that at 125 mph wind the numerical solution was unstable, which means that failure at the toe-nail connection has already been initiated. By comparing this model with the previous ones (Models A and B), it can be noted that the wind speed causing failure was reduced slightly.

Figure 5.11: 3-D roof structure

0

0.5

1

1.5

2

2.5

1 4 7 10 13

step

disp

lace

men

t (m

m)

M odel AM odel B

233E

2E

323

3E

2E

3


Figure 5.12 illustrates how to calculate the toe-nail axial forces in a roof truss structure loaded by wind pressure. The design principle uses a simply supported structure with the wind loads uniformly applied based on tributary area of the roof truss spacing (=2 feet in this study). By applying ASCE7-05 and using wind speed 125 mph, two uniformly distributed loads are applied: p1 = 59.5 psf and p2 = 40.46 psf The maximum reaction (uplift) force in the toe-nail is:

R* = 0.75 (0.5L cosα) (w1) + 0.25 (0.5L cosα) (w2) Substituting L = 27 ft, S = 2 ft and α=18.40 (12:4 roof-slope), the toe-nail force is:

R* = 701 lbs = 3.12 kN

Figure 5.12: 2-d roof truss analysis

If the toe-nail uplift load as a function of various wind speed is plotted, the critical wind speed can be calculated (Figure 5.13). In this case using Ru = 2.41 kN (average peak load from the uplift-connection test), the critical wind speed based on this simple calculation is found to be around 110 mph. Comparing with the calculated critical wind speed (125 mph) obtained through numerical modeling presented above, the system effect is evident.

Figure 5.13: Wind speed vs uplift load based on the simple 2-d roof truss analysis

0.000.501.001.502.002.503.003.50

85 90 95 100 105 110 115 120 125 130

wind speed (mph)

uplif

t loa

d (k

N)

L

R R*

wind direction

w1=p1S

w2=p2S

p1, p2=wind pressures (ASCE-7-05); S =roof truss spacing; R* =max uplift reaction

L

R R*

wind direction

w1=p1S

w2=p2S

p1, p2=wind pressures (ASCE-7-05); S =roof truss spacing; R* =max uplift reaction


Table 5.4 summarizes the critical wind speed results for the structures analyzed, including a comparison with simple design analysis to determine uplift (reaction) force of a roof-truss structure subjected to wind distributed pressure. Detailed results for distribution of toe-nail forces as a function of wind speed can be found in Appendix A. As expected, the critical wind speed is higher (110 mph vs 125 mph) when the structure is analysed as a 3-d system, indicating the benefit of the system effect. It can be noted in Table 5.4 that the influence of wall flexibility is negligible (125 mph vs 128 mph). Surprisingly, the presence of internal partition does not appear to influence the critical wind speed for both one- and two-storey buildings. The height of the building also does not affect the critical wind speed.

Table 5.4: Critical wind speed

Structure analysed Wind speed (mph) Remark

Simple 2d truss analysis 110

Design calculation typically performed by designers

3-d roof structure 125

Roof trusses are assumed toe-nailed to rigid walls

One-storey with full partitions 128 -- One-storey without full partition 128 -- Two-storey with full partitions 128 -- Two-storey without full partition 128 --

5.6.2 Effect of strengthening using hurricane metal connectors The analyses were extended to investigate the effects of using stronger connectors i.e. hurricane tie (metal), to replace toe-nailed connections. Figure 5.14 shows the hurricane ties used in this study. Normally, in new construction (structure) the hurricane ties are installed along with two toe-nails which are used for positioning. But, for retrofitting existing structures, the hurricane ties are installed in addition to the typical existing three toe-nail connections. In the analysis here only one N-link element was assigned to each roof-to-wall connection and no attempts were made in modeling to separate the toe-nail and hurricane ties. Because there is no existing suitable connection data for use as input into the numerical model, three types of connection (uplift) stiffness were simulated. The first one was a fully rigid connection. The other two were semi-rigid with differing stiffness and strength values that were scaled from those of the toe-nail (Figure 5.15). Based on the allowable shear (lateral) strength of existing hurricane ties in the market place, the lateral resistance is lower than the uplift resistance (Simpson Strong-Tie, 2005). Hence, in the assumed connection models, the connection lateral stiffness was assumed to be half of that in the uplift direction. The purpose of the analyses conducted here was to identify the critical wind speeds and location of first failure in the structures. For the 3-D analysis, only the one-storey structures (Models A and B) and the roof assembly (Figure 5.11) were studied. As a comparison with design practice, 2-D roof truss structure shown in Figure 5.12 was also analysed.


Figure 5.14: Example of hurricane metal connector (Simpson Strong Tie)

Figure 5.15: Assigned hurricane ties stiffness (uplift direction) Note : H-tie#1 and H-tie#2 are 1.5 and 2.0 times stiffer and stronger than those of the toe-nail.

Table 5.5: Critical wind speed for structures strengthened with hurricane tie

Critical wind speed (mph) Structure analysed

Regular toe-nail

Hurricane tie#1

Hurricane tie #2

Fully rigid connector

Remarks

2-d roof truss 110 135 157 N/a Could fail either at connectors or other components

3-d roof structure 125 155 180 N/a Could fail either at connectors or other components

Model A 128 160 180 210 Failed within nailed wall connection

Model B 128 160 180 210 Failed within nailed wall connection

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

slip (mm)

laod

(kN

) Test dataH-tie#1H-tie#2


The analysis results are summarized in Table 5.5. As is expected, system effect was also observed when hurricane tie connector was applied in the roof-to-wall connection. It can be seen that increase in the stiffness and associated ultimate load in the connectors leads to increase in the critical wind speed that the structure can sustain. Critical wind speed was not determined for the 2-d and 3-d roof structures for the case of fully rigid connectors, because the analysis was not extended to check the strengths of structural components. It should be noted that the connection between the roof sheathing and roof frame was modeled as rigid. In practice, the roof sheathing connections were designed to hold much larger wind pressure relative to the roof-to-wall connections, since nail spacing can be made much closer to each other; but this is not the case with the roof truss spacing. For Models A and B, modeling rigid roof-to-wall connections led to a shifting of the location of the failure, from the bottom plate to stud connections. Again, this was based on the assumption that failure does not occur at members (stud frames, wall sheathing plates).

5.6.3 Effect of varying internal wall locations So far the discussion has focused on the failure analysis by determining whether the roof-to-wall or other structural connections failed. This section describes how the applied wind load is distributed to wall frame components when the structure is near failure, or specifically when the internal axial (uplift) forces in the link element(s) have reached the peak resistance of the toe-nail or hurricane tie connections. To find the force distribution, internal shear and axial forces in the link elements between the exterior wall frames located at the building corners, including between the exterior wall frame and gable-roof, were extracted from the load-deformation responses (Figure 5.16a). Figure 5.16b shows the lateral load distribution in LFWS due to wind pressure (p) commonly used in current design practice. Rigid roof diaphragm behaviour relative to the wall components was assumed in the analysis (CWC, 2001). For illustrative purposes, in Figure 5.16 no wind pressure was included on the roof surface. In actual design practice, resultant of the different wind-suction values on the roof surface results in additional lateral force that will be carried by the wall components. The wall receiving the wind pressure distributes the top half of its horizontal wind load to the roof and the bottom half to the foundation. The portion of the load applied to the roof tends to cause the roof to move laterally, and the end walls resist this lateral movement. As is shown in Figure 5.5, the wind suction/pressure applied to the walls is normally non-uniform with one wall edge receiving larger suction/pressure in a particular wind direction. Using Figure 5.16, the load distributed to the windward (front) wall is simply

2Hpw = (force / length)

and the shear force distributed to the end walls is

BwLv2

= )/( lengthforce

where: H= height of the wall , B= width of building, and L= length of building.


(a) end wall force distribution from the 3-d model (b) design practice

Figure 5.16: Force distribution in the wall components due to wind load Figure 5.17 (a-d) shows the building layout with varied internal wall partitions including the lateral forces acting on the external and internal walls. The previous model (Model B, which included no internal partitions) was used as comparison (Figure 5.17a). Table 5.6 shows the values of these forces and the total lateral forces obtained from the numerical model. It can be seen that the exterior walls (V1 and V2) receive smaller forces than those within the internal walls (V3 or V4) when these internal walls were applied continuously from the windward and leeward walls (Figures 5.17a&b). The total lateral force is simply the summation of these forces (V1 to V4), and theoretically should equal to the applied lateral external wind forces but act in opposite direction. The total resultant of the lateral wind force is 11.30 kN. It can be noted that the total lateral forces is not the same. The largest difference in terms of the total lateral force comparison was obtained in the case of the structure without any internal wall partitions (Figure 5.17a). This is due to very flexible long walls (windward and leeward), causing portion of the lateral forces to be absorbed by other link elements located in the windward and leeward walls. It should be noted here that V1 is always larger than V2 because the wind pressure applied along the edge strip of the windward wall (indicated by 1E region in Figure 5.5) is larger (ASCE, 2005). In actual design, the larger wind load needs also to be applied on the V2 side and the larger value of the two will define the critical force used for the wall design. With respect to the shear wall capacity range, the numerical values obtained are relatively small. For example, using smallest applicable nails for wall and edge nail spacing of 150 mm, the specified shear strength based on CSAO86-01 is 4.9 kN/m (or 41.9 kN for 9.3 m wall). Even after multiplying it with other design factors (e.g. resistance factor =0.7), the largest calculated value (V1) is still below the capacity range. This indicates that at this wind speed (125 mph), shear wall failure would not be the governing condition.

w

pvw

vL

B

H

ww

pvw

vL

B

H

pvw

vLL

BB

HH

vvv


Table 5.6: Lateral force distribution to the walls

Structure analysed V1 (kN)

V2 (kN)

V3 (kN)

V4 (kN)

Total lateral force (kN)

Figure 5.17a (no partitions) 4.83 3.38 - - 8.21 Figure 5.17b (one partition) 3.22 2.51 4.27 - 10.01 Figure 5.17c (two partitions) 2.36 1.34 4.09 4.38 12.16 Figure 5.17d (two discontinuous partitions) 4.02 2.51 2.44 1.61 10.58

Figure 5.17 (a) No internal wall partition

Leeward wall

Windward wall

Left gable Right gable

Wind load*

V1 V2

Note: * The wind load sign just indicates the direction. The actual wind loads were applied both in the windward and leeward walls.


Figure 5.17 (b) An internal wall partition (V3) located at 1/3 of the building total length from the

left gable position (V1)

Figure 5.17 (c) Two internal wall partitions (V3 & V4) located at 1/3 and 2/3 of the building

total length from the left gable position (V1), respectively

Leeward wall

Windward wall


Wind load

V1 V2

V3

Leeward wall

Windward wall


Wind load

V1 V2

V3 V4


Figure 5.17(d) Two short-internal wall partitions (V3 & V4) located at 1/3 and 2/3 of the

building total length from (V1), respectively (Note: The length of the internal partitions are half of the left/right gable wall, which is 8.53 m)

Figure 5.17: Layout of the structures with varying wall partitions locations The lateral force distributions obtained from the 3-D numerical model above were compared with those obtained using analytical methods used by design engineers. These methods are based on the use of either tributary area or relative stiffness. In the tributary area approach the main assumption is that the floor/roof diaphragms are flexible compared to the shear walls. The shear walls are modeled as structural supports having assigned rigidity (stiffness) and the resulting reaction forces are basically the total shear forces acting on the shear walls. In contrast, the relative stiffness approach assumes that the floor/roof diaphragm is rigid, whereby the applied loads are distributed to the shear walls based on their relative stiffness. In this project, four methods were used including: (1) tributary area method itself; (2) simple and continuous beam methods; (3) relative stiffness without torsional effect; (4) relative stiffness with torsional effect (rigid beam on elastic foundation). Figure 5.18 illustrates the lateral force distribution in the wall due to wind load determined using these analytical methods. Only one internal wall partition is included in this diagram, but the concept applies to more than one internal walls. In the tributary area method (Figure 5.18a), the diaphragm is assumed flexible so that the lateral forces are distributed in proportion to the tributary area associated with the shear walls. As shown in Figure 5.18(a), this method treats the structure as a series of flexible beams resting on rigid supports. This is the simplest analytical method and can lead to either conservative or unconservative results. The simple and continuous beams method can be considered as a special case of the tributary area method. In this method, a series of simple or continuous beams loaded by a uniform line load equal to the total wind load divided by the length of the building was used (Figures 5.18b,c). Finding the reaction forces for the continuous beam method can be done using structural analysis table or simple numerical finite element analysis.

Leeward wall

Windward wall


Wind load

V1 V2

V3

V4


In the relative stiffness methods (Figure 5.18d,e), the diaphragm is assumed as rigid and the lateral forces are distributed in proportion to the stiffness of the shear walls. If it is assumed that no significant torsional effect takes place in the building, then the lateral force distribution is calculated directly based on the shear wall stiffness proportion, without any need to include beam modeling (Figure 5.18d). When the rotation of the building is considered, the torsional stiffness needs to be accounted for through incorporating rigid beam supported by elastic spring/foundation (Figure 5.18e). The shear wall stiffness can be obtained using 2-d finite element analysis or from the semi-analytical model to find shear wall deformation.

(a) Tributary Area

(b) Simple Beam

(c) Continuous Beam

(d) Relative Stiffness Without Torsion

(e) Relative Stiffness With Torsion (Rigid Beam on Elastic Foundation)

Figure.5.18: Various analytical methods to obtain lateral load distribution to walls

K1 K2 K3

K1 K2

K3


Tables 5.7-5.10 summarise the results, while the detailed calculations can be seen in Appendix B. The values in parentheses are the values obtained from the 3-d numerical model. In general, relative to the 3-d numerical models, the analytical methods could result in values that are either conservative or unconservative. The same situations were obtained when comparing the results amongst the analytical methods. The main reason is due to the simplification in assuming shear wall rigidity, neglect of the effects of wall opening and semi-rigid connection within the shear wall components. With respect to the exterior wall design, using the tributary area method and neglecting the contribution of the internal wall partitions leads to a safe solution (Figure 5.16b). It can also be seen that for the exterior wall design, the use of relative stiffness or rigid-beam-on foundation methods always leads conservative solutions. However, attention should be paid to the design of the internal wall partitions because they can potentially attract more forces than assumed by simplified calculation procedures.

Table 5.7: Lateral force distribution (tributary area method/simple beam method vs 3-d numerical model)


V2 (kN)

V3 (kN)

V4 (kN)


Figure 5.17a (no internal wall partitions)

5.65 (4.83)

5.65 (3.38) - -

11.30 (8.21)

Figure 5.17b (one continuous wall partition)

1.88 (3.22)

3.77 (2.51)

5.65 (4.27) -

11.29 (10.01)

Figure 5.17c (two continuous wall partitions)

1.88 (2.36)

1.88 (1.34)

3.76 (4.09)

3.76 (4.38)

11.28 (12.16)

Figure 5.17d (two discontinuous wall partitions)

1.88 (4.02)

1.88 (2.51)

3.76 (2.44)

3.76 (1.61)

11.28 (10.58)

Note: The shear wall force signs in the analytical methods (see Appendix B) were adjusted to be consistent with the 3-d numerical model.

Table 5.8: Lateral force distribution (continuous beam method vs 3-d numerical model)


V2 (kN)

V3 (kN)

V4 (kN)



5.65 (4.83)

5.65 (3.38) - -

11.30 (8.21)


0.49 (3.22)

3.07 (2.51)

7.74 (4.27) -

11.30 (10.01)


1.51 (2.36)

1.51 (1.34)

4.14 (4.09)

4.14 (4.38)

11.30 (12.16)


1.51 (4.02)

1.51 (2.51)

4.14 (2.44)

4.14 (1.61)

11.30 (10.58)


Table 5.9: Lateral force distribution to the walls (relative stiffness method without torsion vs 3-d numerical model)


V2 (kN)

V3 (kN)

V4 (kN)



5.65 (4.83)

5.65 (3.38) - -

11.30 (8.21)


4.34 (3.22)

4.34 (2.51)

2.61 (4.27) -

11.29 (10.01)


3.52 (2.36)

3.52 (1.34)

2.12 (4.09)

2.12 (4.38)

11.28 (12.16)


4.54 (4.02)

4.54 (2.51)

1.09 (2.44)

1.09 (1.61)

11.26 (10.58)

Table 5.10: Lateral force distribution to the walls (rigid beam on elastic foundation vs 3-d numerical model)


V2 (kN)

V3 (kN)

V4 (kN)



5.65 (4.83)

5.65 (3.38) - -

11.30 (8.21)


3.94 (3.22)

4.80 (2.51)

2.56 (4.27) -

11.29 (10.01)


3.53 (2.36)

3.53 (1.34)

2.12 (4.09)

2.12 (4.38)

11.28 (12.16)


4.54 (4.02)

4.54 (2.51)

1.12 (2.44)

1.12 (1.61)

11.32 (10.58)

5.4 Concluding remarks Non-linear (failure) analysis of LFWS under wind load was performed based on the implicit numerical scheme embedded in the solution algorithm of the finite element program SAP2000-NonLinear version 11. The results indicate that the roof-to-wall (toe-nail) connections are the critical components under wind load, when the structural geometry produces uplift forces. The finding that wind causes failure to typical toe-nailed roof-to-wall connections is consistent with practical experience (Cheng 2004). It was also obtained that the effect of internal wall partitions to the wind speed that caused failure is not significant, considering that the structures analysed are limited to typical one- and two-storey wood frame buildings. However, system effect needs to be accounted for when the roof-truss connection is designed as 2-d structural component loaded with wind load. For the case of roof-to-wall strengthening using hurricane metal connectors, the failure location could shift to other locations. However, this heavily depends on the type of hurricane connector used and associated connection characteristics (stiffness and strength).


Lateral forces carried by the internal wall partitions could be larger than those received by the exterior walls, and assumed by commonly used method of analyses. This issue requires further examination. Designing appropriate connection between the exterior and interior walls is important. It should be noticed that in this project no connections were assigned between the internal walls and the roof structure, and creating link elements between these components would yield different force distribution to the exterior walls. So far only one wind direction and one pressure distribution have been considered for one and two-storey LFWS buildings. In reality turbulence in wind creates temporally and spatially varying pressures on building surfaces rather than uniformly distributed pressures as specified in typical building codes. However, because of area averaging effects on pressures and averaging effects of the three-dimensional system response, this should not invalidate deductions about wind speeds causing failures in roof anchorages, but it does mean that the model may not reliably represent the wind speed at which exterior sheathing materials will be dislodged. Therefore pressure contours obtained from Computational Fluid Dynamics (CFD) analysis or wind tunnel tests need to be investigated as well as simple loading idealizations.


6 Testing of connection components in LFWS 6.1 Background Connections are arguably the most important part of light-frame wood structures (LFWS). They hold structural components together and transfer forces from one component to another. The majority of connections in LFWS are composed of nail connections, which in general can be divided into two parts: (1) sheathing-to-lumber frames connections; and (2) lumber frame-to-lumber frame connections. The response of nail connection under applied load is normally non-linear and depends on various parameters such as wood moisture content, wood species, loading direction (parallel or perpendicular to wood grain) and fastener geometry and configuration. Accurate predictions from analytical or numerical models of LFWS depend largely on the availability of accurate connection properties, which are usually derived from connection test or detailed numerical modeling of connection (Kasal, 1992). The main connection property required for numerical modeling is the load-deformation (slip) response (Figure 6.1d). Several data points in the curve are needed to represent the non-linear response until a peak load or post-peak load is reached. In the numerical model using finite element, the connection property is represented by non-linear spring composed of axial, shear and rotational degrees of freedom. Figure 6.1 shows an illustrative example of roof-to-wall joint represented by this type of spring behaviour.

(a) house structure (b) roof-to-wall connection (detail A)

Toe-nail connectionToe-nail connectionA


(c) spring element model (d) load-slip response

Figure 6.1: Connection modeling process

Most of the connection test data available in the literature have been used for deriving connection design values (yield load, ultimate load, ductility), and there is limited amount of connection load-deformation data for use in whole-building numerical models. The main purpose of this connection test program is to fill gaps in input data to 3-D numerical models of LFWS, pertaining specifically to non-linear load-deformation (slip) response under static load. After reviewing and examining available connection test data in the literature particularly related to nail connections in shear wall sub-assembly (e.g. Mi, 2004 and Winkel, 2006), it was identified that there is need to conduct the following tests:

• Roof-to-wall connection: toe-nail joint between bottom chord of roof truss and double top plate,

• Internal-to-external wall connection: nail joint between internal wall-stud and external wall-stud frames, and

• Wall-to-floor connection: nail joint between bottom plate and floor joist.

In this study, the test setups were developed based on ASTM D1761 ‘Testing Mechanical Fasteners in Wood’ (ASTM, 2001) with adjustments in boundary conditions and load application. Although in the numerical model only the average response of load-slip is needed, all related properties, including failure mechanism, ultimate load, yield load, and ductility, were studied.

6.2 Roof-to-wall connection 6.2.1 Test description The first part of the test program was to study the behaviour of roof-to-wall connection subjected to static load. Common method of connecting roof to wall components is by toe-nailing the bottom chord element (2x4) of roof-truss to the double top-plate (2-2x4) of wall using 3-8d or 2-16d common nails (CMHC, 2005). In this study, since the wall frame system consisted of 2x6 lumber including the double top-plate, 3-16d common nails were used. The test was designed to accommodate independent loading in each major direction of the toe-nail connection, one in uplift and two in shear (Figure 6.2). The loading direction here is referred to the wood grain direction of the roof-truss. For example, shear perpendicular means the load is applied perpendicular to the wood-grain of the 2x4 bottom chord lumber. No combined loads were applied in this test. As shown in Figure 6.2, symmetrical test arrangements were employed to avoid rotational movements induced by eccentric (un-symmetric) loading.

connection modeled as spring element with:• two lateral/shear stiffness properties• withdrawal/uplift stiffness property

connection modeled as spring element with:• two lateral/shear stiffness properties• withdrawal/uplift stiffness property

slip

load

slip

load


(a) toe-nail connection with possible load scenarios (b) uplift test

(b) shear parallel (c) shear perpendicular

Figure 6.2: Roof-to-wall toe-nail connection test

Wood specimens included 2x4 (roof truss) and 2x6 (wall double top-plate) S-P-F lumber of No 2 grade or better. The specimens were conditioned in environmental chamber at 65% RH and 200 C for adjustment of the lumber MC to 12 percent. The specific gravity (SG) was computed from the dimensions and weight of the specimen at time of test and MC. These lumber pieces were all cut into 300 mm length. The lumbers were connected using 3-16d common nails (diameter=4.1 mm, length= 89 mm) using toe-nailing technique. To avoid wood splitting, pilot holes were drilled into the 2x4 lumber of the specimen assembly at 30 degrees at marked locations using a drilling tool. Plastic sheets were inserted between the 2x4 member and supports to prevent excessive friction that could influence the slip response of the connection (Figure 6.2b). Once the specimen was assembled in a universal test machine, compression loading mode was applied to the 2x4 component, except for the shear-parallel applied on the 2x6 element (Fig. 6.2b), at a rate of 3 mm/minute until failure was reached or until excessive separation (gap) between the connected elements was detected. Two displacement transducers (LVDTs) were attached symmetrically with respect to the centre line of loading to record slip between the two connected

Roof-truss bottom cord (2x4)

Wall double top-plate (2x6)

Toe-nail

Roof-truss bottom cord (2x4)

Wall double top-plate (2x6)

Toe-nail

3-16d toe-nails2x4

double 2x6 top-plate

Load

support3-16d toe-nails2x4

double 2x6 top-plate

Load

support

2x4

double 2x6

double 2x6

support

support 3-16d toe-nails

load

2x4

double 2x6

double 2x6

support

support 3-16d toe-nails

load

double 2x6

double 2x62x4

3-16d toe-nails

¼” steel plateload

support

double 2x6

double 2x62x4

3-16d toe-nails

¼” steel plateload

support


components. The connection slip is determined using the average value of the two LVDTs. Ten specimens were tested for each loading direction.

6.2.2 Test results Failure mode provides important information regarding whether the connection can be appropriately modeled using the non-linear spring element. If the failure mode is brittle (e.g. wood splitting), the connection load-slip response is generally linear and can be adequately represented by the initial connection stiffness. As was expected, test results indicated that the failure mode for the toe-nail connections was ductile, indicated by nail withdrawal for the uplift load case and excessive bending of nails for the lateral (shear) load cases. No splitting of wood was observed in the test. Table 6.1 shows a summary of the test results, which includes peak load (Pu), yield load (Py), and slip at yield (δy), slip at peak (δu), and ductility ratio for each load direction. Yield load was computed as the intersection point between the load-slip curve and a line having the same slope as initial load-slip curve and is offset horizontally by 5% of the fastener diameter (ASTM 2001). Displacement at yield was also determined to investigate the ductility response of the connection, which is defined as the ratio between displacements at peak and yield. Maximum loads were taken as peak values irrespective of the associated displacements. In general, it can be noted that the variability in the connection response under uplift load was higher compared to those of the lateral loads. Also, as was anticipated, the peak load values are lower in the uplift load case compared to those of the lateral loads.

Table 6.1: Roof-to-wall toe nail connection

Load-slip curves provide important information on the overall response of the connection under load. Figure 6.3 shows the average responses of load-slip curves for each loading direction determined using curve-fitting least-square method. An overall observation is that the connection should be modeled as ductile (non-linear) in the three directions. To be useful as input in the numerical models, several data points in the curve need to be selected in a way that closely reflect the characteristics of the curve. For example, at low load level small interval between the data points in the horizontal axis (slip) is needed to capture the linear response indicated by an abrupt change in the vertical axis (load) values. Table 6.2 summarizes the data points selected for each loading direction that were used for the numerical modeling input, and detail of the load-slip curves for each toe-nail specimen can be seen in Appendix C. (Note: As a comparison, the corresponding response for hurricane metal connector with and without toe-nails can be seen in Appendix D.)

SG, C.o.V

Pu (kN), C.o.V

Py (kN), C.o.V

δu (mm), C.o.V

δy (mm), C.o.V

Ductility, C.o.V

Uplift 0.42 (0.05)

2.45 (0.29)

2.07 (0.29)

4.19 (0.38)

0.78 (0.24)

5.83 (0.51)

Shear parallel

0.42 (0.05)

4.73 (0.05)

2.95 (0.16)

6.14 (0.11)

0.83 (0.42)

8.12 (0.26)

Shear perpendicular

0.42 (0.05)

3.29 (0.06)

2.13 (0.17)

8.38 (0.34)

1.7 (0.4)

5.6 (0.7)


Figure 6.3: Average load-slip curve for roof-to-wall connection.

uplift

Shear parallel

Shear perp


Table 6.2: Data points used as input for numerical modeling

6.3 Interior-to-exterior wall connection

6.3.1 Test description Figure 6.3a illustrates one of few ways in connecting 2x4 interior wall-frame to 2x6 exterior wall-frame of LFWS, and Figure 6.3b illustrates its connection modeled as spring element. In the test, again symmetrical loading arrangement was built by connecting two-2x4 studs to a 2x6 stud with one-16d common nail on each side (Figures 6.4c, d). Plasterboard of thickness 3/8” (9.5mm) was inserted between these two studs. Two lateral (shear) loads were applied with respect to the wood grain direction in the 2x6 stud, one perpendicular and another parallel. No axial load direction (with respect to the nail position) was applied, since there are some previous data available that can be used to closely represent the nail withdrawal behaviour between studs (Winkel, 2006; Mi, 2004). To reduce rotation during the perpendicular loading, the plasterboard was extended beyond the 2x4 side surface area and frictionless plastic material was inserted (Figure 6.4b). The lumber used was SPF grade No. 2. Both lumber sizes (24 and 2x6) were cut into the same lengths of 300 mm. Note that in practice nailing between interior and exterior studs were applied at a spacing between 12” and 24” (300-600mm). Two LVDTs were attached to record the slips between the 2x6-stud and the plasterboard and between the plasterboard and the 2x4 stud. Loading was applied at the same rate as the previous toe-nail test, 3mm/minute until

slip/def (mm)

Shear Perpendicular*

(kN)

Shear Parallel*

(kN)

Uplift (kN)

0 0.01 0.52 0.02 0.5 1.62 4.56 1.69 1 2.98 6.22 2.10

1.5 4.03 7.07 2.21 2 4.77 7.68 2.27 3 5.53 8.61 2.40 4 5.79 9.09 2.37 5 5.96 9.25 2.34 6 6.17 9.35 2.30 7 6.40 9.41 2.29 8 6.55 9.33 2.27 9 6.58 9.11 2.26

10 6.50 8.88 2.25 11 6.42 8.70 2.21 12 6.37 8.44 2.15 13 6.33 8.10 2.08 14 6.28 7.88 2.06

Note: * denotes the overall connection response with 3-16d common nails toe-nailing on each side of the top-plate (symmetrical arrangement). In the numerical model, this implies the loads are half of these values recorded.


failure was observed or until excessive slip or big separation between connection components was obtained. Ten specimens were used for each loading direction.

(a) Interior-to-exterior walls connection (b) connection spring model

(c) perpendicular loading (d) parallel loading

Figure 6.4: Interior-to-exterior walls connection

6.3.2 Test result The majority of the test results indicated that ductile failure mode in the form of excessive bending of nail in combination with wood and plasterboard crushing was observed when the load was applied parallel to the wood grain. Few specimens failed in brittle mode indicated by wood splitting in 2x6 member when the load was applied perpendicular to the grain. Table 6.3 summarizes the test results including peak load (Pu), yield load (Py), and slip at yield (δy), slip at peak (δu), and ductility ratio for each loading direction. Figure 6.5 shows the average load-slip

Exterior wall

Internal wall

16d nail 12” o.c.

Exterior wall

Internal wall

16d nail 12” o.c.

plasterboard

OSB

Int-ext wall spring model

plasterboard

OSB

Int-ext wall spring model

Exterior wall

Internal wall

16d nail 12” o.c.

Exterior wall

Internal wall

16d nail 12” o.c.

2x6 2x42x4

Gypsum wallboardsupport support

16d nail

load

Frictionless plasticmaterial

2x6 2x42x4

Gypsum wallboardsupport support

16d nail

load

Frictionless plasticmaterial


responses determined using least-square curve fitting method. The load-slip responses plotted were the total slips recorded between the 2x4 and 2x6 studs, which were assumed by simply adding the two slip signals recorded with two LVDTs. In general, ductility ratios determined were higher than those obtained from the previous toe-nail connection test, meaning that the connection response needs to be modeled non-linearly. It can also be noted that the connection stiffness at low load level between the parallel and perpendicular are almost the same. Table 6.4 shows the data points representing connection load-slip response used as into the numerical models.

Table 6.3: Test result

Figure 6.5: Average load-slip curve for interior-to-exterior walls connection.

SG, C.o.V

Pu (kN), C.o.V

Py (kN), C.o.V

δu (mm), C.o.V

δy (mm), C.o.V

Ductility, C.o.V

Perpendicular 0.42 (0.05)

1.77 (0.10)

0.88 (0.14)

11.7 (0.23)

1.7 (0.46)

9.5 (0.53)

Parallel 0.42 (0.05)

1.60 (0.10)

1.02 (0.06)

14.5 (0.38)

2.1 (0.22)

7.4 (0.55)

perpendicular

parallel


Table 6.4: Data points as input for numerical modeling

6.4 Wall-to-floor connection 6.4.1 Test description The third part of the test program was conducted to obtain the connection response between wall and floor frames. Figure 6.6a shows a typical external wall-to-floor connection using 2-16d common nails spaced at 300 mm along the bottom wall plate. Figure 6.6b illustrates the modeling strategy for the wall-to-floor connection involving lumber studs, sheathing, and nails. No wall sheathing and its nails are shown here. The bottom plate (2x6) and 5/8” (15.5 mm) OSB sub-floor were joined using 2-16d nails on each side of the 2x10 joist (Figures 6.6c, d). As the previous two connection tests, all lumber pieces used were SFP grade No 2 or better grade. These lumber pieces (2x6s and 2x10s) were cut into the same length, 300mm. Loading rate was 3mm/minute until failure was reached or excessive separation between components was observed. Ten specimens were tested for each loading direction.

slip/def (mm)

Perpendicular (kN)

Parallel (kN)

0.0 0.06 0.26 0.5 1.42 1.03 1.0 1.83 1.50 1.5 2.01 1.80 2.0 2.17 2.01 3.0 2.49 2.30 4.0 2.72 2.53 5.0 2.88 2.71 6.0 3.03 2.83 7.0 3.15 2.91 8.0 3.24 2.98 9.0 3.33 3.04

10.0 3.40 3.09 11.0 3.43 3.12 12.0 3.44 3.14 13.0 3.44 3.14 14.0 3.42 3.13 15.0 3.37 3.11 16 0 3 30*) 3 10*)

Note: *) In the non-linear modeling analysis with load control, one data point after the peak load point is reached is the minimum requirement to complete the load-slip path due to numerical instability reaching post peak analysis. This is not the case if displacement control is used.


(a) wall-floor connection (b) connection model around the wall-floor connection

(c) test of perpendicular loading (d) test of parallel loading

Figure 6.6: Testing of wall-to-floor connection

6.4.2 Test result Table 6.5 summarizes the results for the wall-floor connection test. Based on the ductility ratios and the total load-slip curves (Figure 6.7), the connection responses are quite ductile, despite a few of the connection specimens failing in a brittle manner. This is due to small edge distance of nails drilled at the edge of 2x10 joist member creating a tendency of wood to split (Figure 6.8b). The ductile failure mode is the same as the previous two tests; excessive nail bending and wood crushing near the nail area (Figure 6.8a).

support

5/8” OSB2x10

2x6

support

2-16d commonnail

load

support

5/8” OSB2x10

2x6

support

2-16d commonnail

load 2x62x6 5/8” OSB

2x10 Joist

2-16d commonnail

load

2x62x6 5/8” OSB

2x10 Joist

2-16d commonnail

load

Floor joist

sub-floor

2-16d common nails

wall studs

Floor joist

sub-floor

2-16d common nails

wall studs studs

bottom plate

Joists

OSB sub-floor

Wall-floor connection spring model

studs

bottom plate

Joists

OSB sub-floor

Wall-floor connection spring model


Table 6.5: Test result

Figure 6.7: Average load-slip curve of wall-to-floor connection.

SG, C.o.V

Pu (kN), C.o.V

Py (kN), C.o.V

δu (mm), C.o.V

δy (mm), C.o.V

Ductility, C.o.V

Perp 0.42 (0.05)

2.72 (0.09)

1.23 (0.07)

10.5 (0.27)

1.06 (0.29)

11.0 (0.5)

Parallel 0.42 (0.05)

3.06 (0.06)

1.68 (0.06)

20.4 (0.14)

2.37 (0.36)

9.4 (0.29)

perpendicular

parallel


(a) ductile (b) brittle (wood splitting)

Figure 6.8: Failure observed in wall-floor connection

Table 6.6: Data points as input for numerical modeling

slip/def (mm)

Perpendicular (kN)

Parallel (kN)

0.0 0.41 0.22 0.5 1.88 1.60 1.0 2.66 2.48 1.5 3.10 3.03 2.0 3.40 3.38 3.0 3.87 3.82 4.0 4.29 4.15 5.0 4.64 4.48 6.0 4.88 4.79 7.0 5.04 5.06 8.0 5.19 5.27 9.0 5.34 5.42

10.0 5.49 5.53 11.0 5.61 5.61 12.0 5.67 5.69 13.0 5.68 5.77 14.0 5.64 5.84 15.0 5.59 5.92 16.0 5.54 5.97 17.0 5.47 6.01 18.0 5.35 6.04 19.0 5.10 6.05 20.0 4.59 6.04


6.5 Numerical modeling implication 6.5.1 3-D structural model To study the implication of the connection responses obtained from isolated laboratory tests to the overall (system) response of LFWS, a 3-D whole-building structural model was developed. In this study, a 9.3m x 14m (28ft x 42ft) one-storey LFWS was modeled using commercial FE software SAP2000 as shown in Figure 6.9 (CSI, 2007). The arrangement followed the so-called platform frame construction method with selection of the structural members and other components based on construction guidelines from the Canada Mortgage and Housing Corporation (CMHC, 2005). Detailed numerical modeling techniques including types of element used, material and connection properties, boundary conditions applied, and numerical failure analysis can be seen in Chui et al (2008) and Asiz et al (2008). The models developed in those papers have been updated with the connection properties obtained from the test conducted in this study. Load applied was only wind pressure derived based on ASCE7-05 (ASCE, 2005). The wind direction used is the critical one, acting perpendicular to the long axis of the structure leading to uplift pressure on its roof surfaces. Other wind data used were: wind with exposure category B; importance factor I=1.00; topographic factor Kzt=1 (flat region); and wind directionality factor Kd=0.85. The basic wind speed used was varied until the critical one causing failure to the structure was obtained. Figure 6.9c illustrates the deformed shape and contour of displacement magnitude of the structure under 125-mph wind. The blue colour indicates the most deformed region, which is in the peak of the roof structure.

(a) whole building model (b) internal and external wall

(c) deformed shape and displacement contour

Figure 6.9: 3-D finite element analysis

Notes: Selected connection responses observed A: roof-to-wall connection, B: external-to-internal wall connection, C: wall-to-floor connections

A

B

C


6.5.2 Connection response After running the 3-D model extensively using various wind speeds, it was found that 125 mph was the crucial wind speed causing one of the roof-to-wall (toe-nail) connection reaching its peak load. Figure 6.10 shows the connection response under this wind speed in selected locations as indicated in Figure 6.9. It can be seen that the uplift response of the toe-nail connection between the roof and wall is the most critical one compared to other type of connections, because the uplift peak load was already reached. As expected, the shear response of the toe-nail connection is well below the yield load limit, i.e. at the initial linear range (Figure 6.9a). This is due to the lateral wind-loading configuration at the roof surface that almost canceled out each other, in addition to the contribution of internal wall partitions that absorb this lateral load (Asiz, 2008). As shown in Figure 6.9c, yield load is almost reached for the wall-to-floor connection indicated in the structure.

0.0

1.0

2.0

3.0

4.0

5.0

0.0 2.0 4.0 6.0

deformation (mm)

load

(kN

)

uplif t shear

uplif t-test shear-test

0.0

1.0

2.0

3.0

4.0

0.0 4.0 8.0 12.0 16.0 20.0

deformation (mm)

load

(kN

)shear

shearconnect test

(a) A: roof-to-wall joint** (b) B: internal-external connection*/

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 5.0 10.0 15.0 20.0

deformation (mm)

load

(kN

)

shear

shear test

withdrawal

withdrawal-test

(c) C: wall-floor connection*//

Figure 6.10: Selected connection response

Notes: • **: only shear response

perpendicular to the long-building axis was plotted, since there is no wind pressure loads applied in the parallel direction.

• */: ditto • *//: the withdrawal connection test

data was quoted from Winkel (2006).


6.6 Concluding remarks

• From the connection tests conducted in this study, it can be concluded that the majority of the connection responses are ductile, indicated by excessive bending of nail and wood crushing around it. Consequently, in modeling the connection response within LFWS, the load-slip response needs to be represented as non-linear.

• From the 3-d numerical modeling, it was observed that the connection responses in the structure under wind load vary depending on the location. The most critical one is in the roof-to-wall toe-nail connection under uplift load showing highly non-linear response up to the peak load. Therefore, failure identification of LFWS should be initiated from this connection.

• Future connection tests need to include other proprietary fastening systems such as hold-downs, and slender-type of screws for connecting roof and walls. This is important to know how the critical forces flow from one location to another when strengthening mechanism via these connectors is imposed.


7 Full-scale test of LFWS 7.1 Background Light-frame wood structure (LFWS) are normally constructed from several diaphragms such as walls, floors, and roofs; interconnected by nails, metal plates, anchor bolts, and other proprietary fasteners to form a folded type of light-plate structure, making them efficient to resist gravity loads. In the last few years, a large number of residential structures in North America have failed structurally under lateral loads from major wind events such as windstorm, tornados, hurricane; and considerable damages and failures have been reported. This has generated interest to study the failure behaviour of LFWS under this kind of extreme wind load.

Failure analysis of LFWS under wind load is a difficult task due to several factors, including complexity of wind load action, nonlinear nature of connection system, and high variability of material properties and construction techniques. The main objectives of this study are: (1) to investigate the progressive failure mechanism of simple LFWS subjected to wind load under full-scale and controlled laboratory test, and (2) to validate and improve developed numerical models using test results. Of specific interest in this study was to evaluate the model’s ability to predict the progressive failure of light wood-frame structures.

The test concept was developed based on a simple box-type structure loaded with cornering wind as shown in Figure 7.1. Based on predicted pressure distribution derived from wind tunnel test (Figure 7.1a), only three sides of the structure were loaded, two front wall surfaces and whole roof surface (Figure 7.1b). The wall sides were loaded with pressure forces and the roof side with a suction force. With respect to the roof-to-wall connections, which were expected to be the critical part during the loading-to-failure process, two types of connections were used in the test, traditional toe-nailed connection and proprietary hurricane metal connectors. The test was conducted at the Insurance Research Lab for Better Homes, University of Western Ontario (UWO) in London, ON.

(a) 3d view of pressure distribution (b) Wind loading direction on test structure

Figure 7.1: Test concept

Wind directionWind direction

450Pressure

Suct

ion Suction (uplift)

on the roof

No load

No

load

450450Pressure

Suct

ion Suction (uplift)

on the roof

No load

No

load


7.2 Overview of test program 7.2.1 Test specimen description The dimensions of the test structure are 12’x 7’x 8’ (3.65m x 2.13m x 2.44m) with small overhangs on the roof side to simulate actual roof truss/rafter joint system (see Figure 7.2). Since in accordance with field experience and numerical modeling simulation that the dominant failure mechanism is in the connection between roof and wall, no floor framing was included in the test set-up. All wall frame components were anchored directly to steel beams that are rigidly connected to the laboratory strong floor system. Opening (2’x4’) on the structure was created on the non-loading side to provide an easy access to the inside of the structure for installation and instrumentation purposes.

(a) test structure

(b) wall frame component

Roof joists @610 mm o/c

OSB roof sheathing

OSB sheathing

Studs @610 mm o/c

Steel beam

Bottom plate

Double top plate

Load cells

Roof joists @610 mm o/c

OSB roof sheathing

OSB sheathing

Studs @610 mm o/c

Steel beam

Bottom plate

Double top plate

Load cells

12 ‘

7 ‘

8 ‘

12 ‘

7 ‘

8 ‘

12 ‘

7 ‘

8 ‘


(c) during construction (d) load cells

Figure 7.2: Test structure As can be seen in Figure 7.2, the framing for each wall consisted of double top plates, a single bottom plate, and vertical studs spaced at 24” (600 mm) o.c. All framing members were 2 by 4 (38mm x 89mm) spruce-pine-fir stud grade lumber. The outer wall sheathing was ½” thick OSB connected to the studs using 6d-common nails spaced at 6” o.c. (150mm) along the edges and 12” o.c (300mm) for the intermediate studs. No plasterboards were included in the test. The roof system consisted of 2 by 8 joists (38mm x 184mm) spaced at 24” o.c. (600 mm). Each of the roof-joist was connected to the wall using 3-16d-common nails driven at approximately 300-angle through the roof-joist and into the top plate of the wall. Two of the nails were driven into one side of the joist, while the third nail was driven into the other side. Predrilled holes were created in the joists to prevent splitting. The roof sheathing was ½” thick OSB connected to the joists using 3½” long screws at 6” o.c. (150mm) along the edges and 12” o.c. (300mm) at the intermediate joists. Washers were used to ensure that screws were adequately attached and no failure would be expected at the connection between the roof sheathing and joists under wind-suction load.

7.2.2 Loading and instrumentation Pressure loading actuators (PLA) were used to replicate time-varying wind induced pressures on the surface of the structure (Figure 7.3a). The actuator can create controlled pressure and suction forces via a controlled high-power fan and valve system. The actuators were connected via hoses to airbags that were sealed on the building surfaces and mounted in the steel reaction frame (Figure 7.3b). In total, there were 14 airbags installed with the following distribution: 6 airbags installed on the roof (suction), 2 on the north wall (suction), and 6 on the west wall (pressure and suction). Figure 7.4 shows the wind tunnel-based pressure history used in this test, and Figure 7.5 shows the airbags numbering system. The average pressure at each air bag taken over 0.9 second prior to the attainment of peak/failure load is shown in Table 7.1.


(a) PLA unit (b) airbags installed on the test structure

Figure 7.3: Loading system using pressure loading actuator (PLA)

Figure 7.4: Wind pressure time history used


(a) roof (b) side wall (west) (c) side wall (north)

Figure 7.5: Airbags distribution

Table 7.1: Average of the airbag pressure (kPa) taken over 0.9 second prior to observed peak/failure load

20 m/s 30 m/s 35 m/s 40 m/s 45 m/s Airbag #1 -0.50 -1.13 -1.55 -1.91 -1.69 Airbag #2 -0.58 -1.22 -1.71 -2.09 -1.95 Airbag #3 0.33 0.77 1.07 1.30 2.61 Airbag #4 0.31 0.71 0.96 1.17 2.42 Airbag #5 0.03 0.13 0.19 0.20 1.47 Airbag #6 0.43 0.96 1.32 1.62 2.93 Airbag #7 0.48 1.04 1.44 1.73 2.77 Airbag #8 0.20 0.47 0.67 0.75 1.95 Airbag #9 -0.88 -1.88 -2.58 -3.25 -3.79 Airbag#10 -0.59 -1.31 -1.82 -2.22 -2.43 Airbag#11 -0.87 -1.91 -2.61 -3.30 -3.69 Airbag#12 -0.83 -1.59 -2.19 -2.71 -3.26 Airbag#13 -0.84 -1.79 -2.46 -3.08 -3.20 Airbag#14 -0.74 -1.64 -2.25 -2.78 -3.24

The test structure was heavily instrumented with displacement transducers (LVDTs) to record deformations at the crucial locations such as roof-wall junctions and corners. In total there were 37 LVDTs installed: 14 at the junction between the roof-joist and stud; 12 at the junction

910

12 11

14 13

0.675 m

3@0.

9125

m

1.458m

910

12 11

14 13

910

12 11

14 13

0.675 m0.675 m

3@0.

9125

m

1.458m

8 5

7 4

6 3

[email protected] m

8 5

7 4

6 3

8 5

7 4

6 3

[email protected] m

1

2

2@1.

124

m

1.829m

1

2

2@1.

124

m

1

2

1

2

2@1.

124

m

1.829m


between the top-plate and stud; 8 near the building corners; and 3 at the selected junction between the bottom-plate and stud. Eight load cells were installed between the test base and steel-frame support to record force distribution from the superstructure to the base/foundation. Because of the presence of the airbag system, all LVDTs were installed inside the structure, except 4 which were located at the end of the two roof joists. The load cell type used was three-directional load cells with a capacity of 16 kips (vertical) and 8 kips (horizontal). Figure 7.6 shows a schematic placement of LVDTs and load cells. All loading actuators and sensors were connected to a high-speed computer and data logger equipped with data acquisition software. Two high-speed digital camera recorders were mounted inside the structure to observe visually the progressive failure process. (Note: Few of the LVDT’s locations were changed at different stages during the test.)

(a) LVDTs

(b) load cells

Figure 7.6: Placement and numbering of the LVDTs and load cells

SE_EW

NE_EW

SE_NSSW_NS

N

NW_EW

SW_EW

NE_NSNW_NS

SE_EW

NE_EW

SE_NSSW_NS

NN

NW_EW

SW_EW

NE_NSNW_NS

E1, LE1

E2, LE2

E3, LE3

E4

E5

E6

E7

W1, LW1

W2, LW2

W3, LW3

W4

W5

W6

W7

NW

NW

NE

NE

SW

SW

SE

SE

N

E1, LE1

E2, LE2

E3, LE3

E4

E5

E6

E7

E1, LE1

E2, LE2

E3, LE3

E4

E5

E6

E7

W1, LW1

W2, LW2

W3, LW3

W4

W5

W6

W7

NW

NW

NE

NE

SW

SW

SE

SE

NN

Notes: E= East, W=West, N=North, S=South,

Notes: E= East, W=West, N=North, S=South,


7.2.3 Test sequences Table 7.2 shows the test procedure, which was performed in three sequences. For Test #1, the structure was loaded in five different increments started from low wind pressure corresponding to 20m/s wind speed until failure was reached at a wind speed of 45 m/s. After each 15 minute-trace of wind load application, visible damages or excessive deformations were recorded before increasing to the next increment of wind speed. For Test #2, the failed and highly deformed (yielded) toe-nail connections on the west wall were replaced by hurricane ties (Figure 7.7a). Any damage found in other parts of the structure was repaired and restored as close as possible to the pre-loading in Test #1. The load was applied only on the roof surface at wind speed that caused failure in Test #1 (45 m/s wind). The intent was to have a complete failure at the previously yielded toe-nail connections on the east wall of Test #1. For Test # 3, hurricane ties with strap extended to the wall stud below the plate (Figure 7.7b) were used for all roof-joist and wall connections. Due to practical difficulties, toe-nails were not added to the hurricane tie connections. The purpose of Test#3 was to investigate whether failure mechanism was shifted from the roof-to-wall junction to other location(s).

Table 7.2: Testing stages

Test No. Type of the roof-to-wall connection

Increments of wind speed application

1 Toe-nails on both sides of the roof-joist

15 minute traces at 20, 30, 35, 40, and 45 m/s

2 Short-type of hurricane ties on one side and toe-nail on the other side

15 minute traces at 45 m/s

3 Long-type of hurricane ties on both sides of the roof-joist

15 minute traces at 40 and 45 m/s

(a) short-type (b) long-type

Figure 7.7: Hurricane ties used in the test


7.2.4 Test results 7.2.4.1 Test #1 After about 5 minutes loading simulating a 45m/s wind-speed, the structure failed as indicated by a sudden disintegration in the wall and roof junction components. The loading trace was shut down manually to avoid total collapse of the structural system. By observing carefully the video replay of the failure process, it was found that the shear connection failure was initiated between the stud and top plate located at the mid-wall (beneath roof-joist #4 on the west wall, see Figure 7.6). This was followed by splitting of the adjacent stud located beneath roof-joist #5, indicating bending failure due to excessive loading carried by this stud. Seconds after these two failures, the toe-nail connection on roof-joist #4 (on the west wall) failed, which was indicated by nail withdrawal and complete separation between the bottom side of the roof-joist and the top plate. Figure 7.8 illustrates the failure mechanism. Figure 7.9 shows wind speed versus uplift deformation at toe-nail or roof-wall connections. The associated load was also estimated based on the tributary area method of wind pressure applied for simply supported span of the roof joists. Ideal situation would be having load cells that can record the forces experienced by the toe-nail joint. Due to highly time-varying wind and associated deformation values, the deformations plotted were averaged over period of 0.9 second prior to the attainment of peak or failure load. It can be seen in Figure 7.9a that at failure the deformation at the junction between the roof and west-wall (WW_4) reached about 25 mm, which completely separated the toe-nails from the top plate. On the east wall (EW_4), the deformation shows a snap-back as load increased because of large rotation induced by the excessive uplift deformation on the other toe-nail connection, creating a compression load that counter-acted the uplift force. Similar deformation pattern was observed in the toe-nail connections that did not fail, but with much smaller deformation values (Figure 7.9b).

(a) wall (b) toe-nail connection


Figure 7.8: Failure mechanism for Test #1

(a) roof-joist #4 (b) roof-joist #2

Figure 7.9: Wind speed vs deformation at toe-nail connection

7.2.4.2 Test #2 With only the roof surface loaded (no load was applied to the wall) under 45 m/s wind, the toe-nail failure was observed in roof joist #4 (Figure 7.10), but this time the failure was on the east wall because the west side was strengthened with the short-type of hurricane tie. From this finding, it can be noted that there was no structural dependency between the wall-studs and toe-nail failures as was suspected in Test #1, since with no loading applied on the wall surfaces and that the toe-nail failure was confirmed. 7.2.4.3 Test # 3 Under 40m/s wind, no significant damage or distress was found in the structural components. However, the structure failed under 45 m/s wind indicated by connection failure in the hurricane tie located beneath roof-joist #4 of the west side wall. As can be seen in Figure 7.11, the failure was row-shear parallel to the grain in the stud side that was connected with the hurricane tie. This type of brittle failure was due to five nails crowding near the end of the stud creating planes of shear weakness. In practice, 3 to 4 nails are normally used for hurricane tie connection in addition to 2 to 3 toe-nails (Simpson Strong Tie, 2008).

05

101520253035404550

-5 0 5 10 15 20

slip (mm)

win

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eed

(m/s

)

WW_2EW_2

2.6

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ce (k

N)

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N)

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)

WW_4EW_4

2.6

1.81.3

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uplif

t for

ce (k

N)

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slip (mm)

win

d sp

eed

(m/s

)

WW_4EW_4

2.6

1.81.3

0.6

2.2

uplif

t for

ce (k

N)


Figure 7.10: Failure mechanism for Test #2

Figure 7.11: Failure mechanism for Test #3 7.3 3-d numerical model 7.3.1 Model description Finite element (FE) structural analysis software SAP2000 was used in this study (CSI, 2007). Figure 7.12 shows a 3-d model of the test structure at UWO. Structural members and other components were as described in section 7.2. The modelling technique was in principle the same as those described in Chapter 5. Linear-elastic orthotropic shell elements were used to model the sheathing panels attached to wall, roof and floor framing. Those elements had four nodes with six degrees of freedom at each node. Wall studs, plates, and roof joist framing members were modelled using two-node linear frame elements with six degrees of freedom at each node. Mechanical properties and element types used were taken from Asiz et al (2008). All nailed sheathing-to-framing and framing-to-framing connections were modelled using non-linear link elements composed of internal springs with axial, shear and rotational degrees of freedom. Properties of the link elements for each degree of freedom were derived from experimental load-deformation responses and obtained from the connection test program described in Chapter 6. Boundary conditions represented by the load cells were modelled using structural hinge which allows for free rotation but resists translational forces in three orthogonal directions. The small opening on the west side wall including its framing was included in the model. Load applied was mainly from wind pressure distributed to the wall and roof surfaces according to the airbag loading arrangement. The wind pressure applied was based on average value of time-varying pressure during a 0.9s period prior the peak or failure load. Because wind speed increments used were good enough to represent data points for plotting load deformation response, only Test #1 configuration was modelled in this study.

Non-linear static analysis was performed using load-controlled method to investigate failure behaviour of the test structure. The load-controlled method was used because that is most


appropriate for wind effects. All loads on elements were applied incrementally from zero to a user-specified target value, which is wind pressure causing failure (45 m/s). The response of the structure under wind speeds lower than 45 m/s (20, 30, 35, and 40m/s) can be determined from the incremental response of the 45 m/s wind application by matching the incremental steps with the incremental wind speeds.

7.3.2 Test results vs model predictions

(a) before loading (b) deformed shape under loading prior to failure

Figure 7.12: 3-d FE model of the test structure Figure 7.12b illustrates the deformed shape of the structure under 45m/s wind. The predicted largest deformation was found in the stud located at the west wall #4, which was around 36 mm. No comparison with the test data was made here, because the bending failure type was not anticipated to occur in this stud, hence no LVDT was placed to record the stud-bending deflection. However, by checking the predicted maximum moment in this stud, the value (0.9 kNm) is smaller than the unfactored moment capacity of 2x4 SPF stud (1.27/0.8=1.6 kNm) shown in CSAO86-01. This is in accordance with the test observation that the failure was not initiated by bending (splitting) failure in the stud.

Figure 7.13 shows a comparison of the total base reactions between recorded load cell and predicted values. It can be seen that the predicted response is close to the test data when the loading regime is very small (20-30m/s wind). This is partly because the load cells were modeled as hinges and not as springs that could have non-linear responses. Testing isolated response of the load cells fastened in wood material and loaded under static (or cyclic load) in the future would be helpful in determining their actual responses that can be used as input in the model. Figure 7.14 shows a comparison of the deformation responses between the model and test at the four corners of the structure. It can be seen that the predicted values show linear response while the test result shows non-linear response. Again, this is partly due to modeling the boundary conditions (load cells) as hinges.


(a) test (b) model

(a) test (b) model

Figure 7.13: Total base reaction forces

(a) test (b) model

Figure 7.14: Deformation at the corners Note: The vertical axes (‘wind speed’ and ‘step’) were scaled using the same 10-grid scale for comparison purpose.

7.3.3 Load-deformation at the toe-nail connections The non-linear scheme in the model adopts the ‘implicit method’ to define the failure mechanisms in the structural elements. The analysis for each increment of load checks all elements that have already reached post-linear (post-yield) response. However, since only nailed connections were defined as having non-linear load-deformation response, attention was focused on checking link elements such as those in the toe-nail connections. When individual elements yielded, load re-distributions to adjacent elements were automatically applied within the solution algorithm. This was accomplished by applying a localized self-equilibrating condition near any element that sustained loading beyond its peak force capacity. The solution algorithm became unstable when more than one element became overloaded in a particular region where the self-equilibrating condition had previously been applied. It was assumed that progressive failure of

04.5

913.5

1822.5

2731.5

3640.5

45

-30 -10 10 30

sum of forces (kN)

win

d sp

eed

(m/s

)

Sum-FXSUM-FYSUM-FZ

0123456789

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step

NE_EW

NE_NS

NW_EW

NW_NS

SE_EW

SE_NS

SW_EW

SW_NS

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SE_EW

SE_NS

SW_EW

SW_NS

0123456789

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sum of forces (kN)

step SUM-FX

SUM-FYSUM-FZ


the complete structure would ensue. This may not necessarily reflect actual behaviour but as yet alternative assumptions have not been investigated.

Under a 45 m/s wind, the modelling result has shown that the numerical solution obtained was stable indicating no failure occurred in the structure, particularly in the top plate to stud nail and the toe-nail connections. Figure 7.15 shows a comparison of load-slip in the toe-nail connections between model and test result at roof joist #4 (WW4 and EW4) and #2 (WW2 and EW2). It should be noted that the loads here were estimated values determined by calculating the reaction forces of a simply supported roof joist loaded with distributed wind load determined using a simple tributary area method (Figure 7.16). This simple approach was used because during the test there were no sensors/load cells installed to record the axial forces in the toe-nail connections. Table 7.3 shows the wind speed and the maximum reaction force that represents the maximum axial forces in the toe-nail connection. It can be seen that in general the model predicted the load well at small load levels (linear range), but over-predicted just after the non-linear range (yield location) was reached. The model was not able to predict snap back mechanism that occurred in EW4 and WW2, because no geometric non-linearity was included in the model.

(a) west and east walls #4 (b) west and east wall #2

Figure 7.15: Toe-nail connection responses

0.000.280.550.831.101.381.651.932.202.482.75

0 5 10 15 20 25

slip (mm)

load

(kN

)

WW4_model

EW4_model

WW4_test

EW4_test

0.000.280.550.831.101.381.651.932.202.482.75

-5 0 5 10 15 20

slip (mm)

load

(kN

)WW2_model

EW2_model

WW2_test

EW2_test

R1R2

0.523 mRoof joist

w1w2

1.829 m 0.152 m0.152 m

R1R2

0.523 m0.523 mRoof joist

w1w2w1w2

1.829 m 0.152 m0.152 m 1.829 m 0.152 m0.152 m


Figure 7.16: Simply supported roof-joist under wind load and corresponding estimated axial load ’test’ value (R1, maximum uplift reaction force)

Table 7.3:Wind speed vs reaction (R1)

Note: The w1 and w2 were calculated based on the joist spacing of 24” o.c.

7.4 Discussion The test results indicate that failure of simple LFWS is complex, and is a combination of ductile and brittle modes. The ductile failure mode was the result of failure in nailed connection such as nail within wall components and nail connections between the roof and wall components. In this test, progressive failure was initiated by shear failure in the nail connection between the top-plate and wall stud located at the high pressure area (midwall) followed by bending failure of wall stud near it, and at the same time pull-out of the toe-nail connection. However, it was confirmed that the toe-nail failure and nail shear failure are independent.

So far by comparing with the test results, the numerical model has predicted the structural response poorly, particularly in the non-linear behaviour range. This is because the main source of non-linearity was assumed for the nail connection response, and mechanical properties of wood framing members and sheathing panels were modeled as linear-elastic materials. Also, no geometric non-linearity was incorporated in the model. As was observed during the test, the structures had undergone large deformation before failure, which could indicate that the geometric non-linearity may become a more significant factor near failure. 7.5 Concluding remarks Future test will incorporate loading the same structure using an equivalent a code specified uniformly distributed load. By comparing the responses to the two loads (actual and an equivalent uniformly distributed load) test programs, conclusions can be drawn regarding the differences in structural response and failure mechanism when a light wood frame structure is loaded under an actual wind loading excitation and under an equivalent code load. Detail future test instrumentation should be able to capture the force distribution to the critical components such as in the roof-to-wall connections. To do this load cells between the roof and wall components need to be installed, at least to capture force in the linear regime before conducting destructive test using actual toe-nail and toe-nail with metal strap connections between roof and wall.

speed (m/s) p1(kPa) p2 (kPa) w1 (kN/m) w2 (kN/m) R1 (kN) 20 -0.87 -0.83 -0.53 -0.51 0.63 30 -1.91 -1.59 -1.16 -0.97 1.29 35 -2.61 -2.19 -1.59 -1.34 1.77 40 -3.30 -2.71 -2.01 -1.65 2.22 45 -3.69 -3.26 -2.25 -1.99 2.57


8 3-d numerical model of LFWS under earthquake (dynamic) load

This chapter presented a seismic reliability analysis of a one-story light-frame building using the response surface method with importance sampling. The peak inter-story drifts were selected as the performance criteria to estimate the structural failure probability. The randomness involved in ground motions, structural mass and response surface fitting errors was considered in the formulation of the performance function. The structural mass carried by the building was assumed to be 160 kg/m2, which was relatively high compared with other studies (Wang and Foliente, 2006). Under the assumed serviceability hazard level with exceedance probability of 50% in 50 years (50%/50y), this building had a reliability index around 1.87 with respect to the 23 serviceability performance criteria. And it had much higher seismic reliability indices, 3.04 and 3.36, with respect to the life safety and collapse prevention criteria, respectively. Under the assumed ultimate limit state hazard level with exceedance probability of 10% in 50 years (10%/50y), this building had a low reliability index, only about 0.39 with respect to the serviceability performance criteria. And it had reliability indices of 1.61 and 1.95 with respect to the life safety performance criteria and the collapse prevention performance criteria, respectively. The seismic reliabilities of a 2.44 m (8-foot) long shear wall selected from the building were also estimated. By comparing failure probabilities of the wall considering the system effect and the isolated wall, the system effect was evaluated. It was found the effective mass carried by the wall considering the system effect was much smaller than the tributary mass carried by the isolated wall. The seismic reliability of the wall with the system effect was significantly higher than the isolated wall. For example, under the seismic hazard level of 50%/50y, the wall considering the system effect had a reliability index of 2.22 with respect to the serviceability performance criteria, much higher than 1.59 of the isolated walls. Similarly, under the seismic hazard level of 10%/50y, the wall considering the system effect had a reliability index of 1.55 with respect to the life safety performance criteria, much higher than 1.02 of the isolated wall. Therefore, the estimated seismic reliabilities of the isolated wall are lower bound values considering its actual performance in the building system. Detail report analysis of this chapter can be seen in Appendix E.


9 System reliability analysis Focus of this activity was on the development of system-based design in LFWS using reliability analysis with a long-term goal of implementing it in Canadian wood design standard (CSAO86-01). Before discussing wood system reliability analysis, general design procedure in other construction material with emphasis in steel structure was presented. That also included the development of system reliability analysis in the design of steel structures.

9.1 Design procedure in steel structure The general design approach embodied in the current design of steel structures is the load and resistance factor design (LRFD) concept (AISC, 1999, CSA, 2001). Therein structural components are designed taking into consideration various possible limiting states including ultimate load (strength, stability) and serviceability conditions. Appropriate load and resistance factors are used to achieve certain nominal levels of structural reliability under various loading conditions at the element/component level. In the LRFD format, the design equation of a structural component is expressed as

nRiQi Φ≤∑ λ (1)

where λi is the load factor for the nominal load component Qi, and Φ is the resistance factor for the nominal resistance Rn. Current design procedures in steel structures are still component (member, connection) based. In the general provisions, however, it is explicitly mentioned that the design of steel members and connections shall be consistent with the intended behaviour of structural framing systems and basic assumption made in the structural analysis (AISC, 1999; CSA, 2001). This is equivalent to statements made in codes for design with other structural materials including wood. The specification of methods for structural analysis was included for the first time in the 1999 edition of the American Institute of Steel Construction LRFD code (AISC, 1999). Past editions did not specify how analysis was to be performed, and therefore the basic assumptions about strength and behaviour of elements were independent of how any structural system was modelled. The revision was motivated and made possible by vast developments in numerical modeling software for the structural analysis of steel structures. Specification of how structural analysis is to be performed implies that how steel structural systems behave is known and can be controlled. This specification of how analysis is to be performed includes issues of structural stability, second order (plastic/inelastic) analysis, lateral load performance of systems, and connection behaviour (Deierlien, 1997). Recommendations have been given by researchers to incorporate system effect in designing steel (frame) structures, with structural reliability assessment as the main vehicle. The simplest proposed way to handle systems effect in a structure is to introduce an adjustment (modification) factor Φs into the resistance factor in equation (1), i.e.


nRiQi sΦΦ≤∑ λ (2)

The numerical value of this system factor could be derived based on a structural member’s ductility or strength reserve (material response), structural geometry (redundancy), or classification of limiting states. In the late 1980’s (Galambos, 1990) it was proposed to incorporate a system factor in LRFD-based steel design using classification of limit states according to the level of structural damage permitted and the target level of reliability (Table 9.1). Each damage category was classified based on possible failure modes and consequences. For example, ‘slight damage’ could be indicated by yielding of a tension member without excessive deflection; ‘complete damage’ could be indicated by frame instability. Current LRFD specifications for Φ factors are based approximately on the target reliability index βT = 2.5, which corresponds to the system factor associated with moderate damage. Table 9.1: Classification of limit states (Galambos, 1990)

Limit state classification βT Φs

Slight damage 2.0 1.1 Moderate damage 2.5 1.0 Serious damage 3.0 0.9 Complete damage (no loss of life) 3.5 0.8 Complete damage (loss of life) 4.0 0.7

Note: βT = target reliability index

Hendawi and Frangopol (1994) suggested incorporating subsystem and entire system effects into the overall system factor via a strength reserve classification (Table 9.2). From this, Φs = Φs1 x Φs2 where Φs1 and Φs2 correspond to structural system and subsystems factors, respectively. Using a two-level systems effect, or even more, would result in a more discriminating and rational system assessment and improved consistency in reliability of components and complex structural systems. This practice may be appropriate for implementation in light-frame wood buildings, which are mostly composed of various components and subsystems. The approach of Hendawi and Frangopol (1994) is conceptually similar to ideas for wood systems proposed by Smith et al (2006). Table 9.2: Strength reserve classification (Hendawi and Frangopol, 1994)

Resistance system Level of system strength reserve factor Nil Low Medium High Φs1 0.80 0.90 1.00 1.10 Φs2 0.90 0.95 1.00 1.05

The majority of structural reliability research in steel structures has focused on providing a basis for code calibration at the component level. Work in Canada by Bartlett et al (2003a&b) that developed new values for load factors and load combination factors in the 2005 edition of National Building Code of Canada (NRC 2005) is an example of code calibration activity on the


load side of equation (1) using component-based reliability analysis. Their work was intended to achieve more consistent and uniform reliability with target reliability indexes in the range β = 2.8 to 3.0 for steel components under various load combinations. It was found that reliability indices obtained for the pre-1995 editions of the NBCC 1995 code were relatively high and non-uniform (β = 2.8 to 4.0) because of the definition imposed on the live load that includes both snow load and occupancy loads acting concurrently at their maximum values (which is highly unlikely). Research work on understanding comparative performance between system and member reliability using actual structural systems has been scarce in the literature. Zhou and Hong (2004) addressed this issue by performing reliability assessment of actual planar (2D) moment-resisting steel frames designed according to AISC LRFD specifications. In that study the reliability of structural components was determined using simple reliability analysis methods like First Order Reliability Methods (or FORM for short), with member forces calculated from elastic analysis. The limit state condition for the complete structural frame was determined based on the so-called collapse load factor calculated from Second Order Methods incorporating inelastic/plastic response analysis. The system reliability analysis was determined from FORM and Monte Carlo probabilistic simulation. Result suggests that the system reliability is much higher than the reliability of the most critical members due to redundancy effects and force redistribution capabilities of the structural arrangement. This is an indication that the system aspect needs to be incorporated in the steel design code.

9.2 Design of LFWS System behaviour in LFWS has been recognized in repetitive member systems such as wood floor-joists, rafter and roof trusses, and wood-stud walls. The current design procedure for these members have already incorporated system reliability concept through a so-called system factor, similar to system factor effect described in equation (2) above. For example, in designing closely spaced, repetitive bending members such as floor joist, system factor ranging from 1.1 to 1.4 were used in the Canadian code, depending on joist spacing, nail spacing, and joist (lumber) quality (CSA, 2005). In general, these system factors were derived based on system reliability analysis that applied simple approach in defining failure criterion (ultimate state). For example, the ultimate limit state in wood floor system was defined as either failure of two adjacent members or failure of a set number of members (e.g. Foschi, 1982). Because of load-sharing capability in highly redundant wood floor or other sheathed wood frame systems, the ultimate limit state should consider load re-distribution when one or two members fail. Most of the research in wood system reliability analysis has been focused on incorporating these issues. However, as in the steel structure, techniques for conducting system reliability analysis in wood-structural systems require simplified behavioural models or vast numerical modeling resources. As was indicated in the numerical modeling chapter regarding the large number of elements used in the deterministic analysis, it is not feasible using present computer technology to conduct system reliability simulation of 3-d LFWS (e.g. Monte Carlo). Therefore, a simplified approach that combines load redistribution and ultimate-state definitions is needed. Once this is established, a system reliability analysis using first or second order method or using a combination of simulation and close-form solutions can be performed.


Unlike in the previous wood system reliability research, in this project system factor is proposed to be incorporated in the wood diaphragms (wall and roof) design. For example, in the shear wall design, the shear resistance of nailed shear wall is (CSA, 2005):

Vrs = Φ vdKDKSF KH JubJspJhdLw where KH is the proposed system factor, which is likely dependent on system characteristics, including: building configuration and shape, hold-down (Jhd), presence of certain load path, and presence of ductile elements. To determine this system factor, similar system reliability analysis procedure as in the steel or wood-joist floor using simplified system behaviour can be implemented. More extensive research is required in order to develop this KH factor.

9.3 Concluding remarks Two important findings from this activity are:

• Application of reliability concepts for element based design (existing codes for steel and other materials) are based on nominal reliability and not true reliability. The target reliability indices (β values) and resistance factors (Φ values) that are derived from reliability studies are those values that cause combined application of particular design loads, material design properties and structural analysis methods to replicate traditional design solutions. This is relatively straightforward to apply at element or even subsystem levels, but not at the level of full system. An implication is that system design methods should be based on consideration of true rather than nominal reliability estimates which in turn implies that knowledge of loads must be precise. This reflects that right and left sides of design equations like equations (1) and (2) above cannot be regarded as independent.

• Details of system effects can be expected to be very different between steel and wood systems because structural forms used differ and because of differences in ductility and brittleness of materials used. However, there is no reason why fundamentals of methods should differ.

Significant challenges exist in studying system behaviour and assessing reliability of systems. The challenges include:

- ability to predict what failure modes will govern systems, - ability to predict load redistributions as systems deform and begin to fail, - finding a limit state (performance measure) of an overall structural system (which will be

a function of structural form and failure modes for components), - obtaining statistical correlation amongst failure modes, and - balancing ability of systems to withstand different types of response demands associated

with alternative load combinations. This last factor has strong implications with respect to ability to optimise efficient use of materials. As is well understood, simple systems with parallel components or subsystems subjected to simple loadings have far greater reliability than the reliability of the most critical element in the system (Ditlevsen and Bjerager, 1986; Nowak and Collins, 2000). However, reliability


assessment of actual structural systems subjected to a wide spectrum of static and dynamic loads will need a more comprehensive approach than what currently exists. There is also need to ensure consistency between design at components, subsystems and system levels. Closed form design solutions for systems will be impossible, except for trivial design situations. Advanced computer models that embrace finite element methods and reliability analysis can do what is needed (e.g. Pellissetti and Schueller, 2006; Mahadevan and Haldar, 1991). Alternatively there will have to be acceptance that closed form solutions are approximate (but still undoubtedly much better than what the current generation of design codes yield). Thus an important question is what type of analytical tools it can be assumed that designers should use. Discussion of this should recognise of course that implementation of any generalised system level design of buildings built primarily of steel, wood or other materials will not happen in Canada before 2010 or even not before 2015.


10 Conclusions Based on the activities performed in this project the following conclusions are drawn: 1. From the 3-d numerical modeling of one- and two-storey LFWS subjected to high wind load,

the critical component is in the roof-to-wall connections fastened using toe-nails. This finding strengthens previous field observations after post-failure events such as hurricane and windstorm. Load redistribution in the toe-nail connections was also observed when one or more toe-nails have already reached their peak load, while the applied wind load is increased.

2. Based on the structures analysed in this project, it is found that the critical wind speed causing failure in the roof-to-wall connections is 125 mph. This corresponds to Category 4 (131-155mph) of commonly used Saffir-Simpson Hurricane Scale. It should be noticed here that the 3-d modeling exercise is based on presumption that no defect or construction error was simulated in the modeling. Other findings are:

a. No significant increase in the wind speed failure was found between one and two-storey LFWS.

b. No significant increase in the wind speed failure was found between the 3-d structures with and without any internal wall partitions.

c. System effect was observed in 2-d roof structure, 3-d roof or full structure analyses.

d. Strengthening the roof-to-wall connection using hurricane metal connector leads to an increase in the critical wind speed that causes failure and a shift in failure mechanism from roof-wall connection to other parts of LFWS.

e. Relative to the exterior walls, larger lateral forces are carried by the internal wall partitions, especially those that extend the full length of the structure.

f. Current analytical methods to calculate lateral force distribution to the walls could lead to either conservative or unconservative results depending on structural details.

3. Testing of isolated roof-to-wall connections under static monotonic load indicates ductile failure response in the three major directions, but large variability in the response was observed in the uplift direction.

4. Full-scale testing result of a simple LFWS subjected to wind load indicated that the failure mechanism was initiated in the wall component followed by the roof-to-wall connection. However, the failure within the wall components and the toe-nails were independent. Simple calculation method to find the roof-to-wall connection capacity is adequate for this simple LFWS. The 3-d numerical model shows over-predicted stiffness in the structural system and failure load.

5. Based on the reliability analysis of one-storey LFWS under seismic load, the reliability of the whole structural system is higher than that of an isolated wall component, indicating system effect.

Recommended future work is as follow: 1. The developed 3-d model should be used to evaluate a broader range of structural details to

evaluate the influence structural redundancy on load distribution.


2. The 3-d model should also be extended to incorporate system reliability analysis with certain degree of numerical modeling simplification. This will allow the system design factor for shear walls and diaphragms to be developed using reliability theory.

Practical design implication and impacts/benefits to the wood industry resulting from findings of this project are: 1. Better knowledge on the system behaviour of LFWS under lateral loads (wind and

earthquake). 2. Identification of major technical issues that need to be addressed if system design factors for

shear walls and diaphragms are to be developed for CSAO86. 3. Creation of technical database for advanced 3-d numerical models of LFWS that can be used

as a basis to answer what-if scenarios in wood construction industry. 4. Creation of technical database for connections in LFWS including connection characteristic

and performance under isolated condition.


References Chapters 4&5: Literature review Cheng, J. 2004. Testing and analysis of the toe-nailed connection in the residential roof-to-wall system, Forest Products Journal, 54(4): 58-65. Collins, M., Kasal, B., Paevere, P., Foliente, G.C. 2005a. Three-dimensional model of light frame wood building. I: Model description, ASCE Journal of Structural Engineering, Vol. 131, No. 4, pp 676-683. Collins, M., Kasal, B., Paevere, P., Foliente, G.C. 2005b. Three-dimensional model of light frame wood building. II: Experimental investigation and validation of the analytical model, ASCE Journal of Structural Engineering, Vol. 131, No. 4, pp 684-692. Folz, B., Filiatrault, A. 2004a. Seismic analysis of woodframe structures. I: Model formulation, ASCE Journal of Structural Engineering, Vol. 130, No. 9, pp 1353-1360. Folz, B., Filiatrault, A. 2004b. Seismic analysis of woodframe structures. I: Model implementation and verification, ASCE Journal of Structural Engineering, Vol. 130, No. 9, pp 1353-1360. Gupta, A.K., Kuo, G.P. 1987. Modeling of a wood-framed house, ASCE Journal of Structural Engineering, Vol. 113, No. 2, pp 260-278. Kasal, B., Leichti, R.J., Itani, R., Y. 1994. Nonlinear Finite-element model of complete light-frame wood structures, ASCE Journal of Structural Engineering, Vol. 120, No. 1, pp 100-119. Kasal, B. 1992 A nonlinear three-dimensional model of a light-frame wood structure, Doctoral dissertation, 316p, Dept. of Forest Product, Oregon State University, Corvallis, OR. Liska, A.J., Bohannan, B. 1973. Performance of wood construction in disaster areas, Journal of the Structural Division, ASCE, Vol.99, No. ST12. Nateghi, F. 1988. Analysis of wind forces on light-frame timber structures, Doctoral Dissertation, 194p, Dept. of Civil Engineering, University of Missouri, Columbia, MO. Patton-Mallory, M., Wolfe, R., Soltis, L., Gutkowski, R. 1985. Light-frame shear wall length and opening, ASCE Journal of Structural Engineering, Vol. 111, No. 10, pp 2227-2239. Phillips, T.L. 1990. Load sharing characteristics of three-dimensional wood diaphragms, Master thesis, Dept. of Civil Engineering, 236p, Washington State University, Pullman, WA. Tarabia, A.M. (1994), Response of light-frame buildings to earthquake loadings, Doctoral dissertation, pp 187, Dept. of Civil Engineering, Washington State University, Pullman, WA.


Tarabia, A.M., Itani, R.Y. (1997), Seismic response of light-frame wood buildings, ASCE Journal of Structural Engineering, Vol. 121, No. 11, pp 1470-1477. Tuomi, R.L., McCutcheon, W.J. (1974), Testing of a full-scale house under simulated snowloads and windloads, USDA Forest Service Research Paper, FPL 234, 32p, Madison, WI. Yoon, T.Y. (1991), Behaviour and failure modes of low-rise wood-framed buildings subjected to seismic and wind forces, Doctoral dissertation, 392p, Dept. of Civil Engineering, North Carolina State University, Raleigh, NC. Chapter 6: Connection test

American Society of Civil Engineers (ASCE). 2005. Minimum Design Load for Building and Other Structures, ASCE7-05, ASCE, Reston, VA.

Asiz, A, Chui, Y.H., Smith, I. 2008. Failure Analysis of Light Wood Frame Structure Under Wind Load, International Council for Research and Innovation in Building and Construction Working Commission W18-Meeting 41, St. Andrews, New Brunswick, August 25-28.

Chui, Y.H., Asiz, A., Smith, I., Bartlett, M. 2008. Post-yielding and Load Redistribution Behaviour of Light-frame Wood Structures Under Wind Loads, Proceeding of the Annual Conference of the Canadian Society for Civil Engineers, June 10-14, Quebec City, Quebec.

American Society for Testing and Materials (ASTM). 2001. Standard Test Methods for Mechanical Fasteners in Wood, Annual Book of ASTM Standard, Vol. 04.10, D1761, ASTM, West Conshohocken, PA.

Canada Mortgage and Housing Corporation (CMHC). 2005. Canadian wood-frame house construction, Canada Mortgage and Housing Corporation, Ottawa, Ontario.

Kasal, B. 1992. A non-linear three-dimensional model of a light-frame wood structure, PhD Thesis, Department of Forest Products, Oregon State University, Corvallis, OR, 316p.

Mi, H. 2004. Behaviour of unblocked wood shear walls, Master Thesis, University of New Brunswick, Fredericton, Canada, 220p.

Winkel, M. 2006. Behaviour of light-frame wall subject to combined in-plane and out-of plane loads, Master Thesis, University of New Brunswick, Fredericton, Canada, 191p.

Chapter 7: Full-scale test of LFWS Asiz, A., Chui, Y.H. (2008), Development of Advanced System Design Procedures for the Canadian Wood Design Standard, UNB01 Progress Report-Year 1, Natural Resources Canada under the Value-to-Wood Program, Ottawa, ON, p 84. Asiz, A., Chui, Y.H., Smith, I. (2008), Failure Analysis of Light Wood Frame Structures Under Wind Load, International Council for Research and Innovation in Building and Construction, Working Commission W18-Timber Structure, Aug 24-28, St. Andrews, Canada, Paper 41-15-5.

CWC (2005), Wood Design Manual, Canadian Wood Council, Ottawa, ON. CSI (2007), Structural Analysis Program SAP2000-NonLinear version 11-User Guide. Computer and Structures, Inc., Berkeley, CA.


Simpson Strong Tie (2008), Specification for hurricane ties installation, California. Chapter 9: System Reliability American Institute of Steel Construction (AISC). 1999. Specification for the load and resistance factor design of structural steel buildings, 3rd ed., Chicago, IL.

Bartlett, F.M., Hong, H., Zhou, W. 2003a. Load factor calibration for the proposed 2005 edition of the National Building Code of Canada: Statistics of loads and load effects, Canadian Journal for Civil Engineering, 30: 429-439.

Bartlett, F.M., Hong, H., Zhou, W. 2003b. Load factor calibration for the proposed 2005 edition of the National Building Code of Canada: Companion-action load combinations, Canadian Journal for Civil Engineering, 30: 440-448.

Canadian Standard Association (CSA). 2001. CAN/CSA S16-01: Limit States Design of Steel Structures, Rexdale, Ontario.

Deierlien, G.G. 1997. Steel frame structures, Progress in Structural Engineering and Materials, Vol. 1(1): 10-17.

Ditlevsen, O., Bjerager, P., (1986). Methods of structural systems reliability, Structural Safety, 3: 195-229.

Galambos, T.V. 1990. System reliability and structural design, Structural Safety, 7: pp 101-108.

Hendawi, S., Frangopol, D.M .1994. System reliability and redundancy in structural design and evaluation, Structural Safety, 16: 47-71.

Kulak, G.L., Adams, P.F., Gilmor, M.I. 1995. Limit States Design in Structural Steel, Canadian Institute of Steel Construction, Alliston, Ontario.

Mahadevan, S., Haldar, A. 1991. Practical random field discretization in stochastic finite element analysis, Structural Safety, 9: 283-304.

National Research Council. 2005. National Building Code, NRC, Ottawa.

Nowak, A.S., Collins, K.R. 2000. Reliability of Structures, McGraw Hill, Boston.

Pellissetti, M.F., Schueller, G.I. 2006. On general purpose software in structural reliability – An overview, Structural Safety, 28: 3-16.

Salmon, C. G. 1996. Steel structures: design and behaviour, 4rd ed., Prentice Hall, New Jersey.

Smith, I., Chui, Y.H., Quenneville, P. 2006. Overview of a new approach to handling system effects in timber structures. Working Commission W18 - Timber Structures Paper 39-8-1, International Council for Building Research Studies and Documentation, Rotterdam, The Netherlands. Zhou, W., Hong, H.P. 2004. System and member reliability of steel frames, Steel and Composite Structures, Vol. 4(6): 419-435.


Appendix A: Critical wind speeds and toe-nail force

distributions of the LFWS studied


(a) uplift forces developed in the toe-nail joints (b) wind pressure distribution

Figure A.1: Modeling 3-d roof truss only

(a) uplift forces developed in the toe-nail joints (b) wind pressure distribution Figure A.2: One-storey whole building numerical model with internal partitions

(a) uplift forces developed in the toe-nail joints (b) wind pressure distribution Figure A.3: One-storey whole building numerical model without any internal partition

1

2

34

1E

2E

3E4E

1

2

34

1E

2E

3E4E

0

0.5

1

1.5

2

2.5

1 3 5 7 9 11 13 15 17 19 21


axia

l for

ce (k

N) 90 mph100 mph110 mph120 mph125 mph

233E

2E

323

3E

2E

3

0.000

0.500

1.000

1.500

2.000

2.500

1 3 5 7 9 11 13 15 17 19 21


axia

l for

ce (k

N) 90 mph


1

2

34

1E

2E

3E4E

1

2

34

1E

2E

3E4E

0.000

0.500

1.000

1.500

2.000

2.500

1 3 5 7 9 11 13 15 17 19 21


axia

l for

ce (k

N) 90 mph


roof-truss toe-nail joint analysed


(a) uplift forces developed in the toe-nail joints (b) wind pressure distribution Figure A.4: Two-storey whole building numerical model with full internal partitions

(a) uplift forces developed in the toe-nail joints (b) wind pressure distribution Figure A.5: Two-storey whole building numerical model without any internal partition*

Note: * longitudinal load bearing wall included as support for the second storey

1

23

4

1E

2E

3E4E

1

23

4

1E

2E

3E4E

0

0.5

1

1.5

2

2.5

1 3 5 7 9 11 13 15 17 19 21


axia

l for

ce (k

N) 90 mph


1

23

4

1E

2E

3E4E

1

23

4

1E

2E

3E4E

0.00

0.50

1.00

1.50

2.00

2.50

1 3 5 7 9 11 13 15 17 19 21


axia

l for

ce (k

N) 90 mph



Appendix B: Detail calculation using analytical method of the

lateral force distribution due to wind load


Detail calculation using analytical method for the lateral force distribution to the walls due to wind load

1. One internal partition Figure 1 shows the layout of the building being analysed, 14m (42ft) long by 9.3m (28ft) wide. The interior wall was located at one third of the longitudinal. The walls being analyzed were designated as exterior wall 1 (W1), internal wall 2 (W2), and exterior wall 3 (W3). The design wind load is 11.30 kN.

Figure 1 Plan dimensions of the wood frame house 1.1 Tributary Area Method This method, which is the simplest one, assumes that the horizontal roof and floor diaphragms are flexible and each shear wall is assumed to act independently. Therefore, the lateral forces are distributed in proportion to the tributary area associated with the shear wall. No consideration is given to the influence on the lateral force distribution of the shear wall stiffness (see Figure 2).

Figure 2 Tributary Area Method

From Figure 1 and the building height information,


the tributary area associated with wall 1 is 24.267 8.534 18.22

m× =

the tributary area associated with wall 2 is 24.267 8.535 8.534 54.632 2

m⎛ ⎞+ × =⎜ ⎟⎝ ⎠

the tributary area associated with wall 3 is 28.535 8.534 36.4232

mm× =

Thus, the total area is 212.8 8.534 109.23mm× = According to the Tributary Area Method, the shear force resisted by W1 is simply:

1 18.2 11.30 1.88109.23

The tributary area associated with wall Force kNThe total area

× = × =

and the shear forces resisted by W2 and W3 can be obtained respectively as follow:

2 54.63 11.30 5.65109.23


× = × =

3 36.423 11.30 3.77

109.23The tributary area associated with wall Force kN

The total area× = × =

Figure 3 shows the sketch of the force distribution based on this method. It is obvious that the assumption of horizontal roof and floor diaphragm are flexible often contradicts the reality when the building is not symmetrical and has different stiffness between each shear wall. The oversimplified assumption may lead to conservative or non-conservative results.

Figure 3: Tributary Area Method

1.2 Continuous and Simple Beam Methods The continuous and simple beam methods could be regarded as a subset of the tributary area method (Figure 4). The simple beam method consider the structure as a series of simple beams subjected to a uniform line load which is equal to the total lateral load divided by the length of the building.


The continuous beam method uses a continuous beam over simple supports with a uniform line load, which is equal to the total lateral load divided by the length of the building, to do the calculation. In these two cases, the force distribution has nothing to do with the roof and floor configurations.

(a) The simple beam method

(b) The continuous beam method

Figure 4: Continuous and Simple Beam Methods

From the building geometry:

The length of the building is 4.267 8.535 12.8m+ = .

The uniform line load is 11.30 0.883 /12.8 12.8

Ff kN m= = =

Thus, the shear forces resisted by each shear wall are (Figure 4a):

The shear force resisted by wall 1:

4.2670.883 1.882

kN× =


(4.267 8.535)0.883 5.652

kN+× =


8.5350.883 3.77

2kN× =

To calculate the reactions for the continuous beam method, standard structural analysis table or simple numerical model can be used. A uniform line load 0.883 /kN m is applied to the beam. The results can be seen in Figure 4b.


(a) The simple beam method (b) The continuous beam method

Figure 4: The simple and continuous beam methods

1.3 Relative Stiffness Method without Torsion As was described before, in the tributary area method the lateral forces are distributed in proportion to the tributary area associated with the shear wall, rather than the stiffness. The relative stiffness method is based on an assumption that the horizontal roof and floor diaphragm are rigid, such that the lateral forces are distributed in proportion to the stiffness of the shear wall. The approach used to estimate the shear wall stiffness is based on the finite element modeling. Finite element model of all the walls were developed using the SAP2000 software. The material properties and connection properties were based on the 3D finite element model of the one-story house conducted in chapter 5 of this report. Figure 5 illustrates the FE model for the end wall and Figure 6 shows the FE model for the interior wall. Unit load was applied along the wall height in the direction of the applied wind, and the deformation was determined. The stiffness of shear wall is simply the load divided by the racking deformation of the wall, and designated as K1, K2, and K3. After running the model, it was obtained that K1= K3=6.6kN/mm, K2=3.97kN/mm.

Figure 5: The model of the end wall

Figure 6: The model of the end wall


Then, the shear force resisted by each can be calculated as follow (see Figure 7 for the diagram):

Wall 1: 1

1 2 3

6.6 11.3 4.346.6 6.6 3.97

K F kNK K K

× = × =+ + + +

Wall 2: 2

1 2 3

3.97 11.3 2.616.6 6.6 3.97

K F kNK K K

× = × =+ + + +

Wall 3: 3

1 2 3

6.6 11.3 4.346.6 6.6 3.97

K F kNK K K

× = × =+ + + +

Figure 7: Relative Stiffness Method without Torsion 1.4 Relative stiffness method with torsion (rigid beam on elastic foundations) These two methods are substantially the same. If the structure’s center of gravity and the center of rigidity of the shear wall do not coincide, the torsional stiffness will effect the lateral force distribution. In these two methods, the structure is represented as a rigid beam on linear springs, as shown in Fig.4. Linear springs are used to represent the shear walls. Using the same wall stiffness obtained previously, the shear forces resisted by each shear wall can be calculated. Again, standard structural analysis table or simple numerical model can be used for this purpose. The results can be seen in Figure 9.

Figure 8: Relative Stiffness Method with Torsion (Rigid Beam on Elastic Foundations)


Figure 9: Relative Stiffness Method with Torsion (Rigid Beam on Elastic Foundations) 2. Two internal wall partitions The interior walls were located at one third and two thirds of longitudinal wall (Figure 10).

Figure 10: Two internal wall partition

2.1 Tributary area method:

Based on Figure 10:

The tributary area associated with wall 1 is 24.267 8.534 18.22

m× =

The tributary area associated with wall 2 is 24.267 4.267 8.534 36.422 2

m⎛ ⎞+ × =⎜ ⎟⎝ ⎠


m⎛ ⎞+ × =⎜ ⎟⎝ ⎠


m× =

The total area is 212.8 8.534 109.23mm× =


The shear forces resisted by wall 1 and wall 4 are:

1(4) 18.2 11.30 1.88109.23


× = × =

The shear forces resisted by wall 2 and wal3 are: 2(3) 36.42 11.30 3.76



Figure 11: Tributary Area Method 2.2 Simple beam and continuous beam method: The length of the building is 4.267 8.535 12.8m+ = .

The uniform line load is. 11.30 0.883 /12.8 12.8

Ff kN m= = =

For the simple beam method, the shear forces resisted by each shear wall are:

The shear force resisted by wall1 and wall 4:

4.2670.883 1.88 /2

kN m× =

The shear force resisted by wall 2 and wall3:

(4.267 4.267)0.883 3.76 /2

kN m+× =


Figure 12: Simple Beam Method

Using the same procedure as before, the shear force distribution for the continuous beam method is shown in Figure (Note: W1=W4, and W2=W3).

Figure 13: Continuous Beam Method 2.3 Relative Stiffness Method without Torsion: Using K1= K4=6.6kN/mm, K2=K3=3.97kN/mm:

The shear force resisted by each wall 1and wall 4: 1(4)

1 2 3 4

6.6 11.3 3.526.6 3.97 3.97 6.6

KF kN

K K K K× = × =

+ + + + + +

The shear force resisted by each wall 2 and wal3:

2(3)

1 2 3 4

3.97 11.3 2.126.6 3.97 3.97 6.6

KF kN

K K K K× = × =

+ + + + + +


Figure14: Relative Stiffness Method without Torsion

2.4 Relative Stiffness Method with Torsion (Rigid Beam on Elastic Foundations)

Figure15: Relative Stiffness Method with Torsion (Rigid Beam on Elastic Foundations) 3. Two discontinuous internal walls The interior walls were located at one third and two thirds of longitudinal wall and the interior walls are not continuous (Figure 16).

Figure 16: Building layout with two discontinuous internal walls

3.1 Tributary Area Method:



m× =


m⎛ ⎞+ × =⎜ ⎟⎝ ⎠


m⎛ ⎞+ × =⎜ ⎟⎝ ⎠


m⎛ ⎞+ × =⎜ ⎟⎝ ⎠

The total area is 212.8 8.534 109.23mm× = Thus, the shear forces resisted by wall 1 and wall 4 are:

1(4) 18.2 11.30 1.88109.23


× = × =

and the shear forces resisted by wall 2 and wal3 are: 2(3) 36.42 11.30 3.76



Figure 17: Tributary Area Method

3.2 Simple and Continuous Beam Method: The length of the building is 4.267 8.535 12.8m+ = .

The uniform line load is. 11.30 0.883 /12.8 12.8

Ff kN m= = =

Thus, the shear forces resisted by each shear wall are (Figure 18):

The shear force resisted by wall1 and wall 4:

4.2670.883 1.88 /2

kN m× =

The shear force resisted by wall 2 and wall3:

(4.267 4.267)0.883 3.76 /2

kN m+× =


Figure 18: Simple Beam Method

Using the uniform line load 0.883 /kN m the support reaction forces, which are the lateral force of each wall can be obtained. So according to the Continuous Beam Method, the shear forces resisted by each shear wall are shown in Figure 19.

Figure 19: Continuous Beam Method

3.3 Relative Stiffness Method without Torsion: Using K1= K4=6.6kN/mm, K2=k3=1.59kN/mm, the shear force resisted by each wall 1and wall4:

1(4)

1 2 3 4

6.6 11.3 4.556.6 1.59 1.59 6.6

KF kN

K K K K× = × =

+ + + + + +

and the shear force resisted by each wall 2 and wal3:

2(3)

1 2 3 4

1.59 11.3 1.096.6 1.59 1.59 6.6

KF kN

K K K K× = × =

+ + + + + +


Figure 20: Relative Stiffness Method without Torsion

3.4 Relative Stiffness Method with Torsion (Rigid Beam on Elastic Foundations)

Figure 21: Relative Stiffness Method with Torsion (Rigid Beam on Elastic Foundations)

4. No interior wall (Model B as in the main report) All the methods gave the same results, in which

The shear force resisted by wall 1: 5.65kN The shear force resisted by wall 2 and wall3: 5.65kN


Appendix C: Test results of the toe-nail connection


C.1 Uplift direction

Load Vs. Deflection (RTUP)

00.5

11.5

22.5

33.5

44.5

0 2.5 5 7.5 10 12.5

15 17.5

20 22.5

25 27.5

Deflection (mm)

Load

(kN)

RTUP#1RTUP#2RTUP#3RTUP#4RTUP#5RTUP#6RTUP#7RTUP#8RTUP#9RTUP#10


C.2 Shear direction (perpendicular)

Load Vs. Deflection (RTSHX)

012345678

0 5 10 15 20 25

Deflection (mm)

Load

(kN)

RTSHX#1RTSHX#2RTSHX#3RTSHX#4RTSHX#5RTSHX#6RTSHX#7RTSHX#8RTSHX#9RTSHX#10


C.3 Shear direction (parallel)

Load Vs. Deflection

0

2

4

6

8

10

12

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5

Deflection (mm)

Load

(kN)

RTSHY#1RTSHY#2RTSHY#3RTSHY#4RTSHY#5RTSHY#6RTSHY#9RTSHY#10RTSHY#8RTSHY#7


Appendix D: Test of roof-to-wall connection with hurricane metal connector


Overview of the roof-to-wall connection test using hurricane metal

connector 1. Objective The objective of this test was to study the behavior of roof-to-wall connection with hurricane metal connector subjected to the static load. As was described in the main report, common method of connecting roof to wall components in LFWS is by toe-nailing the bottom chord element of roof to the double top-plate of wall using 3-8d or 2-16d common nail. In this test, the bottom chord element of the roof, the double top-plate and the stud element of wall were connected using hurricane metal connector produced by Simpson Strong-tie (Figure 1). Ideally as in the toe-nail test, all major directions should be considered in the test. But, due to limited hurricane metal connectors available, only uplift direction was considered. 2. Test preparation and set up Wood specimens included 2x8 (roof truss) and 2x6 (wall stud and double top-plate) S-P-F lumber of No. 2 or better grade. The specimens were conditioned in an environmental chamber at 65% RH and 20EC for adjustment of the lumber MC to 12 percent. The specific gravity (SG) was determined from the dimensions and the weight of the specimen at the time of test and MC. These lumber pieces were cut into 300mm length. The double top plates were connected to each other using 4-8d nails to ensure uniform contact within the double top plates during the test. The wall stud was connected to top plate using 8-8d nails (38.1mm-long) that were inserted in the available five holes of the Simpson Strong-tie metal connector. To avoid wood splitting, pilot holes were drilling into the lumber at the marked location using a drilling tool. Once the specimen was assembled in the INSTRON test machine, compression loading mode was applied to the 2x8 component at a rate of 3mm/minute until failure was reached or until excessive separation between the connected elements was detected. To avoid rotational movement induced by eccentric loading, two Simpson Strong-ties connectors were used in one specimen. Two displacement transducers (LVDTs) were attached to the sample to record slip between the double top plates and the bottom chord element of roof. The connection slip was determined using the average value of the two LVDTs. Ten specimens were tested. Additional three specimens using both the Simpson Strong-ties connectors and two 16d toe nails were also tested for comparison purpose.

Figure1: Roof-to-wall connection test


Figure 2: Photo of the test set up

3. Test results The main failure mode observed was the tearing of the sharp angle of the Simpson Strong-ties hurricane connector (Figure 3). Slight bending of the nails connecting the Simpson Strong-tie connector and lumber members was also observed. Tables 1 and 2 summarize the test results. Table 1 shows the results of Simpson Strong-tie connector only, while Table 2 shows the result for Simpson Strong-tie connector plus toe nails. Figures 4 and 5 show the load-slip curves for all test specimens. One curve (RTUP*8) in Figure 4 appears an outlier, which could be due to LVDT malfunction. Comparing with the roof-to-wall connection using toe-nails only, as expected the uplift connection strength with hurricane metal fasteners is larger, but with decreasing ductility response. Also, a small CoV with respect to the strength was observed, since the failure occurred at the hurricane metal connector. A slight increase (16%) in the connection strength was observed when toe-nails were also applied together with Simpson Strong-tie connector.

Figure 3: Failure mode


Table 1 Roof-to-wall Simpson Strong-tie connection

Specimen Bottom chord element of truss density (kg/m3)

Wall element density (kg/m3)

Peak load*, 2Pu

(kN)

Slip at peak (mm)

RTUP*1 460.7 365.7 9.31 8.417 RTUP*2 444.2 355.6 9.22 10.03 RTUP*3 412.8 414.4 8.80 9.83 RTUP*4 492.9 436.5 9.13 8.31 RTUP*5 396.6 406.2 9.30 10.92 RTUP*6 467.2 396.9 9.33 10.2 RTUP*7 447.0 461.4 9.34 9.64 RTUP*8 424.5 455.6 9.26 19.93 RTUP*9 397.6 385.0 9.21 9.80 RTUP*10 450.9 392.9 9.46 9.01

Avg 439.4 407.0 9.24 10.60

CoV 0.07 0.09 0.02 0.32 Note: * The ultimate load per metal connector is Pu, since the symmetrical arrangement was used in the test.

Table 2 Roof-to-wall Simpson Strong-tie plus toe nail connection

Specimen Bottom chord

element of truss density(kg/m3)

Wall element density (kg/m3)

Peak load, 2Pu (kN)

Slip at peak (mm)

RTUP**1 502.2 422.8 11.03 9.73 RTUP**2 424.2 414.4 11.48 10.14 RTUP**3 451.9 405.5 10.94 8.85

Avg 459.4 414.3 11.13 9.57 CoV 0.09 0.02 0.03 0.07


012345678910

0 5 10 15 20 25 30Di spl acement (mm)

Load(kN)

RTUP*1RTUP*2RTUP*3RTUP*4RTUP*5RTUP*6RTUP*7RTUP*8RTUP*9RTUP*10

Figure 3: Load-slip curve for each specimen (Simpson Strong-tie only)

0

2

4

6

8

10

12

14

0 5 10 15 20Di spl acement (mm)

Load(kN) RTUP**1

RTUP**2RTUP**3

Figure 4: Load-slip curve for each specimen (Simpson-Strong tie and toe-nail)


Appendix E: 3-d numerical model of LFWS under earthquake load

(University of British Columbia Team)

1

Seismic Reliability Analysis of a Light-frame Wood Building

Minghao Li and Frank Lam

1. Introduction

To estimate the safety of wood buildings under different seismic hazard levels,

probabilistic or reliability-based approach represents not just a better option but a

necessity because of the high uncertainties inherent in earthquakes and structural systems.

Few researchers studied the reliability of wood based shear wall against seismic hazard

(Foliente (2000), Rosowsky (2002), van de Lindt and Walz (2003), van de Lindt et al.

(2005), Gu (2006), and Li et al. (2009)). Very limited work has been reported on the

seismic reliability study of wood buildings due to the difficulties in characterizing the

uncertainties, defining the performance criteria, and developing computer models for

wood buildings. Wang and Foliente (2006) reported a study on the seismic reliability of

low-rise nonsymmetric woodframe buildings. They used the inter-story drift as the

performance criteria to formulate the performance function and a very simple power-law

formula was used to represent the drift demand through the spectral displacement of

earthquake records.

In this study, a computer model “PB3D” was used to simulate the seismic response

of a light-frame building with different combinations of uncertainties. With the seismic

simulation database, the response surface (RS) method with importance sampling (IS)

was used to approximate the structural seismic response of interest and to formulate an

2

explicit performance function, thus estimating the structural failure probability. Attempt

was also made to evaluate the influence of the building system effect on a type of shear

wall from the perspective of seismic reliability.

2. Earthquake hazards

The term “seismic hazard” stands for the probability that the seismic intensity

measure, such as peak ground acceleration (PGA) and spectral acceleration, exceeds a

specified value during a period of time. For example, three seismic hazard levels can be

defined based on 50%, 10% and 2% exceedance probabilities within 50 years. Their

corresponding return periods are 75 years, 475 years and 2475 years, respectively. For

wood buildings, FEMA 356 recommended four performance levels: serviceability,

immediate occupancy, life safety and collapse prevention with the corresponding inter-

story drift ratios of 0.5%, 1%, 2% and 3% (FEMA, 2000).

The simplest probabilistic approach to model the occurrence of earthquakes during a

period of time is the Poisson process. Although the Poisson process provides an

elementary model of the occurrence of earthquakes, it has been found to be consistent

with historical earthquakes that are of engineering interest in structural applications

(Algermissen 1983). In the U. S., the Poisson process is also used to map the seismic

hazards and model the rate of earthquake occurrence (USGS, 2008). The Poisson process

has the probability mass function (Pinto et al. 2004).

{ } ( ) tk

r ektkP λλ −=!

(1)

3

where k is the number of earthquakes; t is the period of time (e.g. in years); andλ is the

annual arrival rate of earthquakes.

If no earthquakes occur over the time period t, Eq. (1) can be rewritten as:

( ) tr eP λ−=0 (2)

Thus, the probability of occurrence of one earthquake or more is

( ) tr ekP λ−−=≥ 011 . (3)

Now consider the annual probability, i.e. t = 1 year. If the probability of occurrence of an

earthquake with a specified intensity is EP , then the annual arrival rate of such an

earthquake is EPλ . This is called the compound Poisson procedure. Therefore, the annual

exceeding probability becomes

EPa eP λ−−= 01. (4)

Two examples of defining seismic hazard levels are shown as follows:

(1) Earthquakes for serviceability limit state.

It is assumed that these earthquakes have an arrival rate λ=0.05/year and the exceedance

probability of the design earthquake aGd is 50% in 50 years.

( ) ( )( ) 505005001 ..exp. =⋅>−−=> GdGEGdGa aaPaaP

Thus, ( )GdGE aaP > =0.27726 and the corresponding standard normal variate is RN=0.591.

Assuming that the PGA has a lognormal distribution with COV of 0.6 and the design

earthquake aGd=0.15g, one has

( )( ) gRaa aN

a

Gd 15011

2

2.lnexp =+

+= ν

ν; and,

( )( ) gR

aa

aN

aGd 12601

12

2

.lnexp

=+

+⋅=

ν

ν

4

(2) Earthquakes for ultimate limit state

It is assumed that these earthquakes have an arrival rate λ=0.01/year and the exceedance

probability of the design earthquake aGd is 10% in 50 years.

( ) ( )( ) 105001001 ..exp. =⋅>−−=> GdGEGdGa aaPaaP

Thus, ( )GdGE aaP > =0.21072 and the corresponding standard normal variate is RN=0.804.

Assuming that the PGA has a lognormal distribution with COV of 0.6 and the design

earthquake aGd=0.40g, one has

( )( ) gRaa aN

a

Gd 40011

2

2.lnexp =+

+= ν

ν; and,

( )( ) gR

aa

aN

aGd 29801

12

2

.lnexp

=+

+⋅=

ν

ν

3. Response surface (RS) method with importance sampling (IS)

For a well-designed structure with low failure probability, the crude Monte Carlo

Simulation (MCS) requires a large number of simulations to achieve reasonable

estimations. For nonlinear dynamic problems of complicated systems, this approach

might not be suitable since it is very computational intensive. In order to improve

computational efficiency, researchers have developed other approaches such as the RS

method, local interpolation and neural network to estimate the seismic reliability of

nonlinear systems.

The RS method was originally proposed by Box and Wilson (1954) in order to find

the operating conditions of a chemical process in which some of the responses were

optimized. When applied to structural problems, this method replaces the actual structural

response with explicit functions of the random variables of interest. To study the seismic

5

performance of a building, the random variables can include ground motions, gravity load,

and structural properties, etc. By performing dynamic analyses on the sampling points of

the random variables, this method can facilitate the seismic reliability analysis of

complicated nonlinear structures by reducing the required intensive computational effort.

The structural response R such as displacements, internal forces, inter-story drifts or

other damage indicators can be represented as a function of a series of intervening

random variables X1, X2, X3 …Xn,

( ) ( )nXXXX ,...,, 321RXR = (5)

For a nonlinear dynamic problem, the implicit function R can be replaced by an explicit

function in the RS method:

( ) ( )nXXXX ,...,, 321FXF = (6)

Quadratic polynomial functions are commonly used as the explicit function:

( ) ( ) ( ) ( )0000 XXbXXXXaFXF −−+−+= TT (7)

where 0F is the structural response evaluated at the random variable vector 0X , a and b

are unknown coefficient vectors:

( )Tnaaaa ...,,, 321=a (8)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=

nb

bb

...2

1

b (9)

At least 2n+1 sampling points including 0X are needed to determine the coefficient

vectors a and b.

In this study, peak inter-story drifts of the building, which are rational indicators for

6

the structural damages under seismic loads, are used to formulate the performance

function:

( )γδ ,,, raMG GΔ−= (10)

where δ is the structural capacity, which in this case is the building inter-story drift

capacity under a specified performance expectation; Δ is the inter-story drift demand,

also a function of the random variables of interest which are, in this study, the structural

carried mass M; earthquake PGA aG, earthquake frequency contents r, and the response

surface fitting error γ. The frequency content r is usually difficult to quantify;

nevertheless, it should be linked to the performance functions. Therefore, it was assumed

that the characteristics of earthquakes except for PGA can be fully represented by a suite

or ensemble of earthquake records.

The RS method applied in this study is introduced as follows. First, a simulation

database is established by running the seismic simulations repetitively for the selected

combinations of random variables over a defined domain. For each combination, a time-

history analysis was performed for each earthquake record. A set of mean smΔ and

standard deviation smΔσ of the peak structural response (maximum inter-story drift) can

be obtained over the suite of earthquake records. Therefore, for all the combinations of

random variables, a number of sets of smΔ and smΔσ can be established. Then, two third-

order polynomial functions Eq (11a) and Eq. (11b) are used to fit the mean smΔ and

standard deviation smΔσ of the peak structural response over the specified domain of the

random variables, respectively. A boundary condition has been applied herein since the

7

structural response will vanish if the carried mass M or PGA aG is equal to zero (Möller

and Foschi, 2003).

337

326

235

224

23

221 GGGGGGGrs aMaaMaaMaaMaMaaaMaMaa ++++++=Δ (11a)

337

326

235

224

23

221 GGGGGGGrs aMbaMbaMbaMbMabaMbMab ++++++=Δσ (11b)

where Ga is PGA; M is the carried mass; 1a to 7a and 1b to 7b are coefficients which can

be evaluated by the squared error F between the response fitting and simulations:

∑∑= = ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+++

+++−Δ=

M GaN

i

N

j GjiGjiGji

GjiGjiGjiGjiij

aMaaMaaMa

aMaaMaaMaaMaF

1 1

2

337

326

235

224

23

221 (12)

where ijΔ is the mean of the peak drifts from the simulations over the suite of earthquake

records with mass iM and PGA Gja ; NM and NaG are the total numbers of sampling

points for mass and PGA, respectively.

The squared error is minimized by

0=∂∂

iaF (13)

in which i=1,2,…,7. Solving the seven linear equations simultaneously, 1a to 7a can be

evaluated and the explicate response surface of rsΔ can be obtained. Similarly, the

coefficients 1b to 7b can be evaluated for the response surface of rsΔσ .

Now taking into account the response surface fitting errors, the mean and standard

deviation of the peak response are adjusted to

( )( )Δ

−++++++=Δ γ1337

326

235

224

23

221 GGGGGGG aMaaMaaMaaMaMaaaMaMaa

(14a)

8

( )( )Δ

−++++++=Δ σγσ 1337

326

235

224

23

221 GGGGGGG aMbaMbaMbaMbMabaMbMab

(14b)

where Δ

γ and Δσ

γ are the random variables representing the response surface fitting

errors, which are assumed to follow the normal distribution. The fitting errors of the ith

combination of the random variables can be calculated by

irs

ism

irsi

ΔΔ−Δ

=Δ

γ (15a)

irs

ism

irsi

Δ

ΔΔ −=

Δ σσσ

γσ (15b)

For all the combinations of the random variables, the mean and the standard deviation of

the fitting errors can be obtained.

It is assumed that the peak response follows a lognormal distribution. Therefore, Eq.

(10) can be rewritten as

( )( )2

21

1Δ

Δ

++

Δ−= ν

να lnexp NRHG (16)

where Hα is the specified drift capacity (α is drift ratio limit and H is the story height);

Δ is the mean of peak drift demand; Δν is the COV, ΔΔ /σ ; and RN is the normal

variate ( )10,NR . Δ and Δσ are given in Eq. (14a) and Eq. (14b), respectively. Now, Eq.

(16) involves five random variables: PGA Ga , carried mass M, two response surface

fitting errors Δ

γ and Δσ

γ ; and the normal variate ( )10,NR .

Once this explicit response surface is obtained, the failure probability with the

associated reliability index β can be calculated by first order reliability method or second

9

order reliability method (FORM/SORM).

In some problems with high nonlinearity of the performance function, to improve the

accuracy of the reliability estimation, the importance sampling method can be further

used by centering the sampling distribution near so called “design point”. The sampling is

done in region of most importance or likelihood of non-performance, which is around the

design point (Faravelli 1989; Bucher and Bourgund 1990). Rewriting the integration

function of failure probability following the importance sampling method, one has

( ) ( ) ( )[ ] ( )∫=D

f dhhfIP xxxxx / (17)

where index ( )xI is defined such that ( ) 0=xI if structure is safe and ( ) 1=xI if structure

fails; ( )xf is the joint density function of random variables X, centered at the means;

( )xh is the joint density function of random variables X, centered at the design point dX .

And this function can be a normal joint density function. Thus, the failure probability can

be estimated by the average of the function ( ) ( ) ( )[ ]xxx hfI / over the new sampling

domain around the design point:

( ) ( ) ( )[ ]∑= xxx hfIN

Pf /1 (18)

4. Case studies

The uncertainties considered in this study involve the randomness of ground motions,

structural mass and the response surface fitting errors. The structural system of the

building was assumed to be deterministic. The variability in the computer model

predictions have not been considered since there is no information available to account

for the level of the model prediction variability.

10

Table 1 gives a suite of ten historical earthquake records used for simulations. The

first eight records were selected from the Pacific Earthquake Engineering Research

Center NGA database (PEER, 2009). The last two records from Japan were selected from

the internet-based Kyoshin Network strong ground motion database (K-NET, 2004). The

time-history acceleration records are shown in Appendix I.

Table 1 Historical earthquake records used for reliability analysis

No Earthquake Year Component PGA (g) Station 000 0.1194 1 Cape Mendicino,

Fortuna Blvd 1992 090 0.1146

CDMG 89486

180 0.3129 2 Imperial Valley, El Centro 1940 270 0.2148 USGS 117

021 0.1560 3

Kern County, Taft Lincoln school tunnel

1952 111 0.1778 USGS 1095

000 0.2737 4 Landers, Joshua Tree Station 1992 090 0.2882 CDMG 22170

000 0.8774 5 Northridge, Simi Valley Catherine 1994 090 0.6404 USC 90055

035 0.6169 6

Northridge, Beverly Hills 12520 Mulhul

1994 125 0.4444 USC 90014

225 0.1559 7 Superstition Hills, Brawley 1987 315 0.1160 USGS 5060

045 0.1213 8 Superstition Hills, Plaster city 1987 135 0.1858 USGS 5052

000 0.6312 9 Kobe-JMA 1992 090 0.8365 JMA

000 0.6114 10 Kobe-Takatori 1992 090 0.6155 CUE

4.1 Seismic reliability of the building

In this study, to cover the possible domain of the input variables, five structural mass

levels (120 kg/m2, 140 kg/m2, 160 kg/m2, 180 kg/m2 and 200 kg/m2) and ten PGA levels

(0.1 g, 0.2 g, 0.3 g, 0.4 g, 0.5 g, 0.6 g, 0.7 g, 0.8 g, 0.9g, and 1.0g) were selected as the

sampling points of the input variables. Since the response surface is represented by the

11

polynomial functions (Eq. 11a and Eq. 11b), the number of the selected sampling points

is more than sufficient to establish the coefficients of the functions. Alternatively, a

statistical based design of computer experiment approach (Koehler and Owen, 1996;

Sacks et al. 1989) can be used to select these representative variables and construct the

response database.

Two horizontal components of each earthquake record were input simultaneously to

simulate the seismic response of the building. The building is relatively weaker along the

y direction since it has fewer shear walls in this direction (Fig. 1). Therefore, the ground

motion component with higher PGA was used as the input along the y direction of the

building. The seismic record was scaled so that its PGA along the y direction of the

building matched the specified PGA levels (0.1g, 0.2g, …, 1.0g).

Figure 1 Wall layout of the one-story building

In this study, a total of 50 combinations of mass and PGA were calculated. Similar to

Y

X

12

the incremental dynamic analysis (IDA) (Vamvatsikos and Cornell, 2001), for each mass

level, the building was subject to ten earthquake records, each scaled to the multiple

levels of seismic intensity. Therefore, the relationship between the structural response and

the intensity level can be thoroughly investigated by the IDA curves of individual records.

In total, 500 nonlinear time-history analyses were conducted for this building. For

each combination of PGA and structural mass, over ten earthquake records, a set of mean

smΔ and standard deviation smΔσ of the peak inter-story drift response can be obtained.

Table 2 gives 50 sets of mean smΔ and standard deviation smΔσ corresponding to 50

combinations of PGA and structural mass.

Table 2 Mean and standard deviation of peak inter-story drifts

120kg/m2 140kg/m2 160kg/m2 180kg/m2 200kg/m2 PGA (g)

(mm)

(mm) (mm) (mm)

(mm) (mm)

(mm)

(mm)

(mm) (mm)

0.1 1.62 0.44 2.07 0.63 2.46 0.66 2.85 0.73 3.15 0.79 0.2 3.97 1.17 4.99 1.52 5.99 1.68 6.90 1.84 7.96 2.38 0.3 7.21 2.35 8.99 2.57 11.14 3.17 13.67 4.27 16.35 5.50 0.4 11.41 3.50 15.17 4.93 19.48 7.05 23.93 9.40 28.45 12.04 0.5 17.73 6.26 23.96 9.37 30.71 12.94 37.51 17.58 43.13 20.97 0.6 26.20 10.45 35.27 15.67 44.17 20.97 53.17 28.96 60.27 34.88 0.7 36.62 16.36 50.20 27.21 60.17 33.25 68.94 40.08 78.63 46.99 0.8 50.67 27.53 67.07 41.43 76.99 46.39 87.88 52.29 98.04 57.97 0.9 66.50 40.11 83.92 55.01 95.81 59.10 109.35 67.11 123.86 74.60 1.0 84.61 57.46 101.89 68.10 117.20 73.87 137.30 85.85 154.67 98.19

Under each structural mass level, the IDA curves for ten earthquake records were

also plotted to present the relationship between PGA and the peak inter-story drift, as

shown in Fig. 2. Each line represents the peak inter-story drift response with respect to

ten PGA levels for each record.

14

Figure 2 IDA curves of peak inter-story drift (120kg/m2~200kg/m2)

The coefficients a1 to a7, b1 to b7 for the fitted third-order response surfaces of the

mean and standard deviation of the peak inter-story drift responses are given in Table 3.

And the corresponding response surface fitting errors Δ

γ and Δσ

γ are given in Table 4.

Figure 3 shows the comparisons between the fitted polynomial response surface and the

model simulation results. In this figure, if all the points are located on the 45º straight line,

a perfect fitting without fitting errors is achieved. It can be seen that the polynomial

response surface fitting agreed very well with the computer simulation database.

15

Table 3 Polynomial coefficients of peak inter-story drift response surface

Response surface of mean a1 a2 a3 a4 a5 a6 a7

-0.2131 0.1563e-02 0.5089 0.2095e-02 -0.7104e-05 0.1162e-02 -0.5343e-05 Response surface of stdev

b1 b2 b3 b4 b5 b6 b7 -0.7357e-01 0.1040e-03 0.2340 -0.3040e-02 0.2374e-04 0.6911e-02 -0.3580e-04

Table 4 RS fitting errors of peak inter-story drift response

Response surface of mean Response surface of stdev μ σ μ σ

0.1025e-02 0.5945e-01 -0.8410e-02 0.2014

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160

RS fi

tting

(mm

)

Simulation results (mm)

Peak inter-story drift (mean)

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160

RS fi

tting

(mm

)


Peak inter-story drift (stdev)

Figure 3 Response surface fitted peak inter-story drifts vs model simulation results

In the case study, the failure probability was estimated with respect to two seismic

hazard levels (50% exceedance probability in 50 years or 50%/50y; and 10% exceedance

probability in 50 years or 10%/50y) and four performance expectations (serviceability,

immediate occupancy, life safety, and collapse prevention). The assumptions on the two

seismic hazard levels have been introduced in Section 2. The building mass was assumed

to follow a lognormal distribution with mean of 160 kg/m2 and COV of 0.1.

The reliability analysis software RELAN (Foschi, et al. 2007) was used to estimate

the failure probability by evaluating the explicit performance function using FORM and

16

IS. Table 5 gives the reliability estimations with respect to the abovementioned two

hazard levels and four performance criteria. feP and eβ are the event-based failure

probability and the associated reliability index. The numbers in parentheses are the results

estimated by IS, which were very close to the results by FORM.

Table 5 Seismic failure probability of the building (event)

Serviceability (drift 0.5%)

Imme. Occu. (drift 1% )

Life Safety (drift 2%)

Collapse Prev. (drift 3%)

Seismic hazard level Pfe βe Pfe βe Pfe βe Pfe βe

50%/50y 0.0324 (0.0286

1.846 (1.901)

0.0070 (0.0064)

2.456 (2.490)

0.0012 (0.0011)

3.030 (3.052)

0.40e-3 (0.37e-3)

3.352 (3.372)

10%/50y 0.3546 (0.3395)

0.373 (0.414)

0.1572 (0.1504)

1.006 (1.035)

0.0548 (0.0518)

1.600 (1.628)

0.0266 (0.0251)

1.933 (1.958)

4.2 System effect on the shear wall reliability

It is well recognized that the seismic performance of walls in building systems

compare favorably with the isolated walls due to system effect. However, no prior work

has been reported on evaluating the contribution of system effect in light-frame buildings

from the perspective of seismic reliability. In this study, the influence of the system effect

on the seismic reliability of an 8-foot long wall in this building was studied (Fig.4).

Figure 4 Location of the selected 8-foot long wall in the building

Y

X

8 foot wall

17

The seismic response of the isolated 8-foot wall was also simulated by running the

“pseudo-nail” shear wall model. The detailed introduction about this shear wall model

can be found in the literature (Gu and Lam, 2004; Li and Lam, 2009). The ten earthquake

records in Table 1 were also used as the input ground motions for the wall. Since the wall

was oriented along the y direction of the building, the record component along the y

direction of building was used only to do the wall simulations.

Table 6 gives the summary of the peak drift responses of the wall with respect to ten

PGA levels (0.1g, 0.2g, 0.3g, …, 1.0g) and six structural mass levels (500kg/m, 750kg/m,

1000kg/m, 1250kg/m, 1500kg/m, 1750kg/m). The IDA curves for each mass level and

each record are shown in Fig. 5.

Table 6 Mean and standard deviation of peak drift response of the isolated 8ft wall

500kg/m 750kg/m 1000kg/m 1250kg/m 1500kg/m 1750kg/m PGA (g)

(mm)

(mm) (mm)

(mm)

(mm)

(mm)

(mm)

(mm)

(mm)

(mm)

(mm)

(mm)

0.1 0.55 0.16 0.85 0.18 1.27 0.35 1.70 0.45 2.18 0.56 2.79 0.830.2 0.99 0.24 1.88 0.56 3.40 1.05 5.27 1.96 7.40 2.69 10.26 4.180.3 1.69 0.44 3.95 1.36 7.87 3.07 12.99 5.73 19.18 9.08 25.61 12.580.4 2.85 0.84 8.13 2.90 15.84 7.72 26.37 13.42 39.49 24.26 57.33 52.430.5 4.76 1.55 14.56 6.73 28.98 15.27 46.86 28.83 80.59 86.10 85.31 87.510.6 7.68 3.06 23.50 12.08 47.80 29.34 70.41 46.58 103.37 103.29 120.64 107.080.7 12.21 6.26 37.53 21.75 74.91 59.11 98.72 70.32 135.71 113.04 164.15 128.310.8 18.68 10.14 54.84 35.57 94.18 70.70 129.48 94.67 175.14 131.56 199.68 130.050.9 26.29 13.74 76.09 54.04 126.87 91.50 168.71 121.09 207.69 128.65 231.37 131.941.0 35.69 19.14 102.20 78.04 162.04 118.51 202.44 127.38 236.59 129.82 246.34 126.73

18

0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250 300

PG

A (g

)

Peak Wall Drift (mm)

500kg/m- IDA curves

0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250 300

PGA

(g)


750kg/m- IDA curves

0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250 300

PGA

(g)


1000kg/m- IDA curves

19

0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250 300

PGA

(g)



0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250 300

PGA

(g)



0.00.10.20.30.40.50.60.70.80.91.0

0 50 100 150 200 250 300

PGA

(g)



Figure 5 IDA curves of peak wall drift (500kg/m~1750kg/m)

20

The coefficients a1 to a7, b1 to b7 for the polynomial response surfaces of the mean

and standard deviation of the peak wall drifts are given in Table 7. And the corresponding

fitting errors Δ

γ and Δσ

γ are given in Table 8. Figure 6 shows the comparisons between

the fitted polynomial response surfaces and the wall model simulation results, which

indicates a reasonably good fitting.

Table 7 Polynomial coefficients of peak wall drift response surface

Response surface of mean a1 a2 a3 a4 a5 a6 a7

-0.2039e-03 -0.2867e-04 -0.5463e-01 0.1788e-03 0.5289e-07 0.1888e-03 -0.1822e-06 Response surface of stdev

b1 b2 b3 b4 b5 b6 b7 -0.2192e-01 -0.3349e-04 -0.4067e-01 0.1678e-03 0.9747e-07 0.1659e-03 -0.2280e-06

Table 8 RS fitting errors of peak wall drift response

Response surface of mean Response surface of stdev μ σ μ σ

-0.498e-2 0.1432 0.5884e-01 0.2105

0

50

100

150

200

250

0 50 100 150 200 250

RS fi

tting

(mm

)


Peak wall drift (mean)

0

50

100

150

200

250

0 50 100 150 200 250

RS fi

tting

(mm

)


Peak wall drift (stdev)

Figure 6 Response surface fitted peak wall drifts vs model simulation results

According to the mean and standard deviation of the wall peak drift responses

retrieved from the building simulation database, the effective mass carried by the wall can

21

be estimated by Eq. (11a) and Eq. (11b) given the PGA value. Table 9 gives the estimated

effective mass corresponding to each PGA level. Therefore, the mean and standard

deviation of the effective mass was then used to estimate the seismic reliability of the

wall considering the building system effect.

Table 9 Summary of the wall peak drift in the building with associated effective mass

PGA(g)

Mean (mm)

Stdev (mm)

Eff. massa (kg/m)

Eff. massb (kg/m)

Eff. mass. avg. (kg/m)

Eff. mass. stdev. (kg/m)

0.1 1.45 0.51 1089 11000.2 4.11 1.33 1057 10890.3 8.86 3.05 1029 10640.4 16.70 6.85 987 9120.5 27.16 12.28 946 8410.6 40.36 21.13 919 8280.7 56.16 33.96 899 8400.8 72.85 47.26 871 8340.9 91.65 59.62 846 8091.0 113.29 75.08 827 799

929 107

aEffective mass was estimated by the response surface of drift mean (11a); and bEffective mass was estimated by the response surface of drift standard deviation (11b).

Alternatively, the carried mass by the isolated wall can be calculated by distributing

the total structural mass among the shear walls proportional to the lateral resistance of

individual walls or to the tributary areas of individual walls. In this building, the layout of

the walls along the y direction is almost symmetrical. The total shear wall length along

the y direction of the building is 40 feet (12.2 m). The selected wall is 8 feet (2.44m) long.

If the total structural mass is M, then, the tributary mass carried by the wall is about 0.2M.

The construction area is about 109 m2 and the distributed structural mass is 160 kg/m2. So,

the total structural mass is 17,440 kg. Therefore, the wall carries a mass of 3488 kg, i.e.,

1429 kg/m with respect to its length.

22

Table 10 shows the comparisons of the event-based seismic reliability of the 8-foot

wall carrying the effective mass and the tributary mass under two seismic hazard levels

with respect to four performance criteria. The failure probabilities with the associated

reliability indices were evaluated by FORM. The seismic reliabilities of the wall

considering the system effect were significantly higher than the isolated wall carrying the

tributary mass.

Table 10 Comparison of the shear wall failure probabilities with/without system effect

Serviceability (drift 0.5%)

Imme. Occu. (drift 1% )

Life Safety (drift 2%)

Collapse Prev. (drift 3%)

Seismic hazard levels

Wall mass (kg/m)

Pfe βe Pfe βe Pfe βe Pfe βe Eff. 929 0.0134 2.215 0.0044 2.621 0.0012 3.043 0.486e-3 3.298 50% in

50years Trib. 1429 0.0561 1.589 0.0236 1.985 0.0081 2.406 0.0039 2.664 Eff. 929 0.2354 0.721 0.1283 1.134 0.0601 1.554 0.0357 1.803 10% in

50years Trib. 1429 0.4302 0.176 0.2776 0.590 0.1542 1.019 0.1005 1.279

5. Conclusions

This report presented a seismic reliability analysis of a one-story light-frame building

using the response surface method with importance sampling. The peak inter-story drifts

were selected as the performance criteria to estimate the structural failure probability. The

randomness involved in ground motions, structural mass and response surface fitting

errors was considered in the formulation of the performance function. The structural mass

carried by the building was assumed to be 160 kg/m2, which was relatively high

compared with other studies (Wang and Foliente, 2006).

Under the assumed serviceability hazard level with exceedance probability of 50% in

50 years (50%/50y), this building had a reliability index around 1.87 with respect to the

23

serviceability performance criteria. And it had much higher seismic reliability indices,

3.04 and 3.36, with respect to the life safety and collapse prevention criteria, respectively.

Under the assumed ultimate limit state hazard level with exceedance probability of 10%

in 50 years (10%/50y), this building had a low reliability index, only about 0.39 with

respect to the serviceability performance criteria. And it had reliability indices of 1.61 and

1.95 with respect to the life safety performance criteria and the collapse prevention

performance criteria, respectively.

The seismic reliabilities of a 2.44 m (8-foot) long shear wall selected from the

building were also estimated. By comparing failure probabilities of the wall considering

the system effect and the isolated wall, the system effect was evaluated. It was found the

effective mass carried by the wall considering the system effect was much smaller than

the tributary mass carried by the isolated wall. The seismic reliability of the wall with the

system effect was significantly higher than the isolated wall. For example, under the

seismic hazard level of 50%/50y, the wall considering the system effect had a reliability

index of 2.22 with respect to the serviceability performance criteria, much higher than

1.59 of the isolated walls. Similarly, under the seismic hazard level of 10%/50y, the wall

considering the system effect had a reliability index of 1.55 with respect to the life safety

performance criteria, much higher than 1.02 of the isolated wall. Therefore, the estimated

seismic reliabilities of the isolated wall are lower bound values considering its actual

performance in the building system.

24

6. References

• Algermissen, S. T. (1983). “An introduction to the seismicity of the United States: monograph series.” Earthquake Engineering Research Institute, Berkeley, CA, U.S.

• Box, G., and Wilson, K. B. (1954). “The exploration and exploitation of response surfaces: some general considerations and examples.” Biometrics, 10:16-60.

• Bucher, C. G., and Bourgund, U. (1990). “Fast and efficient response surface approach for structural reliability problems.” Structural Safety 7(1): 57-66.

• Faravelli, L. (1989). “Response-surface approach for reliability analysis.” Journal. of Eng. Mech. 115(12): 2763-2781.

• FEMA. (2000). “Prestandard and commentary for the seismic rehabilitation of buildings.” Report No. 356, Federal Emergency Management Agency, Washington, D. C., U.S.

• Foliente, G. C. (2000). “Reliability assessment of timber shear walls under earthquake loads.” Proc., 12th World Conf. on Earthquake Engineering, Paper No. 612.

• Foschi, R. O., Li, H., Folz, B., Yao, F., and Zhang, J. (2007). “Relan- Reliability Analysis Software, V8.0.” Department of Civil Engineering, University of British Columbia, Vancouver, Canada.

• Gu, J. (2006). “An efficient approach to evaluate seismic performance and reliability of wooden shear walls.” Ph.D. thesis, University of British Columbia, Vancouver, Canada.

• Gu, J., and Lam, F. (2004). “Simplified mechanics-based wood frame shear wall model.” Proc., 13th World Conf. on Earthquake Engineering, Vancouver, Canada. Paper No. 3109.

• K-NET. (2004). “Kyoshin network - strong-motion database.” National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan. <http://www.k-net.bosai.go.jp>.

• Koehler, J. R., and Owen, A. B. (1996). “Computer experiments. Handbook of statistics 13.” Elsevier, NY, U.S., 261-308.

• Li, M. and Lam, F. (2009) “Lateral performance of nonsymmetric diagonal-braced wood shear walls”, ASCE Journal of Structural Engineering, 135(2): 178-186.

• Li, M ., F. Lam and R.O. Foschi. (2009) Seismic Reliability Analysis of Diagonal-braced and Structural-panel-sheathed Wood Shear Walls. Journal of Structural Engineering. ASCE. (in press).

• Möller, O., and Foschi, R. O. (2003). “Reliability evaluation in seismic design: a response surface methodology.” Engineering Spectra, 19(3): 579-603.

25

• PEER - Pacific Earthquake Engineering Research Center: NGA database (2009). <http://peer.berkeley.edu/nga/search.html>.

• Pinto, P. E., Giannini, R., and Franchin, P. (2004). “Seismic reliability analysis of structures.” IUSS Press, Pavia, Italy.

• Rosowsky, D. (2002). “Reliability-based seismic design of wood shear walls.” Journal of Structural Engineering, ASCE, 128(11): 1439-1453.

• Sacks, J., Welch, W. J., and Mitchell, T. J., and Wynn, P. (1989). “Design and analysis of computer experiments.” Statistical Science, 4(4): 409-435.

• USGS – U. S. Geological Survey Earthquake Hazard Program. (2008). <http://earthquake.usgs.gov/research/hazmaps/haz101/index.php>.

• van de Lindt, J. W., Huart J. N., and Rosowsky, D. V. (2005). “Strength-based seismic reliability of wood shear walls designed according to AF&PA/ASCE 16.” Journal of Structural Engineering, 131(8): 1307-1312.

• van de Lindt J. W., and Walz M. A. (2003). “Development and application of wood shear wall reliability model.” Journal of Structural Engineering, ASCE, 129(3): 405-413.

• Vamvatsikos, D., and Cornell, C. A. (2001). “Incremental dynamic analysis.” Earthquake Engineering and Structural Dynamics, 31(3): 491-514.

• Wang, C., and Foliente G. C. (2006). “Seismic reliability of low-rise nonsymmetric woodframe buildings.” Journal of Structural Engineering, ASCE, 132(5): 733-743.

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Appendix I

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