DIRECT STRENGTH DESIGN FOR COLD-FORMED STEEL MEMBERS WITH PERFORATIONS

Solicited proposal submitted to:The American Iron and Steel Institute (AISI)

Principal Investigator:Ben Schafer

Assistant Professor

Department of Civil EngineeringThe Johns Hopkins University

Baltimore, Maryland

June 2004

AbstractThe recently adopted Direct Strength Method has opened the potential for the Specification to encourage the creation of highly optimized and efficient cold-formed steel members by integrating numerically determined elastic buckling loads directly into the design process. A significant current shortcoming of Direct Strength design is that it does not apply to members with perforations (holes). Perforations are commonly used in nearly all cold-formed steel applications and therefore extension of Direct Strength design to members with holes is sorely needed. A three phase (year) proposal is proposed herein to address this shortcoming. The first phase focuses on using existing data coupled with finite element analysis to efficiently provide a means to bring conventional members with holes into the Direct Strength procedures. Phases 2 and 3 focus on more in-depth theoretical challenges and experimental validation so that a rational analysis method can be provided for any cold-formed steel member with perforations, including unique configurations such as flanged holes, slotted holes, and the like. Specific budgets are provided for the three separate phases. A rational analysis method for designing any cold-formed steel member with holes stands to significantly increase the flexibility of cold-formed steel applications and allow industry and practicing engineers to take full advantage of the potentials of the Direct Strength design method.

Direct Strength Design for Cold-Formed Steel Members with Perforations 1

1. BackgroundPerforations in cold-formed steel members come in a variety of different forms, as shown in Figure 1. The two most common types of perforations are isolated holes, and patterned holes. Isolated holes include load bearing studs with holes for services and/or bridging (Figure 1a), and isolated holes in joists, purlins, and girts (Figure 1a). Patterned holes include those in pallet rack post uprights for tabbed beam connections (Figure 1b). Other more unique situations exist for cold-formed steel members with perforations; including isolated holes that include formed-in flanges for increased stiffness around the hole (Figure 1c) and new ideas for better thermal behavior using small patterned perforations (Figure 1d).

(a) Isolated holes in studs, may also be found in joists, purlins, and girts, several holes may exist along the length, though spacing is generally far apart

(b) Patterned perforations in rack posts, and in some rack beams, in addition other specialty industries include such perforations (picture from UNARCO product catalog)

(c) Isolated flanged holes in joists, purlins; holes stiffened through transverse and possibly longitudinal external stiffeners also relevant (picture from Dietrich web site)

(d) Specialty perforations as found in slitted cross-sections used in Europe for improved thermal performance (Sections tested and analyzed in Kesti 2000, picture from Kesti 2000)

Figure 1 Examples of perforation patterns found in cold-formed steel systems

Current Specification (NAS 2001) methods for designing members with holes are limited. For isolated circular holes in lipped channel columns the experiments of Ortiz and Peköz (1981) are used to define a reduced effective width for geometries in the tested range only. Isolated holes in lipped channel beams follow Shan et al. (1994), Langan et al. (1994), Uphoff (1996), and Deshmukh (1996) and are used to define a hole size which is small enough to be ignored – design for other hole sizes conservatively require the effective width to be calculated assuming the hole creates unstiffened elements on either side, i.e., the classic solution for a long plate simply supported on three sides and free on the third (the hole) is used for finding the effective width. Alternatively, and with much greater accuracy for local buckling, stub column testing may be performed. This is common practice for members with patterned perforations only. However, testing is only done at short lengths, and distortional buckling which dominates at intermediate lengths, is problematically not considered (Hancock et al. 1994). Thorough compilations of other relevant work are provided in Kesti (2000) and

Direct Strength Design for Cold-Formed Steel Members with Perforations 2

Shanmugam and Dhanalakshmi (2001). Existing methods have an intentionally limited range of applicability, but may be excessively conservative in some situations and ignore important limit states in other situations. A consistent design approach is needed.

Perforations (holes) are a common need in cold-formed steel systems; whether for services in buildings, for convenient connection of other members, or other uses. The main Specification (NAS 2001) covers specific cases of members with holes, but the use is effectively limited to the testing performed. Further, in some cases the Specification methods are known to be overly conservative. The Direct Strength Method (DSM) was created to provide a means to efficiently design highly optimized cross-sections; cross-sections that could not be readily handled by the design method of the Specification. Extension of the Direct Strength Method is needed in order to provide a general method for the efficient design of members with perforations (holes).

2. Elastic buckling and the Direct Strength MethodThe basic premise of the Direct Strength Method may be expressed for a column as:

Pn=f(Pcr,Pcrd,Pcre,Py) (Eq. 1)where:Pn=nominal column strengthPcr=axial load at which elastic local buckling occursPcrd=axial load at which elastic distortional buckling occursPcre=axial load at which global column buckling (flexural, torsional, flexural-torsional occurs)Py=axial load at which yielding occurs (squash load).

The development of functional expressions (the “f” of Eq. 1) preceded from considering the large amount of available experimental data and empirically fitting limit-state specific strength curves for global buckling, distortional buckling, and local-global buckling.

For members without holes the primary means for examining the elastic buckling loads employed the classical finite strip method (FSM), e.g., CUFSM. However, this method cannot discretely handle the presence of holes without significant modifications. Thus, when considering members with holes the more general finite element method (FEM) using shell elements is typically preferred. Recent work by Sarawit (2003) on patterned perforations for rack posts (Figure 1b) and by Kesti (2000) on small patterned perforations for a unique stud with better thermal properties (Figure 1d) has shown how the finite element method may be used for elastic buckling prediction of members with holes. For example, Figure 2 shows an open source tool developed by Sarawit for isolated plates and demonstrates the reduction in the elastic local plate buckling coefficient. Figure 3 extends the analysis to full members with a general purpose FE package, ABAQUS, for elastic buckling in the local, distortional, and global buckling modes.

Figure 2 and Figure 3 demonstrate, at least visually, that members with holes have elastic buckling modes similar to members without holes. But, what these figures fail to show is (1) many more buckling modes may exist – particularly for larger holes and (2) determining which of the myriad of buckling modes should be defined as “local” or “distortional” or “global” without the aid of the half-wavelength vs. load factor plot that finite strip provides is difficult at best and impossible at worst. The finite element method is less restricted than the finite strip method, with this generality comes much complication. A methodology is needed to post-process finite element analysis (FEA), similar to that used in finite strip analysis, so that specific modes can be identified and even isolated. A consistent approach to identifying elastic buckling modes in members with holes is a key challenge in the work proposed herein.

Direct Strength Design for Cold-Formed Steel Members with Perforations 3

Figure 2 FE predications of elastic plate buckling coefficients for isolated plates with rack post patterned perforations completed by Sarawit 2003

Figure 3 FE predictions of the elastic buckling modes of rack post columns with patterned perforations (a) Local (b) Distortional (c) Flexural-torsional, completed by Sarawit 2003

Direct Strength Design for Cold-Formed Steel Members with Perforations 4

3. Ultimate strength and the Direct Strength MethodDevelopment of the Direct Strength Method relied on the wide body of available experimental data on members without holes. Strength curves were selected that connected elastic buckling loads to ultimate strength, for example, for a column in distortional buckling the expression is:

(Eq. 2)

Consider the rack post of Figure 3b, the question for members with holes is, if Pcrd is properly calculated to reflect the reduction due to the holes will the same strength expression (Eq. 2) be applicable to this member? It is certainly possible that this will be the case, but it is not guaranteed, as theoretically the presence of the hole will influence the elastic buckling response (represented by Pcrd) and the post-buckling response (handled through Eq. 2). While a clear means exists to account for the change in elastic buckling, and thus the reduced Pcrd due to the hole, needed modifications to the Direct Strength expressions, such as Eq. 2, remain unknown.

Use of the available experimental data on members with holes from Ortiz and Peköz (1981), Shan et al. (1994), Langan et al. (1994), Uphoff (1996), Deshmukh (1996) and others available in the literature will be crucial to initially evaluating the Direct Strength expressions. For each existing test (1) general purpose finite element models will have to be built to determine the elastic buckling loads in the presence of the holes (2) the FE elastic buckling modes will have to be mapped appropriately to local, distortional, and global buckling values and only then can we (3) determine the accuracy of existing Direct Strength expression and evaluate the necessity of potential modifications to those expressions.

4. Statement of Work and Work PlanObjective: Development of a general design method for cold-formed steel members with perforations.

The developed design method is envisioned as an extension to the Direct Strength Method. While it is believed that completion of the entire project plan is required in order to fully implement the Direct Strength Method for members with perforations it is recognized that funding may not be available for this complete effort immediately. Therefore, the project has been specifically broken into three years, each year with separate tasks and goals so that the funding and effort levels can be matched appropriately.

Year 1: Benefiting from existing experimental data $66,056

Objective: Efficiently extend DSM to members with holes that are already covered in the Specification and insure that DSM, at least in a limited sense, can be applied to products already on the market: metal studs, rack posts, etc., at least where test data is already readily available.

Survey current industry use on members with perforations Evaluation of existing experimental results

- Gather all existing experimental data- Elastic FEA of existing experimental results- Identification of local, distortional, and global modes for perforated members- Evaluation of existing Direct Strength expressions

Design examples

Specification ballot on Direct Strength Method for conventional members with perforations

Direct Strength Design for Cold-Formed Steel Members with Perforations 5

Year 2: Tackling theoretical challenges and extending experiments $62,617

Objective: Formalize identification of buckling modes for members with holes. Increase understanding of post-buckling mechanisms for members with holes. Extend DSM as a rational analysis method for any cold-formed member with holes; including unique members with flanged or stiffened holes.

Identification/isolation of buckling modes in a general FEA- Extension of Adany and Schafer work on modal identification from finite strip to FEA

Extension of existing experimental results- Nonlinear FEA models of experiments to verify and validate implemented FEA model- Additional parametric studies for ultimate strength of members with perforations (focus on unusually large holes, boundary between isolated holes and patterned holes, etc.)- Examination/extension of Direct Strength expressions- Detailed evaluation of post-buckling response (using nonlinear FEA)

Evaluation of flanged or stiffened holes- Collection of existing experimental data, as available- Complete elastic buckling and nonlinear FEA of typical sections- Examination/extension of Direct Strength expressions- Design examples

Specification ballot on members with flanged or stiffened holesResearch tool for the direct identification of buckling modes for members with holesDraft ballot on rational analysis method for any member with holes

Year 3: Experimental validation and developing open-source tools $81,104

Objective: Experimentally validate DSM as a rational analysis method for any cold-formed member with holes; including unique members with flanged or stiffened holes. Develop open-source tools that engineers may use for easy application of DSM to members with holes.

Experiments on beams and columns with holes Beam testing would use the existing rig at JHU and column testing would employ the 100 kip universal testing machine. If the DSM beam-column proposal is funded this work would have significant synergy with that proposal – and the developed testing rig from that proposal could be used for the testing here. Since only a 1 year testing program is envisioned the FEA work and existing tests would be used to carefully select a small subset of cross-sections and hole patterns of interest. A total of approximately 36 tests is envisioned, 3 tests at each of 3 lengths for four different cross-sections, this allows the influence of a critical hole to be gauged for local, distortional, and global buckling.Development of an open-source computational tool for members with perforations

- stand-alone tool for elastic buckling of members with perforations and/or- post-processing tools for general purpose FE programs (ANSYS, ABAQUS, etc.)- integrate work on modal identification work from year 2

Design examples

Ballot on rational analysis method for any member with holesOpen-source computational tool for members with holes

Direct Strength Design for Cold-Formed Steel Members with Perforations 6

The order of the work in years 2 and 3 is somewhat more flexible than year 1. The project may be thought of as consisting of 3 phases, each with the proposed budget provided.

As discussed in the elastic buckling section previously, a key theoretical challenge, addressed in year 2 of the work, is the identification/isolation of individual buckling modes from a general purpose FEA; currently no tool exists for this purpose. Consider a simple model of a lipped channel (without holes) as shown in Figure 4. At a given length, the number of total degrees of freedom determines the number of possible modes. For Figure 4

FSM: 15 nodes × 4 DOF/node = 60 modes, andFEA: 15 nodes in a section × 9 sections along the length × 4 DOF/node = 540 modes.

In general the situation is actually much worse than this calculation indicates, because FEA is performed on a much longer length model with many more elements. Members with holes require the convenience of FEA to incorporate discontinuities (like holes) along the length but methods are needed for post-processing FEA runs to effectively deal with the large number of modes and to identify modes of actual interest.

finite element finite strip

Figure 4 FEM/FEA vs. FSM

0

0,2

0,4

0,6

0,8

1

1,2

10 100 1000 10000buckling length (mm)

(Pcr

/Py)

all-modeglobaldist.local

Figure 5 FSM analysis with modal constraints

Recently Adany and Schafer (2004) have shown how to use the mechanical assumptions of Generalized Beam Theory (Davies et al. 1994, Silvestre and Camotin 2002a,b) in order to restrain general purpose analysis tools like FSM to the analysis of a single mode. As an example, FSM analysis of a lipped channel in pure compression is shown in Figure 5, the “all-mode” curve is the traditional FSM analysis; note that distortional buckling cannot be readily identified in this curve because no minimum exists. However, in the subsequent curves we have restricted the FSM analysis via a series of mechanical assumptions (deformation constraints) and generated curves which are unique to the traditional buckling modes. These curves provide exact definitions for the individual buckling modes and allow isolation of the modes.

Extension of the technique employed by Adany and Schafer to FEM is possible, and would provide a means to isolate the FEA on individual modes. This would allow one to directly identify the influence of a hole, or series of holes on a particular buckling mode. Without such a tool proper identification of the modes, given a myriad of possible choices in the FEA and the subtle differences between the modes, would rely solely on the experience of the analyst. Such a method is possible in some cases, but can introduce significant approximation and a loss of transparency and generality for the approach.

Direct Strength Design for Cold-Formed Steel Members with Perforations 7

5. Impact on IndustryThe metal stud and rack manufacturing industries, which use perforations in most of their products, need this research to bring the potential short- and long-term advantages of the Direct Strength Method to their industries. Unique innovations involved with perforations in members, such as flanged holes, and slotted holes need this research to provide a recognized design approach in the Specification.

Cold-formed steel members require perforations. The development of the Direct Strength Method provides a means to highly optimize cold-formed sections. Extending the application of the Direct Strength Method to members with holes provides a means for industry to move towards highly optimized sections, more readily embrace high strength steels, and increase the flexibility of cold-formed steel applications.

6. Work ProductProgress reports will be provided to AISI every 6 months at the AISI-COS meetings. A report will be provided upon completion of the project. Upon review and comments from the AISI a final report will be provided. Test data and reports will be made available in electronic format to AISI and other researchers.

7. BudgetA summary of the proposed budget is provided in Table 1. Support for a student and 1 month of faculty salary is requested in all 3 years. In year 1, funding for a computer is requested, and in year 3 funding for performing experiments is requested. A detailed breakdown of the budget is provided in the Appendix.

Table 1 Summary budgetBUDGET BREAKDOWN Year 1 Year 2 Year 3 TotalFaculty 17,993 18,712 19,461 56,166Student 41,745 43,087 44,475 129,308Travel/Dissemination 0 0 0 0Experiment 0 0 16,350 16,350Computation 6,318 818 818 7,953

66,056 62,617 81,104 209,776

* Budget notes: (1) Equipment costing greater than $5K is not subject to overhead(2) The Department supports first-year graduate students, therefore the student on this project will be a second year student when joining the research (this provides a means to fund a student for 4 years with only 3 years worth of money).

8. FacilitiesComputer: Computing resources at Johns Hopkins University are nearly completely de-centralized. Computers in current use in the PI’s research group were purchased through startup funds and other grants. All of my current graduate students have Dell workstation class Intel machines varying from 1 to 2 years old. In addition I have 2 machines used primarily for finite element analysis with ABAQUS; two 2 GHz Dell workstation with 2 GB of memory running Linux. Three computers with A/D boards and 1 laptop have also been purchased to support efforts in the lab. These resources will be available to support the research initiatives proposed herein. The proposed computational efforts will be aided by purchasing a new Linux workstation for parametric studies using CUFSM and ABAQUS.

Laboratory: The Department of Civil Engineering maintains a structural testing laboratory in the building. The structural laboratory is approximately 20 ft x 40 ft in plan and has a 20 ft. ceiling. The laboratory includes regularly spaced floor tie-downs, an electric over head crane, and a large adaptable reaction frame consisting of heavy hot-rolled steel sections. Additionally, the laboratory includes sinks,

Direct Strength Design for Cold-Formed Steel Members with Perforations 8

gas and vacuum lines, and is served by an MTS hydraulic pump for running either of the 2,000 lbf or 20,000 lbf actuators or one 100,000 lbf universal testing machine – all controlled by the same MTS 407 controller. An adjoining laboratory of approximately the same size includes an additional 8,000 lbf hydraulic universal testing machine for dynamic testing, and a 10,000 lbf screw-driven universal testing machine – all available for use in this proposal. Laboratory sensors include, load cells, LVDTs, position transducers, extensometers, accelerometers and other sensors. Data acquisition capabilities include 3 computers with National Instruments A/D boards, 1 laptop with an A/D PCMCIA card, and a National Instruments SCXI system for conditioning and reading strain gauges, LVDTs, accelerometers and 20 other analog channels along with LabView. Miscellaneous supporting equipment for field instrumentation is also available. The PI has experience using this equipment in his research efforts to date. In addition, the department was recently donated 10 Parker Series 2HX Actuators with 42 in. stroke, along with 2 enclosed pumps which can be used in the development of unique testing rigs. The Department shares an on-site machine and wood shop with Mechanical Engineering.

Technician and admin. support: The Department has a full-time lab technician available to support the experimental testing proposed herein. Additionally the department has a part-time staff member in the machine shop available to aid in the manufacturing of fixtures and specimens. The Department hires a private consultant for computational support. The Department also has two full-time administrative staff which are available for help on an as-needed basis.

9. PersonnelIn addition to the principal investigator one graduate student is requested for supporting the research proposed herein. The Department of Civil Engineering supports all first-year graduate students, therefore the student selected for this work would not be brought on to the project until their second year of research. This insures far greater productivity for the research and is a form of cost sharing that the Department extends to all funded research projects. A three year project would allow the graduate student to completely focus their efforts on this work and provide funding towards a Ph.D. A one page resume of the PI is attached.

10. ReferencesABAQUS (2003). ABAQUS/Standard Users Manual version 6.3, ABAQUS, Inc. (formerly Hibbitt,

Karlsson Sorensen, Inc.) www.abaqus.com (referenced on 21 July 2003).Ádány, S., Schafer, B.W. (2004). “Buckling mode classification of members with open thin-walled

cross-sections.” CIMS ’04, Fourth International Conference on Coupled Instabilities in Metal Structures, Rome, Italy, 27-29 September, 2004

Davies, J.M., Leach, P., Heinz, D. (1994). “Second-order Generalized Beam Theory.” J. of Constructional Steel Research, Elsevier. 31 (2-3) 221-241.

Deshmukh, S.U. (1996). Behavior of Cold-Formed Steel Web Elements with Web Openings Subjected to Web Crippling and Combination of Bending and Web Crippling for Interior-One-Flange Loading. M.S. Thesis. University of Missouri-Rolla. Rolla, MO.

Hancock, G.J., Y.B. Kwon, E.S. Bernard, (1994). “Strength Design Curves for Thin-Walled Sections Undergoing Distortional Buckling.” J. of Constructional Steel Research, Elsevier. 31 (2-3) 169-186.

Kesti, J. (2000). Local and Distortional Buckling of Perforated Steel Wall Studs. Ph.D. Thesis, Helsinki University of Technology, Espoo, Finland.

Langan, J.E., LaBoube, R.A., Yu, W.W. (1994). Structural Behavior of Perforated Web Elements of Cold-Formed Steel Flexural Members Subjected to Web Crippling and a Combination of Web Crippling and Bending. Cold-Formed Steel Series, Department of Civil Engineering, University of Missouri-Rolla, 94 (3).

Direct Strength Design for Cold-Formed Steel Members with Perforations 9

NAS (2001). North American Specification for the Design of Cold-Formed Steel Structures. American Iron and Steel Institute, Washington, DC.

Ortiz-Colberg, R., Peköz, T. (1981). Load Carrying Capacity of Perforated Cold-Formed Steel Columns. Department of Structural Engineering Report, Cornell University, 81 (12).

Sarawit, T.P. (2003). Cold-Formed Steel Frame and Beam-Column Design. Ph.D. Dissertation. Cornell University, Ithaca, NY.

Schafer, B.W. (2003) “CUFSM – Elastic Buckling Prediction” www.ce.jhu.edu/bschafer/cufsm (referenced on 21 July 2003).

Shan, M., LaBoube, R.A., Yu, W. (1994). Behavior of Web Elements with Openings Subjected to Bending, Shear and the Combination of Bending and Shear. Civil Eng. Study Structural Series, University of Missouri-Rolla. 94 (2).

Shanmugam, N.E., Dhanalakshmi, M. (2001). “State-of-art review and compilation of studies on perforated thin-walled structures.” International J. of Structural Stability and Dynamics, World Scientific. 1 (1) 59-81

Silvestre, N., Camotim, D. (2002a). “First-order generalised beam theory for arbitrary orthotropic materials.” Thin-Walled Structures, Elsevier. 40 (9) 755-789.

Silvestre, N., Camotim, D. (2002b). “Second-order generalised beam theory for arbitrary orthotropic materials.” Thin-Walled Structures, Elsevier. 40 (9) 791-820.

Uphoff, C.A. (1996). Structural Behavior of Circular Holes in Web Elements of Cold-Formed Steel Flexural Members. M.S. Thesis. University of Missouri-Rolla. Rolla, MO.

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APPENDIX: BUDGET BREAKDOWN

BUDGET - SPONSORED PROJECT

3 Years - Start Date 06/01/05 YEAR1 YEAR 2 YEAR 306/1/05 -05/31/06 06/1/06 - 05/31/07 06/01/07 - 05/31/08 Total

FacultyBen Schafer (1 month) 8,274 8,605 8,949 25,829Benefits (33%) 2,730 2,840 2,953 8,524Total Direct Salary & Benefits 11,005 11,445 11,903 34,352Total F&A Base 11,005 11,445 11,903 34,352F&A (63.5%) 6,988 7,268 7,558 21,814Total Faculty Costs 17,993 18,712 19,461 56,166

Graduate StudentGraduate Student Salary (1 @12 months) 20,964 21,593 22,241 64,798Tuition (for graduate students) (no F&A) 6,269 6,583 6,912 19,763Health insurance (for graduate students) (no F&A) 1,200 1,200 1,200 3,600Total Direct Graduate Student Costs 28,433 29,375 30,352 88,161F&A Base 20,964 21,593 22,241 64,798F&A (63.5%) 13,312 13,712 14,123 41,146Total Graduate Student Costs 41,745 43,087 44,475 129,308

TravelDissemination of research results (conferences, etc.) 0 0 0 0F&A Base 0 0 0 0F&A (63.5%) 0 0 0 0Total Travel 0 0 0 0

Experimental Support - Equipment & SuppliesTesting Equipment (no F&A)* 0 0 0 0Materials/Supplies (Testing) 0 0 10,000 10,000Total Direct Equipment & Supplies 0 0 10,000 10,000F&A Base 0 0 10,000 10,000F&A (63.5%) 0 0 6,350 6,350Total Equipment & Supplies 0 0 16,350 16,350

Computational Support - Equipment & SuppliesComputer (no F&A)* 5,500 0 0 5,500Software 500 500 500 1,500Total Direct Equipment & Supplies 6,000 500 500 7,000F&A Base 500 500 500 1,500F&A (63.5%) 318 318 318 953Total Equipment & Supplies 6,318 818 818 7,953

Total Direct 45,438 41,320 52,755 139,513Total F&A base 32,469 33,538 44,643 110,650Total F&A 20,618 21,297 28,349 70,263Total Budget 66,056 62,617 81,104 209,776Total All Major Items 66,056 62,617 81,104 209,776

Direct Strength Design for Cold-Formed Steel Members with Perforations 11

BENJAMIN WILLIAM SCHAFER

203 Latrobe Hall e-mail: schafer@jhu.eduDepartment of Civil Engineering voice: (410) 516-7801The Johns Hopkins University fax: (410) 516-7473Baltimore, MD 21218 web: www.ce.jhu.edu/bschafer

EDUCATIONPh.D / M.S. Cornell University (1995–1997) Civil/Structural Eng., Minor: Theoretical and Applied Mech.

Thesis: Cold-Formed Steel Behavior and Design: Analytical and Numerical Modeling of Elements and Members with Longitudinal Stiffeners. Advisor: Teoman Peköz

B.S.E. University of Iowa (1989–1993) Civil Engineering

HONORSResearch Collingwood Prize (2003) (For paper on Distortional Buckling of Columns)

Best Presentation at the ASCE-SEI Structures Congress (2003) – tied for1st PlaceTeaching Robert S. Pond, Sr. Excellence in Teaching Award (2004)

Service Dunn Family Award – from the JHU Student Council (2004)

PROFESSIONALSenior

EngineerSimpson Gumpertz & Heger, Inc., Arlington, MA (1998 – 2000) Eng. Mech. & Infrastructure Division.

Failure Investigations, Buried Structures, Seismic Consulting

RESEARCHAssistant Professor

The Johns Hopkins University (2000 – Present)Active Projects: Design of Structural Systems for Unforeseen Catastrophic Events, Cold-Formed Steel Design Guide for the Direct Strength Method, Experimental Study of Distortional Buckling on C and Z Members in Bending, Historic American Engineering Record: Covered Wooden Bridge StudiesCompleted Projects: Test Verification of the Effect of Stress Gradient on Webs of C and Z Sections, Distortional Buckling of Cold-Formed Steel Columns

Postdoc Cornell University (1997–1998)

TEACHINGAsst. Prof. The Johns Hopkins University (2000 – Present) What is Engineering?, Steel Structures, Structural

Stability, Perspectives on the Evolution of StructuresInstructor Cornell University (1997-1998) Structural Behavior, Modern Structures

SERVICE & ACTIVITIESCommittees American Iron and Steel Institute - Committee on Specifications (AISI-COS) (1995–Present)

ASCE-SEI Committee on Cold-Formed Steel, member (1997-2000) Chairmen (2001–Present)ASCE-SEI Committee on Compression and Flexural Members, member (2001–Present)SSRC TG 13, Thin-Walled Metal Construction, member (2001–2003) Chairmen (2004–Present)

SELECTED PUBLICATIONS:Liu, H., Igusa, T., Schafer, B.W. (2004). “Global Optimization of Cold-Formed Steel Columns by an Original

Knowledge-Based Optimization Method.” Elsevier, Thin-walled Structures Journal (In Press) (doi:10.1016/j.tws.2004.01.001)

Schafer, B.W. (2003). “Advances in Direct Strength Design of Thin-Walled Members.” Advances in Structures: Steel, Concrete, Composite and Aluminum - ASSCCA’03, Sydney, Australia, June 23 - 25, 2003

Yu, C., Schafer, B.W. (2003). “Local Buckling Tests on Cold-Formed Steel Beams.” ASCE, Journal of Structural Engineering. 129 (12) 1596-1606. (doi:10.1061/(ASCE)0733-9445(2003)129:12(1596))

Schafer, B.W. (2002). “Local, Distortional, and Euler Buckling in Thin-walled Columns.” ASCE, Journal of Structural Engineering. 128 (3) 289-299. (doi:10.1061/(ASCE)0733-9445(2002)128:3(289))

Schafer, B.W., Peköz, T. (1999). “Laterally Braced Cold-Formed Steel Flexural Members with Edge Stiffened Flanges.” ASCE, Journal of Structural Engineering. 125 (2) 118-127. (doi:10.1061/(ASCE)0733-9445(1999)125:2(118))

Direct Strength Design for Cold-Formed Steel Members with Perforations 12