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Earthquake Performance of Unreinforced Masonry

Residential Buildings up to 15 m in Height

WILLIS, C. R.1

GRIFFITH, M. C.2

LAWRENCE, S. J.3

1 Postdoctoral Fellow, The University of Adelaide 2 Associate Professor, The University of Adelaide

3 Conjoint Professor, The University of Newcastle; SPL Consulting Pty Ltd

March 2007

i

ABSTRACT

This report presents deemed-to-satisfy solutions for earthquake loading of unreinforced masonry structures up to 15 m in height. The structures under analysis are Importance Level 2 buildings and are hence subject to Earthquake Design Category II (EDC II). This study considers the wall forces and associated actions due to earthquake loads corresponding to the Ballot Version of the Australian Standard for earthquake actions, AS 1170.4 (Standards Australia, 2005). The seismic demands for various loading conditions are compared against the corresponding seismic capacities given by the Australian Standard for masonry structures, AS 3700 (Standards Australia, 2001, including proposed Amendment 3, 2006).

A parametric study was used to examine the effects of a wide range of parameters, including number of stories, wall geometries, support conditions and openings. The results of the parametric study indicate, for a typical office building and a typical home unit building, the range of conditions leading to earthquake failure using the current design criteria of AS 3700.

The following are the main findings:

• Out-of-plane bending tends to govern as wall span (L), site sub-soil class, hazard factor (Z) and the number of levels increase. This applies for both the office building and the home unit building. This finding is based on the failure criterion of the strength of walls in two-way bending being exceeded.

• Out-of-plane shear governs in relatively few cases and, when it occurs, it is in conjunction with out-of-plane bending and/or in-plane shear failure. There is no difference in this respect between the office building and the home unit building.

• In-plane shear in the direction of the short plan dimension of a building is governed by the arrangement of the internal walls. For the assumed wall distributions used in this study, in-plane shear in the short direction was not critical for the office building. However, for the home unit building, in-plane shear occurred in the short direction simultaneously with failure in the long direction, since the tributary areas were equal, giving the same total design capacity in both directions.

• In-plane shear in the long direction is the most significant mode governing structural performance when the failure criterion of onset of sliding at the base of the wall is used. The assumed layout of internal walls was found to be a significant factor influencing behaviour. The onset of sliding does not necessarily constitute failure under seismic action, as it often does not lead to collapse or provide a risk to life. It is the opinion of the authors that this, along with other possible design criteria such as tensile cracking at the heel of a wall and compressive crushing at the toe of a wall are not threats to life-safety and therefore might not be the most appropriate design criteria for earthquake resistance. Further research in this area and a re-examination by the AS 3700 Standards committee is recommended.

ii

NOTATION

Adw combined bedded area of the shear-resisting portion of a member

ai effective floor acceleration at level i

EDC Earthquake Design Category

Fi horizontal static force at level i

fd minimum design compressive stress on the bed joint at the cross-section

f'ms characteristic shear strength of masonry

G crack slope

Gi permanent action (self-weight or ‘dead load’) at level i

Ks factor to account for floor number

kp probability factor

kv shear factor

Mcd diagonal bending moment capacity

Mch horizontal bending moment capacity

n maximum number of levels in structure

Qi imposed action for occupancy on level i

Rf1 rotational restraint factor (edge 1)

Rf2 rotational restraint factor (edge 2)

Sp/µ ratio of structural performance to ductility

Vc design shear capacity

Vd total out-of-plane shear force

V0 shear bond strength of the shear section

V1 shear friction strength of the shear section

Wi seismic weight of the structure at level i

wc total design capacity (out-of-plane load)

wd seismic demand (out-of-plane load)

Z hazard factor

φ capacity reduction factor

ψc combination factor for earthquake imposed action

iii

TABLE OF CONTENTS ABSTRACT……………………………………………………………………………..i NOTATION…………………………………………… ……………………………….ii TABLE OF CONTENTS……………………………………………………………...iii 1 INRODUCTION………………………………………......................................1 2 METHODOLOGY……………………………………………………………..2

OUT-OF-PLANE BENDING…………………………………………...3 OUT-OF-PLANE SHEAR………………………………………………4 IN-PLANE SHEAR……………………………………………………..6

3 PARAMETRIC STUDY………………………………………………………8 4 RESULTS……………………………………………………………………...11

EFFECT OF AN OPENING ON BENDING RESPONSE………...….12 EFFECT OF Ks FACTORS ON BENDING RESPONSE……………..12 EFFECT OF SIDE RESTRAINT FACTORS ON BENDING RESPONSE…………………………………………………………….15

5 CONCLUSIONS………………………………………………………………16 ACKNOWLEDGEMENTS…………………………………………………………..17 REFERENCES………………………………………………………………………..17 APPENDIX A: METHODOLOGY………………………………………………….18 APPENDIX B: CALCULATIONS…………………………………………………..25

TABLE OF FIGURES

1 Seismic load path for a masonry building (Priestley, 1985)…………………3 2 Out-of-plane wall contribution to in-plane shear resistance………………...8 3 Tributary areas for load transfer……………………………………………...9 4 Idealised failure patterns……………………………………………………..12 5 Out-of-plane bending response (site sub-soil class A)………………………13 6 Out-of-plane bending response (site sub-soil class B)………………………13 7 Out-of-plane bending response (site sub-soil class C)………………………14 8 Out-of-plane bending response (site sub-soil class D)………………………14

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1 INTRODUCTION

Residential buildings up to 15 m in height constitute a highly important market segment for the clay masonry industry. Houses of one and two storeys are rarely subjected to engineering design, but three, four and five-storey ‘walk-up’ units require engineering calculations to justify their structural adequacy. The development of panel systems using other materials presents a constant challenge to the market share of clay masonry in this segment.

Following the 1989 Newcastle earthquake and as a result of on-going research and development of standards and building regulations, there has been an increased emphasis placed on design for earthquake forces. At the same time, there has been some criticism of designers for not considering adequately all aspects of behaviour of these types of buildings during an earthquake. In particular, it has been suggested that some designs have not made adequate provision for the transfer of shear forces to the foundation and that the masonry might not perform as expected in an earthquake. The current earthquake loading code AS 1170.4 was published in 1993 and, at the present time, a draft revision is nearing completion. This revision will modify the design requirements for structures, increasing design actions in some cases and requiring all structures (except most houses) to be designed for earthquake forces. In particular, it will move all material-related design and detailing considerations to the appropriate material standards.

In conjunction with the revision of the earthquake loading standard, an amendment to the masonry structures standard AS 3700 (Standards Australia, 2001) has been prepared and is in the final stages leading up to its publication. This amendment includes detailing provisions for masonry structures to resist earthquakes and will therefore have an effect on the design of residential unit buildings.

The cumulative effect of these pending changes to standards and the challenges faced by clay masonry in the marketplace has been to focus attention on the performance of masonry in multi-storey residential buildings and, in particular, the criteria being used for design. The masonry standard has, to date, applied the same design approach and criteria for earthquake loading as for wind loading, but recent research indicates that this might be unnecessarily conservative and that the design criteria relevant to earthquake loading should be re-examined. As a preliminary step, it is necessary to identify the critical actions for the various masonry elements in a multi-storey residential building, covering a range of variables, and this is the primary purpose of the current study.

This study sets out to identify which seismically induced actions are critical to the life-safety design objective embodied in the earthquake loading code. Out-of-plane wall actions are related to the earthquake induced accelerations and in-plane wall actions are related to the earthquake induced in-plane shear force. The 15 m height limit for the study means that typical structures up to and including five stories in height are considered. This also covers all domestic construction (Building Class 1a and 1b), whether less than or greater than 8.5 m tall.

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2 METHODOLOGY

In the Ballot Version of AS 1170.4 (Standards Australia, 2005), the majority of unreinforced masonry buildings whose height is less than or equal to 15 m are covered by the simplified design method for Earthquake Design Category II (EDC II) structures. This approach will be conservative for EDC I structures and was therefore used to develop the deemed-to-satisfy requirements presented in this study. The results will cover the majority of masonry walk-up flats and apartment buildings in all capital cities and throughout most of Australia.

The method used is a parametric study, applying the range of parameters encountered in service to the analysis of masonry buildings under seismic actions. The range of parameters is presented in Section 3. By considering the range of cases analysed, a pattern of critical actions and building elements is developed and the appropriateness of the design criteria can be examined.

The seismic actions that are considered in this study include:

• out-of-plane bending;

• out-of-plane shear; and,

• in-plane shear.

The method by which each of these actions is analysed and the key assumptions used are presented in the following sections. The threshold at which the seismic capacity equals demand defines the limit for the deemed-to-satisfy conditions.

The foundation of a masonry structure transmits seismic motion from the ground to the stiffest elements, the in-plane structural walls. The structural walls excite the floor diaphragms that in turn excite the out-of-plane walls (Figure 1). The seismic load path is the reverse of this energy input. Strictly speaking, the out-of-plane loading is not constant for a single floor level. However, it is not excessively conservative to assume that the out-of-plane load, which may be directly related to ground acceleration, is uniform over the storey height (Priestley, 1985). Hence, for the analysis of masonry it is assumed that the out-of-plane load induced by seismic effects may be represented as an equivalent static uniformly distributed load. The method given in AS 3700 (Standards Australia, 2001) is consistent with this approach. To determine an equivalent static load produced by seismic activity, factors including the location of the wall in the building, the level of ground acceleration and the dynamic response of the building must be accounted for (Page, 1995).

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groundacceleration

energy input

Figure 1: Seismic load path for a masonry building (Priestley, 1985)

2.1 Out-of-plane Bending

Walls loaded in the out-of-plane direction must resist their own inertia forces, determined from the wall self-weight multiplied by the acceleration at the mid-height of the wall. The critical storey is taken as the top floor because earthquake induced accelerations increase with height. Walls in the top storey of masonry buildings were assessed for their total design capacity, wc, using AS 3700 (Standards Australia, 2001) and compared to the seismic demand, wd, specified in AS 1170.4 (Standards Australia, 2005). For deemed-to-satisfy limit state conditions to exist, wc ≥ wd.

Seismic Demand (AS 1170.4 Analysis)

The wall in the top storey, i, is supported at its base by the floor at level i-1 and at its top by the roof at level i. Hence, the acceleration at its mid-height is approximated as the average of the accelerations at levels i-1 and i. The horizontal static force at level i is given by (1) (AS 1170.4, Equation 5.4), hence the acceleration at level i is given by (3).

ipp

si WSZk

KF

=

µ (1)

where:

icii QGW ∑∑ += ψ (2)

4

Ks = Factor to account for floor number

kp = Probability factor

Z = Hazard factor

Sp/µ = Ratio of structural performance to ductility

Wi = Seismic weight of the structure at level i

Gi = Permanent action (self-weight or ‘dead load’) at level i

ψc = Combination factor for earthquake imposed action

Qi = Imposed action for occupancy on level i

[ ]µppsi

ii SZkK

W

Fa ==

(3)

The out-of-plane load (seismic demand), wd, is given by the wall self-weight multiplied by the acceleration at its mid-height (4). From AS 1170.1 (Standards Australia, 2002) Table A2, the force per unit area for ‘brick masonry, solid - burnt clay’, per 10 mm thickness is 0.19 kN/m2. Hence, for a wall thickness of 110 mm, the wall self-weight is 2.09 kN/m2.

2/)( kPa 09.2 1d ii aaw +×= − (4)

Total Design Capacity (AS 3700 Analysis)

For out-of-plane bending it is assumed that the entire vertical load is on the inner leaf, which supports the slab, hence the outer leaf does not benefit from superimposed compressive stress and is therefore critical. The total compressive stress, fd, at the mid-height of the wall in the top storey is given by the self-weight of the outer leaf. The horizontal and diagonal bending moment capacities, Mch and Mcd, are calculated and used to determine the total design capacity for the outer leaf, wc.

2.2 Out-of-plane Shear

Out-of-plane (i.e. through-thickness) shear is proportional to the earthquake induced accelerations acting on a wall and as accelerations increase with height, the critical storey is again taken as the top floor. For out-of-plane shear at the wall edges in the top storey it is assumed that the out-of-plane load from both leaves is shed to the inner leaf, hence the inner leaf is critical. Walls in the top storey of masonry buildings were assessed for their total design capacity, Vc = V0 + V1 (shear bond and friction strengths of the shear section), using AS 3700 (Standards Australia, 2001) and compared to the total out-of-plane shear (seismic demand), Vd, given in AS 1170.4 (Standards Australia, 2005). For deemed-to-satisfy limit state conditions to exist, Vc ≥ Vd.

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The seismic demand for out-of-plane shear, Vd, is given by the seismic demand for out-of-plane bending, wd, multiplied by the face area of the wall over which it acts, for each leaf of the wall in cavity construction. There will not always be connectors at the vertical wall edges and the shear bond component at these edges is considered questionable. As a result, most of the resistance is provided by the top and bottom wall edges, where there is potentially shear bond and friction from the vertical load, hence it is conservatively assumed that all of the load will be equally distributed to these two edges.


The out-of-plane shear capacity is given by (5).

where:

dwms0 AfV ′= φ (6)

dwdv1 AfkV = (7)

V0 = Shear bond strength of the shear section

V1 = Shear friction strength of the shear section

φ = Capacity reduction factor

f'ms = Characteristic shear strength of masonry

Adw = Combined bedded area of the shear-resisting portion of a member

kv = Shear factor

fd = Minimum design compressive stress on the bed joint at the cross-section

In addition to assuming that the load on both leaves must be resisted along the top and bottom edges of only the inner leaf, it was also assumed that a damp-proof course or slip joint would be located at the base of the inner leaf. The total compressive stress, fd, at the base of the wall in the top storey is given by the compressive stress due to the ceiling and roof and the self-weight of the inner leaf. The characteristic shear strength of masonry, f'ms, is taken as zero at a damp-proof course or slip joint, hence the shear bond strength, V0, is also zero. As a result, the design shear capacity (V0 + V1) must rely solely on the shear friction strength, V1, to resist the shear demand, Vd.

10c VVV += (5)

6

2.3 In-plane Shear

Walls loaded in the in-plane direction must resist all the earthquake induced shear forces applied in the structure above that level (Figure 1). Hence, the critical storey is the ground storey because the storey shear forces (internal actions) become larger moving down the building. The in-plane shear force in a wall due to earthquake loading is computed and compared to its respective design capacity given by AS 3700 (Standards Australia, 2001). The in-plane shear capacity of the ground storey walls is computed assuming a damp-proof course joint at the base of each wall; hence the shear capacity is given by shear friction only. The in-plane shear strength design criterion at the base of masonry walls is currently seen by AS 3700 (Standards Australia, 2001) to be a necessary design criterion for earthquake loading.

In considering the in-plane action, it has been assumed that overturning of the wall will be restrained by the weight of the structure above. Also, it is clear that shear failure within the masonry will not occur, because f'ms for the mortar joints is greater than the value of zero assumed at the base of the wall. Furthermore, tensile ‘failure’ at the heel of a wall under in-plane shear is normally tolerated as it will, at most, result in only minor cracking, and experience shows that crushing at the toe of a wall will not occur. It has therefore been assumed that the behaviour is governed by sliding on the base.


The equivalent horizontal static earthquake force applied at level i in a building is given by (8).

ipp

si WSZk

KF

=

µ (8)

where:

icii QGW ∑∑ += ψ (9)

Ks = Factor to account for floor number

kp = Probability factor

Z = Hazard factor

Sp/µ = Ratio of structural performance to ductility

Wi = Seismic weight of the structure at level i

Gi = Permanent action (self-weight or ‘dead load’) at level i

ψc = Combination factor for earthquake imposed action

Qi = Imposed action for occupancy on level i

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The relationship for Fi (8) is based on the assumption that the mass at each floor level can be lumped together, i.e. the weight of the walls (i.e. both leaves of the external walls in cavity construction and the internal partition walls) for half a storey above and below each floor level are included in this lumping process.

For the top level, n, the total load includes the weights of the roof (terracotta tiles), ceiling (Portland cement plaster, 13 mm thick) and half the walls spanning between levels n-1 and n.

For levels 1 to n-1, the total load includes the live load (residential, conservatively taken as 2.0 kPa), and weights of the floor slab (concrete, 175 mm thick), flooring (pine flooring overlay, 15 mm thick) and the walls for half a storey above and below each floor level. It is assumed that the inertia forces due to the weights of half the walls between the base and level 1 plus the base slab and flooring are transmitted directly to the footings and these are therefore not included in the calculations. The total force, Fi, for each level is then determined using (8). The shear demand, Vd = ΣFi, must be resisted by the ground storey walls running parallel to the earthquake motion.


For in-plane loading, all load from the slabs (and both leaves) are assumed to accumulate to the inner leaf, with the outer leaf not contributing to the shear resistance. The shear resistances of the inner leaves are checked for the structure in both the short and long directions. The relationship that must be satisfied for shear capacity requirements is given by (10).

where:

dwms0 AfV ′= φ (11)

dwdv1 AfkV = (12)

V0 = Shear bond strength of the shear section

V1 = Shear friction strength of the shear section

φ = Capacity reduction factor

f'ms = Characteristic shear strength of masonry

Adw = Combined bedded area of the shear-resisting portion of a member

kv = Shear factor

fd = Minimum design compressive stress on the bed joint at the cross-section

10cd VVVV +=≤ (10)

8

It is also assumed that a damp-proof course or slip joint would typically exist at the base of each ground storey wall. Hence the shear bond strength, V0, is zero at this location. As a result, the design shear capacity (V0 + V1) is based solely on the shear friction strength, V1.

To determine the compressive stress, fd, acting on each of the walls contributing to the shear resistance, the gravity load transmitted to each leaf was considered by assuming that the weights of the external leaves are transmitted directly to the foundation and hence are excluded from the total vertical compressive load on the inner leaves of the structure at ground level. It is conservative to exclude the outer leaves since a proportion of their weight is likely to be transferred to the inner leaf through nibs on the slab or shelf angles. Each critical inner leaf is assumed to support the live load and ceiling, roof and floor slab weights in proportion to their respective tributary areas, plus its own self-weight.

The actual in-plane resistance is modified to account for ‘flange effects’, whereby a proportion of the walls orthogonal to the in-plane walls (a nominal length of 25% of the span on each side of the in-plane wall was assumed) will contribute to shear strength through the Adw term in (12). For this action, the in-plane wall is envisaged as the ‘web’ of an I-section, and the out-of-plane walls are envisaged as the ‘flanges’ of the section (Figure 2).

In-plane wall('web')

Out-of-plane wall('flange')

Direction ofin-plane shear

L

0.25 L0.25 L

Figure 2: Out-of-plane wall contribution to in-plane shear resistance

3 PARAMETRIC STUDY

For the formulation of the deemed-to-satisfy solutions for masonry structures up to 15 m in height, two types of structure were investigated, i.e. a home unit (four occupancies per level) and an office building.

Table 1 details the overall geometries for the structures considered in the parametric study. For the determination of the total length of walls in each direction, the external cavity walls are counted twice due to the assumption of

9

double leaf construction. In addition, to calculate the design shear capacity, the proportion of tributary area in each direction is required to determine the compressive stress, fd. For office buildings, the internal walls running parallel to the short direction are assumed to be double the length of the orthogonal walls, hence the tributary area for load transfer to each wall is taken as 75% of the total floor area for the short direction and 25% for the long direction (Figure 3 (a)). For home units, the wall lengths in the orthogonal directions are assumed to be approximately equal, and hence the tributary areas are taken as 50% in each direction (Figure 3 (b)).

Table 1: Overall structural geometries

Parameter Unit Office

Length of Building (Short Direction) m 11 12

Length of Building (Long Direction) m 32 50

Total Length of Walls (Short Direction) m 120 180

Total Length of Walls (Long Direction) m 180 250

Proportion of Tributary Area (Short Direction) 0.5 0.75

Proportion of Tributary Area (Long Direction) 0.5 0.25

12 m

A B

CD

50 m

75% of areaABCD to shortdirection walls

Longdirection

Shortdirection

2 L1

L1

11 m

A B

CD

32 m

L2

L2

50% of areaABCD to shortdirection walls

(a) Office building (b) Home unit

Figure 3: Tributary areas for load transfer

Table 2 and Table 3 indicate respectively the parameters that were varied and those held constant for the parametric study. The methodology and spreadsheet calculations for an example case are presented in Appendix A and Appendix B, respectively.

The range of earthquake hazard factor, Z, covers the major population centres in Australia, from 0.05 (e.g. Brisbane, Gold Coast) to 0.12 (e.g. NW Western Australia). Other capital cities (Adelaide 0.10, Darwin 0.09, Melbourne 0.08, Perth 0.09, and Sydney 0.08) fall within this range. Hobart (0.03) does not have significant earthquake risk.

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AS 1170.4 (Standards Australia, 2005) defines site sub-soil class as follows:

• Class A - Strong rock;

• Class B - Rock;

• Class C - Shallow soil; and,

• Class D - Deep or soft soil.

A fifth class (E - Very soft soil) is not considered in this study and would generally require special consideration for design.

AS 3700 (Standards Australia, 2001) defines the rotational restraint factor for lateral load design of masonry walls as varying from 0 (a simply-supported edge) to 1 (a fully restrained edge). Intermediate values are permitted, indicating partial restraint, and are often used for designs where edges are restrained by return walls or continuity. For this study, an intermediate value of 0.5 is used, along with the values of 0 and 1.

Table 2: Variable parameters

Parameter Values

Length of Wall L 4, 6, 8, 10 m

Length of Opening L o 0, 1.2 m

Hazard Factor Z 0.05, 0.08, 0.10, 0.12

Site Sub-soil Class A, B, C, D

Total Number of Storeys 2, 3, 4, 5

Rotational Restraint Factor R f1 0, 0.5, 1.0

Rotational Restraint Factor R f2 0, 0.5, 1.0

Table 3: Constant parameters

Parameter Value

Shear Strength of Masonry f 'ms 0 MPa *

Flexural Tensile Strength of the Masonry f 'mt 0.2 MPa *

Lateral Modulus of Rupture of the Brick Unit f 'ut 0.8 MPa *

Height of Wall H 3 m

Probability Factor (500 Year Reference Period) k p 1.0

Shear Factor k v 0.3

Ratio of Structural Performance to Ductility Sp/µ 0.62

Thickness of Mortar Joint t j 10 mm

Capacity Reduction Factor φ 0.6

Combination Factor for Earthquake-Imposed Action ψ c 0.3

Unit Dimensions h u × l u × t u 76 × 230 × 110 mm

Density of Masonry (per 10 mm thickness ) 0.19 kN/m2

Number of External Wall Leaves (Cavity Wall) 2

Slab Thickness 175 mm

Timber Flooring Thickness (Overlay on Concrete Slab) 15 mm

* Characteristic

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4 RESULTS

Table 4 and Table 5 indicate the results for a wall with no opening that is partially supported on four sides (rotational restraint factors, Rf1 = Rf2 = 0.5), within an office building and home unit respectively. The numbers in the cells indicate failure criteria as follows:

(1) out-of-plane bending;

(2) out-of-plane shear;

(3) in-plane shear (short direction); and,

(4) in-plane shear (long direction).

The shaded cells indicate that there was no failure under these conditions of earthquake loading.

Table 4: Parametric study - office building

2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5

0.050.080.100.12

0.050.080.10 10.12 4 4 4 1,4 1 1 10.050.08 1 10.10 4 4 4 4 4 1,4 1 1,4 1,4 1 10.12 4 4 4 4 4 4 1,4 1,4 1,4 1 1,4 1,4 1,4 10.050.08 1 1 1 10.10 4 4 4 4 4 4 4 4 4 1,4 1,4 1,4 1,4 1,4 1,4 1,40.12 4 4 2,4 2,4 4 4 1,2,4 1,2,4 1,4 1,4 1,2,4 1,2,4 1,4 1,4 1,2,4 1,2,4

No. of Levels

D

4 m

A

B

C

10 mNo. of Levels

Length of Wall, L 6 mNo. of Levels

8 mNo. of LevelsHazard

Factor, ZSite Sub-Soil

Class

Table 5: Parametric study - home unit

2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5

0.050.080.100.12

0.050.080.10 10.12 1 1 1 10.050.08 1 10.10 1 1 1 1 1 10.12 3,4 3,4 3,4 3,4 1,3,4 1,3,4 1 1 1,3,4 1,3,4 1 10.050.08 1 1 1 10.10 1 1 1 1 1 1 10.12 3,4 3,4 2,3,4 2,3,4 3,4 3,4 All All 1,3,4 1,3,4 All All 1,3,4 1,3,4 All All

10 mSite Sub-Soil

ClassHazard

Factor, ZNo. of Levels No. of Levels No. of Levels No. of Levels

Length of Wall, L 4 m 6 m 8 m

A

B

C

D

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4.1 Effect of an Opening on Bending Response

For the range of parameters investigated, the results for a wall with a 1.2 m opening central in the wall panel that is partially supported on four sides are the same as those indicated in Table 4 and Table 5 for an office building and home unit respectively.

For the 4 m long wall, the out-of-plane bending capacity was reduced by the presence of an opening. However, the seismic demand was not sufficient to exceed the capacity and cause failure. For the longer walls (L = 6, 8, 10 m) the out-of-plane bending capacity was not changed by the presence of an opening due to the design approach adopted in AS 3700 (Standards Australia, 2001). Figure 4 shows the assumed idealised failure patterns. The crack slope, G, governs the formation of the diagonal crack lines, based on brick unit geometry for half-overlap stretcher-bonded masonry. For walls 3 m in height, with an opening width of 1.2 m, and a crack slope of G = 0.717, the diagonal cracks do not intersect the opening for wall lengths greater than approximately 5.39 m and therefore develop their maximum lengths and capacities. The horizontal crack along the bed joint at mid-height is neglected in the calculation of the total design capacity; hence, any reduction in length due to an opening does not affect the results.

L > 5.39 mL = 4.0 m

G = 0.717

Intersection of diagonalcrack with opening

Lo = 1.2 m

H = 3.0 m

Lo = 1.2 m

Figure 4: Idealised failure patterns

4.2 Effect of Ks Factors on Bending Response

Table 6 indicates the out-of-plane bending results for a wall with no opening that is partially supported on four sides (rotational restraint factors, Rf1 = Rf2 = 0.5). The ratio of capacity to demand, wc/wd, is reported for the same range of parameters investigated previously for Table 4 and Table 5. The results are applicable to both an office building and home unit. Figure 5 to Figure 8 indicate the results of Table 6 graphically for site sub-soil classes A, B, C and D respectively. The vertical dashed line at wc / wd = 1.0 represents the equality of capacity to demand, i.e. wc = wd, hence to the right of the line (wc / wd > 1) is deemed to be safe for design. Note the change in the scale of the x-axis (wc / wd) between figures for clarity.

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Table 6: Out-of-plane bending response (wc / wd)

2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 50.05 8.67 7.99 8.67 9.26 5.03 4.63 5.03 5.37 3.50 3.23 3.50 3.74 2.69 2.48 2.69 2.870.08 5.42 4.99 5.42 5.79 3.14 2.90 3.14 3.36 2.19 2.02 2.19 2.34 1.68 1.55 1.68 1.800.10 4.34 4.00 4.34 4.63 2.51 2.32 2.51 2.68 1.75 1.61 1.75 1.87 1.34 1.24 1.34 1.440.12 3.61 3.33 3.61 3.86 2.09 1.93 2.09 2.24 1.46 1.35 1.46 1.56 1.12 1.03 1.12 1.200.05 7.03 6.27 6.68 7.28 4.07 3.63 3.87 4.22 2.84 2.53 2.70 2.94 2.18 1.94 2.07 2.260.08 4.39 3.92 4.18 4.55 2.55 2.27 2.42 2.64 1.77 1.58 1.69 1.84 1.36 1.22 1.30 1.410.10 3.51 3.13 3.34 3.64 2.04 1.82 1.94 2.11 1.42 1.27 1.35 1.47 1.09 0.97 1.04 1.130.12 2.93 2.61 2.78 3.03 1.70 1.51 1.61 1.76 1.18 1.06 1.13 1.23 0.91 0.81 0.86 0.94

0.05 5.51 4.48 4.79 5.16 3.19 2.60 2.78 2.99 2.23 1.81 1.94 2.08 1.71 1.39 1.49 1.600.08 3.44 2.80 3.00 3.22 2.00 1.62 1.74 1.87 1.39 1.13 1.21 1.30 1.07 0.87 0.93 1.000.10 2.75 2.24 2.40 2.58 1.60 1.30 1.39 1.50 1.11 0.90 0.97 1.04 0.85 0.69 0.74 0.800.12 2.29 1.87 2.00 2.15 1.33 1.08 1.16 1.25 0.93 0.75 0.81 0.87 0.71 0.58 0.62 0.67

0.05 5.51 4.48 4.00 3.70 3.19 2.60 2.32 2.15 2.23 1.81 1.61 1.50 1.71 1.39 1.24 1.150.08 3.44 2.80 2.50 2.32 2.00 1.62 1.45 1.34 1.39 1.13 1.01 0.94 1.07 0.87 0.77 0.720.10 2.75 2.24 2.00 1.85 1.60 1.30 1.16 1.07 1.11 0.90 0.81 0.75 0.85 0.69 0.62 0.570.12 2.29 1.87 1.66 1.54 1.33 1.08 0.97 0.89 0.93 0.75 0.67 0.62 0.71 0.58 0.52 0.48

B

C

D

A

4 mNo. of Levels No. of Levels

Length of Wall, LSite Sub-Soil

ClassHazard

Factor, ZNo. of Levels No. of Levels

6 m 8 m 10 m

0

0 1 2 3 4 5 6 7 8 9 10Ratio of Capacity to Demand, w c / w d

Haz

ard

Fac

tor,

Z

0.05

0.08

0.10

0.12

5432

No. of Levels

L = 10 m 8 m 6 m 4 m

Figure 5: Out-of-plane bending response (site sub-soil class A)

0

0 1 2 3 4 5 6 7 8Ratio of Capacity to Demand, w c / w d

Haz

ard

Fac

tor,

Z

0.05

0.08

0.10

0.12

5432

No. of Levels

L = 10 m 8 m 6 m 4 m

Figure 6: Out-of-plane bending response (site sub-soil class B)

14

0

0 1 2 3 4 5 6Ratio of Capacity to Demand, w c / w d

Haz

ard

Fac

tor,

Z

0.05

0.08

0.10

0.12

5432

No. of Levels

L = 10 m 8 m 6 m 4 m

Figure 7: Out-of-plane bending response (site sub-soil class C)

0

0 1 2 3 4 5 6Ratio of Capacity to Demand, w c / w d

Haz

ard

Fac

tor,

Z

0.05

0.08

0.10

0.12

5432

No. of Levels

L = 10 m 8 m 6 m 4 m

Figure 8: Out-of-plane bending response (site sub-soil class D)

The general trend displayed by the data points for site sub-soil classes A, B and C (Figure 5, Figure 6 and Figure 7 respectively) indicates that the ratio of wc / wd is a minimum for a three-storey building. For class D (i.e. deep or soft soil) sites, the ratio is least for a five-storey building. The reason for this trend is that the fundamental period of vibration of a three-storey unreinforced masonry building is expected to be closest to resonance with the anticipated earthquake ground motion frequencies for sub-soil classes A, B and C, whereas on soft soil sites such as sub-soil class D the building period for a five-storey building will be longer and more closely matched with the soft soil ground motion frequencies.

For example, for a four-storey building, a wall in the top storey is supported at its base by the floor at level 3 and at its top by the roof at level 4. Hence, the acceleration (i.e. load or demand) at wall mid-height is approximated as the average of the accelerations at levels 3 and 4. The acceleration at each level is proportional to the factor, Ks, given in Table 7 for each level in a structure for various sub-soil classes. Thus, for a four-storey building on soil class C, the acceleration at wall mid-height is determined to be Ks = 4.25 (being the average

15

of 4.9 and 3.6). For a structure located on site class C with a hazard factor of 0.10 (Figure 7), the average Ks factors over the top level of two, three, four and five-storey buildings are 3.7, 4.6, 4.3 and 4.0 respectively. Since the seismic capacity, wc, remains constant, the ratio of wc / wd will vary inversely proportionally to the value of wd. Hence, because the ‘demand’ at the top storey of the three-storey building is the greatest (Ks = 4.6) the wc / wd ratio is least for the three-storey building.

This also explains the trends shown in Table 4 and Table 5. For example, consider a structure located in site class B, with a hazard factor of 0.10, and a wall length of 10 m. Out-of-plane failure is deemed to occur in the top level of a three-storey building, but not for a building with 2, 4 or 5 levels. This is also shown graphically in Figure 6.

Table 7: Ks factor (AS 1170.4)

5 4 3 2 1A 2.5 1.9 1.4 1.0 0.5B 3.1 2.5 1.8 1.2 0.6C 4.4 3.5 2.6 1.7 0.9D 6.1 4.9 3.6 2.5 1.2A - 2.7 2.0 1.4 0.6

B - 3.5 2.6 1.7 0.9C - 4.9 3.6 2.5 1.2D - 5.8 4.4 3.0 1.4A - - 3.1 2 1.0B - - 3.9 2.6 1.3C - - 5.5 3.6 1.8D - - 5.5 3.6 1.8A - - - 3.1 1.6B - - - 3.9 1.9C - - - 4.9 2.5

D - - - 4.9 2.5A - - - - 2.3B - - - - 3.0C - - - - 3.6D - - - - 3.6

1

5

4

3

2

Total number of

stories

Sub-soil type

K s factorStorey under consideration

4.3 Effect of Side Restraint Factors on Bending Response

Table 8 indicates the out-of-plane bending results for a wall supported on four sides with no opening. The ratio of capacity to demand, wc/wd, is reported for three values of the rotational restraint factors, Rf1 and Rf2, where 0, 0.5 and 1.0 correspond to conditions of simple, partial and rigid rotational restraint respectively. While a value of 1.0 provides an upper bound estimate for capacity, it is suggested that such restraint can not be achieved in practical situations. The same range of parameters for hazard factor and number of levels were investigated as done previously, however the typical case of site sub-soil class B and wall length of 6 m were selected for comparison purposes. The results are applicable to both an office building and home unit.

16

Table 8: Out-of-plane bending response (wc / wd with Rf1, Rf2 varied)

2 3 4 5 2 3 4 5 2 3 4 50.05 3.45 3.08 3.28 3.58 4.07 3.63 3.87 4.22 4.69 4.19 4.46 4.860.08 2.16 1.93 2.05 2.24 2.55 2.27 2.42 2.64 2.93 2.62 2.79 3.040.10 1.73 1.54 1.64 1.79 2.04 1.82 1.94 2.11 2.35 2.09 2.23 2.430.12 1.44 1.28 1.37 1.49 1.70 1.51 1.61 1.76 1.96 1.74 1.86 2.03

0.5 1.06 mLength of Wall, L

Restraint, R f1 = R f2 0

B

Site Sub-Soil Class

Hazard Factor, Z

No. of Levels No. of Levels No. of Levels

With reference to Table 8 the following observations can be made:

• Increasing Rf1 = Rf2 from 0 to 0.5 increases the ratio of wc/wd by 18%; and

• Increasing Rf1 = Rf2 from 0 to 1.0 increases the ratio of wc/wd by 36%.

5 CONCLUSIONS

With reference to Table 4 and Table 5, the following conclusions can be made:

• Out-of-plane bending tends to govern as wall span (L), site sub-soil class, hazard factor (Z) and the number of levels increase. An increase in wall span reduces the total design capacity, wc, and increasing the other three factors increases the seismic demand, wd. There is no difference in results between the office building and home unit. This finding is based on the failure criterion of cracking at the extreme tension fibre in bending.

• Out-of-plane shear governs in relatively few cases. The combinations of factors that resulted in failure were four and five-storey buildings, for site sub-soil class D and a hazard factor (Z) of 0.12. This failure criterion occurred simultaneously with out-of-plane bending and/or in-plane shear. There is no difference in results between the office building and home unit.

• In-plane shear in the short direction is governed by the arrangement of the internal walls. As discussed above, for office buildings, the tributary area for load transfer to each wall was taken as 75% of the total floor area for the short direction and 25% for the long direction. For home units, the tributary areas were taken as 50% in each direction. As a result, in-plane shear in the short direction was not critical for office buildings for the range of parameters investigated, however for home units, in-plane shear occurred simultaneously in the two orthogonal directions since the tributary areas were equal, giving the same total design capacity in both directions.

• In-plane shear in the long direction is the most significant mode governing structural performance. The effects become less significant as the number of levels increases, which increases the total design in-plane shear capacity at a greater rate than the seismic demand due to the increase in compressive stress, fd. The assumed wall layout was found to be a significant factor influencing behaviour. For example, for office buildings, there was a problem for site sub-soil class B and for Z = 0.10, however failure did not occur for home units in this case. This was due to the assumed reduced tributary areas for fd calculations in the long direction walls for office buildings compared to the home unit building. This finding is based on the

17

failure criterion of onset of sliding at the base of the wall. It should be noted that this does not normally constitute failure under seismic action, as it often does not lead to collapse or provide a risk to life.

While the in-plane shear strength design criterion at the base of masonry walls is currently seen by AS 3700 (Standards Australia, 2001) to be a necessary design criterion for earthquake loading, it is the opinion of the authors that this, along with other possible design criteria such as tensile cracking at the heel of a wall and compressive crushing at the toe of a wall are not necessarily threats to life-safety and therefore might not be the most appropriate design criteria. If a wall slips at its base it will ideally limit the amount of acceleration that can be induced into the building, thereby reducing the amount of inertia forces experienced by the structure. The critical question then becomes, “how far will it slip and how much slip is acceptable?”. Further research in this area and a re-examination of the earthquake design criteria by the AS 3700 Standards Committee are recommended.

ACKNOWLEDGMENTS

This research was conducted with the financial support of the Australian Clay Brick and Paver Institute. Their support is gratefully acknowledged. The comments and findings in this report are those of the authors, and not necessarily those of the sponsor.

REFERENCES

1 Standards Australia (2005), AS 1170.4: Earthquake actions in Australia (Ballot draft), Standards Australia, Sydney, April 2005.

2 Standards Australia (2001), AS 3700-2001: Masonry structures (including proposed Amendment 3), Standards Australia, Sydney, 2001.

3 Standards Australia (2002), AS/NZS 1170.1: Structural design actions - Permanent, imposed and other actions, Standards Australia, Sydney, 2002.

4 Page, A. W. (1995), “Unreinforced Masonry Structures - An Australian Overview”. Proceedings of the Pacific Conference on Earthquake Engineering, Parkville, Victoria, Australia, November 1995, pp. 1-16.

5 Priestley, M. J. N. (1985), “Seismic Behaviour of Unreinforced Masonry Walls”. Bulletin of the New Zealand National Society for Earthquake Engineering, Vol.18, No.2, June 1985, pp. 191-205.

APPENDIX A: METHODOLOGY

18

1. Selection of Structure

The structure under analysis is an Importance Level 2 building, and is hence subject to earthquake design category II (EDC II): • Four (4) storey office building • Length of building (short direction) = 12 m • Length of building (long direction) = 50 m • Total length of walls (short direction) = 180 m • Total length of walls (long direction) = 250 m

The wall under analysis has the following characteristics: • Length of wall, L = 4.00 m • Height of wall, H = 3.00 m • Supported on four sides • No openings • Loadbearing • 110/50/110 mm cavity wall

2. Reference Period

Reference Period used in the analysis is 500 years

3. Hazard Factor

AS 1170.4, Table 3.2: Z = 0.10 (Adelaide)

4. Probability Factor

AS 1170.4, Table 3.1:

Annual Probability of Exceedance

P Probability Factor

kp 1/500 1.0

5. Site Sub-soil Class

Select Class D: Deep or soft soil site

6. AS 1170.4 Analysis (Out-of-plane Bending)

Walls loaded in the out-of-plane direction must resist their own inertia forces, i.e. wall self-weight multiplied by the acceleration at the mid-height of the wall.

The critical storey is taken as the top floor as accelerations increase with height. The wall in the top storey is supported at its base by the floor at level 3 and at its top by the roof at level 4. Hence, the acceleration at its mid-height is approximated as the average of the accelerations at levels 3 and 4. The horizontal static force at level ‘i ’ is given by AS 1170.4, Equation 5.4:

[ ] ippsi WSZkKF µ=

Hence the acceleration at level ‘i’ is given by:

[ ]µppsi

ii SZkK

W

Fa ==

Ks = 4.4 Table 5.1, 3rd of 4 storeys, Sub-soil D = 5.8 Table 5.1, 4th of 4 storeys, Sub-soil D

Sp/µ = 0.62 Table 6.2, Masonry Structures, URM

19

2728.062.010.00.14.43 =×××=a

3596.062.010.00.18.54 =×××=a

From AS 1170.1, Table A2, the force per unit area for ‘brick masonry, solid - burnt clay’, per 10 mm thickness is 0.19 kN/m2. Hence, for a wall thickness of 110 mm, this equates to 2.09 kN/m2.

The out-of-plane load is given by the wall self-weight multiplied by the acceleration at its mid-height:

2/)( kPa 09.2 43 aawd +×=

Hence the seismic demand is 0.66 kPa.

7. AS 3700 Analysis (Out-of-plane Bending)

For out-of-plane bending it is assumed that the entire vertical load is on the inner leaf, which supports the slab, hence the outer leaf is critical and does not benefit from superimposed compressive stress.

Parameters

Vertical edges supported Y

Top edge supported YOpening NUnit length of wall b mm 1000Design compressive stress f d MPa 0.029Flexural tensile strength of masonry f mt MPa characteristic 0.2

Lateral modulus of rupture of brick unit f ut MPa characteristic 0.8

Height of wall H mm 3000Height of opening H o mm -

Height of brick unit h u mm 76

Length of wall L mm 4000Length of opening L o mm -Length of brick unit l u mm 230

Thickness of mortar joint t j mm 10Thickness of masonry section t u mm 110

Capacity reduction factor φ 0.6Compressive stress σ v MPa 0

Force Per Unit Area (per 10 mm thickness) kN/m20.19

One-way Horizontal BendingPerpend spacing factor kp 1.00

Section modulus of the bedded area Z d mm3per metre width 2016667

Horizontal bending moment capacity (i) kNm per metre width 1.24

(ii) kNm per metre width 2.16(iii) kNm per metre width 0.56

Horizontal bending moment capacity M ch kNm per metre width 0.56

Diagonal BendingAspect factor a f 1.47

Height factor B mm 69.9Equivalent torsional strength f t MPa characteristic 1.01

Crack slope G 0.717Design height H d mm 1500Coefficients k1 0.54

k2 2.82Design length L d mm 2000

Restraint factors Rf1 0.5Rf2 0.5

Equivalent torsional section modulus Z t mm3per mm crack length 878.6

Slope factor α 0.96Diagonal moment capacity M cd kNm per m crack length 0.53Total design capacity w c kPa 1.32

Hence the design capacity is 1.32 kPa.

20

8. Deemed-to-Satisfy Result (Out-of-plane Bending)

wd (0.66 kPa) < wc (1.32 kPa)

The seismic demand of 0.66 kPa is less than the design capacity of 1.32 kPa, therefore for out-of-plane bending, the wall in the 4th storey is OK .

9. AS 3700 Analysis (Out-of-plane Shear)

For out-of-plane shear at the wall edges in the top storey it is assumed that the out-of-plane load from both leaves is shed to the inner leaf, hence the inner leaf is critical. The seismic demand on each leaf is 0.66 kPa (calculated in Section 6) acting over a face area of (4.0 × 3.0) m2 hence the total out-of-plane shear is given as follows:

Total out-of-plane shear = 2 × 0.66 kPa × (4.0 × 3.0) m2 (multiply by 2 since two leaves)

= 15.86 kN

Most of the resistance is provided by the top and bottom wall edges, where there is shear bond and friction from the vertical load, hence it is conservatively assumed that all of the load will go to these edges. There will not always be connectors at the sides and the shear bond component at these edges is considered questionable.

Assuming the shear is equally distributed to both edges, the total out-of-plane shear (seismic demand), Vd, for the top and bottom edge is therefore:

= 0.5 × 15.86 kN = 7.93 kN

The relationship that must be satisfied for out-of-plane shear capacity requirements is given by AS 3700, Equation 7.5.1(1):

1o VVVd +≤

Vo = the shear bond strength of the shear section

= φ f'ms Adw

φ = 0.6 Table 4.1 f'ms = 0 MPa Clause 3.3.4(a), for damp-proof course or slip joint Adw = 0.44 m2 1 inner leaf wall × 4.0 m × 0.110 m

Vo = 0 kN

V1 = the shear friction strength of the shear section

= kv fd Adw

kv = 0.3 Table 3.3

The total compressive stress, fd, at the base of the wall in the top storey is given by the compressive stress due to the ceiling and roof and the self-weight of the wall. The level of compressive stress acts to increase the total design capacity, hence to be conservative, the lower bound will be assumed. It is assumed that the shortest wall span is 4 m in each orthogonal direction.

The tributary area of ceiling and roof for load transfer to inner leaf can be shown to be = 2L - 4 = 4.0 m2

Pressure due to ceiling + roof = 0.29 + 0.57 = 0.86 kN/m2 (AS 1170.1 Table A2)

21

( ) ( )( ) MPa 0648.010

m 0.11 m 4.0

wallofheight m 0.3 wallof width m 0.4 kPa 2.09m 0.4kN/m 86.0 3-22

d =××

××+×=f

Clause 7.5.1(a), not greater than 2 MPa

V1 = 8.56 kN

Vo + V1 = 8.6 kN

10. Deemed-to-Satisfy Result (Out-of-plane Shear)

Vd (7.9 kN) < Vo + V1 (8.6 kN)

The seismic demand on one wall of 7.9 kN is less than the design capacity of 8.6 kN, therefore for out-of-plane shear, the wall in the 4th storey is OK . Hence, friction is sufficient to satisfy demand and edge connectors are not required.

11. AS 1170.4 Analysis (In-plane Shear)

Walls loaded in the in-plane direction must resist all the forces applied in the structure above that level.

The critical storey is taken as the ground storey level as the storey shear forces (internal actions) get larger as you go down the building.

The horizontal static force at level ‘i’ is given by AS 1170.4, Equation 5.4:

[ ] ippsi WSZkKF µ=

where:

icii QGW ∑∑ += ψ Equation 6.2(6)

The relationship for Fi (Equation 5.4) is based on the assumption that the mass at each floor level can be lumped together, i.e. the weight of the walls for half a storey above and below each floor level are included in this lumping process.

For level 4, the total load includes the weights of the roof, ceiling and half the walls spanning between levels 3 and 4.

Total Load for Level 4: W4 Permanent Action, G

AS 1170.1

Ceiling Portland cement plaster, 13 mm thick 0.29 kN/m2 600.0 m2 174.0 kN Table A2

Roofs Tiles – Terracotta 0.57 kN/m2 600.0 m2 342.0 kN Table A2

Walls Brick masonry, solid –

burnt clay, per 10 mm of thickness 0.19 kN/m2 Table A2

Short direction walls 2.09 kN/m2 270.0 m2 564.3 kN

Long direction walls 2.09 kN/m2 375.0 m2 783.8 kNΣΣΣΣ 1864.1 kN

Imposed Action, QNone ΣΣΣΣ 0 kN

Earthquake-Imposed Action Combination Factor, ψψψψ c 0.3

Total Action, W W 4 = 1864.1kN

TotalMaterial or Construction Force/unit area Area

22

For levels 1-3, the total load includes the live load, and weights of the floor slab, flooring and the walls for half a storey above and below each floor level.

The weights of half the walls between the base and level 1 and the base slab and flooring are transmitted to the footings and are therefore not included in the calculations.

Total Load for Levels 1-3: W1, W2, W3 Permanent Action, G

AS 1170.1

Concrete Floor slab, 175 mm thick 24.0 kN/m3 105.0 m3 2520.0 kN Table A1

Timber Pine flooring, 15 mm thick 5.3 kN/m3 9.0 m3 47.7 kN Table A1




Long direction walls 2.09 kN/m2 750.0 m2 1567.5 kNΣΣΣΣ 5263.8kN

Imposed Action, Q

Residential General areas (conservatively taken) 2.0 kPa 600 m2 1200.0 kN Table 3.1ΣΣΣΣ 1200.0kN

Earthquake-Imposed Action Combination Factor, ψψψψ c 0.3

Total Action, W W 1 = W 2 = W 3 = 5623.8kN

Total

Material or Construction Weight/cubic metre Volume Total

Force/unit area Area

Material or Construction Uniformly Dist. Actions Area

Now determine the total force, Fi, for each level:

kp = 1.0 Table 3.1 Z = 0.10 Table 3.2 Sp/µ = 0.62 Table 6.2, Masonry Structures, URM

From AS1170.4, Table 5.1, 4 storey structure, Sub-soil D, Ks factors are given in the following table:

Hence, the Total Base Shear, V = ΣΣΣΣFi = 3738.7 kN.

This total base shear, V, must be resisted by the walls running parallel to the earthquake motion.

12. AS 3700 Analysis (In-plane Shear)

For in-plane loading, all load from the slabs (and both leaves) will accumulate to the inner leaf, and the outer leaf does not contribute to the shear resistance, hence the inner leaf is critical.

The relationship that must be satisfied for in-plane shear capacity requirements is given by AS 3700, Equation 7.5.1(1):

1o VVVd +≤

Level Ks Factor Wi (kN) Fi (kN) 1 1.4 5623.8 488.1 2 3.0 5623.8 1046.0 3 4.4 5623.8 1534.2 4 5.8 1864.1 670.3

Σ Σ Σ Σ 18735.5 3738.7

23

Short Direction .

Vo = the shear bond strength of the shear section = φ f'ms Adw

φ = 0.6 Table 4.1 f'ms = 0 MPa Clause 3.3.4(a), for damp-proof course or slip joint Adw = 19.8 m2 180 m (total short direction walls) × 0.110 m

Vo = 0 kN


= kv fd Adw

kv = 0.3 Table 3.3

To determine the compressive stress, fd, acting on each of the walls contributing to the shear resistance, consider the load transmitted to each leaf. The weights of the external leaves are excluded from the total load of the structure. It is conservative to exclude the outer leaves since a proportion of their weight is likely to be transferred to the inner leaf through nibs on the slab or shelf angles.

18735.5 – [2 × (12 m + 50 m) × 3.00 m × 2.09 kPa] = 17958.0 kN

Each critical inner leaf wall supports the live load and ceiling, roof and floor slab weights in proportion to their respective tributary areas, plus their own self-weight.

The internal walls running parallel to the short direction of the building are assumed to be double the length of the orthogonal walls, hence the tributary area of roof and ceiling for load transfer to each wall is taken as 75% of the total floor area. Therefore, the compressive stress, fd, for each leaf is approximately:

MPa 680.010m 0.110 m 180

kN 0.1795875.0 3 =××

×= −df Clause 7.5.1(a), not greater than 2 MPa.

V1 = 4040.5 kN

The actual in-plane resistance is modified to account for ‘flange effects’, whereby a proportion of the walls orthogonal to the in-plane walls (a nominal length of, say, 25% to each side of the in-plane wall) will contribute to shear strength. For this action, the in-plane wall is envisaged as the ‘web’ of an I-section, and the out-of-plane walls are envisaged as the ‘flanges’ of the section.

kN 4.6730.1795825.05.03.01 =×××=′V

• multiply by 0.5 since 25% to each side of the orthogonal wall • multiply by 0.25 since the long direction walls take 25% of the tributary area

Vo + V1 + V'1 = 4714.0 kN

Long Direction .

Vo = the shear bond strength of the shear section

= φ f'ms Adw

φ = 0.6 Table 4.1 f'ms = 0 MPa Clause 3.3.4(a), for damp-proof course or slip joint Adw = 27.5 m2 250 m (total long direction walls) × 0.110 m

Vo = 0 kN


= kv fd Adw

24

kv = 0.3 Table 3.3

The internal walls running parallel to the short direction of the building are assumed to be double the length of the orthogonal walls, hence the tributary area of roof and ceiling for load transfer to each wall is taken as 25% of the total floor area. Therefore, the compressive stress, fd, for each leaf is approximately:

MPa 163.010m 0.110 m 250

kN 0.1795825.0 3 =××

×= −df Clause 7.5.1(a), not greater than 2 MPa.

V1 = 1346.8 kN

The actual in-plane resistance is modified to account for ‘flange effects’, whereby a proportion of the walls orthogonal to the in-plane walls (a nominal length of, say, 25% to each side of the in-plane wall) will contribute to shear strength.

kN 3.20200.1795875.05.03.01 =×××=′V

• multiply by 0.5 since 25% to each side of the orthogonal wall • multiply by 0.75 since the short direction walls take 75% of the tributary area

Vo + V1 + V'1 = 3367.1 kN

13. Deemed-to-Satisfy Result (In-plane Shear)

Short Direction .

Vd (3738.7 kN) < Vc (4714.0 kN)

The total base shear demand of 3738.7 kN is less than the design shear capacity of 4714.0 kN, therefore for in-plane loading in the short direction, the walls in the base storey are OK .

Long Direction .

Vd (3738.7 kN) > Vc (3367.1 kN)

The total base shear demand of 3738.7 kN is greater than the design shear capacity of 3367.1 kN, therefore for in-plane loading in the long direction, the walls in the base storey are NOT OK .

26

APPENDIX B: CALCULATIONS

25

1. PARAMETERS

Variable Parameters

Structure Type 1 Office

Length of Wall L 4 10000mm

Length of Opening L o 1 0 mm

Hazard Factor Z 4 0.12 AS 1170.4 Table 3.2

Wall Edge Support (Top) 2 Simple

Wall Edge Support (Left) 4 Partial

Wall Edge Support (Right) 4 Partial

Site Sub-soil Class 4 D AS 1170.4 Clause 4.2

Storey Under Consideration 5 5

Total Number of Storeys 4 5

Unit Type 1 A

Unit Dimension (Height) h u 76 mm

Unit Dimension (Length) l u 230 mm

Unit Dimension (Width) t u 110 mm

Rotational Restraint Factor R f1 0.5 AS 3700 Clause 7.4.4.2

Rotational Restraint Factor R f2 0.5 AS 3700 Clause 7.4.4.2

Constant Parameters

Length of Building (Short Direction) 12 m

Length of Building (Long Direction) 50 m

Total Length of Walls (Short Direction) 180 m

Total Length of Walls (Long Direction) 250 m

Proportion of Tributary Area (Short Direction) 0.75

Proportion of Tributary Area (Long Direction) 0.25

Unit Length of Wall b 1000 mm

Design Compressive Stress f d 0.0285MPa

Shear Strength of Masonry f' ms 0 MPa * AS 3700 Clause 3.3.4 (a)

Flexural Tensile Strength of the Masonry f' mt 0.2 MPa * AS 3700 Clause 3.3.3 (a) (i)

Lateral Modulus of Rupture of the Brick Unit f' ut 0.8 MPa * AS 3700 Clause 1.5.2.9

Height of Wall H 3000 mm

Probability Factor kp 1.0 AS 1170.4 Table 3.1

Shear Factor k v 0.3 AS 3700 Table 3.3

Ratio of Structural Performance to Ductility Sp /µ 0.62 AS 1170.4 Table 6.2

Thickness of Mortar Joint t j 10 mm

Capacity Reduction Factor (a) (ii) φ 0.6 AS 3700 Table 4.1

Earthquake-Imposed Action Combination Factor ψ c 0.3 AS 1170.4 Clause 6.2.2

Force Per Unit Area (per 10 mm thickness) 0.19 kN/m2 AS 1170.1 Table A2

Force Per Unit Area 2.09 kN/m2 per metre width of wall

Number of Wall Leaves (Cavity) 2

Reference Period 500 years

Slab Thickness 175 mm

Timber Flooring Thickness 15 mm

* Characteristic

Note: at least one wall

edge must be supported

Note: opening is central in wall panel

10000

D

5

0.12

5

A

Simple

Partial

Partial

0

Office

26

2. OUT-OF-PLANE BENDING

AS 1170.4 Analysis

Factor to Account for Floor (Upper) K s (upper) 6.1 AS 1170.4 Table 5.1

Factor to Account for Floor (Lower) K s (lower) 4.9 AS 1170.4 Table 5.1

Acceleration at Level i (Upper) a i 0.45Acceleration at Level i -1 (Lower) a i -1 0.36

Seismic Demand (Out-of-plane Load) w d 0.86 kPa

AS 3700 Analysis

One-way Horizontal Bending

Perpend Spacing Factor k p 1.00 AS3700 Clause 7.4.3.4

Section Modulus of the Bedded Area Z d 2016667mm3per metre width

Horizontal Bending Moment Capacity (i) 1.24 kNm per metre width

(ii) 2.16 kNm per metre width

(iii) 0.56 kNm per metre width

Horizontal Bending Moment Capacity M ch 0.56 kNm per metre width

Diagonal Bending

Opening No

Number of Vertical Edges Supported Both

Slope Factor α 2.39 AS3700 Clause 7.4.4.2 (a)

Case 1-6 (Table 7.4) 2

Aspect Factor a f 2.78

Coefficients k 1 0.50 AS3700 Table 7.4

k 2 2.95 AS3700 Table 7.4

Height Factor B 69.9 mm AS3700 Clause 7.4.4.2 (b)

Equivalent Torsional Strength f' t 1.01 MPa * AS3700 Clause 7.4.4.2 (b)

Crack Slope G 0.72 AS3700 Clause 7.4.4.2 (a)

Design Height H d 1500 mm AS3700 Clause 7.4.4.2 (a)

Design Length L d 5000 mm

Equivalent Torsional Section Modulus Z t 878.6mm3per mm crack length

Diagonal Moment Capacity M cd 0.53 kNm per m crack length

Total Design Capacity (Bending) w c 0.41 kPa = 0.48wd Clause 7.4.4.2 (a)

Deemed-to-satisfy Result

(Seismic Demand) wd > w c (Total Design Capacity) NOT OK

27

3. OUT-OF-PLANE SHEAR

AS 3700 Analysis

Total Out-of-plane Shear 51.31 kN

Seismic Demand (Shear at Base of Wall) V d 25.66 kN

Area of a Shear-resisting Portion of a Member A dw 1.1 m2

Shear Bond Strength of the Shear Section V o 0.00 kN

Minimum Design Compressive Stress f d 0.0648MPa

Shear Friction Strength of the Shear Section V 1 21.39 kN

Total Design Capacity (Shear) V o + V 1 21.39 kN

Deemed-to-satisfy Result

(Seismic Demand) V d > V o + V 1 (Total Design Capacity) NOT OK

Friction IS NOT sufficient to satisfy demand hence EDGE CONNECTORS are required

28

4. IN-PLANE SHEAR

AS 1170.4 Analysis

Total Load for Level 5

Permanent Action, G

AS 1170.1

Ceiling Portland cement plaster, 13 mm thick 0.29 kN/m2 600.0 m2 174.0 kN Table A2

Roofs Tiles – Terracotta 0.57 kN/m2 600.0 m2 342.0 kN Table A2




Long direction walls 2.09 kN/m2 375.0 m2 783.8 kN

ΣΣΣΣ 1864.1 kN

Imposed Action, Q

None ΣΣΣΣ 0 kN

Total Action, W 1864.1 kN

Total Load for Levels 1 - 4

Permanent Action, G

AS 1170.1

Concrete Floor slab 24.0 kN/m3 105.0 m3 2520.0 kN Table A1

Timber Pine flooring 5.3 kN/m3 9.0 m3 47.7 kN Table A1




Long direction walls 2.09 kN/m2 750.0 m2 1567.5 kN

ΣΣΣΣ 5263.8 kN

Imposed Action, Q

Residential General areas (conservatively taken) 2.0 kPa 600.0 m2 1200.0 kN Table 3.1

ΣΣΣΣ 1200.0 kN

Total Action, W 5623.8 kN

Total force, F i , for each level: Level K s

1 1.2 5623.8 kN 502.1kN

2 2.5 5623.8 kN 1046.0kN

3 3.6 5623.8 kN 1506.3kN

4 4.9 5623.8 kN 2050.2kN

5 6.1 1864.1 kN 846.0kN

ΣΣΣΣ 24359.3 kN 5950.6 kN

Total Base Shear (Seismic Demand) Vd 5950.6 kN = 0.24W

Material or Construction

F i


W i

Volume

Unif. Dist. Actions Area Total

Force/unit area

Weight/cubic metre

Area

Total

Force/unit area Area Total


29

Short Direction

AS 3700 Analysis




Shear Friction Strength of the Shear Section V 1 5305.9kN

Shear Friction Strength of the Shear Section (Flange Effects) V 1' 884.3kN

Total Design Capacity (Shear) V o + V 1 + V 1' 6190.2 kN = 1.04V d

Deemed-to-satisfy Result(Seismic Demand) V < V o + V 1 + V 1' (Total Design Capacity) OK

Long Direction

AS 3700 Analysis




Shear Friction Strength of the Shear Section V 1 1768.6kN

Shear Friction Strength of the Shear Section (Flange Effects) V 1' 2652.9kN

Total Design Capacity (Shear) V o + V 1 + V 1' 4421.6 kN = 0.74V d

Deemed-to-satisfy Result(Seismic Demand) V > V o + V 1 + V 1' (Total Design Capacity) NOT OK

FAIL: Friction IS NOT sufficient to satisfy demand

Friction IS sufficient to satisfy demand

earthquake performance of unreinforced masonry residential … · · 2013-12-02earthquake...

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