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The Masonry Society

AIA Provider: 50119857

Analysis of Masonry Shear Walls Using Strut-and-Tie Models

Patrick B. Dillon, Ph.D., P.E.Project EngineerWDP & Associates

Fernando S. Fonseca, Ph.D., S.E.ProfessorBrigham Young University

The Masonry Society is a registered Provider with the

American Institute of Architects Continuing Education

Systems. Credit earned on completion of this program will be

reported to CES Records for AIA members. Certificates of

completion for non-AIA members are available upon request.

This program is registered with AIA/CES for continuing

professional education. As such, it does not include content

that may be deemed or construed to be an approval or

endorsement by the AIA of any material of construction or any

method or manner of handling, using, distributing or dealing

in any material or product.

Questions related to specific materials, methods, and services

will be addressed at the conclusion of this presentation.

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Course Description

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This presentation describes ongoing research that has the objective to develop strut-and-tie modeling procedures for masonry.

Introduction

� Stress Fields� A stress field is a region in a body for which the stress is

defined at every point.

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Introduction

�Lower Bound Plasticity Theorem� Provided that the stress fields

� satisfy the boundary conditions,

� are in equilibrium, and

� do not violate the yield criterion of the material,

then the predicted strength is a lower bound for the ultimate strength of the material.

�Members divided into B-regions and D-regions

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B-Regions

�B stands for Bernoulli

�Linear strain distribution

�Traditional analysis methods apply

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D-Regions

�D stands for:� Discontinuity

� Disturbance

� Detail

�Nonlinear strain distribution

�Regions near:� Concentrated loads

� Geometric discontinuities

� Openings

� Bends

� Corners

� St. Venant’s Principle

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St. Venant’s Principle The localized effects caused by a load acting on the body will dissipate within regions that are sufficiently away from the point of load application.

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D-region D-region D-regionB-region

This distance away from load application can be taken as the member depth

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St. Venant’s Principle

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Structural Analysis

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=

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Strut and Tie Modeling

� Strut-and-tie models represent a complex structural member as an appropriate simplified truss model.

� Struts:

� Compression

�Ties:

� Tension

�Nodal zones:

� Transfer stresses11

Adapted from: McGregor & Wight

Applications

Reinforced Concrete

12Images adapted from: McGregor & Wight

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Applications

Deep Steel Sections

� Struts� Stiffeners

�Ties

� Web

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Source: http://www.lusas.com/products/bridge_tour_analysis.html

Ties

Struts

Applications

Traditional Masonry Design

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�Thrust Lines� Struts

�No tension

� No ties

Adapted from: https://static.cambridge.org/resource/id/urn:cambridge.org

:id:binary:90293:20160706011842795-0639:05935fig8_118.png

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Applications

Masonry Design

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D-regions

�D-regions prevail� STM is an ideal tool!

Application

Summary

� Suitable for design of:� Reinforced concrete

� Deep steel sections

� Masonry!

�Not really useful for:� Timber design

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These material groupings all share another similarity…

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Application

…flammability!

17Source: http://www.fireengineering.com/articles/print/volume-169/issue-1/features/massive-fire-destroys-new-jersey-lightweight-wood-frame-apartment-building.html

Strut-and-Tie Modeling

�There is no single, unique S&T model for most design situations encountered.

�There are, however, some techniques and rules that can help the designer develop an appropriate model.

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S&T Guidelines for Masonry

Reinventing the Wheel?

�No!

�The existing guidelines of ACI 318 have been used as a starting point for developing strut-and-tie modeling guidelines for masonry.

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ACI 318-14

� §23.2.1 - Strut-and-tie models shall consist of struts and ties connected at nodes to form an idealized truss.

� §23.2.2 - Geometry of the idealized truss shall be consistent with the dimensions of the struts, ties, nodal zones, bearing areas, and supports.

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ACI 314-18

� 23.3 – Design Strength

� §23.3.1 - For each applicable factored load combination, design strength of each strut, tie, and nodal zone in a strut-and-tie model shall satisfy ϕ Sn ≥ U, including (a) through (c):

a) Struts: ϕ Fns ≥ Fus

b) Ties: ϕ Fnt≥ Fut

c) Nodal zones: ϕ Fnn ≥ Fus

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ACI 318-14

�23.4 – Strength of struts

� §23.4.1 The nominal compressive strength of a strut, Fns, shall be calculated by (a) or (b):

� (a) Strut without longitudinal reinforcement

Fns = fce Acs

� (b) Strut with longitudinal reinforcement

Fns = fce Acs + Aʹs fʹs� §23.4.3 Effective compressive strength of concrete

in a strut, fce, shall be calculated by:fce = βs (0.85 fʹc)

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ACI 318-14

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Table 23.4.3-Strut coefficient βs

Strut geometry and location Reinforcement crossing a strut βs

Struts with uniform cross-

sectional area along length (prismatic

struts)

NA 1.0

Struts located in a region of a member

where the width of the compressed

concrete at midlength of the strut can

spread laterally (bottle-shaped struts)

Satisfying 23.5 0.75

Not Satisfying 23.5 0.60λ

Struts located in tension members or the

tension zones of membersNA 0.40

All other cases NA 0.60λ

Masonry Struts

�The effective compressive strength is taken as

fʹs = 0.8 βs βα fʹm

where

�� - strut efficiency factor

�� - strut inclination factor

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Strut Efficiency Factor, ��

� βs = 1.0 for struts that are principally prismatic

� βs = 0.75 for bottle-shaped struts crossed by at least one reinforcing bar

� βs = 0.60 for bottle-shaped struts not crossed by at least one reinforcing bar

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Strut Inclination Factor, ��

�The values for βα

(strut inclination factor) were assumed to follow a bilinear approximation:� 1.0 at a strut inclination

of 0°, decreasing to

� 2/3 at an inclination angle of 35°, and

� 2/3 for inclination >35°

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Nodal Zones

�Transfer stresses between struts or between struts and

ties

� Provide anchorage for reinforcement ties

�The effective strength of nodal regions is taken as

fʹn = 0.8 βn fʹm

where

�� – node efficiency factor

� �� = 1.0 for nodal zones anchoring one tie

� �� = 0.6 for nodal zones anchoring two ties27

Anchorages

�Nodal zone provide anchorage for reinforcement

�Development length requirements must be satisfied

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Analysis

The current study constructed strut-and-tie models for the fully grouted specimens presented by Voon (In–Plane Seismic Design of Concrete Masonry Structures. Ph.D. thesis, University of Auckland, Auckland)

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Results

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Wall

Ultimate Shear

Load (kN)

Strut-and-Tie Models TMS 402

EquationIncluding βα

Excluding βα

Min Max Avg Vn (kN) Vexp/Vn Vn (kN) Vexp/Vn Vn (kN) Vexp/Vn

A1 205 215 210 183 1.15 194 1.08 235 0.89

A2 177 195 186 187 0.99 205 0.91 219 0.85

A4 201 233 217 203 1.07 215 1.01 237 0.92

A7 261 263 262 229 1.14 245 1.07 274 0.96

A8 244 250 247 212 1.17 225 1.10 258 0.96

A9 204 207 206 156 1.32 172 1.19 288 0.71

A10 572 598 585 578 1.01 622 0.94 596 0.98

Mean 1.12 Mean 1.04 Mean 0.90

COV 0.100 COV 0.093 COV 0.105

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Discussion

�The ability of strut-and-tie models to consider the subtle differences in reinforcement placement and wall geometry makes them more precise at describing and predicting the shear behavior of masonry walls than the TMS shear equation.

�The improved precision of the strut-and-tie modeling method comes at the expense of requiring more effort and understanding on the part of the designer.

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Discussion

�Developing strut-and-tie models for masonry walls is straightforward and can be mastered quickly with some practice.

�The most important principles of developing strut-and-tie models are:

� All forces and reactions be in equilibrium

� The design strength of all members meet or exceed the ultimate factored load applied to them

� The geometry of all members should be considered in apportioning loads and calculating design strength

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Summary

�The results show that the strut-and-tie model guidelines based on the methodology for RC are valid for masonry design with minor adaptations.

�The shear strength predictions from the proposed strut-and-tie modeling methodology out-perform those of the TMS shear strength equation.

�The vertical reinforcement nearest the trailing edge of the wall and the horizontal reinforcement in the middle half of the wall are most effective in contributing to the shear capacity of masonry shear walls.

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The Masonry Society

This concludes The American Institute of Architects

Continuing Education Systems Course

Patrick B. Dillon, Ph.D., P.E.

pdillon@wdpa.com

Fernando S. Fonseca, Ph.D., S.E.

fonseca@byu.edu

Thank you