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

Transcription

1 Analysis of Masonry Shear Walls Using Strut-and-Tie Models Patrick B. Dillon, Ph.D., P.E. Project Engineer WDP & Associates Fernando S. Fonseca, Ph.D., S.E. Professor Brigham Young University The Masonry Society AIA Provider: 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. 2 1

2 Course Description This presentation describes ongoing research that has the objective to develop strutand-tie modeling procedures for masonry. 3 Introduction Stress Fields A stress field is a region in a body for which the stress is defined at every point. 4 2

3 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 5 B-Regions B stands for Bernoulli Linear strain distribution Traditional analysis methods apply 6 3

4 D-Regions D stands for: Discontinuity Disturbance Detail Nonlinear strain distribution Regions near: Concentrated loads Geometric discontinuities Openings Bends Corners St. Venant s Principle 7 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. This distance away from load application can be taken as the member depth D-region B-region D-region D-region 8 4

5 St. Venant s Principle 9 Structural Analysis = 10 5

6 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 stresses Adapted from: McGregor & Wight 11 Applications Reinforced Concrete Images adapted from: McGregor & Wight 12 6

7 Applications Ties Deep Steel Sections Struts Stiffeners Ties Web Struts Source: 13 Applications Traditional Masonry Design Thrust Lines Struts No tension No ties Adapted from: :id:binary:90293: :05935fig8_118.png 14 7

8 Applications Masonry Design D-regions prevail STM is an ideal tool! D-regions 15 Application Summary Suitable for design of: Reinforced concrete Deep steel sections Masonry! Not really useful for: Timber design These material groupings all share another similarity 16 8

9 Application flammability! Source: 17 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. 18 9

10 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-andtie modeling guidelines for masonry. 19 ACI Strut-and-tie models shall consist of struts and ties connected at nodes to form an idealized truss Geometry of the idealized truss shall be consistent with the dimensions of the struts, ties, nodal zones, bearing areas, and supports

11 ACI Design Strength For each applicable factored load combination, design strength of each strut, tie, and nodal zone in a strut-and-tie model shall satisfy ϕ S n U, including (a) through (c): a) Struts: ϕ F ns F us b) Ties: ϕ F nt F ut c) Nodal zones: ϕ F nn F us 21 ACI Strength of struts The nominal compressive strength of a strut, F ns, shall be calculated by (a) or (b): (a) Strut without longitudinal reinforcement F ns = f ce A cs (b) Strut with longitudinal reinforcement F ns = f ce A cs + Aʹs fʹs Effective compressive strength of concrete in a strut, f ce, shall be calculated by: f ce = β s (0.85 fʹc) 22 11

12 ACI Table Strut coefficient β s Strut geometry and location Reinforcement crossing a strut β s Struts with uniform crosssectional 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 Not Satisfying λ Struts located in tension members or the tension zones of members NA 0.40 All other cases NA 0.60λ 23 Masonry Struts The effective compressive strength is taken as fʹs = 0.8 β s β α fʹm where - strut efficiency factor - strut inclination factor 24 12

13 Strut Efficiency Factor, β s = 1.0 for struts that are principally prismatic β s = 0.75 for bottle-shaped struts crossed by at least one reinforcing bar β s = 0.60 for bottle-shaped struts not crossed by at least one reinforcing bar 25 Strut Inclination Factor, The values for β α (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 >

14 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 β n fʹm where node efficiency factor = 1.0 for nodal zones anchoring one tie = 0.6 for nodal zones anchoring two ties 27 Anchorages Nodal zone provide anchorage for reinforcement Development length requirements must be satisfied 28 14

15 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) 29 Results Wall Ultimate Shear Load (kn) Strut-and-Tie Models TMS 402 Including β α Excluding β α Equation Min Max Avg V n (kn) V exp /V n V n (kn) V exp /V n V n (kn) V exp /V n A A A A A A A Mean 1.12 Mean 1.04 Mean 0.90 COV COV COV

16 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. 31 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-andtie 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 32 16

17 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. 33 Thank you This concludes The American Institute of Architects Continuing Education Systems Course Patrick B. Dillon, Ph.D., P.E. The Masonry Society Fernando S. Fonseca, Ph.D., S.E. 17