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# Analysis of Confined Masonry part 1

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### Analysis of Confined Masonry part 1

1. 1. Short Course on Seismic Design of Reinforced and Confined Masonry Buildings February 17-21, 2014, IIT Gandhinagar, India
2. 2. Acknowledgments Kiran Rangwani, IIT Gandhinagar, India EERI Confined Masonry Network – authors of the confined masonry guide: Roberto Meli and others
3. 3. Topics Part 1: Simplified Method (Svetlana Brzev) Part 2: Wide Column Model (J.J. Perez Gavilan)
4. 4. The Simplified Method (SM) Based on an idealized distribution of lateral seismic forces in regular shear wall structures with rigid diaphragms. Shear strength of all walls at any floor level is required to exceed the seismic demand (applied shear force due to earthquake ground shaking)
5. 5. Assumptions 1.It is assumed that all walls at each floor level fail simultaneously. 2.The walls have shear-dominant behaviour (the effect of bending is ignored). 3.The method assumes rigid diaphragm behaviour. 4.The method ignores torsional effects.
6. 6. Theoretical Background The goal: Shear strength of all walls at any floor level (VR ) should exceed the seismic shear force demand (Vx) at the same level
7. 7. Seismic Shear Force Demand Interstorey shear force Vx  ix QV
8. 8. Seismic Force Distribution to Individual Walls Wall shear demand Vjx
9. 9. Seismic Force Distribution to Individual Walls xN j jx jx xjxjx V k k DkV   1 j jAEj jx H AFG k      N j jAEj jAE xjx AF AF VV j 1
10. 10. Wall resistance VRj Storey Shear Resistance Seismic load Ap Aw Wall cross-section Aj
11. 11. Storey Shear Resistance 1AEF when 33.1 L H 2 33.1        H L FAE when 33.1 L H AEjsRj FAfV 
12. 12. Wall Density Index (d) One of the key indicators of seismic resistance p w A A d  Seismic load Ap Aw
13. 13. Wall Density Index Derivations Goal: resistance greater than demand ws N j jsR AfAfV  1 ThB WAV  pT nwAW  s h f wnA d   BR VV 
14. 14. Wall Density Index – India Allowable shear stress (N/mm2) Floor weight (kN/m2) Number of storeys Seismic Zone III IV V 0.3 6.0 1 1.6 2.4 3.6 2 3.2 4.8 7.2 3 4.8 7.2 10.8 0.4 1 1.2 1.8 2.7 2 2.4 3.6 5.4 3 3.6 5.4 8.1 0.5 1 1.0 1.5 2.2 2 2.0 2.9 4.4 3 2.9 4.4 6.5 0.3 8.0 1 2.2 3.2 4.8 2 4.3 6.4 9.6 3 6.5 9.6 14.4 0.4 1 1.6 2.4 3.6 2 3.2 4.8 7.2 3 4.8 7.2 10.8 0.5 1 1.3 2.0 2.9 2 2.6 3.9 5.8 3 3.9 5.8 8.7
15. 15. Assumptions 1. 𝑅=2.5 for confined masonry (currently not addressed by IS 1893) 2. 𝑆𝑎 𝑔 = 2.5 assuming the fundamental period range from 0.1 to 0.4 sec 3. Importance factor 𝐼=1 assuming regular importance 4. Allowable masonry shear stress (fs): from 0.3 to 0.5 N/mm2 5. Floor weight (w) – two values: 6.0 kN/m2 (light-weight floor structure) and 8.0 kN/m2 (heavy-weight floor structure e.g. RC slab).
16. 16. Further Reading  Attached writeup (document) on the Simplified Method  Seismic Design Guide for Low-Rise Confined Masonry Buildings, EERI, 2011 www.confinedmasonry.org