1. Comparative Study of Chord forces in Flat Slabs due to Seismic loads in buildings of different plan aspect ratios
Aman Gupta (B.Tech. student)
Dr. S. Mandal (Associate Prof.)
IIT(BHU), Varanasi

2. INTRODUCTION
Traditionally, slabs were designed only for gravity loads; means vertical loads, there were less consideration on the effect of lateral load on slabs. In case of earthquake, in-plane stresses are developed in the slabs and these stresses lead to formation of cracks and depletes the slab capacity, which sometimes leads to failure of the structure.
This presentation compares the variation of chord forces for buildings having different plan aspect ratios using STAAD.Pro software.
Plan aspect ratio: Length to Width ratio of a building

3. What are “Chord Forces”?
During earthquake, the slabs act as deep beams and these slabs undergoes in-plane bending, resulting into the normal tensile and compressive forces in slabs.
These tensile and compressive forces are called Chord Forces.

5. How to calculate chord forces?
The chord force can be calculated by dividing the slab into finite small elements (Using Finite Element Method). The net chord forces has been evaluated by summing the force in each element algebraically (Dhar and Sengupta, 2010; Naeim and Boppana, 2001). C = T = ∑ σzzAi +Pz These forces have been calculated by structural analysis and design software STAAD.Pro in this presentation.

6. Buildings Specifications
Table 1 Member dimension for the building modeled
Member
Breadth (mm)
Depth (mm)
Thickness (mm)
Slab
250
125#
Shear Wall
150
Columns in ground and first storeys
350
600
Columns in second to four storeys
500
Columns in fifth and sixth storeys
400
#For building 2A

7. Buildings Specifications cont..

8. Buildings Specifications cont..
Buildings with plan aspect ratio 1 and 2

9. Load Calculation 1. Earthquake load is calculated as per IS 1893:2002.
Parameters for calculating base shear 1.
Zone factor, Z
0.36 (for Seismic zone V) 2.
Response reduction factor, R
4 (Ordinary shear wall with SMRF) 3.
Importance Factor, I
1.5 (For important building) 4.
Time Period, T
0.075h0.75 = 0.075x = 0.76 second 5.
Spectral acceleration coefficient, Sa/g
1.36/T = 1.36/0.76 =1.79 (For medium soil) 6.
Horizontal seismic coefficient (Ah)
(Z/2)(I/R)(Sa/g) = 0.12
SMRF = Special Moment Resisting Frame
2. The dead load (density of concrete= kg/m3),
live load (4 kN/m2 on nominal floor and 2 kN/m2 on roof floor) is applied.

10. RESULTS AND DISCUSSIONS
Chord Forces in different floor levels in buildings of plan aspect ratio 1 and 2
Chord Forces Increases non-linearly with increase in Plan aspect ratio of buildings (Length to width ratio of a building).

11. Contours showing the variation of chord stresses along the chord
Chord stresses varies parabolically along the chord.
3-D building showing contours of chord stresses
floor slab showing contours of chord stresses

12. Chord stress at different floor levels of a building along the chord
The chord stresses in flat slab vary parabolically along the length of chord also these stresses increases as we go up the floor level.

13. Effect of shear wall
The maximum chord forces are higher in upper floors (i.e., in 5th, 6th floor and roof) of building with shear wall which is caused by the presence of shear wall.

14. Effect of slab thickness on chord forces
Chord forces remain unchanged with the change in slab thickness

15. Effect of slab thickness on chord stresses
Chord stresses increases with decrease in slab thickness

16. Conclusions
The magnitude of chord forces in flat slab increases non-linearly with increase in plan aspect ratio of buildings. So for buildings with larger plan aspect ratio, there is need of consideration of Chord forces while designing it.
The chord stresses in flat slab vary parabolically along the length of chord, also these stresses increases as go up the floor level. So higher emphasis is given to Chord forces in higher floors.
The maximum chord forces developed is higher in upper floors in case of buildings with shear wall than framed buildings without shear wall.
Chord forces are independent of the thickness of slab, however stresses developed due to chord force increases with decrease in slab thickness.

17. References
IS 1893: 2002, “Indian Standard Criteria for Earthquake Resistant Design of Structures”, Part 1, Bureau of Indian Standards, New Delhi.
IS 13920:1993, “Indian Standard Ductile Detailing of Reinforced Concrete Structures Subjected to Seismic Forces”, Bureau of Indian Standards, New Delhi.
Sengupta A. K. and Shetty A. D. (2011): “Analysis of Chord Forces in Floors with Large Openings or Re-Entrant Corners in Reinforced Concrete Buildings”, ICI Journal, Indian Concrete Institute, July-September, vol.12, pp 7-16.
Dhar S. and Sengupta A. K. (2010): “Analysis of Chord Forces in Reinforced Concrete Buildings with Flat Slabs”, ICI Journal, Indian Concrete Institute, January- March, Vol.10, No.4, pp

18. Moehle J. P. , Hooper J. D. , Kelly D. J. , and Meyer T. R
Moehle J. P., Hooper J. D., Kelly D. J., and Meyer T. R. (2010): “Seismic Design of Cast-in-Place Concrete Diaphragms, Chords, and Collectors” A Guide for Practicing Engineers, National Earthquake Hazards Reduction Program (NEHRP), pp1-14.
Naeim F. and Boppana R. R. (2001): “Seismic Design of Floor Diaphragms”, The seismic Design Handbook, Edited by Naeim F., 2nd Edition, Springer Science + Business Media, pp (Bibliography).