1. University of Palestine
Advance Design of RC Structure
University of Palestine
Lecture 4
Shear Wall Design
Dr. Ali Tayeh

2. Design Loads Reinforcement Shear force – maximum at the base
Bending moment – maximum at the base
Axial load – including its own weight
Reinforcement
Special reinforced concrete walls are to be provided with reinforcement in two orthogonal directions in the plane of the wall.
At least two curtains of reinforcement shall be used in wall if:
Vu exceeds
The wall thickness is more than 250 mm
Reinforcement spacing each way in structure wall shall not exceed the large of 450 mm & 3  wall thickness

3. The minimum reinforcement ratio for both the vertical & horizontal reinforcement is:If
The minimum vertical reinforcement ratio
V = for No. 16 bars or smaller, fy  420 MPa
= for other bars, fy  420 MPa
The minimum horizontal reinforcement ratio
h = for No. 16 bars or smaller, fy  420 MPa
= for other bars, fy  420 MPa
Vu is obtained from the lateral load analysis in accordance with the factored load combinations.
Acv is the gross area of concrete section bounded by the web thickness & length of section in the direction of the shear force considered

4. Shear Strength
The nominal shear strength Vn
Where c is for hw/Lw  1.5
0.17 for hw/Lw  2
varies linearly between 0.25 & 0.17 for hw/Lw between 1.5 & 2
hw = height of entire wall of wall considered
Lw = length of entire wall in the direction of shear force
For all wall piers sharing a common lateral force Vn shall not be taken larger than

5. Design for Flexural & Axial Loads
For individual wall piers Vn shall not be taken larger than
Acw is the area of concrete section of the individual pier considered
Design for Flexural & Axial Loads
The compression zones must include special boundary elements when

6. Where
C = distance from the extreme compression fiber to the neutral axis calculated from the factored axial force & nominal moment strength, consistent with the design displacement u, resulting in the largest neutral axis
Lw = length of the entire wall considered in the direction of the shear force
δu = design displacement & it is determined by multiplying the deflections from an elastic analysis under the prescribed seismic forces by a deflection amplification
hw = height of entire wall or of the segment of wall considered

7. When special boundary elements are required, they must extend horizontally from the extreme compression fiber a distance not less than the large of C-0.1Lw & C/2
In the vertical direction the special boundary elements must extend from the critical section a distance greater than or equal to the large of Lw or Mu/4Vu.
This distance is based on upper bound estimates of plastic hinge lengths.

8. The compression zone shall include special boundary elements where the maximum extreme fiber stress corresponding to the factored forces, including earthquake effects, exceeds 0.2fc’
Special boundary elements can be discontinued where the compressive stress is less than 0.15fc’.

9. When special boundary elements are not required & if the longitudinal reinforcement ratio at the wall boundary is greater than 2.8/fy, the maximum longitudinal spacing of transverse reinforcement in the boundary shall not exceed 200mm. Except when
If the wall subjected to axial load smaller than the producing balanced failure, the following approximate equation can be used to determine the design moment capacity of the wall:

10. Ast = total area of vertical reinforcement
lw = horizontal length of wall
Pu = factored axial compressive load
fy = yield strength of reinforcement

11. fc ' = compressive strength of concrete
β1 = factor relating depth of equivalent rectangular compressive stress block to the neutral axis depth= 0.85 for fc’= 17 to 28 MPa & = 0.8 for fc’ > 28 MPa
fc ' = compressive strength of concrete
h = thickness of wall
φ = 0.90 (strength primarily controlled by flexure with low axial load)

12. Detailing reinforcement for boundary Zone
Dimension
The minimum section dimension of the boundary zone shall be lw/16.
Boundary zones shall have a minimum length of 450mm (measured along the length) at each end of the wall or portion of wall.
In I-, L-, C- or T-section walls, the boundary zone at each end shall include the effective flange width and shall extend at least 250mm. into the web.
Confinement Reinforcement
All vertical reinforcement within the boundary zone shall be confined by hoops or cross-ties having a steel cross sectional area Ash> 0.09S.bc. fc′ / fy

13. Minimum for vertical reinforcement
All Hoops and cross-ties shall have a vertical spacing,
(diameter of largest vertical bar within boundary zone)
The length-to-width ratio of the hoops shall not exceed 3 and all adjacent hoops shall be overlapping.
Cross-ties or legs of overlapping hoops shall not be spaced farther apart than 250mm along the wall.
Alternate vertical bars shall be confined by the corner of a hoop or cross-tie.
Minimum for vertical reinforcement
Av > area of boundary zone or two no. 16 bars at each edge of the boundary zone

14. Reinforcement details for special boundary elements

15. Load Combination
ACI required that structure, their components, & their foundation be designed to have strength not less than the most severe of the following combination of loads:
U = 1.4(D + F )
U = 1.2(D + F + T) + 1.6(L + H) + 0.5(Lr or S or R)
U = 1.2D + 1.6(Lr or S or R) + (1.0L or 0.8W)
U = 1.2D + 1.6W + 1.0L + 0.5(Lr or S or R)
U = 1.2D + 1.0E + 1.0L + 0.2S
U = 0.9D + 1.6W + 1.6H
U = 0.9D + 1.0E + 1.6H
Where:
U = required strength to resist the factored loads
D = dead load
L = live load
W = wind load
E = earthquake load

16. The effect of seismic load E is defined as follows:
F = load due to fluids with and maximum heights well-defined pressures
H = load due to soil pressure
T = load due to effects of temperature, shrinkage, expansion of shrinkage
compensating concrete, creep, differential settlement, or combinations thereof.
Lr = roof live load
S = snow load
R = rain load
The effect of seismic load E is defined as follows:
E = the effect of horizontal and vertical earthquake-induced forces,
SDS = the design spectral response acceleration at short periods
D = the effect of dead load
ρ = the reliability factor
QE = the effect of horizontal seismic forces

17. If the there is a vertical discontinuities of the structure system that resisting the seismic load the effect of seismic load E is defined as follows:
where Ωo is the system over strength factor. The value of Ωo varies between 2 to 3 as give in table depending on the type of lateral force resisting system

18. Example Design the shear wall section at the basement
Determine minimum vertical & horizontal reinforcement requirements in the wall
100t
784t.m
5m0.25m
D.L = 120t
L.L = 50t
980kN
7840kN.m
1176kN
490kN
Check if two curtains of reinforcement are required.
According to the above equation, no need for two curtains but as the wall thickness is 250mm the code recommend to use two curtains of reinforcement.

19. The minimum reinforcement ratio
Therefore the minimum reinforcements ration are
Minimum steel area
Use 100cm in both sides of the wall & in the vertical & horizontal directions

20. Smax = the smaller of 325 = 75cm & 45cm
Smax = 45cm > S = 36 cm O.K.
Use 35cm in each side of the wall in the vertical & horizontal direction

21. Determine reinforcement requirements for shear
Shear strength of wall
c = for hw/Lw = 18/5 = 3.6  2
Therefore, the 35cm in the vertical & horizontal direction would be enough for the shear

22. Determine reinforcement requirements for combined flexural & axial loads
Determine if special boundary elements are required
Pu = 1.2D + 1.0E + 1.0L or
Pu = 1.2D + 1.6L
There is a vertical load comes from the earthquake which can be computed by Ev = 0.2Sds*D (D is the total dead load)
Pu = 1.2D + 1.0(0.2Sds*D) +1.0 L
= 1.2 0.333 = 1980 kN

23. Pu = 1.2 490 = 2195 kN
Therefore Pu = 2195 kN
Therefore, special boundary elements are required

24. Special boundary length
Lager of C/2, C – 0.1Lw cm or Lw/16

25. Check moment capacity Mn
Lw/16 = 500/16 = 31cm
Take the boundary length as 45cm as it’s the minimum
Check moment capacity Mn

26. Therefore additional reinforcements are required for flexural
Mn = 6.95MPa < Mu = 7.84MPa
Therefore additional reinforcements are required for flexural
= 316
216 at each edge of the boundary zone is the minimum vertical reinforcement in the boundary zone

27. Confinement Reinforcement
Confinement of the boundary elements
Maximum Hoops and cross-ties vertical spacing
Smax = smaller of 150mm or 6largest bar diameter(16mm) = 96mm
Smax = 90mm
Reinforcement cross-section area long direction
Use 9cm parallel to the wall

28. Reinforcement cross-section area short direction
Use 9cm perpendicular to the wall
45cm
416
212
35cm