- Minimum reinforcement ratios and requirements for reducing ratios based on shear load are outlined. Wall thickness requirements vary from 8 inches minimum to 16 inches minimum depending on wall type. - Slender and squat wall behavior is described in relation to their height-to-length aspect ratios. Ductile behavior is preferred to avoid shear failure. - Design of the critical section and boundary element is discussed, including requirements for reinforcement and extending the boundary element. - An iterative process is described for selecting reinforcement within the boundary element length to satisfy strength requirements.

1. 6 November 2015

2. • Minimum reinforcement ratio , ρl and ρt = 0.0025
• ρl and ρt are permitted to be reduced if Vu ≤ 2 Acv λ √f’c
• If hw/lw ≤ 2, ρt is not to be less than ρl
2
Ref: NIST GCR 11-917-11REV-1

3. • ACI 318 has no prescriptive minimum thickness.
• Minimum thickness of 8 in. is a practical lower limit for special
structural walls.
• Construction and performance are generally improved if wall
thickness is at least 12 in. where special boundary elements
are used.
• Walls with conventional coupling beams require minimum
thickness of 14 in.
• Walls with diagonal reinforced coupling beams require
minimum thickness of 16 in.
3

4. • Slender walls (hw/lw ≥ 2)
– Tend to behave much like flexural cantilevers
– Preferred inelastic behavior is ductile flexure yielding, without shear
failure.
• Squat walls (hw/lw ≤ 0.5)
– Resist lateral force in diagonal strut mechanism
– Concrete and distributed horizontal and vertical reinforcement resist
shear
• Wall behavior transitions between above extremes for
intermediate aspect ratios.
4

6. • For slender walls, ductile
flexural yielding at the base
of wall
• For slender coupled walls,
ductile yielding of coupling
beams plus ductile flexural
yielding at the base of wall.
• Wall shear failure,
diaphragm failure and
foundation failure should be
avoided.
6
Ref: NIST GCR 11-917-11REV-1

7. • Design selected critical section to have strength in flexure and
axial closely matching the required strengths, with some
overstrength provided at other locations.
• Special details for ductile response can be concentrated
around the selected critical section, with relaxed detailing
elsewhere.
• In very tall buildings, higher mode response may cause some
flexural yielding in intermediate stories.
7

8. • Axial force well below the balanced point
• UBC 97
– Pu ≤ 0.35 P0, which corresponds approximately to the balanced axial
force in a symmetric wall.
• ACI 318
– No limit for wall axial force.
– Avoid concrete reaches strain of 0.003 before tension reinforcement
yields
8

9. 9
-70
-60
-50
-40
-30
-20
-10
0
10
-0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004
Stress(MPa)
Strain
Concrete Stress-Strain Curve

10. • Mn,CS = Pu xp + Ts1 j1 lw +
Ts2 j2 lw
• j1 lw = 0.4 lw
• j2 lw = 0.8 lw
• Ts2 = minimum
reinforcement
• Find Ts1.
10
Ref: NIST GCR 11-917-11REV-1

11. • Special boundary element
– High compressive demand on the edge
• Ordinary boundary element
– As,be/Ag,be > 400/fy
11

12. • Design for single critical
section
• Determine top level
displacement, u
• c ≥ lw / (600 x u/ hw)
• Extend vertically above
and below critical
section a distance not
less than the greater of
lw and Mu,CS/4Vu,CS
12
Ref: NIST GCR 11-917-11REV-1

13. 13
Ref: NIST GCR 11-917-11REV-1

14. • Can be used for any wall
• If nominal concrete stress exceeds 0.2 f’c, boundary element
required.
• Extend until compressive stress drops below 0.15 f’c.
14

15. 15
Ref: NIST GCR 11-917-11REV-1

16. 16
Ref: NIST GCR 11-917-11REV-1

17. 17
C-01
C-02
C-03
C-04
C-05
C-06
C-07
C-08
C-09
C-10
C-11
C-12
C-13
C-14
C-15
C-16
C-17
-10
0
10
20
30
40
50
60
70
-0.006 -0.004 -0.002 0.000 0.002 0.004
StoryLevel
Axial Strain (mm/mm)
Wall Axial Strain (C-02)
STG
TAB
UNI
KOC
DUZ
STL
LGP
Average
Steel Yielding
Strain
Max. Comp.
Strain Limit

18. 18
Determine type of boundary
element required.
Determine boundary
element length
Select trial boundary element
reinforcement size and spacing
Select trial size and spacing
of vertical reinforcement
Determine P-M strength
Use P-M analysis to check
assumed boundary element
length
Note:
Spacing of vertical reinforcement is
dictated by arrangement of
confinement reinforcement

19. • Select the vertical reinforcement and spread it within the
required boundary element length.
• Layout the transverse reinforcement to support verticals and
confine the core.
• Iterate until all requirements are met.
19

20. • Vn = Acv (αc λ √f’c + ρt fy)
– Acv = lw bw
– αc = 3.0 if hw/lw ≤ 1.5
– αc = 2.0 if hw/lw ≥ 2.0
• Upper limit
– 8Acv √f’c, for all vertical wall segments resisting common lateral force
– 10Acv √f’c, for individual vertical wall segments
20

21. 21
0
10
20
30
40
50
60
70
80
-0.01 0 0.01 0.02 0.03 0.04
Story
Coupling Beam Rotation
Coupling Beam Shear Hinge Rotation at V1
LOM_STG
TAB
UNI
KOC
DUZ
STL
LOM_LGP
Average

22. 22
Ref: ACI 318-11

23. 23
Shear Wall Reinforcement Details