Structural Concrete - Hassoun

20.5 Special Requirements in Design of Structures Subjected to Earthquake Loads 853
No. 4 ties
No. 4 hoop
24 in.
24 in.
Figure 20.36
Example 20.8: Boundary element reinforcement.
From the interaction diagram,
M n
f ′ c A g h = 0.162
M n = 0.162 × 4000 × 5760 × 28 × 12 = 104,509 kip ⋅ ft > 69,230 kip ⋅ ft
(OK)
4. Special boundary element requirements. The shear-based approach is used to determine whether
the special boundary elements are required.
A g = 5376 in. 2
16 ×(28 × 12)3
I g = = 50,577,408 in. 4
12
l w 28 × 12
= = 168 in.
2 2
Maximum compressive stress in the wall is given as
P u
+ M u l w
= 4,000,000 +
A g I g 5376
45,000,000 × 12
168 = 2538 psi
50,577,408
0.2f c ′ = 0.2 × 4000 = 800 psi < 2538 psi
A special boundary element is needed. Transverse reinforcement of boundary element should
be designed as for members of special moment frame subjected to axial load and bending
(Fig. 20.36).
Use no. 4 hoops and crossties around longitudinal bars in both directions. Maximum spacing
of transverse reinforcement should be determined as follows:
⎧
⎪0.25 × (smallest member dimension) = 0.25 × 24 = 6in.
⎪6 ×(diameter
s max = ⎨ (
of longitudinalbar)
)
=6 × 1.41 = 8.5in.
⎪ 14 − hx
( ) 14 − 6
s
⎪ x = 4 +
= 4 + = 6.67 in.
3
3
⎩
Use s = 6 in. (governs).