Structural Concrete - Hassoun

5.9 Shear Force Due to Live Loads 211
Example 5.3
A 10-ft-span cantilever beam has a rectangular section and carries uniform and concentrated factored
loads (self-weight is included), as shown in Fig. 5.15. Using f c ′ = 4 ksi normal-weight concrete and
f y = 60 ksi, design the shear reinforcement required for the entire length of the beam according to the
ACI Code.
Solution
1. Calculate the shear force along the beam due to external loads:
V u (at support) =5.5(10)+20 + 8 = 83 K
( ) 20.5
V ud (at d distance) =83 − 5.5 = 73.6K
12
V u (at 4 ft left) =83 − 4(5.5) =61 K
V u (at 4 ft right) =61 − 20 = 41 K
V u (at freeend) =8K
The shear diagram is shown in Fig. 5.15.
2. Calculate φV c :
φV c = 2λ √ √
f c ′ bd = 2(0.75)(1) 4000(12)(20.5) =23.34 K
1
2 φV c = 11.67 K
24"
18"
23.34 K
8
8 K
38.5" 25.5"
8.0"
Figure 5.15 Example 5.3.