Structural Concrete - Hassoun

560 Chapter 16 Continuous Beams and Frames
Test on a continuous reinforced concrete beam. Plastic hinges developed in the positive and negative
maximum moment regions.
Location 1 2 3 4 5 6
Moment coefficient − 1 + 1 − 1 + 1 − 1 + 1 16
14
10
16
11
16
M u (K ⋅ ft) −158.7 181.4 −276.5 187.5 −272.7 187.5
4. Determine beam dimensions and reinforcement.
a. Maximum negative moment is −276.5 K ft. Using ρ max = 0.016, R u = 740 psi
R u,max = 820 psi ρ max = 0.01806 (Table 4.1) φ = 0.9
√ √
M
d = u 276.5 × 12
R u b = 0.74 × 12 = 19.3in.
For one row of reinforcement, total depth is 19.3 + 2.5 = 21.8 in., say, 23 in., and actual d is
20.5 in. A s = 0.016 × 12 × 19.3 = 3.7 in. 2 ; use four no. 9 bars in one row. Note that the total
depth used here is 23 in., which is more than the 22 in. assumed to calculate the weight of the
beam. The additional load is negligible, and there is no need to revise the calculations.
b. The sections at the supports act as rectangular sections with tension reinforcement placed
within the flange. The reinforcements required at the supports are as follows:
c. For the midspan T-sections, M u =+187.5 K ⋅ ft. For a = 1.0 in. and flange width = 72 in.,
A s =
M u
φf y (d − a∕2) = 187.5 × 12
0.9 × 60(20.5 − 1∕2) = 2.1in.2