Structural Concrete - Hassoun

880 Chapter 21 Beams Curved in Plan
Solution
Apartment building.
1. For a rectangular section with the sides ratio, y/x = 2, λ = 3.39. For this beam θ = π/4.
(
)
M c = wa2 sin 2 θ
6 sin 2 θ + λ cos 2 θ
(
)
M c = wa2 0.5
= 0.038wa 2
6 0.5 + 3.39 × 0.5
= 0.038 × 6(10) 2 = 22.8K⋅ ft
2.
M A = M c − w a2
2 = 0.038wa2 − 0.5wa 2 =−0.462wa 2
=−277.2K⋅ ft
M N = 0 when M c − w x2
2 = 0
or 0.038 wa 2 −0.5 wx 2 = 0, so x = 0.276a = 2.76 ft measured from c.
3. T A = 0.038 wa 2 = 0.038 × 600 = 22.8 K⋅ft
T C = M C cot θ