Structural Concrete - Hassoun

21.7 V-Shape Beams Subjected to Uniform Loading 879
90 ∘ V-shape beams, London, Ontario, Canada.
where
λ = EI/GJ
a = half total length of beam (length AC)
θ = half angle between two sides of V-shape beam
The torsional moment at the centerline section is
T c =
M c
sin θ cos θ = M c cot θ (21.42)
2. The bending and torsional moments at any section N along half the beam AC or BC at a
distance x measured from section C are calculated as follows:
M N = M c − w x2
(21.43)
2
T N = T c =
M c
sin θ × cos θ = M c cot θ (21.44)
To compute the moments at the supports, let x = a. Then
M A = M c − w a2
2
T A = T c = M c cot θ
Example 21.5
Determine the bending and torsional moments in a V-shape beam subjected to a uniform load of 6 K/ft.
The length of half the beam is a = 10 ft and the angle between the V-shape members is 2θ = π/2. The
beam section is rectangular with a ratio of long side to short side of 2.