Civil Engineering MCQJE Level Civil Engineering
The 'collapse load' for a fixed-fixed beam of span L under central point load W is:
Strength of MaterialsStrength of MaterialsHARD
Choose the correct answer
A
W = 8Mp/L
B
W = 16Mp/L — three hinges (both ends + midspan) mechanism gives collapse load
C
W = 4Mp/L
D
W = 12Mp/L (this applies to fixed-pinned)
Correct Answer
B. W = 16Mp/L — three hinges (both ends + midspan) mechanism gives collapse load
Why is this the answer?
Fixed-fixed beam under central W: collapse mechanism needs 3 plastic hinges (both fixed ends + midspan). At collapse: W×L/4 = Mp (from virtual work: W×δ = Mp×θ + Mp×2θ + Mp×θ = 4Mp×θ, δ = L/4×θ). So W_collapse = 16Mp/L. For fixed-pinned: W = 12Mp/L (2 hinges only). Plastic analysis always > elastic analysis because Mp > Me.
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