GATE CE 2014 Set 2 — Question 44
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Structural Engineering → Connections & Plastic Analysis → Plastic Analysis (Beams)
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Question
A prismatic beam (as shown below) has plastic moment capacity of , then the collapse load of the beam is
Correct answer
(C) (6Mₚ)/(L)
Solution
To find the collapse load , we consider all possible independent collapse mechanisms and choose the one that gives the minimum load.Mechanism 1: Collapse of the first span (Span 1)
In this mechanism, plastic hinges form at the location of the load and at the middle support (since it's a continuous beam).
Let be the rotation at the left support. The displacement under load is .
The rotation at the plastic hinge under is .
The rotation at the plastic hinge at the middle support is .
Due to the rotation at the middle support, the overhang moves upwards by .
External Work ():
Internal Work ():
Equating :
Mechanism 2: Collapse of the overhang
In this mechanism, a plastic hinge forms only at the middle support. The first span remains stationary.
Let be the rotation of the overhang downwards.
External Work ():
Internal Work ():
Equating :
The collapse load is the minimum of the two: .Thus, the correct option is (C).
In this mechanism, plastic hinges form at the location of the load and at the middle support (since it's a continuous beam).
Let be the rotation at the left support. The displacement under load is .
The rotation at the plastic hinge under is .
The rotation at the plastic hinge at the middle support is .
Due to the rotation at the middle support, the overhang moves upwards by .
External Work ():
Internal Work ():
Equating :
Mechanism 2: Collapse of the overhang
In this mechanism, a plastic hinge forms only at the middle support. The first span remains stationary.
Let be the rotation of the overhang downwards.
External Work ():
Internal Work ():
Equating :
The collapse load is the minimum of the two: .Thus, the correct option is (C).
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