GATE CE 2021 Set 1 — Question 51
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Structural Engineering → Indeterminate Analysis & Influence Lines → Matrix Methods
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Question
Employ stiffness matrix approach for the simply supported beam as shown in the figure to calculate unknown displacements/rotations. Take length, ; modulus of elasticity, ; moment of inertia, .
The mid-span deflection of the beam (in mm, round off to integer) under in downward direction will be ___________
Correct answer
100 to 130
Solution
Using the unit load method or stiffness assembly:
Deflection
For a point load at mid-span, the bending moment is for .
The unit load moment is for .
Given: , , , .
.
Rounding to the nearest integer, the deflection is .
Deflection
For a point load at mid-span, the bending moment is for .
The unit load moment is for .
Given: , , , .
.
Rounding to the nearest integer, the deflection is .
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