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Sufficient Condition for an Extrema

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Question

what is the shape of influence line diagram for the maximum bending moment in respect of a simply supported beam?

A

Triangular

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B

Parabolic

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C

Circular

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D

Rectangular

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Solution

The correct option is B Parabolic
The maximum bending moment for any position of load occur under the load. So the equation for maximum bending moment is

$M_{m a x} = \frac{x (L - x)}{L}$

Thus the ILD for maximum bending moment is parabolic. This is also called envelop of maximum bending moment.

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