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Step By Step Answers with Explanation

To solve the problem of the deflection under the P applied load using the moment area method, we must first draw the shear force diagram (SFD) and bending moment diagram (BMD) for the beam.

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The bending moment diagram is shown below:

PL/2

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Step 2: Calculate the M/EI diagram

The M/EI diagram is simply the bending moment diagram divided by the flexural rigidity, EI, of the beam. In this case, EI is constant, so the M/EI diagram is the same as the bending moment diagram.

δ_L/2 = ∫PL/2EI dx from L/2 to L

Evaluating the integral, we get:

The deflection under the P applied load is:

δ_L/2 = PL^2 / 8EI