Shear and Bending Moment Diagrams

Example: Use Method 2 to calculate the shear and bending moment

along the beam

Strategy: Use dV/dx = w(x) to determine the slope of the shear diagram.

The slope of the shear force, dV/dx, equals the change in distributed loading.

Use dM/dx = V(x) to determine the slope of the moment diagram. Note: The slope of the moment diagram equals the value of the shear force.
Also note: By integration, the area under the shear diagram represents the change in the moment. i.e

M(x) = ʃ V(x) dx

Example: Calculate the shear and bending moment diagram for the symmetrically loaded simply supported (pin at A and roller at C) beam shown below.

Recall the sign conventions for shear force and bending moment (shown below).

So at x = 0 the shear force is + P/2 and remains constant until x = L/2 when
it drops to ˗ P/2 and remains at that value until x = L when it returns to zero.

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