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Calculation of Shear and Bending Moment Diagrams using Direct Method

In a Nut Shell: The calculation of shear and bending moment diagrams using the

direct method involves the following steps:

Step 1

Construct a free body diagram (FBD) of the entire beam and use equilibrium

to determine the support reactions. These support reaction yield the shear

force and bending moment at each end of the beam.

Step 2

Construct a free body diagram (FBD) at each section along the beam where

the external loading changes. Then use the equations of equilibrium to

determine the shear and bending moment at each section.

Step 3

Plot the shear and bending moment distribution using the sign convention.

Step 4

Check that the values of shear and bending moment in the diagrams agree

with the values at the supports determined in step 1. Disagreement means

that there is an error in plotting the shear or bending moment diagrams.

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