Direct Integration of A Beam - Integrating

Integrating

Each time an integration is carried out, a constant of integration needs to be obtained. These constants are determined by using either the forces at supports, or at free ends.

For internal shear and moment, the constants can be found by analyzing the beam's free body diagram.

For rotation and displacement, the constants are found using conditions dependent on the type of supports. For a cantilever beam, the fixed support has zero rotation and zero displacement. For a beam supported by a pin and roller, both the supports have zero displacement.