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.
Read more about this topic: Direct Integration Of A Beam