Construction of Shear Diagram & Bending Moment Diagram

Consider a general beam segment AB

Relations derived from the equilibrium equations are.

  and 

The equations of shear and bending moment in the beam derived from a beam segment AB can be used for constructing the shear diagram and bending moment diagram. These equations can be applied for beam segment with any type of loading by setting the corresponding loads to zero when these loads are not available.

Start drawing the shear diagram and bending moment diagram from left end to right end.  And the considered beam segment is assumed to be fixed at the rightmost edge of the beam segment considered and the load applied on the rightmost edge of the beam segment is ignored as usual. 

Summary of stability and determinacy of planar truss:

Free End at the Leftmost End Beam Segment Shear Diagram Bending Moment Diagram Shear  Bending Moment

Free End with Applied Force at the Leftmost End Beam Segment Shear Diagram Bending Moment Diagram Shear  Bending Moment

Free End with Uniformly Distributed Load at the Leftmost End Beam Segment Shear Diagram Bending Moment Diagram Shear  Bending Moment

Free End with Variable Trianglar Distributed Load at the Leftmost End Beam Segment Shear Diagram Bending Moment Diagram Shear  Bending Moment

Free End with Concentrated Couple at the Leftmost End Beam Segment Shear Diagram Bending Moment Diagram Shear  Bending Moment

Free End with Uniformly Distributed Moment at the Leftmost End Beam Segment Shear Diagram Bending Moment Diagram Shear  Bending Moment

Free End with Reaction Force at the Leftmost End Beam Segment Shear Diagram Bending Moment Diagram Shear  Bending Moment

Shear and Bending Moment at the Left Only Beam Segment Shear Diagram Bending Moment Diagram Shear  Bending Moment