7.7 : Bending Moment Diagram

A bending moment diagram is a graphical representation of the bending moments experienced by a beam under load along the beam length. It is an essential tool for engineers and designers to analyze structures and ensure they can withstand applied forces. The steps to create the bending moment diagram for a beam are listed below.

Determine reactive forces and couple moments: Calculate all the reactive forces and couple moments acting on the beam. In certain cases, when the beam is inclined at an angle, these forces are resolved into their components acting perpendicular and parallel to the beam's axis.

Section the beam and draw the free-body diagram: Consider an arbitrary distance from the beam's left end. This arbitrary distance can be extended in different regions along the beam's length. At each assumed distance, section the beam and create a free-body diagram of one of the segments. Ensure that the bending moment (M) is shown acting in their positive sense, according to the established sign convention.

Calculate bending moment: Apply the moment equilibrium equations and obtain the bending moment (M) about the sectioned end of the segment.

Plot the moment diagram: Create the moment diagram (M versus x) from the obtained bending moment along the beam length. If computed values of the functions describing M are positive, plot the values above the x-axis. Conversely, if the values are negative, plot them below the x-axis.

Following this procedure, you can construct accurate shear and bending moment diagrams for any beam. These diagrams are crucial in designing structural elements, such as shelving arms, that resist the forces and moments induced by applied loads.