Shear and Moment Diagrams

Shear and bending moment diagrams give a graphical representation of the internal forces developed in flexural members, i.e., members designed to resist transverse loads. Generally, bending moment controls the sizing of flexural members and moment-resisting connection details while shear controls the details of shear tab connections.

Background

Coming into this lecture, you should be able to:

Solve for the reactions of determinate beams
Work with the differential equation of beam equilibrium

New Concepts

After this lecture, you should be able to:

Draw the internal shear force diagram for a beam using the graphical approach
Draw the internal bending moment diagram for a beam using the graphical approach

Down the Road

Beyond this course, you will see the concepts from this lecture in the following courses:

CE 382 - moment diagrams are essential for computing beam deflections and rotations by virtual work
CE 383 - moment diagrams are required for designing steel beams
CE 481 - moment diagrams are required for designing reinforced concrete beams; in addition, the sign of the moment diagram indicates which side of a beam requires steel reinforcement

Sign Convention

The sign convention for internal shear force and bending moment is different from that for external forces and moments, respectively. The sign convention we will use for internal shear and moment on a differential beam slide is shown in Figure 2.1.

Positive internal shear force acts down on the right side of the slice and up on the left side
Positive bending moment puts the top of the beam into compression and bottom into tension

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