Shear and Moment Diagrams

Shear and bending moment diagrams are analytical tools used in structural analyses and structural design to determine the value of shear force and bending moment at different length of an element. Using these diagrams type and size of a member can be determined easily. Another application of shear and moment diagrams is that the deflection can be easily determined using either the moment area method or the conjugate beam method.

Convention

Normal Convention

The normal convention used in most engineering applications is to label a positive shear force one that spins an element clockwise (up on the left, and down on the right). Likewise the normal convention for a positive bending moment is to warp the element in a "u" shape manner (Clockwise on the left, and counterclockwise on the right).

Normal positive shear force convention (right) and normal bending moment convention (left).

Concrete Design Convention

An exception to using the normal convention is used when designing concrete structures. Since concrete is weak in tension the most important part of designing a member with a high bending moment is to show whether the top or bottom of the concrete member is in tension. Because of this the positive moment diagram is alway drawn such that the tension on top is defined to be positive. This is opposite of the normal convention. The shear convention remains the same.

Vertical and Angled Members

For vertical members deciding the convention is to start from the bottom and move up in the same way that horizontal members start from the left and move to the right. In this way a force pushing to the left from the bottom will inspire a positive shear moment which will also be drawn to the left. For angled members if there is a conflict of interest between the normal convention and the vertical convention most often an engineer will follow the normal or horizontal reaction but either can be followed and the engineer should make note of which convention they are following.

For concrete in either vertical or angled members the shear diagrams are drawn as stated above but the the moment diagram should be drawn to show which side the tension of the member will be on.