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► Determine support reactions (FBD).
Draw V vs. x and M vs. x axis under FBD.
Section the beam at various values of x and draw FBD for the section.
Evaluate V by summing all forces perpendicular to x axis.
Evaluate M by summing all moments about the sectioned end of segment.
Plot on graph (pay attention to sign convention).
Repeat for new position. Graphical Method for V And BM Diagrams
Graphical Method for V And BM Diagrams
► Consider the following element from a beam with arbitrary loading. Shear and Bending Moment Diagrams
Shear and Bending Moment Diagrams
► Slope of moment diagram at each point is the value (+ or ) of the shear. ► Slope of the shear diagram at each point is the opposite sign of the distributed load intensity at each point. Shear and Bending Moment Evaluation
Shear and Bending Moment Evaluation
► We integrate the loading and shear diagrams to determine the changes in shear and bending moment. ► Note: if w(x) is a curve of degree n, then V(x) will be a curve of degree n+1.
Note: if V(x) is a curve of degree n, then M(x) will be a curve of degree N+1. ► Regions of Concentrated Force and Moment
Regions of Concentrated Force and Moment
► ► ► ► The application of a concentrated force causes a discontinuity in the shear diagram of magnitude F.
Downward force equals negative jump in shear.
The application of a concentrated moment causes a discontinuity in the BM curve of magnitude M .
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- Fall '13