This video explains how to draw the shear force SFD and bending moment diagram BMD for a beam under a distributed load.
Here are the steps you should follow when drawing a shear force and bending moment diagram for a beam.
Step 1: Determine the support reactions from the free body diagram of entire beam.
Step 2: Divide the beam into segments so that the loading within each segment is continuous.
Perform the following steps for each segment of the beam.
Step 3: Introduce an imaginary cutting plane within the segment, locating at a distance x from the left end of the beam, that cuts the beam into two parts.
Step 4: Draw free body diagram for the segment of the beam. Show the shear force and bending moment on the cut section.
Step 5: Write the equilibrium equation, obtainable from the free body diagram.
Step 6: Solve the equilibrium equation for the shear force and the bending moment.
Step 7: Plot the curves for shear force and bending moment. It is desirable to draw the shear force diagram below the entire beam and then draw the bending moment diagram below the shear force diagram.
Beams
Beams are structural members which are designed to support loadings applied perpendicular to their axes. In general, beams are long, straight bars having a constant cross-sectional area. Often they are classified as to how they are supported. For example, a simply supported beam is pinned at one end and roller-supported at the other, and a cantilevered beam is fixed at one end and free at the other and overhanging beam as shown in figure. The actual design of a beam requires a detailed knowledge of the variation of the internal shear force V and bending moment M acting at each point along the axis of the beam.
Shear force(V) ##
Shear force is the force in the beam acting on the cross-section, perpendicular to its longitudinal (x) axis.
Bending moment.(M)##
A bending moment is the reaction induced in a beam when an external force or moment is applied to the beam causing the beam to bend.
The variations of V and M as functions of the position x along the beam's axis can be obtained by using the method of sections discussed in here, however, it is necessary to section the beam at an arbitrary distance x from one end rather than at a specified point. If the results are plotted, the graphical variations of V and M as functions of x are termed the shear diagram and bending-moment diagram, respectively.
In general, the internal shear and bending-moment functions will be discontinuous, or their slopes will be discontinuous at points where a distributed loads changes or where concentrated forces or couple moments are applied. Because of this, these functions must be determined for each segment of the beam located between any two discontinuities of loading.
Sign Convention.
Before presenting a method for determining the shear and bending moment as functions of x and later plotting these functions (shear and bending-moment diagrams), it is first necessary to establish a sign convention so as to define a "positive" and "negative" shear force and bending moment acting in the beam. Here the positive directions are denoted by an internal shear force that causes clockwise rotation of the member on which it acts, and by an internal moment that causes compression or pushing on the upper part of the member. Also, positive moment would tend to bend the member if it were elastic, concave upward. Loadings that are opposite to these are considered negative.