Shear Force and Bending Moment Diagrams:
A Shear Force diagram for a structural member is a diagram that shows the values of shear forces at several sections of the member.
A bending moment diagram for a structural member is a diagram that illustrated the values of bending moment at several sections of the member.
The shear force & bending moment, at any section, might be obtained analytically. The values of shear force & bending moment are plotted as ordinates against the location of the cross section of the beam as abscissa. Such ordinates are drawn at significant points of the beam & a straight line or a curve is drawn joining the tops of all of such ordinates. These diagrams provide the clear picture of the distribution of shear forces & bending moment along the length of the beam.
Process for Drawing the SF Diagram (SFD) & BM Diagram (BMD)
Step 1
Determine the reaction of any one of the support, by taking moments about the hinged or pinned support and equating to zero (∑M = 0).
Step 2
Discover the reactions of other supports by means of static equilibrium equation
(∑V = 0, ∑H = 0).
Step 3
Illustrate a base line of length equal to the length of the beam to some of scale.
Step 4
Starting from one end (left end), calculate the shear force at all salient points. If there is a vertical load (including reaction) at a section, calculate the shear force just left as well as right of the vertical load (or reaction). The shear force diagram will increase or decrease suddenly at the point of application of load depending upon the direction of load, that means by a vertical straight line at the section.
Step 5
Determine the bending moment at salient points.
Step 6
Plot the positive values of shear force & bending moment above the base line & negative below it. The bending moment diagram & shear force diagram might be obtained by joining these ordinates.
The following points must be kept in mind for drawing the shear force & bending moment diagrams :
(a) If there is no loading on the part of the beam the shear force diagram shall be horizontal. The bending moment diagram shall be inclined. The shear force diagram shall remain unchanged among any two vertical loads provided there is no loading among the vertical loads.
(b) If there is a uniformly distributed load among two sections, the shear force diagram shall be inclined straight line & the bending moment diagram shall be a curve.
(c) The bending moment shall be zero at the free end of the cantilever & at the two supports of simply supported beam.
(d) The bending moment diagram shall consist of either straight lines or smooth curves.