A Beam is defined as a structural member subjected to transverse shear loads during its functionality. Due to those transverse shear loads, beams are subjected to variable shear force and variable bending moment.
Shear force at a cross section of beam is the sum of all the vertical forces either at the left side or at the right side of that cross section.
Bending moment at a cross section of beam is the sum of all the moments either at the left side or at the right side of that cross section.
1. Simple Supports
2. Fixed Supports
(a) Roller Support – resists vertical forces only
(b) Hinge support or pin connection – resists horizontal and vertical forces
(c) Fixed support or builtin end
Note: The distance between two supports is known as “span”.
The following are the important types of load acting on a beam:
Or if the shear force tries to rotate the element clockwise then it is takes as positive & if the shear force tries to rotate the element anticlockwise then it is takes as negative.
Important Points for Drawing Shear Force and Bending Moment Diagrams
Relation between Load, Shear Force and Bending Moment
A beam is carrying a uniformly distributed load of w per unit length. Consider the equilibrium of the portion of the beam between sections 11 and 22. This portion is at a distance of x from left support and is of length dx.
F = Shear force at the section 11
F + dF = Shear force at the section 22,
M = Bending moment at the section 11,
M + dM = Bending moment at the section 22.
The forces and moments acting on the length ‘dx’ of the beam are:
The portion of the beam of length dx is in equilibrium. Hence resolving the forces acting on this part vertically, we get
–dF = w.dx
dF / dx = w
The above equation shows that the rate of change of shear force is equal to the rate of loading.
Taking the moments of the forces and couples about the section 22, we get
Neglecting the higher powers of small quantities, we get
F.dx = dM
F = dM / dx
The above equation shows that the rate of change of bending moment is equal to the shear force at the section.
Some Examples:
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 