What is Bending Moment? Equation Example Calculation and Diagram

What is Binding Moment?

Bending moment formed as the result of the external as well as the self load acting on a beam is called the bending moment. This is called so because it tends to bend a beam. To find the magnitude of the bending moment at the section of a beam. It is the product-sum of all the forces applying on it from one end of the beam to that section and the perpendicular distances (arms of the forces). In addition to this bending moment. The maximum bending moment is also calculated. In the case of cantilever beam. This maximum bending moment acts at the fixed end of the beam. While it is always zero at its free end. In the case of simply supported and over –hanging beams. It zero at the ends of the beams. While maximum bending moment is that section of the beam between the supports where the shear force changes its sign. I.e. from positive to negative or vice versa. For different beams, maximum bending moments due to different loads are given in the table of bending moment coefficients.

1. Cantilever Beam :
(a) Point load at free end,
B.M (max) = Wl

What is Bending Moment? Equation Example Calculation and Diagram

(b) U.D.L at entire span
B.M. (max) =W.l2/2

2. Simply Supported Beam:
a) Point load at mid-span
B.M(max) = W.l/4

(b) U.D.L at entire span
B.M (max) = w.l2/8

Note: For unsymmetrical simply supported beams and over-hanging beams, reactions are determined at the supports by taking moments about the support, then actual shear diagram is drawn then maximum bending moment is determined at the point where shear force changes its sign.

Example for Bending Moment

Draw shear force and bending moment diagram for the beam loaded as shown in the figure.

Solution:
Shear force at section A, B = S.FAB = -1000 lbs
Shear force all point B = S.FB= -1000-2000=-3000lbs
Shear force at point C (max) = -3000(1000*2) =-5000lbs
Bending Moment:
Bending moment at point A = B.MA = 0
Bending moment at point B = B.MB =1000+2000=3000lbs
Bending moment at point C = B.MC =
1000*4+2000*2+ (1000*2)*1=4000+4000+2000=10000lb:ft
Note: it’s maximum Bending Moment

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