Bending Moment and Fixed Moment Calculations

Bending Moment and Shear Force diagrams

What is Bending Moment?

The element bends when a moment is applied to it. Every structural element has bending moment. Concept of bending moment is very important in the field of engineering especially Civil engineering and Mechanical Engineering.

Unit of measurement: Newton-metres (N-m) or pound-foot or foot-pound (ft.lb)

Bending moment is directly proportional to tensile and compressive stresses. Increase in tensile and compressive stresses results in the increase in the bending moment. These stresses also depend on the second moment of area of the cross section of the element.

What is Shear stress?

Shear stress is defined as the measure of force per unit area. Shear stress occurs in shear plane. There are many planes possible at any point in a structure which can be defined to measure stress.

Stress = Force/Unit area

Example: Bending Moment and Shear Force Calculations

Simply supported bending moment

M_ab = wl²/8 = (22×4.14×4.14)/8

= 47.13 KN-m

M_bc = wl²/8 = (22×4.14×4.14)/8

= 47.13 KN-m

Fixed Moments

Moment about B

wl²/12 = (22×4.14×4.14)/12

= 31.4 KN-m

Support reactions

R_A+R_B+R_C = 2(22×4.14)

= 182.16 KN

3R_A = 182.16

R_A = 60.72KN

R_A = R_B = R_C = 60.72 KN

Also check out: Introduction to Load Calculations