Basic formula for maximum bending moment, Mechanical Engineering

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Q. Write down the basic formula for maximum bending moment in some ideal cases.

Sol.:

 

Berm together with nature of load

Maximum B.M.

Section when maximum B.M. occurs

1.

 

 

 

 

 

 

Cantilever loaded with 1 point load wat the free end.

WL

It occurs at fixed end.

1562_bending moment.png

 

2.

 

 

 

 

 

 

 

Cantilever loaded with U.D.L. over entire length.

WL2

2

here

W = total value of U.D.L.

20 × l

 

It occurs at fixed end.

 

w/unit length

758_bending moment1.png

 

Berm together with nature of load

Maximum B.M.

Section when maximum B.M. occurs

 

3.

 

 

 

 

Boam loaded with 1 point load at the mid-span.

WL

4

where

W = point load placed at mid-span.

 

If occurs at mid-span.

 

 

 

2340_bending moment2.png

 

4.

 

WL2

8

where

W = total value of U.D.L.

= 20 × l.

 

If occurs at mid-span.

w/unit length

 

 

l


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