Expert: Veto Varma - 2/7/2008

Question
hi,
i want to know why the bending moment of the cantilever beam with uniform load will be like 1/3 of rectangle..why cont it be like 2/3 of rectangle.i'll not be able to give fig. to you.

Answer
Hi Siva,

To understand the bending moment it is best to draw it and write the equation for it. For uniformly loaded beam the equation for moment at any point is wx2/2  where x is the distance from the free end. This is an equation of  the parabola. Now if you take few points and draw it you will find the parabola going inside not outside, what it means, that the bending moment at the free end dies very slowly and gradually and the value is not much. This is the actual behaviour of the cantilever.  The area of this shape of parabola is 1/3 of the rectangle and that's why the bending moment is 1/3 of the rectangle. If the parabola is of different shape then the area of the parabola will be different.

I hope this answers your question.

Regards
Veto