(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Refer to the attachment provided

2. Relevant equations

Just taking force and moment equilibium of whatever component I choose.

3. The attempt at a solution

I assumed a uniform force distribution.

Set the origin at the leftmost end. For [tex]0< x < \frac{L-a}{2}[/tex]

The shear force acting is [tex]+qx[/tex] and the bending moment is [tex]\frac{-qx^{2}}{2}[/tex]

Note that the situation is symmetrical w.r.t the centre of the beam.

Now for [tex]\frac{L-a}{2}< x < L/2[/tex]

The relevant force equilibrium equation is

[tex]-qx+\frac{qL}{2}+V=0 \Rightarrow V=qx-\frac{qL}{2}[/tex]

The bending moment can be similarly found and is given by

[tex]\frac{qLx}{2}-\frac{qx^{2}}{2}-\frac{qL(L-a)}{4}[/tex]

Thus the maxima of the above two moments are

[tex]\frac{q(L-a)^{2}}{8}[/tex] and [tex]\frac{qL(L-a)}{4}[/tex]

Both of which give a=L is when it is minimized. That isn't the answer at the back of the book!

I don't think we should take it as a uniform distribution.

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# Homework Help: Minimizing the maximum bending moment

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