- #1
gpavanb
- 12
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Homework Statement
Refer to the attachment provided
Homework Equations
Just taking force and moment equilibium of whatever component I choose.
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.