Question

The bending moment M of a beam, supported at one end, at a distance x from the support is given by M=12wLx−12wx2 where L is the length of the beam, and w is the uniform load per unit length. Find the point on the beam where the moment is greatest.________

Answer 1

Answer:$x=\frac{L}{2}$

Step-by-step explanation:

Given

Bending Moment of a beam, supported at one end, at a distance x from the support is given by

$M=12wLx-12wx^2$

to get the maximum bending moment differentiate M w.r.t x

$\frac{\mathrm{d} M}{\mathrm{d} x}=12wL-24wx$

Put $\frac{\mathrm{d} M}{\mathrm{d} x}=0$

$12wL-24wx=0$

$L=2x$

$x=\frac{L}{2}$

$M=12wL\cdot \frac{L}{2}-12w(\frac{L}{2})^2$

$M=3wL^2$