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=(L)/(2)`

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=(L)/(2)`

`M=12wL\cdot (L)/(2)-12w((L)/(2))^2`

`M=3wL^2`