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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.________

Respuesta :

Answer:[tex]x=\frac{L}{2}[/tex]

Step-by-step explanation:

Given

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

[tex]M=12wLx-12wx^2[/tex]

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

[tex]\frac{\mathrm{d} M}{\mathrm{d} x}=12wL-24wx[/tex]

Put [tex]\frac{\mathrm{d} M}{\mathrm{d} x}=0[/tex]

[tex]12wL-24wx=0[/tex]

[tex]L=2x[/tex]

[tex]x=\frac{L}{2}[/tex]

[tex]M=12wL\cdot \frac{L}{2}-12w(\frac{L}{2})^2[/tex]

[tex]M=3wL^2[/tex]

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