Hi can any body take me through this problem to help me understand the correct way of tackling such a problem.
The bending moment, M, at position x m from the end of a simply supported beam of length, L m carrying a uniformly distributed load of, w kN m^-1 is given by:
M=w/2*L(L-x) - w/2*(L-x)^2.
Show using the above expression, that the maximum bending moment occurs at the mid point of the beam and determine its value in terms of w and L.
This problem has been causing me considerable grief, if there is anyone out there who may be able to help, it would be greatly appreciated.
Kind Regards,
Phil
The bending moment, M, at position x m from the end of a simply supported beam of length, L m carrying a uniformly distributed load of, w kN m^-1 is given by:
M=w/2*L(L-x) - w/2*(L-x)^2.
Show using the above expression, that the maximum bending moment occurs at the mid point of the beam and determine its value in terms of w and L.
This problem has been causing me considerable grief, if there is anyone out there who may be able to help, it would be greatly appreciated.
Kind Regards,
Phil
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Expanding your expression for M;
M = wL²/2 - wLx/2 - wL²/2 + wLx - wx²/2
dM/dx = -wL/2 + wL - wx
for dM/dx = 0, wL/2 - wx = 0 →
x = L/2
M@L/2 = wL(L - L/2)/2 - w(L - L/2)²/2 = wL²/8
M = wL²/2 - wLx/2 - wL²/2 + wLx - wx²/2
dM/dx = -wL/2 + wL - wx
for dM/dx = 0, wL/2 - wx = 0 →
x = L/2
M@L/2 = wL(L - L/2)/2 - w(L - L/2)²/2 = wL²/8