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A beam of length `l`is supported at oneend. If `W`is the uniform load perunit length, the bending moment `M`at a distance `x`from the end is givenby `M=1/2l x-1/2W x^2dot`Find the point on thebeam at which the bending moment has the maximum value. |
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Answer» `M = ((lx)/(2) - (Wx^(2))/(2)) rArr (dM)/(dx) = ((l)/(2) - Wx) and (d^(2)M)/(dx^(2)) = -W` For a maxima or minima, we have `(dM)/(dx) = 0` Now, `(dM)/(dx) = 0 rArr (l)/(2) - Wx = 0 rArr x = (l)/(2W)` Also, `(d^(2)M)/(dx^(2)) = - W lt 0` for all values of x `:. x = (l)/(2W)` is a point of maxima So, the required point is at a distance of `(l//2W)` from the supporting end. |
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