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I need some clarification on the location of maximum moment. I did some computation on my own and I think (using the parabolic square formula, a^2/R1=
L^2/R1=R2) I think max. moment occurs at x = 3.46. Also, how come again we are using I = bh^3/12 and not bh^3/3. Kindly clarify. Thank you in advance.
The beam is a cantilever with downward triangular load. Generally, the maximum moment of cantilever beam will occur at the fixed support. At the point you mention, x = 3.46 m from the free end, the moment is only 1150 N-m, while at the fixed support, M = 6000 N-m.
For the moment of inertia, the one you are going to use for the bending formula fb = Mc/I is the moment of inertia about the neutral axis. The formula I = bh3/3 is the moment of inertia about the base b of the rectangle, while the moment of inertia at the neutral axis is given by I = bh3/12.
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