# Does max deflection occur at max bending moment?

i thought the maximum deflection of a structure (a beam for example) occured at the same location of the maximum bending moment. But, doing some homework im getting contradicting results.

does max deflection ALWAYS occur at the same location of the max bending moment?

thanks for the responses in advance

PS heres some more details if you need them:

using the 4th derivative method for finding deflection/ slope, i found the second derivative (which should be the moment) and found where it is maximum (using a graphing calculator). the question uses variables instead of number, but that shouldn't matter. later on in the solution to the problem, it says that the maximum deflection is at a different place than i calculated for the max bending moment.

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this makes absolutely no sense to me, unless:

i made a mathematical mistake (unlikely, i checked my work repeatedly)
the location of the max BM is not the same as the location of the max deflection.

ill type up my work if its necessary

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Yes............

PhanthomJay
Homework Helper
Gold Member
The max deflection does not always occur at the max bending moment. Take a simple cantilever for example, with a load at the free end. The max moment occurs at the fixed end, but the max deflection occurs at the free end where M = 0.

The max deflection does not always occur at the max bending moment. Take a simple cantilever for example, with a load at the free end. The max moment occurs at the fixed end, but the max deflection occurs at the free end where M = 0.
thank you that makes sense.

but how about a simply supported beam? as in, a hinge at one end, a roller at the other, and a triangular uniform distributed load on top. so the location of maximum bending moment wouldn't be equal to the location of maximum deflection?

i think if the load isn't symmetrically directed at the center of the structure, the locations aren't the same.

PhanthomJay
Homework Helper
Gold Member
thank you that makes sense.

but how about a simply supported beam? as in, a hinge at one end, a roller at the other, and a triangular uniform distributed load on top. so the location of maximum bending moment wouldn't be equal to the location of maximum deflection?

i think if the load isn't symmetrically directed at the center of the structure, the locations aren't the same.
That is correct.

That is correct.
Thank you!

Keep in mind that the deflection is the second derivative of the bending moment (for simple beam theory). This means that the bending moment need not be maximum for maximum deflection.