Thread: Maxima minima calculus help

Hello,

I'm stuck on the following question. I feel like I've computed the correct results but because my units have cancelled I'm a bit lost. If you refer below (I think) I have computed the correct result for a maximum deflection but I don't know what answer is the position for a maximum deflection. I think it's the first derivative but I'm not sure.

Anyway, here's the question:

If a beam of length L is fixed at the ends and loaded in the centre of the beam by a point load of F Newtons the deflection at a distance x from one end is given by:



Where E = Young's Modulus and I = Second Moment of Area of the beam. Find the position and the value of the maximum deflection of the beam if:

L = 10m

EI =

F = 100kN















Substituting x= (+5) into the initial equation for a maximum deflection:



Now I'm lost on the position?

Thanks in advance

... the deflection at a distance x from one end is given by ...

So it's 5 then?

Yes, the mid-point.

Surely, knowing the load was in the middle we could have said immediately that the maximum deflection would be when x=5

I don't know how the formula for is derived, but had the expression in brackets been for example, the maximum deflection would not have been at the mid-point, (though I would have to admit that from a practical point of view I would have expected it to be).