A simply supported beam with a uniformly distributed load {w}?

Question

has symmetrical overhangs of distance {d}. The total beam length is {L}:
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w ..| | | | | | | | | | | | | | | | | | | | |
.... [__________________]
....... d ^..................... ^ d
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Question: What are the boundary conditions for this problem for solving the Euler-Bernoulli equation?

Answer 1

Your boundary conditions is simply supported meaning there is no vertical or horizontal displacement at the supports (ux = 0 and uy = 0), but the beam can rotate about the supports.

Imagine the support acting as a hinge. The door can swing about the hinge point, but the hinge won't move from it's spot.

Answer 2

do dM/dx=0 dM/dx= (wL/2) (-a million) - (w/2) *2(L-x) (-a million) =0 = -wL/2 +w (L-x)=0 L-x= L/2 x=L-L/2 = L/2 ( on the middle ) even if that's a max , d2M/dx2<0 d2M/dx2= 0 +(w (-a million) = -w <0 , so at x=L/2 M is Max .- M(L/2) = ( wL/2) (L/2) -(w/2) ( L/2)^2= wL^2/4 -wL^2/8 = wL^2/8 ( often that's a straightforward expresion to envision any beam , like a reference )

Answer 3

simply supported

Answer 4

stigma to