mathematical relationship problem - help required!

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bantamm

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peeps, can you possibly help me with an explanation for this question...

What is the mathematical relationship between bending moment, slope and defelection for a loaded beam??

it can be either expressed in equation format or written.



help please.
 

Simple beam theory:

Let
W(x) = force loading per unit length
V(x) = shear
M(x) = moment
Y’(x) = slope
Y(x) = deflection

V(x) = int(W(x))dx
M(x) = int(V(x))dx
Y’(x) = int(M(x))dx / [E*I]
Y(x) = int(Y'(x))dx

You may need a minus sign here or there depending on your convention. Draw a picture and make sure it makes sense.

Solve the constants of integration using your boundary conditions. For example let boundary occur at x=a (typically either 0 or L)
Simply supported: M(a)=0, Y(a)=0
Fixed: Y’(a)=0, Y(a)=0
Free: V(a)=0, M(a)=0
 

thanks for that. but I dont understand your explanation!

can you lay it out simplistically please?
 

Ive done some searches on onlline, but nothing really showing.
 

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