Thread: Deflection Curves

A deflection curve is:

EIy''''=w

E, w, and I are constants.

The downward direction is considered positive.

I have these initial conditions (the beam is fixed at 0 and L):

y(0) = 0
y(L) = 0
y''(0) = 0
y''(L) = 0

I have to find a solution for these conditions and also find the max deflection in the y direction.

I believe I found the solution for y, but I have some constants that I am unable to define, so I am not sure how (or if) I can find the maximum deflection.

I came up with y = (wx^4)/24EI + Ax^3/6 + Bx (A and B are yet to be defined constants)

To find the maximum deflection, I assume I should set y' equal to zero to find the maximum, which gave:

0 = (wx^3)/6EI + (Ax^2)/2 + B

Is there something more I can do to find the maximum deflection?

Thanks

Originally Posted by machi4velli

A deflection curve is:

EIy''''=w

E, w, and I are constants.

The downward direction is considered positive.

I have these initial conditions (the beam is fixed at 0 and L):

y(0) = 0
y(L) = 0
y''(0) = 0
y''(L) = 0

Okay,
y''''=W/EI

Thus, integrating 4 times,
y=W/EIx^4+Ax^3+Bx^2+Cx+D
Where, A,B,C,D are to be determined.

Solve the initial value problem,

D=0,
C=L
B=0
A=L/3

Thus,
y=W/EIx^4+L/3x^3+Lx

To minimize this you need,
y'=0 on 0<=x<=L

Could you possibly explain that further? I am not sure what I may be doing incorrectly, but I got (-1/2)(w/EI)L for A and (-1/12)(w/EI)L^3 for C