Aerstz
Apr13-09, 04:57 AM
1. The problem statement, all variables and given/known data
Two questions are of the same problem (these are taken from a textbook):
EIdy/dx = - (Fx^2)/4 + A
The constant A can be obtained from the boundary conditions: slope dy/dx = 0, x = 1/2L. Thus A = (FL^2)/16 hence
EIdy/dx = - (Fx^2)/4 + (FL^2)/16
My problem 1: I have absolutely no idea why A = (FL^2)/16. If someone could please show me in a few small steps how A was determined, I should be very grateful!
Integrating again (with respect to x), the second constant, B, equals zero thus
EIy = - (Fx^2)/4 + (FL^2)/16 + B
B = 0
y = (Fx/48EI) (3L^2 - 4x^2)
x = 1/2 L thus
ymax = (FL^3)/48EI
My problem 2: I have no idea how the solution for ymax was determined. I Also have no idea why y = (Fx/48EI) (3L^2 - 4x^2) when EIy = - (Fx^2)/4 + (FL^2)/16 + B. Is the equation for y simply the equation for EIy transposed for y? Because when I tried them I ended up with values which did not fit. (Did I make a simple error in my calculating, or is something else going on?)
Please could you explain to me what is going on in the above equations?
Two questions are of the same problem (these are taken from a textbook):
EIdy/dx = - (Fx^2)/4 + A
The constant A can be obtained from the boundary conditions: slope dy/dx = 0, x = 1/2L. Thus A = (FL^2)/16 hence
EIdy/dx = - (Fx^2)/4 + (FL^2)/16
My problem 1: I have absolutely no idea why A = (FL^2)/16. If someone could please show me in a few small steps how A was determined, I should be very grateful!
Integrating again (with respect to x), the second constant, B, equals zero thus
EIy = - (Fx^2)/4 + (FL^2)/16 + B
B = 0
y = (Fx/48EI) (3L^2 - 4x^2)
x = 1/2 L thus
ymax = (FL^3)/48EI
My problem 2: I have no idea how the solution for ymax was determined. I Also have no idea why y = (Fx/48EI) (3L^2 - 4x^2) when EIy = - (Fx^2)/4 + (FL^2)/16 + B. Is the equation for y simply the equation for EIy transposed for y? Because when I tried them I ended up with values which did not fit. (Did I make a simple error in my calculating, or is something else going on?)
Please could you explain to me what is going on in the above equations?