Boundary conditions for a 4th order beam deflection equation

[Xaspire88]

What would the boundary conditions be for a fourth order differential equation describing the deflection (elastic curve) of a propped cantilever beam with a uniform distributed load applied? i.e. a beam with a built in support on the left and a simple support on the right. I need 4 obviously but I am having a hard time coming up with the 4th.

So far I have

1. x = 0 v = 0 (no deflection at the built in support end)
2. x = L v = 0 (no deflection at the simple support end)
3. x = 0 dv/dx = 0 (slope of the deflection at the built in support is 0)

and for the fourth I have seen

x = L d^2v/dx^2=0

but I am having some trouble wrapping my head around that last one. Is it correct?

 

[PhanthomJay]

What would the boundary conditions be for a fourth order differential equation describing the deflection (elastic curve) of a propped cantilever beam with a uniform distributed load applied? i.e. a beam with a built in support on the left and a simple support on the right. I need 4 obviously but I am having a hard time coming up with the 4th.

So far I have

1. x = 0 v = 0 (no deflection at the built in support end)
2. x = L v = 0 (no deflection at the simple support end)
3. x = 0 dv/dx = 0 (slope of the deflection at the built in support is 0)

and for the fourth I have seen

x = L d^2v/dx^2=0

but I am having some trouble wrapping my head around that last one. Is it correct?

yes, at the pinned simple support which is free to rotate, there can be no bending moment, which is what that boundary condition describes (at x = L, v" = M/EI = 0)

 

[Xaspire88]

thanks, I was getting confused because some sites had "common beam" equations that were different than others.. until i realized that the supports were on different sides and thus their coordinate system was changing. now it makes sense.