|Jun28-11, 11:54 AM||#1|
critical load for buckling
1. The problem statement, all variables and given/known data
A rod of leangth L and flexural rigidity EI is pinned at one end by means of torsional spring having a constant beta, and fixed on the other end.
The rod is subjected to a compressive axial force P.
Determine the critical load for instability.(image of the problem is attached)
2. Relevant equations
As far as I understand, the way to solve this problem is:
M(x)=-R*x-P*v(x)+beta*v'(0) , where R is the reaction on the left end at the y direction v(x) is the deflection function and v'(x) is the angle function.
3. The attempt at a solution
the two equations above yields:
v''(x)+(P/EI)*v(x)= (beta*v'(0)-R*x)/EI ->
to find those constants the boundry conditions are: v(o)=0 v(L)=0 v'(L)=0
How do I represent v'(0) which is unknown ?
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