Question

In the study of Buckling of uniform column under an axial load F, the deflection y(x) is obtained from the following equation with no deflections at x=0 and x=L:

Answer 1

@ganeshie8 can u help me

Answer 2

r u getting it sir

Answer 3

characteristic equation is
\(\large r^2 + \gamma ^2 = 0\)

right ?

Answer 4

is it very difficult sir because i tried for a long time but can't get it

Answer 5

u should start with making an auxiliary equation like
\[D^2+\gamma^2=0\]
\[D=(+-)i \gamma\]
so the complementary function will be
\[C.F=C_1\cos(\gamma x)+C_2\sin(\gamma x)\]
like this

Answer 6

and what do u mean by first critical load?

Answer 7

if i do in that i am getting C sqrt(C^2+1)!=C^2+1 and x = (2 (tan^(-1)(C-sqrt(C^2+1))+pi n))/gamma and n element Z

Answer 8

i think here they want to covert to an differential equation n then solve but i don't rely know how to get a differential equation from this @sidsiddhartha

Answer 9

don't know to convert to differential equation sorry for the typing mistake

Answer 10

i think they only asked for the general solution and why u want to convert the diff equation?

Answer 11

i really don't it was a random guess and not good at differentials

Answer 12

i think all they want is the complementary function and that will be the general solution and,sorry i dont have any idea about the crictical load thing