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Exact Solution:
imagex d
dx imaged image. imagexdx
d image. imagex
E dx
d image. f
. E A dx
d image. ( ) . 10 x . 10 L L x
2
. E A
image. 1
( ) . E A
. 5
3 x3 . . 5 L2x C1
Boundary condition: Displacement at (x=0) is equal to zero.
C1 0
Therefore,
image. 1
( ) . E A
. 5
3 x3 . . 5 L2x
image. 1
A
. 5 L2 . 5 x2
A 2 L 60
At x=0, x 0
image. 1
( ) . E A
. 5
3 x3 . . 5 L2x = image0
image. 1
A
. 5 L2 . 5 x2
= image9 103
At x=30, x 30
image. 1
( ) . E A
. 5
3 x3 . . 5 L2x = image0.00825
image. 1
A
. 5 L2 . 5 x2
= image6.75 103
At x=60, x 60
image. 1
( ) . E A
. 5
3 x3 . . 5 L2x = image0.012
image. 1
A
. 5 L2 . 5 x2
= image0