Question

A beam of length 10m is supported at its ends and weighs 100kg/m. The ODE governing Cy" = 100{(x^2)/2 - 5x) where C is a constant. Solve this equation to determine the deflection at x=6m , given that y=0 at x=0 and x=10.

Answer 1

$Cy" = 100(\frac {x^2}{2} - 5x)$

integrating,

$Cy'= 100(\frac {x^3}{6} - 5\frac {x^2}{2})+c_{1}$

again Integrating,

$Cy= 100(\frac {x^4}{24} - 5\frac {x^3}{6})+c_{1} x+c_{2}$

at y=0 at x=0 $c_{2}=0$

and y =0 and x = 10 $c_1=4.17 \times 10^3$

deflection at x=6 m

$y= \frac {12420} {C}$