Answer to Question #249213 in Differential Equations for Micau

Question

Find the midspan deflection as well as the shear and moment at the support of the beam as shown. EI is constant.
W = sin x (kN/m)
L = pi (m)

Answer 1

midspan deflection:

$\delta=\frac{5WL^4}{384EI}=\frac{5\pi^4sinx}{384EI}=1.27\cdot\frac{sinx}{EI}$

bending moment at any point x:

$M_x = WLx/2 -Wx2 /2=(\pi/2-x/2)xsinx$

shear:

$F=M_x/x=(\pi/2-x/2)sinx$