QUESTION ONE

A concrete beam with a cross$-$section shown in Figure Q$1$ is resting on an elastic foundation with

a subgrade modulus of $(K_0)250000k\frac{N}{m^2}\frac{?}{m}.$ The beam is $10m$ long, and it is subjected to a

concentrated load of $300kN$ and to a uniformly distributed load of $2k\frac{N}{m}$ over a length $3000mm$

$(a=b=1500mm)$ at the centre. Neglecting the self$-$weight and assuming freely supported ends,

Determine the following:

a$)$ The maximum deflections

b$)$ Slope

c$)$ Shear force.

d$)$ Maximum Bending stress

Assume Young's modulus, $E_c=28$GPa.

Hint: $k=b{K}_0$