For the beam shown below, let $w_0=180\frac{N}{m},w_1=280\frac{N}{m},$ and $M=140Nm.$ All

dimensions are in m $.$

Figure $1$ Loaded Simply Supported Beam

a$.$ Find the reactions at A and $B.$

b$.$ Find the loading function $q(x)$ using singularity functions.

c$.$ Find the shear and moment functions $V(x)$ and $M(x).$

d$.$ Determine the values of the shear function at $0m,1m,2m,2\mathrm{.}5m,5m,8m,9m,$

$10$ m $.$ If the shear function is discontinuous at any of these points, evaluate it at the $-$

and $+$ locations $($an infinitesimal distance below and above the indicated location$).$

For example, the shear function should have a step at $2$ m $,$ so you will find the values

at $2-m$ and $2+m.$