$5.)$ Consider the $2$D beam supported by a roller at A and a pin at B$.$

EXTERNAL FORCES

a$)$ Draw a FBD$.$ Include all external reaction forces & moments.

b$)$ Solve for the values of all external reaction forces & moments.

INTERNAL FORCES

c$)$ Draw the internal shear force diagram $($SFD$)$ for the beam.

Label the maximum and minimum values on the graph.

d$)$ Draw the internal bending moment diagram $($BMD$)$ for the beam.

Label the maximum and minimum values on the graph.

e$)$ What is the maximum magnitude of bending moment on the beam?

f$)$ Is the maximum $($above$)$ a "sagging" or "hogging" bending moment?

g$)$ At what single point along the beam does this maximum occur?

h$)$ What are the values of internal forces $($ N$,$V$,$M $)$ acting at C $?$

INTERNAL FORCES $-$ EQUATION

i$)$ What is the equation for shear force V$($x$)$ and bending moment M$($x$)$ for

EACH interval $($given below$).$ Assume x$=0$ is at the left end of the beam:

a$.$ From the left edge until point A $?$

b$.$ From A until B $?$