The simply supported beam undergoes a "triangular" distributed load as shown.

a$.$ Show that the support reactions are Ax$=0,$Ay$=8$ kip up$,$ By$=4$ kip up$.$

b$.$ Find expressions for the internal shear force Vint from x$<mn>6</mn>$ft and for $6$ftx$<mn>1</mn><mn>2</mn>$ft$.$

c$.$ Find expressions for the internal moment Mint from x$<mn>6</mn>$ft and for $6$ftx$<mn>1</mn><mn>2</mn>$ft$.$

d$.$ Plot the internal shear force Vint as a function of x from $0$ to $12$ ft $.$ Indicate any jumps due to

external forces or changes in loading, as well as any zeroing crossings, slopes of linear portions,

or local maxima or minima if any such are found.

e$.$ Plot the internal moment Mint as a function of x from $0$ to $12$ ft $.$ Indicate any jumps due to

external forces or changes in loading, as well as any zeroing crossing $\_()$ slopes of linear portions,

or local maxima or minima if any such are found.