$(1)$ Beam Analysis: Internal Loads due to Point Forces and Distributed Loads $(35$ pts$)$ For each of the problems $1A)$ below,

a$)$ Determine the shear force and bending moment equations for the beam.

b$)$ Draw the shear and bending moment diagrams for the beam

c$)$ Confirm that $V_y$ is the derivative of the Moment $M_{bz}$

$1$A: Beam ABC

$1$B: Beam ABC with distributed load

$1$C: Beam ACB with distributed load

$1$D: Beam ABCDE with multiple point loc

$1$E: Beam ABCD with point and distributed lo

Problem $1$F: An unknown loading on the simply supported beam $AB$ generates the shear diagram shown below.

a$)$ Determine the loading on the beam in terms of $P$

b$)$ Determine the bending moment diagram in terms of $P$

Problem $1$G: An unknown loading on the simply supported beam $AB$ generates the moment diagram shown.

a$)$ Determine the shear diagram in terms of $P$

b$)$ Determine the loading on the beam in terms of $P$