To determine the angle of twist of end A with respect to C, we can use the formula:
theta = (T L) / (G J)
where theta is the angle of twist, T is the torque, L is the length of the shaft, G is the shear modulus of elasticity, and J is the polar moment of inertia of the shaft.
The torque can be found from the distributed load. The triangular load can be divided into two parts: a rectangle of width 80 mm and height 1 kN/m, and a triangle of base 80 mm and height 2 kN/m. The area of the rectangle is:
A1 = 80 x 1000 = 80000 N.mm
The area of the triangle is:
A2 = 1/2 x 80 x 80 x 2000 = 640000 N.mm
The total torque is:
T = (80000 + 640000) / 2 = 360000 N.mm
The polar moment of inertia of a solid circular shaft is:
J = pi/32 x D^4
where D is the diameter of the shaft. Substituting the given values, we get:
J = pi/32 x 80^4 = 2.015 x 10^8 mm^4
The shear modulus of elasticity for A-36 steel is 79.3 GPa = 79.3 x 10^3 MPa = 79.3 x 10^3 N/mm^2.
Substituting the given values, we get:
theta = (360000 x 1000) / (79.3 x 10^3 x 2.015 x 10^8) = 0.002 radians
Therefore, the angle of twist of end A with respect to C is 0.002 radians.