Engineering Solid Mechanics Beam Stress Question

[Leighanne]

Homework Statement

Looking for some help in solving this practice problem, I have tried multiple times and can't seem to get to the correct answers.

Relevant Equations

The solid 30 mm diameter steel [E = 200 GPa] shaft shown in Figure supports two pulleys. For the loading shown, use discontinuity functions to compute:

(a) the deflection of the shaft at pulley B.

(b) the deflection of the shaft at pulley C.

answers: (1.539mm, 6.15mm)

 

[erobz]

You are supposed to use the singularity function to find the deflections. You need to write the moment as a function of $x$. Then the deflections come from integrating twice:

$$EI \frac{d^2y}{dx^2} = M(x)$$

Why are you trying to find the shear stress?

 

[Leighanne]

Uploaded the wrong solution attempt whoops!
heres the correct one.

 

[erobz]

Uploaded the wrong solution attempt whoops!
heres the correct one.
View attachment 338230

There should be a constant moment that you have not included in $M(x)$. There may be more, but start there( i.e there is vertical reaction and moment at A under equilibrium).