Question

Consider the following shaft with held by two bearings. The shaft rotations produced the assigned torque, while supporting a 500 lb net pulley force. The shaft is in compression with a 400 lb force. At the location- L/3 the shaft has either a shoulder fillet, grooved, flat-bottom grooved, or with a transverse round hole. 500 lb See case 700 lb-in number Diameter Di 1200 lbǐn 500 lb-in 400 lb 400 lb Diameter D2 Diameter D2 (depends on case number) L/3 L/3

Answer 1

Case (a)

Let the origin be at leftmost point A, y axis is vertically up. Rightmost point is B

Bending Moment Diagram

The equilibrium equations are given by

$R_A+R_B+500=0$

$500(2\frac{L}{3})+R_BL=0$

Or

$500(\frac{2(12)}{3})+12R_B=0$

Or

Hence the equation for bending moment is

$M=-166.67x+500<x-8>$

The bending moment diagram is given below:

Torque Diagram

Let the pulley point be C

The torque from A to C is 1200 lb-i

The torque from C to B is 1200-700=500 lb-in

Torque equation is

$T=1200-700<x-8>^0$

The torque diagram is given below:

Axial force diagram

The axial force is constant and compressive and the equation is

$F=-400$

The plot is given below:

b) The Von Mises stress is given by

The possible critical locations are

1) The point of max bending moment , point C at x=8 in

2) The point of max stress concentration , point D where the change in diameter takes place, x=4 in

(Since only possible loctions of critical stress points are required, the stresses are not calculated as such)

Cases b) and c)

a) The loading diagram remains the same as for case a) above

b) The possible critical points remain the same as for case a) above