# Question: a vertical shaft made from aisi 1040 cold drawn steel...

###### Question details

A vertical shaft, made from AISI 1040 cold drawn
steel, carries pulleys. A schematic of the shaft is shown in a
horizontal position for convenience of plotting axial diagrams. The
tensile forces in the belts under operating conditions are shown.
Also, the shaft carries an axial compressive load of 6.2 kN. The
torque/power is transmitted between each pulley and the shaft by a
key fitted in a sled-runner keyseat type.

The steps listed below will ultimately lead you to the computation
of the maximum
shear stress using the equation

T_max= maximum shear stress at the same point where σ and T
occur

σ= tensile or compressive stress creates by various loads

T= shear stress creates by various loads

(--------)

Direct Compression stress and deformation

1. Using reasonable design assumptions, propose a diameter for the
shaft based on direct normal stress. Be sure to state your safety
factor and reasons for picking that factor.

2. Determine the stress concentration factor K_t for a sled-runner
keyseat (same as in bending).

3. Using the stress concentration factor K_t just determined,
adjust your recommendation for shaft diameter.

4. Based on your recommended diameter, compute the deformation δ_c
due to force P.

Torsional shear stress and deformation

5. Compute the torque T_B and T_C due to tensile forces in the
belts at point B and C, respectively.

6. Draw the torque diagram to show the level of torque in all
segments of the shaft.

7. Based on your recommended diameter found in step 4 above,
compute the nominal torsional stress T_Bnom and T_Cnom on the outer
surface of the shaft for cross sections passing through points B
and C due to the torque T_B and T_C.

8. Compute the angle of twist θ_BC of the cross section passing
through B with respect to that passing through point C.

9. Determine the stress concentration factor K_t, in torsion, for a
sled-runner keyseat.

10. Using the stress concentration factor K_t just determined,
calculate the shear stresses T_B and T_C on the outer surface of
the shaft for cross sections passing through points B and C,
respectively.

11. If necessary, adjust your recommended diameter to allow for the
direct shear stress. Reiterate the calculations for σ, δ_c, and
T_B.

Key Design

12. Determine the force F that the shaft exerts on the key

13. Suggest the dimensions (length, width, and height) of the key
if it was made of steel. ( there are many possible solutions)

Discussion

Are the values of the deformation δ_c due to the compressive force
P, and the angle of twist θ_BC acceptable for a power transmission
shaft such as the one under consideration? Why?

What considerations and standards did you use to determine safety
factors?