A solid shaft of 65mm outside diameter and a hollow shaft of 85mm outside diameter are connected by 6 bolts with the mean pitch of thread being 155mm. The shear stress due to the torque on the shafts is equal to the shear stress on the bolts.

a) Find the diameter of the bolts.

b) Find the inside diameter of the hollow shaft.
Where do I start?

Note: Solid shafts and hollow shafts system are used in low stress,low RPM applications, like a large air fan. The solid shaft comes from the motor and the hollow shaft will be used on the fan.Because of the lighter hollow shaft a smaller driving motor can be used.They are usually connected by a flange welded over the smaller diameter solid shaft. The flange outside diameter is equal to the hollow shaft outside diameter.The shafts are then secured together by bolts.

For the shear stress (in terms of the torque) use

http://www.engineeringtoolbox.com/torsion-shafts-d_947.html
Then use that stress for the diameter of the bolts. Assume the torque is distributed evenly over the bolt cross sectional areas. I don't see what the thread pitch has to do with it.

Thanks... I couldn't figure out why there's is a thread pitch either!!!

To solve this problem, you can start by using the principle of equilibrium to relate the shear stress on the shafts and bolts. The equation for shear stress is given by:

τ = Tc / (d * t)

where:
τ is the shear stress,
Tc is the torque on the shafts, which is assumed to be the same as the torque on the bolts,
d is the diameter of the shaft or bolt, and
t is the thickness of the shaft or bolt.

Since the shear stress on the shafts is equal to the shear stress on the bolts, we can set up the following equation:

τ_shafts = τ_bolts

(Tc / (d_shaft * t_shaft)) = (Tc / (d_bolt * t_bolt))

Now, let's apply this equation to solve for the unknowns.

a) To find the diameter of the bolts (d_bolt), we need to determine the values of Tc, d_shaft, t_shaft, and t_bolt.

The question gives the outside diameter of the solid shaft (65mm) and the outside diameter of the hollow shaft (85mm). To find the thickness of the hollow shaft (t_shaft), we subtract the inside diameter of the hollow shaft from its outside diameter. However, the inside diameter of the hollow shaft is not given, so we need to solve part b) first.

b) To find the inside diameter of the hollow shaft, we can use the relationship between the outside diameter and inside diameter of the hollow shaft. The inside diameter of the hollow shaft is equal to the outside diameter of the solid shaft (65mm). Therefore, the inside diameter of the hollow shaft is 65mm.

Now that we have the inside diameter of the hollow shaft, we can go back to part a) to find the diameter of the bolts.

Plug in the provided values into the equation and solve for d_bolt:

(Tc / (65 * t_shaft)) = (Tc / (d_bolt * t_bolt))

Since Tc cancels out, we have:

1 / (65 * t_shaft) = 1 / (d_bolt * t_bolt)

Simplifying further, we have:

d_bolt = t_bolt / (65 * t_shaft)

Note: Remember to use consistent units throughout the calculation, such as millimeters.

By solving the equations and substituting the given values, you will be able to determine the diameter of the bolts (d_bolt) and the inside diameter of the hollow shaft.