Calculating Inside Diam. & Stress of Hollow Steel Shaft

In summary, the homework statement provided the information of a hollow steel shaft with a torque of 5400 Nm and a torsional shear of 150 MPa. The required values were the inside and outside diameters, as well as the stress on the inside of the shaft. Using the formula 16T/[pi d^3], the inside and outside diameters were calculated to be 64.49 mm and 48.37 mm, respectively. To determine the stress on the inside of the shaft, the formula Tr/J was used, where J is the polar moment of inertia. Since the shaft is hollow, J was calculated to be (π/32)(douter^4-dinner^4). After substitution,
  • #1
darkmagic
164
0

Homework Statement



Given:
hollow steel shaft
Torque = 5400 Nm
Torsional Shear = 150 MPa

Required:
Inside diameter
Outside Diameter
Stress on the inside of the shaft

Homework Equations





The Attempt at a Solution


I solved both the diameters which are 64.49 mm and 48.37 mm.
I don't know what formula to use to determine the stress on the inside of the shaft

I used to 16T/[pi d^3) where d is the inside diameter. Am I correct?
 
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  • #2
In general

T/J = (shear stress)/r

so shear stress = Tr/J

at the outer, r = outer radius

at the inner r = inner radius
 
  • #3
The J and r are already substituted in the formula I used. Ok thanks.
 
  • #4
Is J there the J of the smaller circle, with the inside diameter? I got 243 Mpa which is larger than 150 Mpa.
 
  • #5
darkmagic said:
Is J there the J of the smaller circle, with the inside diameter? I got 243 Mpa which is larger than 150 Mpa.

Your shaft is a hollow one, so the J = (π/32)(douter4-dinner4)
 

1. How do you calculate the inside diameter of a hollow steel shaft?

The inside diameter of a hollow steel shaft can be calculated by subtracting the wall thickness from the outside diameter. The wall thickness can be measured using a caliper or obtained from the manufacturer's specifications.

2. What is the formula for calculating the stress of a hollow steel shaft?

The formula for calculating the stress of a hollow steel shaft is: σ = (M * c) / (π * r^3), where σ is the stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and r is the radius of the shaft.

3. What are the units of measurement for calculating the inside diameter and stress of a hollow steel shaft?

The inside diameter is typically measured in millimeters (mm) or inches (in), while stress is measured in units of pressure, such as pounds per square inch (psi) or megapascals (MPa).

4. Can the inside diameter and stress of a hollow steel shaft be calculated for any shape or only round shafts?

The calculations for inside diameter and stress of a hollow steel shaft can be applied to any shape, as long as the dimensions and material properties are known. However, the formula mentioned in question 2 is specifically for round shafts. Different formulas may be needed for calculating the stress of non-circular shafts.

5. How can the calculated stress of a hollow steel shaft be used in engineering design?

The calculated stress of a hollow steel shaft is an important factor in engineering design as it helps determine the strength and load-bearing capacity of the shaft. Engineers can use this information to select the appropriate material and dimensions for the shaft, ensuring it can withstand the expected loads and operate safely.

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