Torsional Constant
Calculate torsional constant (J) for various cross-sections including circular, hollow circular, rectangular, I-beam, channel, and angle sections. Essential for shaft design and torsional rigidity ...
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Why: Understanding torsional constant helps you make better, data-driven decisions.
How: Enter Shape Type, Dimension Unit, Diameter to calculate results.
Run the calculator when you are ready.
๐ฉ Solid Circular Shaft
Calculate J for 50mm diameter solid steel shaft
๐ Hollow Circular Tube
Find J for pipe: OD=100mm, ID=80mm
๐ Rectangular Bar
Calculate J for 40mm ร 20mm rectangular bar
๐๏ธ I-Beam Section
I-beam: flange=150mm, web=200mm, thicknesses=10mm
๐ฆ Channel Section
Channel: width=100mm, height=200mm, thickness=8mm
Enter Values
Cross-Section Shape
Circular Section Dimensions
Torsional Stiffness (Optional)
For educational and informational purposes only. Verify with a qualified professional.
What is Torsional Constant?
The torsional constant (J), also known as the polar moment of inertia for circular sections, is a geometric property that quantifies a cross-section's resistance to torsional deformation. It determines how much a structural member will twist under an applied torque. The torsional constant is crucial in shaft design, power transmission systems, and any application involving rotational loading.
Shaft Design
Essential for designing drive shafts, axles, and rotating components. Determines angular deflection and stress distribution under torque.
Cross-Section Shape
Different shapes have vastly different torsional constants. Closed sections (circular, hollow) are much more efficient than open sections.
Torsional Stiffness
Combined with material properties (shear modulus G) and length, J determines the torsional stiffness k = GJ/L.
Formulas for Different Shapes
Solid Circular Section
Where d = diameter. This is the exact formula for circular sections.
Hollow Circular Section
Where dโ = outer diameter, dแตข = inner diameter. Excellent for weight reduction.
Rectangular Section (Approximate)
Where ฮฒ depends on aspect ratio (h/b), b = larger dimension, t = smaller dimension. This is an approximation.
Open Sections (I-beam, Channel, Angle)
Simplified formula for thin-walled open sections. Less accurate than closed sections.
Key Concepts
Closed vs Open Sections
- โข Closed sections (circular, hollow circular) have much higher torsional constants
- โข Open sections (I-beam, channel, angle) have lower torsional resistance
- โข Closed sections distribute stress more evenly
- โข Open sections may experience warping and stress concentrations
Design Considerations
- โข Larger J means less twist under the same torque
- โข Hollow sections provide weight savings with minimal J reduction
- โข Rectangular sections are inefficient for torsion - use circular when possible
- โข Consider both J and material properties (G) for complete analysis
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