There is no point reaching for a calculator that cannot show its working. This one starts from radius (r), a, inner semi-major axis (a₀), b, inner semi-minor axis (b₀), rectangle base (a), web height (c), web width (d), rectangle height (b), fillet radius (r), thickness (t), thickness (t₁), one way, if else, torsional constant (k), ellipse length, torsion constant (k) and torsional constant (k) and reports torsional constant (k), t/t₁ = d/b and k₁, so you can see how each answer follows from the numbers you entered.
What Is the Torsional Constant Calculator?
This torsional constant calculator is for the kind of problem where you know the physical quantities but not the number you need. It turns radius (r), a, inner semi-major axis (a₀), b, inner semi-minor axis (b₀), rectangle base (a), web height (c), web width (d), rectangle height (b), fillet radius (r), thickness (t), thickness (t₁), one way, if else, torsional constant (k), ellipse length, torsion constant (k) and torsional constant (k) into torsional constant (k), t/t₁ = d/b and k₁.
Physics calculations go wrong in predictable ways, usually through mixing units or dropping a digit. Work through the result one step at a time and check that the figures are the size you would expect at each stage.
How the Torsional Constant Physics Works
The relationship is applied step by step, and each step is a standard piece of physics rather than a single opaque formula. That means you can check the intermediate values against what the theory predicts, which is usually faster than checking only the final answer.
Keep every value in the same unit system throughout the calculation. Mixing metres and feet part way through is the single most common reason a correct formula gives a wrong answer.
Units, Assumptions and the Limits of the Model
The calculation assumes ideal conditions: no air resistance, no heat loss, and dimensions that do not change while you work. Those assumptions are reasonable for most classroom and engineering estimates, and unreasonable for anything more precise.
Where a value is a rate, it has to be quoted for the same period as everything else. A per-hour figure cannot be combined with a per-day figure without converting one of them first.
A Worked Example
Working through an example, with radius (r) set to 10, a set to 5, inner semi-major axis (a₀) set to 2, the calculator returns torsional constant (k) of 15,707.96327, and q of 0.4, and torsional constant (k) (square) of 87.89063. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out torsional constant (k)?
Enter radius (r), a, inner semi-major axis (a₀), b, inner semi-minor axis (b₀), rectangle base (a), web height (c), web width (d), rectangle height (b), fillet radius (r), thickness (t), thickness (t₁), one way, if else, torsional constant (k), ellipse length, torsion constant (k) and torsional constant (k). The calculator then works through the relationship and reports torsional constant (k), t/t₁ = d/b and k₁.
What does the torsional constant actually calculate?
It takes radius (r), a, inner semi-major axis (a₀), b, inner semi-minor axis (b₀), rectangle base (a), web height (c), web width (d), rectangle height (b), fillet radius (r), thickness (t), thickness (t₁), one way, if else, torsional constant (k), ellipse length, torsion constant (k) and torsional constant (k) and converts them into torsional constant (k), t/t₁ = d/b and k₁ using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter radius (r)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.