This thermal stress calculator takes the figures you already have and applies the relationship behind thermal stress calculations for you, giving change in temperature (δt) and thermal stress (σt) from initial temperature (ti), final temperature (tf), thermal expansion coefficient (α) and young’s modulus (em).
What Is the Thermal Stress Calculator?
This thermal stress calculator is for the kind of problem where you know the physical quantities but not the number you need. It turns initial temperature (ti), final temperature (tf), thermal expansion coefficient (α) and young's modulus (em) into change in temperature (δt) and thermal stress (σt).
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 Thermal Stress 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 initial temperature (ti) set to 10, final temperature (tf) set to 5, thermal expansion coefficient (α) set to 2, the calculator returns change in temperature (δt) of -5, and thermal stress (σt) of -1,000. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out change in temperature (δt)?
Enter initial temperature (ti), final temperature (tf), thermal expansion coefficient (α) and young's modulus (em). The calculator then works through the relationship and reports change in temperature (δt) and thermal stress (σt).
What does the thermal stress actually calculate?
It takes initial temperature (ti), final temperature (tf), thermal expansion coefficient (α) and young's modulus (em) and converts them into change in temperature (δt) and thermal stress (σt) 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 initial temperature (ti)?
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.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.