Thermal Stress Simulator

このコンテンツはまだ日本語訳がありません。

Modified: Jun. 9, 2026

Published: Jun. 5, 2026

A member free to expand develops no stress at all, but fix both ends and even a modest temperature rise creates forces large enough to buckle a rail or shear the bolts in a pipe flange, with no external load anywhere in the picture. The stress builds because constrained expansion is mechanically identical to a compressive load: the wall pushes back on the bar with exactly the force that would have been needed to squeeze it back to its original length. This simulator makes that process visible: a bar sits between two walls with an optional gap, the temperature rises, and you watch free expansion fill the gap stress-free before compressive stress begins to build the moment contact is made. #ThermalStress #ThermalExpansion #SolidMechanics

Open Simulator

What You Can Analyze

Free thermal expansion

See how far the bar would grow if unconstrained: delta = alpha times L times deltaT. Until that growth fills the gap, the stress is exactly zero regardless of temperature.

Constrained thermal stress

Once the gap closes, read the compressive stress and safety factor against yield, computed from the material modulus and the blocked fraction of thermal expansion.

Gap-then-contact behavior

Choose a gap size and watch the stress chart stay flat until the critical temperature, then rise linearly. The design charts show how a larger gap raises that threshold.

Safety check

Find the safe temperature rise to yield, compare it against your applied deltaT, and read the remaining margin, for any of the five built-in materials or a custom configuration.

Key Features

Animated bar between walls A canvas diagram shows the bar growing toward the far wall as temperature rises, with expansion arrows while the gap is open and a color shift to compressive stress once contact is made. The gap and expansion are exaggerated for clarity.
Play to ramp temperature Press Heat and the temperature climbs automatically so you can watch the transition from free expansion to constrained stress in real time, with a teal playhead sweeping the charts.
Live readouts Thermal stress, free expansion, actual expansion, gap state, safety factor, and safe deltaT all update as you drag any slider, with no need to press a compute button.
Four analysis charts in two groups The Response group shows stress magnitude and expansion against temperature rise; the Design group shows how stress and safe temperature change with gap size. A vertical marker tracks your current operating point.
Five preset configurations Steam pipe, rail track, bridge expansion joint, aluminium strut, and copper bar with gap, covering the range from fully fixed structural members to joints with deliberate clearance.
A/B case comparison Save the current curves as Case A, change the material, gap, or length, and overlay both datasets on every chart to compare the effect directly.
Downloadable resources A lab report with all four charts and the bar diagram, a CSV of the full stress and expansion dataset, and a design data sheet with the animation as a WEBM video.

Preset Configurations

Preset	Material	L (mm)	deltaT (degC)	Gap (mm)	Represents
Steam pipe	Steel	3000	150	0	Fixed pipe between flanges, no expansion allowance
Rail track	Steel	1000	45	3	Rail with a small joint gap between sections
Bridge expansion joint	Steel	2000	50	25	Structural member with a deliberate expansion joint
Aluminium strut	Aluminium	500	80	0	Short fixed strut in a high-temperature enclosure
Copper bar with gap	Copper	800	100	5	Busbar with a small clearance to the adjacent block

Equations

Free thermal expansion (no constraint or gap still open):

dFree = alpha * L * dT

When free expansion is less than or equal to the gap, the bar has not yet touched the far wall and no stress exists:

if dFree <= gap:
    sigma = 0
    dActual = dFree

Once the gap closes, the blocked expansion produces compressive stress:

if dFree > gap:
    sigma = -E * (dFree - gap) / L
    dActual = gap

Which can be written explicitly in terms of the inputs:

sigma = -E * (alpha * L * dT - gap) / L
      = -E * (alpha * dT - gap / L)

Safety factor against yield (compressive magnitude versus material yield strength):

SF = yield / |sigma|

Safe temperature rise (the deltaT at which sigma first reaches the yield stress):

dT_safe = (yield * L / E + gap) / (alpha * L)
        = yield / (E * alpha) + gap / (alpha * L)

Material properties used in the simulator (alpha in 1e-6/degC, E in GPa):

Steel:     alpha = 12,  E = 200, yield = 250 MPa
Aluminium: alpha = 23,  E = 69,  yield = 240 MPa
Copper:    alpha = 17,  E = 117, yield = 210 MPa
Brass:     alpha = 19,  E = 100, yield = 200 MPa
Titanium:  alpha = 8.6, E = 114, yield = 880 MPa

Guided Experiments

Work through the Thermal Stress Experiments lesson for structured, Python-verified exercises that pair directly with this simulator:

Thermal Stress Experiments: the hands-on lab that pairs with this simulator.
Thermal Stresses and Strains: the lesson that covers the underlying theory.
Solid Mechanics Analyzer: the full suite of stress-analysis simulators.
Pressure Vessel Simulator and Mohr’s Circle Simulator: neighboring simulators in the same suite.

Comments

Loading comments...