Thermal Stress Calculator

At a glance:Thermal stress is the internal mechanical stress a solid develops from a temperature change. When temperature changes, its length would freely expand/contract by ΔL_free=α·L·ΔT (α linear expansion coefficient, L original length, ΔT temperature change). If the ends are constrained (fixed supports, rigid connection) and cannot move freely, an opposite strain builds inside, producing thermal stress σ=E·α·ΔT (E Young's modulus). Direction: heating while blocked → compressive stress; cooling while blocked → tensile stress. The thermal strain ε=α·ΔT is the free strain from temperature; when constrained it becomes elastic strain ε_el=σ/E, and compatibility gives α·ΔT+σ/E=0 → σ=−E·α·ΔT (sign convention). This tool outputs the magnitude σ=E·α·ΔT. α meaning: elongation per unit length per 1 K. Common α (1/K): Invar 1.2e-6 (watches, gauges, very stable), glass 9e-6, concrete 10e-6, steel 12e-6, copper 17e-6, brass 19e-6, aluminium 23e-6, zinc 30e-6, plastics 50–100e-6. High-α materials are temperature-sensitive (aluminium expands ~2× steel). Typical stress: steel ΔT=50 K → σ=200GPa×12e-6×50=120 MPa (half of 250 MPa yield, not negligible); concrete ΔT=30 K → σ=30GPa×10e-6×30=9 MPa (near its 3–5 MPa tensile strength, so it cracks). History: 18th-century temperature compensation in compasses/watches, 19th-century rail buckling, 20th-century jet-engine thermal-stress analysis. Applications: bridge expansion joints; rail welding and track stability; engine piston/cylinder clearances; toughened glass; electronic packaging fatigue (different α of chip/mold/substrate); building expansion joints every 30–50 m; bimetallic strips (thermostats); quench cracking. Notes: (1) assumes fully constrained ends — partial restraint reduces stress; (2) assumes uniform temperature — gradients add bending stress; (3) beyond elastic limit needs elastoplastic analysis; (4) α, E vary with temperature (integrate at high T); (5) composites need compatibility + equilibrium.