Physics · Mechanical Properties Of Solids · NEET
Because both the free expansion and the stiffness scale the same way with length. Free expansion is ΔL = L·α·ΔT, so thermal strain = ΔL/L = α·ΔT — the L cancels here. Stress = Y × strain = Y·α·ΔT. A longer rod expands more, but it also needs that same larger stretch to be undone, so the strain (and therefore the stress) stays the same. NEET tip: if a question gives you length only to distract you, ignore it for stress. Length matters only if they ask for the FORCE and give you area, or ask for total ΔL.
Thermal expansion is what happens when a rod is FREE: it simply gets longer by ΔL = L·α·ΔT and feels no stress. Thermal stress is what happens when the rod is CLAMPED (both ends fixed): it cannot get longer, so the supports push back and a compressive stress = Y·α·ΔT develops inside. One is a change in length (free), the other is a force per area (blocked). You never get both fully at once — free means expansion with no stress, fixed means stress with no length change.
First find the thermal stress = Y·α·ΔT. Then multiply by the area of cross-section: Force = stress × A = Y·α·ΔT·A. Watch the units: A must be in m² (convert cm² by ×10⁻⁴), ΔT is the rise in temperature (final − initial), and α is per °C or per K (same value). The force does not depend on length.
No — the STRESS (Y·α·ΔT) does not depend on area at all. It depends only on the material (Y and α) and the temperature rise ΔT. Area only enters when you convert stress into FORCE (F = stress × A). So a thin rod and a thick rod of the same material heated by the same ΔT feel the same stress, but the thick rod carries a larger force.
On heating a clamped rod the stress is compressive (the rod wants to grow but is squeezed). On cooling a clamped rod the stress is tensile (the rod wants to shrink but is stretched by the supports). The magnitude is the same: stress = Y·α·|ΔT|. This is why railway lines and bridges are built with expansion gaps — to avoid these stresses in both hot and cold weather.
A metallic bar (Young's modulus Y = 0.5×10¹¹ N m⁻², coefficient of linear expansion α = 10⁻⁵ °C⁻¹, length 1 m, area of cross-section 10⁻³ m²) is heated from 0 °C to 100 °C while clamped so it cannot expand or bend. The compressive force developed in it is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Thermal stress = Y·α·ΔT, where Y is Young's modulus, α is the coefficient of linear expansion, and ΔT is the temperature change. The compressive force is F = Y·α·ΔT·A, where A is the area of cross-section.
When heated, the rod naturally wants to expand by ΔL = L·α·ΔT. The rigid supports prevent this expansion, so they must push inward with just enough force to squeeze the rod back to its original length. This squeeze is the compressive thermal stress.
Yes. Rails are laid with small gaps and expansion joints so that on hot days they can expand freely without developing large compressive thermal stress that could bend or buckle the track.
No. Thermal stress = Y·α·ΔT depends only on the material and the temperature rise. Length and area do not affect the stress; area only affects the total force (F = stress × A).
