Review. On a day that the temperature is 20.0^∘ C, a concrete walk is poured in such a way that

step 1 What is the stress in the cement on a day of temperature 50 .0 .0 Celsius if the cement was pour

Review. On a day that the temperature is 20.0^∘ C, a...

Review. On a day that the temperature is $20.0^{\circ} \mathrm{C},$ a concrete walk is poured in such a way that the ends of the walk are unable to move. Take Young's modulus for concrete to be $7.00 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}$ and the compressive strength to be $2.00 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}$ (a) What is the stress in the cement on a hot day of $50.0^{\circ} \mathrm{C}$ ? (b) Does the concrete fracture?

Key Concepts

Compressive Strength

Compressive strength is the maximum compressive stress that a material can withstand before failure, such as cracking or crushing. This property is fundamental in evaluating whether a material, like concrete, will sustain a load or stress without fracturing, particularly when additional stresses from thermal effects are present.

Young's Modulus

Young's modulus is a measure of the stiffness of a material, quantifying the relationship between tensile or compressive stress and the corresponding strain in the elastic region of the material’s deformation. It is used to determine how much a material will deform under a given load and is key in calculating stress induced by other factors, such as thermal expansion when the material is constrained.

Thermal Expansion

Thermal expansion refers to the phenomenon where materials change their dimensions in response to changes in temperature. When a material is heated, its particles gain kinetic energy and tend to move apart, causing it to expand. This concept is crucial for understanding how temperature variations can lead to strains in a material when expansion or contraction is restricted by external constraints.

Thermal Stress

Thermal stress is the internal force per unit area that develops in a material when its natural tendency to expand or contract due to temperature changes is hindered by constraints. Since the material cannot freely expand or contract, the induced strain is converted into stress, which may lead to deformation or even fracture if it exceeds the material’s strength limits.

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