Conceptual Physics

11.9 - Interactive checkpoint: stress and strain

A 3.50 meter-long rod, composed of a

titanium alloy, has a cross-sectional

area of 4.00×10í^4 m^2. It increases in

length by 0.0164 m under a force of

2.00×10^5 N. What is the stress on the

rod? What is the strain? What is

Young's modulus for this titanium

alloy?

Answer:

stress = N/m^2

strain =

Y = N/m^2

11.10 - Gotchas

Stress equals force. No, stress is always a measure of force per unit surface area. A force stretches a rod by 0.01 meters, so the strain is 0.01 meters. No, strain is always the fractional change (a dimensionless ratio). To calculate the strain, you need to divide this change in length by the initial length of the rod. This is not stated here, so you cannot determine the strain without more information.

11.11 - Summary

An object is in equilibrium when there are no net forces or torques on it. Static equilibrium is a special case where there is also no motion. The center of gravity is the average location of the weight of an object. The force of gravity effectively acts on the object at this point. The concept of center of gravity is very similar to the concept of center of mass. The two locations differ only when an object is so large that the pull of gravity varies across it.

Elasticity refers to an object's shape changing when forces are applied to it. Objects are called elastic when they return to their original shape as forces are removed. Related to elasticity are stress and strain. Stress is the force applied to an object per unit area. The area used to determine stress depends on how the force is applied. Strain is the fractional change in an object's dimensions due to stress. The relationship between stress and strain is determined by a material's modulus of elasticity up to the proportionality limit. An object will become permanently deformed if it is stressed past its elastic limit. It will finally break at its rupture point. Ductile materials are easily deformed, while brittle materials tend to break rather than stretch. Tensile stress is the application of stress causing stretching or compression along a line. Strain under tensile stress is measured as a fractional change in length and stress is measured as the force per unit cross-sectional area. Young's modulus is the tensile stress on a material divided by its strain.

Volume stress acts over the entire surface of an object. The amount of volume stress is calculated as the force per unit surface area, while the strain is the fractional change in volume. The bulk modulus relates volume stress and strain.

Static equilibrium

ȈFx = 0, ȈFy = 0, ȈIJ = 0

Tensile stress

Volume stress