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Because normal strain is the ratio of two lengths, it is a dimensionless quantity, that is, it has no units. Therefore, strain is expressed simply as a number, independent of any system of units. Numerical values of strain are usually very small, because bars made of structural materials undergo only small changes in length when loaded. 0 m. 0 m L In practice, the original units of d and L are sometimes attached to the strain itself, and then the strain is recorded in forms such as mm/m, mm/m, and m/m.

When a material behaves elastically and also exhibits a linear relationship between stress and strain, it is said to be linearly elastic. This type of behavior is extremely important in engineering for an obvious reason—by designing structures and machines to function in this region, we avoid permanent deformations due to yielding. Hooke’s Law The linear relationship between stress and strain for a bar in simple tension or compression is expressed by the equation s ϭ Ee (1-8) in which s is the axial stress, e is the axial strain, and E is a constant of proportionality known as the modulus of elasticity for the material.

Strains are plotted on the horizontal axis and stresses on the vertical axis. (In order to display all of the important features of this material, the strain axis in Fig. * Beyond point A, the proportionality between stress and strain no longer exists; hence the stress at A is called the proportional limit. For low-carbon steels, this limit is in the range 210 to 350 MPa, but high-strength steels (with higher carbon content plus other alloys) can have proportional limits of more than 550 MPa. The slope of the straight line from O to A is called the modulus of elasticity.

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Parts catalog. USAF series YB-35, YB-35A, and YB-49 aircraft by Northrop

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