Material Constants

Overview

Source: Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA

In contrast to the production of cars or toasters, where millions of identical copies are made and extensive prototype testing is possible, each civil engineering structure is unique and very expensive to reproduce (Fig.1). Therefore, civil engineers must extensively rely on analytical modeling to design their structures. These models are simplified abstractions of reality and are used to check that the performance criteria, particularly those related to strength and stiffness, are not violated. In order to accomplish this task, engineers require two components: (a) a set of theories that account for how structures respond to loads, i.e., how forces and deformations are related, and (b) a series of constants that differentiate within those theories how materials (e.g. steel and concrete) differ in their response.

Figure 1: World Trade Center (NYC) transportation hub.

Most engineering design today uses linear elastic principles to calculate forces and deformations in structures. In the theory of elasticity, several material constants are needed to describe the relationship between stress and strain. Stress is defined as the force per unit area while strain is defined as the change in dimension when subjected to a force divided by the original magnitude of that dimension. The two most common of these constants are the modulus of elasticity (E), which relates the stress to the strain, and Poisson's ratio (ν), which is the ratio of lateral to longitudinal strain. This experiment will introduce the typical equipment used in a construction materials laboratory to measure force (or stress) and deformation (or strain), and use them to measure E and ν of a typical aluminum bar.

Procedure

Modulus of Elasticity and Poisson's Ratio

It will be assumed herein that students have been trained in the use and safety precautions required to operate a universal testing machine.

Obtain a rectangular aluminum bar (12 in. x 1 in. x ¼ in.); an aluminum 6061 T6xxx or stronger is recommended. A hole should be drilled about 1 in. from one beam end to serve as a loading point.
Mark a location on the beam about 8.0 in. from the center of

Results

The data should be imported or transcribed into a spreadsheet for easy manipulation and graphing. The data collected is shown in Table 1.

Because the rosette strain gage is not aligned with the principal axes of the beam, the rosette strains need to be input into the equations for ε_1,2 (Eq. 9) and ε (Eq. 10) above to compute principal strains, resulting in the data shown in Table 2. The table shows that the angle between the

Application and Summary

In this experiment, two fundamental material constants were measured: the modulus of elasticity (E) and Poisson's ratio (v). This experiment demonstrates how to measure these constants in a laboratory setting using a rosette strain gage. The values obtained experimentally match well with the published values of 10,000 ksi and 0.3, respectively. These values are key in applying the theory of elasticity for engineering design, and this experimental technique described herein are typical of those used for obtai