10.6 Modulus of Elasticity, Modulus of Rigidity, and Bulk Modulus of Compressibility 285
Note that the physical variables involved include the fundamental base dimensions length and
area from Chapter 7 and the physical variable force from this chapter. Note also from Equa-
tion (10.26) that the modulus of elasticity,E, is inversely proportional to elongationx; the more
the material stretches, the smaller the value ofE. Values of the modulus of elasticityEfor selected
materials are shown in Table 10.5.
Another important mechanical property of material is the modulus of rigidityor shear mod-
ulus. The modulus of rigidity is a measure of how easily a material can be twisted or sheared. The
value of the modulus of rigidity shows the resistance of a given material to shear deformation.
Engineers consider the value of shear modulus when selecting materials for shafts or rods that are
subjected to twisting torques. For example, the modulus of rigidity or shear modulus for alumi-
num alloys is in the range of 26 to 36 GPa, whereas the shear modulus for steel is in the range of
75 to 80 GPa. Therefore, steel is approximately three times more rigid in shear when compared
to aluminum. The shear modulus is measured using a torsional test machine. A cylindrical spec-
imen of known dimensions is twisted with a known torque. The angle of twist is measured and
is used to determine the value of the shear modulus (see Example 10.14). The values of shear
modulus for various solid materials are given in Table 10.5.TABLE 10.5 Modulus of Elasticity and Shear Modulus of Selected Materials
Modulus of Shear
Material Elasticity (GPa) Modulus (GPa)Aluminum alloys 70 –79 26 – 30
Brass 96 –110 36 – 41
Bronze 96 –120 36 – 44
Cast iron 83 –170 32 – 69
Concrete (compression) 17– 31
Copper alloys 110 –120 40 – 47
Glass 48 – 83 19 – 35
Magnesium alloys 41– 45 15 –17
Nickel 210 80
Plastics
Nylon 2.1– 3.4
Polyethylene 0.7–1.4
Rock (compression)
Granite, marble, quartz 40 –100
Limestone, sandstone 20 –70
Rubber 0.0007– 0.004 0.0002 – 0.001
Steel 190 – 210 75 – 80
Titanium alloys 100 –120 39 – 44
Tungsten 340 – 380 140 –160
Wood (bending)
Douglas fir 11–13
Oak 11–12
Southern pine 11–14Source:From Gere. Mechanics of Materials, 5E. © 2001 Cengage Learning, a part of Cengage Learning, Inc.
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