will shorten when pushed (subject to a compressive force). The larger the value of the
modulus of elasticity is, the larger the required force would be to stretch or shorten the
material. For example, the modulus of elasticity of aluminum alloy is in the range of 70
to 79 GPa (giga Pascal, giga 10
9
), whereas steel has a modulus of elasticity in the range
of 190 to 210 GPa; therefore, steel is approximately three times stiffer than aluminum
alloys.
Modulus of Rigidity (Shear Modulus)—Modulus of rigidity is a measure of how easily a
material can be twisted or sheared. The value of the modulus of rigidity, also called shear
modulus, shows the resistance of a given material to shear deformation. Engineers con-
sider the value of shear modulus when selecting materials for shafts, which are rods that are
subjected to twisting torques. For example, the modulus of rigidity or shear modulus for
aluminum 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
than aluminum is.
Tensile Strength— The tensile strength of a piece of material is determined by measuring the
maximum tensile load a material specimen in the shape of a rectangular bar or cylinder can
carry without failure. The tensile strength or ultimate strength of a material is expressed as
the maximum tensile force per unit cross-sectional area of the specimen. When a material
specimen is tested for its strength, the applied tensile load is increased slowly. In the very
beginning of the test, the material will deform elastically, meaning that if the load is
removed, the material will return to its original size and shape without any permanent
deformation. The point to which the material exhibits this elastic behavior is called the
yield point. The yield strength represents the maximum load that the material can carry
without any permanent deformation. In certain engineering design applications, the yield
strength is used as the tensile strength.
Compression Strength— Some materials are stronger in compression than they are in ten-
sion; concrete is a good example. The compression strength of a piece of material is deter-
mined by measuring the maximum compressive load a material specimen in the shape of
rectangular bar, cylinder, or cube can carry without failure. The ultimate compressive
strength of a material is expressed as the maximum compressive force per unit cross-sec-
tional area of the specimen. Concrete has a compressive strength in the range of 10 to
70 MPa ( mega Pascal, mega 10
6
).
Modulus of Resilience—Modulus of resilience is a mechanical property of a material that
shows how effective the material is in absorbing mechanical energy without going through
any permanent damage.
Modulus of Toughness—Modulus of toughness is a mechanical property of a material that
indicates the ability of the material to handle overloading before it fractures.
Strength-to-Weight Ratio—As the term implies, it is the ratio of strength of the material
to its specific weight (weight of the material per unit volume). Based on the application,
engineers use either the yield or the ultimate strength of the material when determining the
strength-to-weight ratio of a material.
Thermal Expansion— The coefficient of linear expansion can be used to determine the change
in the length (per original length) of a material that would occur if the temperature of the
material were changed. This is an important material property to consider when designing58 Chapter 3 Introduction to Engineering Design
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