Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

which someone may subject the part or the structural member, we introduce a factor of safety

(F.S.), which is defined as

(10.27)

wherePmaxis the load that can cause failure. For certain situations, it is also customary to

define the factor of safety in terms of the ratio of maximum stress that causes failure to

the allowable stresses if the applied loads are linearly related to the stresses. The factor of

safety for Example 10.13 using an alumnium alloy with a yield strength of 50 MPa is 3.1.

Example 10.14 A setup similar to the one shown in Figure 10.32 is commonly used to measure the shear mod-

ulus,G. A specimen of known lengthLand diameterDis placed in the test machine. A known

torqueTis applied to the specimen and the angle of twist fis measured. The shear modulus

is then calculated from

(10.28)

Using Equation (10.28), calculate the shear modulus for a given specimen and test results of

T3450 Nm,L20 cm,D5 cm, f0.015 rad.

G

32 TL

pD

4

f



321 3450 N#m 21 0.2 m 2

p 1 0.05 m 2

4

1 0.015 rad 2

75 GPa

G

32 TL

pD

4

f

F.S.

Pmax

Pallowable

288 Chapter 10 Force and Force-Related Parameters

Load range

indicator

Motor

Specimen

Fixed

head

Turning

head

■Figure 10.32 A setup to measure the shear modulus of a material.

Bulk Modulus of Compressibility

Most of you have pumped air into a bicycle tire at one time or another. From this and other

experiences you know that gases are more easily compressed than liquids. In engineering, to see

how compressible a fluid is, we look up the value of a bulk modulus of compressibility of the

62080_10_ch10_p251-302.qxd 5/22/10 12:32 AM Page 288

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