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

18.3 Nonlinear Models 597

Again, note the slope of this model is not constant, that is, for any 5 mph change in speed,

the dependent variableSchanges by different amounts based on where in the speed range you

introduce the change.

We can describe many other engineering situations with second-order polynomials. The

trajectory of a projectile under a constant deceleration, power consumption for a resistive ele-

ment, drag force, or the air resistance to the motion of a vehicle are represented by second-

order models.

Deflection of a Beam The deflection of a cantilever beam is an example of an engineering sit-

uation where a higher-order polynomial model is used. For example, the cantilever beam shown

in Figure 18.8 is used to support a load acting on a balcony. The deflection of the centerline of

the beam is given by the following fourth-order polynomial equation.

y (18.8)

wx

2

24 EI

1 x

2

 4 L x 6 L

2

2

u u

shown: slope

change in stopping distance S

change in speed V



1472  1212

110  52

508  436

55  50

u u

Stopping Sight Distance (ft)

1000

900

800

700

600

500

400

300

200

100

0

0.0 20.0 40.0 60.0 80.0 100.0 120.0

Speed (ft/s)

Speed Speed Stopping Sight

(mph) (ft /s) Distance (ft)

0 0.0 0

5 7.3 21

10 14.7 47

15 22.0 78

20 29.3 114

25 36.7 155

30 44.0 201

35 51.3 252

40 58.7 309

45 66.0 370

50 73.3 436

55 80.7 508

60 88.0 584

65 95.3 666

70 102.7 753

75 110.0 844

80 117.3 941

■Figure 18.7 The stopping sight distance for a car traveling speeds of up to 80 mph.

26 72

5 mph (7.4 ft /s) 5 mph (7.4 ft /s)

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