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

6.20. On a summer day in Phoenix, Arizona, the inside room

temperature is maintained at 68F while the outdoor

air temperature is a sizzling 110F. What is the out-

door – indoor temperature difference in: (a) degrees

Fahrenheit, (b) degrees Rankine, (c) degrees Celsius,

and (d) Kelvin? Is one degree temperature difference

in Celsius equal to one temperature difference in Kel-

vin, and is one degree temperature difference in

Fahrenheit equal to one degree temperature difference

in Rankine? If so, why?

6.21. A cantilever beam shown in the accompanying figure is

used to support a load acting on a balcony. The

deflection of the centerline of the beam is given by the

following equation:

where

ydeflection at a givenxlocation, ( m)

wdistributed load

Emodulus of elasticity (N/m

2

)

Isecond moment of area ( m

4

)

xdistance from the support as shown ( m)

Llength of the beam ( m)

What is the appropriate unit forw, if the preceding

equation is to be homogeneous in units? Show all steps

of your work.

6.22. A model known asstopping sight distanceis used by

civil engineers to design roadways. This simple

model estimates the distance a driver needs in order

to stop his car while traveling at a certain speed after

detecting a hazard. The model proposed by the

y

wx

2

24 EI

1 x

2

 4 Lx 6 L

2

2

American Association of State Highway Officials

(AASHO) is given by

where

Sstopping sight distance (ft)

Vinitial speed (ft /s)

gacceleration due to gravity, 32.2 ft /s

2

fcoefficient of friction between tires and

roadway

Ggrade of road

Tdriver reaction time (s)

What are the appropriate units forfandGif the pre-

ceding equation is to be homogeneous in units? Show

all steps of your work.

6.23. In an annealing process — a process wherein materials

such as glass and metal are heated to high temperatures

and then cooled slowly to toughen them — the follow-

ing equation may be used to determine the tempera-

ture of a thin piece of material after some time t.

where

Ttemperature (C)

hheat transfer coefficient

rdensity (kg /m

3

)

cspecific heat ( J/ kgK)

Lplate thickness ( m)

ttime (s)

TTenvironment

TinitialTenvironment

expa

2 h

rcL

tb

S

V

2

2 g 1 f G 2

TV

Problems 155

w

L

x

Problem 6.21

A cantilever beam.

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