978-0073380292 Chapter 3 Part 7

Statics 2e 383

Part (b)

With the values

WD300 lb

,

kD25 lb=in:

, and

rD20 in:

given in the problem statement,

Eq. (8) contains one unknown, namely

d

. Two strategies for determining the value of

d

that satisfies Eq. (8)

are described.

Problem 3.93

In the cable system shown, point

D

lies in the

y´

plane and force

P

is parallel

to the

´

axis. If

PD500 lb

, determine the force in cables

AB

,

AC

,

AD

, and

AE.

Problem 3.94

In the cable system shown, point

D

lies in the

y´

plane and force

P

is parallel

to the

´

axis. If cables

AB

and

AC

have

500 lb

breaking strength, and cables

AD

and

AE

have

1000 lb

breaking strength, and if all cables are to have a

factor of safety of

1:5

against failure, determine the largest force

P

that may be

supported.

D3

815

12PD15

32P;

(7)

FAC D15

(14)

Only the smallest of the above values of

P

will satisfy all four failure criteria. Hence, the largest value

P

Problem 3.95

Repeat Prob. 3.93 with point Ahaving coordinates A.1; 8; 0/ ft.

Problem 3.96

Repeat Prob. 3.94 with point Ahaving coordinates A.1; 8; 0/ ft.

(11)

Only the smallest of the above values of

P

will satisfy all four failure criteria. Hence, the largest value

P

Problem 3.97

Force

P

is supported by two cables and a bar. Point

A

lies in the

y´

plane,

and points

B

and

C

lie in the

x´

plane. If

PD3kip

, determine the forces

supported by the cables and bar.

Problem 3.98

Force

P

is supported by two cables and a bar. Point

A

lies in the

y´

plane, and

points

B

and

C

lie in the

x´

plane. The compressive load that causes the bar to

buckle and the breaking strength of each cable are specified below. If factors of

safety against failure (see the footnote of Prob. 3.94) of

1:7

and

2:0

are to be

used for cables and bars, respectively, determine the allowable force

P

that can

be supported.

Member Strength

AO 3000 lb compression

AB 6000 lb

AC 5000 lb

Problem 3.99

A photograph of the NASA Apollo 16 Lunar Module

(abbreviated by NASA as the LM) is shown on the

surface of the Moon. Such spacecraft made six

Moon landings during 1969–72. A simplified model

for one of the four landing gear assemblies of the LM

is shown. If the LM has

15;000 kg

mass, and rests on

the surface of the Moon where acceleration due to

gravity is

1:62 m=s2

, determine the force supported

by members

AB

,

AC

, and

AD

. Assume the weight

of the LM is uniformly supported by all four landing

gear assemblies, and neglect friction between the

landing gear and the surface of the Moon.

4.15;000 kg/1:62 m

s2D6075 N:(4)

Vector expressions for the forces are

E

TAB DTAB ErAB

rAB DTAB 1O{1O|C2:2 O

k

2:615 ;(5)

k

Problem 3.100

When in equilibrium, plate

ACDE

is horizontal. The plate weighs

1200 lb

and

is supported by cables

ABC

,

BD

,

BE

, and

BH

. As shown, cable

ABC

wraps

around ring

B

, which has negligible friction. If the coordinates of point

B

are

B .40; 20; 80/ in.

, determine the forces in the four cables. Remark: The system

of equations can be solved manually, but solution by calculator or computer is

recommended.

Solution

B

A

x

z

C

D

E

y

TBH

TBD

TAB

TBC TBE

The FBD for point

B

is shown where all cable forces are positive in

tension. By inspection (or by drawing a FBD of the entire system and

enforcing equilibrium of forces in the vertical direction),

TBH D1200 lb:(1)

Using the geometry provided in the problem statement, the following

position vectors may be written

ErBA D.50 O{C20 O|80 O

k/ in:; (2)

ErBC D.20 O{20 O|80 O

k/ in:; (3)

ErBD D.40 O{20 O|80 O

k/ in:; (4)

ErBE D.40 O{C20 O|80 O

k/ in:(5)

Vector expressions for the forces are

E

TBA DTAB ErBA

rBA DTAB

50 O{C20 O|80 O

k

96:44 ;(6)

E

TBC DTAB ErBC

rBC DTAB

20 O{20 O|80 O

k

84:85 ;(7)

E

TBD DTBD ErBD

rBD DTBD 40 O{20 O|80 O

k

91:65 ;(8)

E

TBE DTBE ErBE

rBE DTBE 40 O{C20 O|80 O

k

91:65 ;(9)

E

TBH D1200 lb O

k: (10)

Note that in writing Eqs. (6) and (7) that the magnitudes of the two forces are the same, namely

TAB

. The

equilibrium equations are

Problem 3.101

Member

OA

buckles when the compressive force it supports reaches

400

N.

Cables

AC

and

AD

each have

300

N breaking strength. Assuming the cabling

between

A

and

B

is sufficiently strong, determine the force

T

that will cause

the structure to fail. Assume the pulleys are frictionless with diameters that are

small enough so that all cables between Aand Bare parallel to line AB.

Problem 3.102

A portable tripod hoist for moving objects into and out of a manhole is shown.

The hoist consists of identical-length bars

AB

,

AC

, and

AD

that are connected

by a socket at

A

and are supported by equal

8ft

length cables

BC

,

BD

, and

CD

to prevent ends

B

,

C

, and

D

of the bars from slipping. Cable FAE passes

around a frictionless pulley at

A

and terminates at winch

E

, which is fixed to

bar

AB

. Idealize points

A

and

E

to be particles where all bar and cable forces

pass through these points. If the tripod is erected on level ground and is

7ft

high, and the object being lifted in the manhole weighs 300 lb,

(a)

Determine the forces in bars

AC

and

AD

and in portion

AE

of bar

AB

.

(b) Determine the force in portion EB of bar AB.

Hint: Define an

xy´

coordinate system where the

x

and

y

directions

lie in the plane defined by points B,C, and

D

, and where the

x

or

y

direction coincides with one of cables

BC

,

BD

, or

CD

. Then de-

termine the coordinates of points

B

,

C

, and

D

. The

x

and

y

coordi-

nates of point

A

are then the averages of the coordinates of points

B

,

C

,

and D.

Problem 3.103

A worker standing on a truck uses rope

AB

to slowly lower object

B

down a

chute. The object weighs

100 lb

and fits loosely against the walls of the chute

and slides with no friction. In the position shown, the center of object

B

is

halfway down the chute. The person’s hand

A

lies in the

xy

plane, and the

chute lies in a plane parallel to the y´ plane.

(a)

Determine the tension in rope

AB

and the reactions between the object

and the chute.

(b)

If the worker wishes to slowly pull the object up the chute, explain how

your answers to Part (a) change.

Problem 3.104

Due to a poorly designed foundation, the statue at point

A

slowly slides

down a grass-covered slope. To prevent further slip, a cable is attached

from the statue to point

B

, and another cable is attached from the

statue to point

C

. The statue weighs

1000 lb

, and idealize the surface

on which the statue rests to be frictionless. Determine the minimum

tensile strength each cable must have, and the magnitude of the reaction

between the statue and the slope.

Problem 3.105

Channel

AB

is fixed in space, and its centerline lies in the

xy

plane. The plane

containing edges

AC

and

AD

of the channel is parallel to the

x´

plane. If the

surfaces of the channel are frictionless and the sphere

E

has

2kg

mass, determine

the force supported by cord

EF

, and the reactions

RC

and

RD

between the

sphere and sides Cand D, respectively, of the channel.