CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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PROBLEMS # 4-SOLUTION

Topics Equilibrium of a rigid body (Chapter 5 in textbook).

Textbook: Engineering Mechanics, by R.C. Hibbeler, Pearson, 12th Edition.

•5–88. Determine the horizontal and vertical components of reaction at pin A and force in the

cable BC. Neglect the thickness of the members.

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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*5–64. The pole for a power line is subjected to the two cable forces of 60 lb, each force

lying in a plane parallel to the plane. If the tension in the guy wire AB is 80 lb,

determine the x, y, z components of reaction at the fixed base of the pole, O.

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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5–91. Determine the normal reaction at the roller A and horizontal and vertical components at pin

B for equilibrium of the member.

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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*5–72. Determine the components of reaction acting at the smooth journal bearings A, B, C.

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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5–74. If the load has a weight of 200 lb, determine the x, y, z components of reaction at the

ball-and-socket joint A (pin) and the tension in each of the wires.

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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Vector Approach:

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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0xF 0xA …….Eq.1

05

40

CDyy FAF

……Eq.2

02005

30

EFCDBDzz FFFAF

……Eq.3

0)4()4(5

3)2(2000

EFCDx FFM

……Eq.4

0)4(200)2()4(5

3)4(0

EFCDBDy FFFM

…..Eq.5

50 lb

Scalar Approach:

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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0)4(5

40

CDz FM

…..Eq.6

01. xAEq

06. CDFEq

02. yAEq

NFEq EF 1004.

NFEq BD 1505.

NAEq z 503.

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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*5–76. The member is supported by a pin at A and a cable BC. If the load at D is 300 lb,

determine the x, y, z components of reaction at the support A (fixed, but it allows rotation around

x) and the tension in cable B C.

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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5-69.The shaft is supported by three smooth journal bearings at A, B, and C. Determine the

components of reaction at these bearings.

Hint: A and B allow translation along y-direction, and C allows translation along x-

direction.

Free-body Diagram

CIE200-Statics Equilibrium of a Rigid Body F.El Meski, PhD, PE

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