# Get questions and answers for Civil Engineering

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Determine the force in each cable used to lift the surge arrester of mass M at constant velocity.
Units Used:
kN = 103 N
Mg = 103 kg

Given:
M = 9.50 Mg
a = 2 m
b = 0.5 m
θ = 45 deg

The cylinder of weight W is supported by three chains as shown. Determine the force in each chain for equilibrium.
Given:
W = 800 lb
r = 1 ft
d = 1 ft

The triangular frame ABC can be adjusted vertically between the three equal-length cords. If it remains in a horizontal plane, determine the required distance s so that the tension in each of the cords, OA, OB, and OC, equals F. The lamp has a mass M.
Given:
F = 20 N
M = 5 kg
g = 9.81 m/s2
d = 0.5 m

Determine the force in each cable needed to support the platform of weight W.

Units Used:

kip = 103 lb

Given:

W = 3500 lb d = 4 ft

a = 2 ft e = 3 ft

b = 4 ft f = 3 ft

c = 4 ft g = 10 ft

A flowerpot of mass M is supported at A by the three cords. Determine the force acting in each cord for equilibrium.

Given:
M = 25 kg
g = 9.81m/s2
θ1 = 30 deg
θ2 = 30 deg
θ3 = 60 deg
θ4 = 45 deg

If each cord can sustain a maximum tension of T before it fails, determine the greatest weight of the flowerpot the cords can support.

Given:
T = 50 N
θ1 = 30 deg
θ2 = 30 deg
θ3 = 60 deg
θ4 = 45 deg

The pipe is held in place by the vice. If the bolt exerts force P on the pipe in the direction shown determine the forces FA and FB that the smooth contacts at A and B exert on the pipe.

Given:
P = 50 lb
θ = 30 deg
c = 3
d = 4

When y is zero, the springs sustain force F0. Determine the magnitude of the applied vertical forces F and -F required to pull point A away from point B a distance y1. The ends of cords CAD and CBD are attached to rings at C and D.

Given:

F0 = 60 lb

k = 40 lb/ft

d = 2 ft

y1 = 2 ft

When y is zero, the springs are each stretched a distance δ. Determine the distance y if a force F is applied to points A and B as shown. The ends of cords CAD and CBD are attached to rings at C and D.

Given:
δ = 1.5 ft
k = 40 lb/ft
d = 2 ft
F = 60 lb

Cord AB of length a is attached to the end B of a spring having an unstretched length b. The other end of the spring is attached to a roller C so that the spring remains horizontal as it stretches. If a weight W is suspended from B, determine the angle θ of cord AB for equilibrium.

Given:
a = 5 ft
b = 5 ft
k = 10 lb/ft
W = 10 lb

The uniform crate of mass M is suspended by using a cord of length l that is attached to the sides of the crate and passes over the small pulley at O. If the cord can be attached at either points A and B, or C and D, determine which attachment produces the least amount of tension in the cord and specify the cord tension in this case.
Given:
M = 50 kg
g = 9.81 m/s2
a = 0.6 m
b = 1.5 m
l = 2 m
c = a/2
d = b/2

The man attempts to pull the log at C by using the three ropes. Determines the direction θ in which he should pull on his rope with a force P, so that he exerts a maximum force on the log. What is the force on the log for this case? Also, determine the direction in which he should pull in order to maximize the force in the rope attached to B. What is this maximum force?

Given:
P = 80 lb
φ = 150 deg

The "scale" consists of a known weight W which is suspended at A from a cord of total length L. Determine the weight w at B if A is at a distance y for equilibrium. Neglect the sizes and weights of the pulleys.

Determine the maximum weight W that can be supported in the position shown if each cable AC and AB can support a maximum tension of F before it fails.

Given:
θ = 30 deg
F = 600 lb c = 12 d = 5

If the spring on rope OB has been stretched a distance δ. and fixed in place as shown, determine the tension developed in each of the other three ropes in order to hold the weight W in equilibrium Rope OD lies in the x-y plane.

Given:
a = 2 ft
b = 4 ft
c = 3 ft
d = 4 ft
e = 4 ft
f = 4 ft
xB = −2 ft
yB = −3 ft
zB = 3 ft
θ = 30 deg
k = 20 lb/in
δ = 2 in
W = 225 lb

The joint of a space frame is subjected to four member forces. Member OA lies in the x - y plane and member OB lies in the y - z plane. Determine the forces acting in each of the members required for equilibrium of the joint.

Given:
F4 = 200 lb
θ = 40 deg
φ = 45 deg

If A, B, and D are given vectors, prove the distributive law for the vector cross product, i.e. A × (B+D) = (A×B) + (A×D).
Prove the triple scalar product identity A⋅ (B × C) = (A × B) ⋅C.
Given the three nonzero vectors A, B, and C, show that if A⋅ (B×C) = 0, the three vectors must lie in the same plane.
Determine the magnitude and directional sense of the resultant moment of the forces at A and B about point O.

Given:
F1 = 40 lb
F2 = 60 lb
θ1 = 30 deg
θ2 = 45 deg
a = 5 in
b = 13 in
c = 3 in
d = 6 in
e = 3 in
f = 6 in

Determine the magnitude and directional sense of the resultant moment of the forces at A and B about point P. Units Used: kip = 1000 lb

Given:
F1 = 40 lb b = 13 in
F2 = 60 lb c = 3 in
θ1 = 30 deg d = 6 in
θ2 = 45 deg e = 3 in
a = 5 in f = 6 in

Determine the magnitude of the force F that should be applied at the end of the lever such that this force creates a clockwise moment M about point O.

Given:
M = 15 Nm
φ = 60 deg
θ = 30 deg
a = 50 mm
b = 300 mm

Determine the angle θ (0
Given:
F = 100 N φ = 60 deg
M 20 = N ∙ m a = 50 mm
θ = 30 deg b = 300 mm

Determine the magnitude and directional sense of the moment of the forces about point O.
Units Used:
kN = 103 N

Given:
FB = 260 N e = 2 m
a = 4 m f = 12
b = 3 m g = 5
c = 5 m θ = 30 deg
d = 2 m FA = 400 N

Determine the magnitude and directional sense of the moment of the forces about point P.
Units Used:
kN = 103 N

Given:
FB = 260 N e = 2 m
a = 4 m f = 12
b = 3 m g = 5
c = 5 m θ = 30 deg
d = 2 m
FA = 400 N

A force F is applied to the wrench. Determine the moment of this force about point O. Solve the problem using both a scalar analysis and a vector analysis.

Given:
F = 40 N
θ = 20 deg
a = 30 mm
b = 200 mm

Determine the magnitude and directional sense of the resultant moment of the forces about point O. Units Used: kip = 103 lb

Given:
F1 = 300 lb e = 10 ft
F2 = 250 lb f = 4
a = 6 ft g = 3
b = 3 ft θ = 30 deg
c = 4 ft φ = 30 deg
d = 4 ft

To correct a birth defect, the tibia of the leg is straightened using three wires that are attached through holes made in the bone and then to an external brace that is worn by the patient. Determine the moment of each wire force about joint A.

Given:
F1 = 4 N d = 0.15 m
F2 = 8 N e = 20 mm
F3 = 6 N f = 35 mm
a = 0.2 m g = 15 mm
b = 0.35 m θ 1 = 30 deg
c = 0.25 m θ 2 = 15 deg

To correct a birth defect, the tibia of the leg is straightened using three wires that are attached through holes made in the bone and then to an external brace that is worn by the patient. Determine the moment of each wire force about joint B.

Given:
F1 = 4 N d = 0.15 m
F2 = 8 N e = 20 mm
F3 = 6 N f = 35 mm
a = 0.2 m g = 15 mm
b = 0.35 m θ 1 = 30 deg
c = 0.25 m θ 2 = 15 deg

Determine the moment of each force about the bolt located at A.

Given:
FB = 40 lb a = 2.5 ft α = 20 deg γ = 30 deg
FC = 50 lb b = 0.75 ft β = 25 deg

Determine the resultant moment about the bolt located at A.

Given:
FB = 30 lb
FC = 45 lb
a = 2.5 ft
b = 0.75 ft
α = 20 deg
β = 25 deg
γ = 30 deg

The elbow joint is flexed using the biceps brachii muscle, which remains essentially vertical as the arm moves in the vertical plane. If this muscle is located a distance a from the pivot point A on the humerus, determine the variation of the moment capacity about A if the constant force developed by the muscle is F. Plot these results of M vs. θ for −60 ≤ θ ≤ 80.
Units Used:
kN = 103 N

Given:
a = 16 mm
F = 2.30 kN
θ = (−60 ... 80)

The Snorkel Co. produces the articulating boom platform that can support weight W. If the boom is in the position shown, determine the moment of this force about points A, B, and C.
Units Used:
kip = 103lb

Given:
a = 3 ft
b = 16 ft
c = 15 ft
θ1 = 30 deg
θ2 = 70 deg
W = 550 lb

Determine the direction θ (0Â° ≤ θ ≤ 180Â°) of the force F so that it produces
(a) The maximum moment about point A and
(b) The minimum moment about point A. compute the moment in each case.

Given:
F = 40 lb
a = 8 ft
b = 2 ft

The rod on the power control mechanism for a business jet is subjected to force F. Determine the moment of this force about the bearing at A.
Given:
F = 80 N θ 1 = 20 deg
a = 150 mm θ 2 = 60 deg

The boom has length L, weight Wb, and mass center at G. If the maximum moment that can be developed by the motor at A is M, determine the maximum load W, having a mass center at G', that can be lifted.

Given:
L = 30 ft
Wb = 800 lb
a = 14 ft
b = 2 ft
θ = 30 deg
M = 20 Ã— 103 lb⋅ ft

The tool at A is used to hold a power lawnmower blade stationary while the nut is being loosened with the wrench. If a force P is applied to the wrench at B in the direction shown, determine the moment it creates about the nut at C. What is the magnitude of force F at A so that it creates the opposite moment about C?

Given:
P = 50 N b = 300 mm
θ = 60 deg c = 5
a = 400 mm d = 12

Determine the clockwise direction θ (0 deg ≤ θ ≤ 180 deg) of the force F so that it produces
(a) The maximum moment about point A and
(b) No moment about point A compute the moment in each case.

Given:
F = 80 lb
a = 4 ft
b = 1 ft

The Y-type structure is used to support the high voltage transmission cables. If the supporting cables each exert a force F on the structure at B, determine the moment of each force about point A. Also, by the principle of transmissibility, locate the forces at points C and D and determine the moments.
Units Used:
kip = 1000 lb

Given:
F = 275 lb
a = 85 ft
θ = 30 de

The force F acts on the end of the pipe at B. Determine

(a) The moment of this force about point A, and

(b) The magnitude and direction of a horizontal force, applied at C, which produces the same moment.

Given:

F = 70 N

a = 0.9 m

b = 0.3 m

c = 0.7 m

θ = 60 deg

The force F acts on the end of the pipe at B. Determine the angles θ (0Â° ≤ θ ≤ 180Â°) of the force that will produce maximum and minimum moments about point A.
What are the magnitudes of these moments?
Given:
F = 70 N
a = 0.9 m
b = 0.3 m
c = 0.7 m

The towline exerts force P at the end of the crane boom of length L. Determine the placement x of the hook at A so that this force creates a maximum moment about point O. What is this moment?
Unit Used:
kN = 103 N

Given:
P = 4 kN
L = 20 m
θ = 30 deg
a = 1.5 m

The towline exerts force P at the end of the crane boom of length L. Determine the position θ of the boom so that this force creates a maximum moment about point O. What is this moment?
Units Used:
kN = 103 N

Given:
P = 4 kN
x = 25 m
L = 20 m
a = 1.5 m

Determine the resultant moment of the forces about point A. Solve the problem first by considering each force as a whole, and then by using the principle of moments.
Units Used:
kN = 103 N

Given:
F1 = 250 N a = 2 m
F2 = 300 N b = 3 m
F3 = 500 N c = 4 m
θ1 = 60 deg d = 3
θ2 = 30 deg e = 4

If the resultant moment about point A is M clockwise, determine the magnitude of F3.
Units Used:
kN = 103 N

Given:
M = 4.8 kN⋅ m a = 2 m
F1 = 300 N b = 3 m
F2 = 400 N c = 4 m
θ1 = 60 deg d = 3
θ2 = 30 deg e = 4

The flat-belt tensioner is manufactured by the Daton Co. and is used with V-belt drives on poultry and livestock fans. If the tension in the belt is F, when the pulley is not turning, determine the moment of each of these forces about the pin at A.

Given:
F = 52 lb
a = 8 in
b = 5 in
c = 6 in
θ1 = 30 deg
θ2 = 20 deg

The worker is using the bar to pull two pipes together in order to complete the connection. If he applies a horizontal force F to the handle of the lever, determine the moment of this force about the end A. What would be the tension T in the cable needed to cause the opposite moment about point A.

Given:
F = 80 lb θ 1 = 40 deg θ 2 = 20 deg a = 0.5 ft b = 4.5 ft

If it takes a force F to pull the nail out, determine the smallest vertical force P that must be applied to the handle of the crowbar. Hint: This requires the moment of F about point A to be equal to the moment of P about A. Why?

Given:
F = 125 lb
a = 14 in
b = 3 in
c = 1.5 in
θ1 = 20 deg
θ2 = 60 deg

The pipe wrench is activated by pulling on the cable segment with a horizontal force F. Determine the moment MA produced by the wrench on the pipe at θ. Neglect the size of the pulley.

Given:
F = 500 N
a = 0.2 m
b = 0.5 m
c = 0.4 m
θ = 20 deg

Determine the moment of the force at A about point O. Express the result as a Cartesian vector.

Given:
F = (60 -30 -20) N
a = 4 m d = 4 m
b = 7 m e = 6 m
c = 3 m f = 2 m

Determine the moment of the force at A about point P. Express the result as a Cartesian vector.

Given:
a = 4 m b = 7 m c = 3 m d = 4 m e = 6 m f = 2 m
F = (60 -30 -20) N

Determine the moment of the force F at A about point O. Express the result as a Cartesian vector.
Units Used:
kN = 103 N
Given:
F = 13 kN
a = 6 m
b = 2.5 m
c = 3 m
d = 3 m
e = 8 m
f = 6 m
g = 4 m
h = 8 m

Determine the moment of the force F at A about point P. Express the result as a Cartesian vector.
Units Used: kN = 103 N
Given:
F = 13 kN
a = 6 m
b = 2.5 m
c = 3 m
d = 3 m
e = 8 m
f = 6 m
g = 4 m
h = 8 m

The curved rod lies in the x-y plane and has radius r. If a force F acts at its end as shown, determine the moment of this force about point O.

Given:
r = 3 m a = 1 m θ = 45 deg
F = 80 N b = 2 m

The curved rod lies in the x-y plane and has a radius r. If a force F acts at its end as shown, determine the moment of this force about point B.

Given:
F = 80 N c = 3 m
a = 1 m r = 3 m
b = 2 m θ = 45 deg

The force F acts at the end of the beam. Determine the moment of the force about point A. Given:
F = (600 300 -600) N
a = 1.2 m
b = 0.2 m
c = 0.4 m

The pole supports a traffic light of weight W. Using Cartesian vectors; determine the moment of the weight of the traffic light about the base of the pole at A.

Given:
W = 22 lb a = 12 ft θ = 30 deg

The man pulls on the rope with a force F. Determine the moment that this force exerts about the base of the pole at O. Solve the problem two ways, i.e., by using a position vector from O to A, then O to B.

Given:
F = 20 N
a = 3 m
b = 4 m
c = 1.5 m
d = 10.5 m

Determine the smallest force F that must be applied along the rope in order to cause the curved rod, which has radius r, to fail at the support C. This requires a moment to be developed at C of magnitude M.

Given:
r = 5 ft
M = 80 lb⋅ ft
θ = 60 deg
a = 7 ft
b = 6 ft

The pipe assembly is subjected to the force F. Determine the moment of this force about point A.

Given:
F = 80 N
a = 400 mm
b = 300 mm
c = 200 mm
d = 250 mm
θ = 40 deg
φ = 30 deg

The pipe assembly is subjected to the force F. Determine the moment of this force about point B.

Given:
F = 80 N
a = 400 mm
b = 300 mm
c = 200 mm
d = 250 mm
θ = 40 deg
φ = 30 deg

The x-ray machine is used for medical diagnosis. If the camera and housing at C have mass M and a mass center at G, determine the moment of its weight about point O when it is in the position shown.
Units Used:
kN = 103 N

Given:
M = 150 kg
a = 1.2 m
b = 1.5 m
θ = 60 deg
g 9.81 m/s2

Using Cartesian vector analysis, determine the resultant moment of the three forces about the base of the column at A.
Units Used:
kN = 103 N
F1 = (400 300 120) N
F2 = (100 -100 -60) N
F3 = (0 0 -500) N
a = 4 m
b = 8 m
c = 1 m

A force F produces a moment MO about the origin of coordinates, point O. If the force acts at a point having the given x coordinate, determine the y and z coordinates.
Units Used: kN = 103 N

Given:
F = (6 -2 1) kN
MO = (4 5 -14) kN ∙ m
x = 1 m

The force F creates a moment about point O of MO. If the force passes through a point having the given x coordinate, determine the y and z coordinates of the point. Also, realizing that MO = Fd, determine the perpendicular distance d from point O to the line of action of F.

Given:
F = (6 8 10) N
MO = (-14 8 2) N ∙ m
x = 1 m

The force F produces a moment MO about the origin of coordinates, point O. If the force acts at a point having the given x-coordinate, determine the y and z coordinates.
Units Used:
kN = 103 N
Given:
x = 1 m

Determine the moment of the force F about the Oa axis. Express the result as a Cartesian vector.
Given:
F = (50 -20 20) N
a = 6 m
b = 2 m
c = 1 m
d = 3 m
e = 4 m

Determine the moment of the force F about the aa axis. Express the result as a Cartesian vector.
Given:
F = 600 lb
a = 6 ft
b = 3 ft
c = 2 ft
d = 4 ft
e = 4 ft
f = 2 ft

Determine the resultant moment of the two forces about the Oa axis. Express the result as a Cartesian vector.

Given:
F1 = 80 lb
F2 = 50 lb
α = 120 deg
β = 60 deg
γ = 45 deg
a = 5 ft
b = 4 ft
c = 6 ft
θ = 30 deg
φ = 30 deg

The force F is applied to the handle of the box wrench. Determine the component of the moment of this force about the z axis which is effective in loosening the bolt.
Given:
a = 3 in
b = 8 in
c = 2 in
F = (8 -1 1) lb

The force F acts on the gear in the direction shown. Determine the moment of this force about the y axis.

Given:
F = 50 lb
a = 3 in
θ1 = 60 deg
θ2 = 45 deg
θ3 = 120 deg

The Roller Ball skate is an in-line tandem skate that uses two large spherical wheels on each skate, rather than traditional wafer-shape wheels. During skating the two forces acting on the wheel of one skate consist of a normal force F2 and a friction force F1. Determine the moment of both of these forces about the axle AB of the wheel.

Given:
θ = 30 deg
F1 = 13 lb
F2 = 78 lb
a = 1.25 in

The cutting tool on the lathe exerts a force F on the shaft in the direction shown. Determine the moment of this force about the y axis of the shaft.
Units Used:
kN = 103 N

Given:
F = (6 -4 -7)kN
a = 30 mm
θ = 40 deg

The hood of the automobile is supported by the strut AB, which exerts a force F on the hood. Determine the moment of this force about the hinged axis y.
Given:
F = 24 lb a = 2 ft b = 4 ft c = 2 ft d = 4 ft

The lug nut on the wheel of the automobile is to be removed using the wrench and applying the vertical force F at A. Determine if this force is adequate, provided a torque M about the x axis is initially required to turn the nut. If the force F can be applied at A in any other direction, will it be possible to turn the nut?

Given:
F = 30 N
M = 14 N ∙ m
a = 0.25 m
b = 0.3 m
c = 0.5 m
d = 0.1 m

The lug nut on the wheel of the automobile is to be removed using the wrench and applying the vertical force F. Assume that the cheater pipe AB is slipped over the handle of the wrench and the F force can be applied at any point and in any direction on the assembly. Determine if this force is adequate, provided a torque M about the x axis is initially required to turn the nut.

Given:
F1 = 30 N M = 14 N ∙ m a = 0.25 m b = 0.3 m c = 0.5 m d = 0.1 m

The bevel gear is subjected to the force F which is caused from contact with another gear. Determine the moment of this force about the y axis of the gear shaft.
Given:
a = 30 mm
b = 40 mm
F = (20 8 -15) N

The wooden shaft is held in a lathe. The cutting tool exerts force F on the shaft in the direction shown. Determine the moment of this force about the x axis of the shaft. Express the result as a Cartesian vector. The distance OA is a.

Given:

a = 25 mm

θ = 30 deg

F = (–5 – 3      8) N

Determine the magnitude of the moment of the force F about the base line CA of the tripod.
Given:
F = (50 -20 -80) N
a = 4 m
b = 2.5 m
c = 1 m
d = 0.5 m
e = 2 m
f = 1.5 m
g = 2 m

The flex-headed ratchet wrench is subjected to force P, applied perpendicular to the handle as shown. Determine the moment or torque this imparts along the vertical axis of the bolt at A.

Given:
P = 16 lb a = 10 in
θ = 60 deg b = 0.75 in

If a torque or moment M is required to loosen the bolt at A, determine the force P that must be applied perpendicular to the handle of the flex-headed ratchet wrench.

Given:
M = 80 lb⋅ in
θ = 60 deg
a = 10 in
b = 0.75 in

The A-frame is being hoisted into an upright position by the vertical force F.
Determine the moment of this force about the y axis when the frame is in the position shown.

Given:
F = 80 lb
a = 6 ft
b = 6 ft
θ = 30 deg
φ = 15 deg

Determine the moment of each force acting on the handle of the wrench about the a axis.
Given:
F1 = (-2 4 -8) lb F2 = (3 2 -6) lb

Determine the moment of each force acting on the handle of the wrench about the z axis.

Given:
F1 = (-2 4 -8) lb F2 = (3 2 -6) lb
b = 6 in
c = 4 in
d = 3.5 in
θ = 45 deg

Determine the magnitude and sense of the couple moment.
Units Used:
kN = 103 N

Given:
F = 5 kN
θ = 30 deg
a = 0.5 m
b = 4 m
c = 2 m
d = 1 m

Determine the magnitude and sense of the couple moment. Each force has a magnitude F.
Given:
F = 65 lb
a = 2 ft
b = 1.5 ft
c = 4 ft
d = 6 ft
e = 3 ft

Determine the magnitude and sense of the couple moment.
Units Used:
kip = 103 lb
Given:
F = 150 lb
a = 8 ft
b = 6 ft
c = 8 ft
d = 6 ft
e = 6 ft
f = 8 ft

If the couple moment has magnitude M, determine the magnitude F of the couple forces.

Given:
M = 300 lb⋅ ft
a = 6 ft
b = 12 ft
c = 1 ft
d = 2 ft
e = 12 ft
f = 7 ft

A clockwise couple M is resisted by the shaft of the electric motor. Determine the magnitude of the reactive forces −R and R which act at supports A and B so that the resultant of the two couples is zero.

Given:
a = 150 mm
θ = 60 deg
M = 5 N ∙ m

The resultant couple moment created by the two couples acting on the disk is MR. Determine the magnitude of force T.
Units Used:
kip = 103 lb
Given:
MR = (0 0 10) kip-in
a = 4 in
b = 2 in
c = 3 in

Three couple moments act on the pipe assembly. Determine the magnitude of M3 and the bend angle θ so that the resultant couple moment is zero.

Given:
θ1 = 45 deg
M1 = 900 N ∙ m
M2 = 500 N ∙ m

The floor causes couple moments MA and MB on the brushes of the polishing machine. Determine the magnitude of the couple forces that must be developed by the operator on the handles so that the resultant couple moment on the polisher is zero. What is the magnitude of these forces if the brush at B suddenly stops so that MB = 0?

Given:
a = 0.3 m
MA = 40 N ∙ m
MB = 30 N ∙ m

The ends of the triangular plate are subjected to three couples. Determine the magnitude of the force F so that the resultant couple moment is M clockwise.

Given:
F1 = 600 N
F2 = 250 N
a = 1 m
θ = 40 deg
M = 400 N ∙ m

Two couples act on the beam. Determine the magnitude of F so that the resultant couple moment is M counterclockwise. Where on the beam does the resultant couple moment act?

Given:
M = 450 lb⋅ ft
P = 200 lb
a = 1.5 ft
b = 1.25 ft
c = 2 ft
θ = 30 deg

Express the moment of the couple acting on the pipe assembly in Cartesian vector form. Solve the problem
(a) Using Eq. 4-13, and
(b) Summing the moment of each force about point O.
Given:
F = (0 0 25) N
a = 300 mm
b = 150 mm
c = 400 mm
d = 200 mm
e = 200 mm

If the couple moment acting on the pipe has magnitude M, determine the magnitude F of the vertical force applied to each wrench.

Given:
M 400 = N ∙ m
a = 300 mm
b = 150 mm
c = 400 mm
d = 200 mm
e = 200 mm

Determine the resultant couple moment acting on the beam. Solve the problem two ways:
(a) Sum moments about point O; and
(b) Sum moments about point A.
Units Used:
kN = 103 N

Given:
F1 = 2 kN θ1 = 30 deg
F2 = 8 kN θ2 = 45 deg
a = 0.3 m
b = 1.5 m
c = 1.8 m

Two couples act on the beam as shown. Determine the magnitude of F so that the resultant couple moment is M counterclockwise. Where on the beam does the resultant couple act?

Given:
M = 300 lb⋅ ft
a = 4 ft
b = 1.5 ft
P = 200 lb
c = 3
d = 4

Two couples act on the frame. If the resultant couple moment is to be zero, determine the distance d between the couple forces F1.

Given:
F1 = 80 lb
F2 = 50 lb
a = 1 ft
b = 3 ft
c = 2 ft
e = 3 ft
f = 3
g = 4
θ = 30 deg

Two couples act on the frame. Determine the resultant couple moment. Compute the result by resolving each force into x and y components and
(a) Finding the moment of each couple (Eq. 4-13) and
(b) Summing the moments of all the force components about point A.

Given:
F1 = 80 lb c = 2 ft g = 4
F2 = 50 lb d = 4 ft θ = 30 deg
a = 1 ft e = 3 ft
b = 3 ft f = 3

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