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The â€œspanner wrenchâ€ is subjected to the force F. The support at A can be considered a pin, and the surface of contact at B is smooth. Determine the reactions on the spanner wrench.
Given:
F = 20 lb
a = 1 in
b = 6 in

The automobile is being towed at constant velocity up the incline using the cable at C. The automobile has a mass M and center of mass at G. The tires are free to roll. Determine the reactions on both wheels at A and B and the tension in the cable at C.

Units Used:

Mg = 103 kg kN = 103 N

Given:

M = 5 Mg d = 1.50 m

a = 0.3 m e = 0.6 m

b = 0.75 m θ 1 = 20 deg

c = 1 m θ 2 = 30 deg

g = 9.81m/s2

The uniform bar has mass M and center of mass at G. The supports A, B, and C are smooth. Determine the reactions at the points of contact at A, B, and C.

Given:

M = 100 kg

a = 1.75 m

b = 1.25 m

c = 0.5 m

d = 0.2 m

θ = 30 deg

g = 9.81m/s2

The beam is pin-connected at A and rocker-supported at B. Determine the reactions at the pin A and at the roller at B. Given:

F = 500 N

M = 800 N ∙ m

a = 8 m

b = 4 m

c = 5 m

Determine the magnitude of the reactions on the beam at A and B. Neglect the thickness of the beam.

Given:

F1 = 600 N

F2 = 400 N

θ = 15 deg

a = 4 m

b = 8 m

c = 3

d = 4

Determine the reactions at the supports.

Given:

w = 250lb/ft

a = 6 ft

b = 6 ft

c = 6 ft

When holding the stone of weight W in equilibrium, the humerus H, assumed to be smooth, exerts normal forces FC and FA on the radius C and ulna A as shown. Determine these forces and the force FB that the biceps B exerts on the radius for equilibrium. The stone has a center of mass at G. Neglect the weight of the arm.

Given:

W = 5 lb

θ = 75 deg

a = 2 in

b = 0.8 in

c = 14 in

The uniform door has a weight W and a center of gravity at G. Determine the reactions at the hinges if the hinge at A supports only a horizontal reaction on the door, whereas the hinge at B exerts both horizontal and vertical reactions.

Given:

W = 100 lb

a = 3 ft

b = 3 ft

c = 0.5 ft

d = 2 ft

The ramp of a ship has weight W and center of gravity at G. Determine the cable force in CD needed to just start lifting the ramp, (i.e., so the reaction at B becomes zero). Also, determine the horizontal and vertical components of force at the hinge (pin) at A.

Given:

W = 200 lb a = 4 ft

θ = 30 deg b = 3 ft

φ = 20 deg c = 6 ft

The drainpipe of mass M is held in the tines of the fork lift. Determine the normal forces at A and B as functions of the blade angle θ and plot the results of force (ordinate) versus θ (abscissa) for 0 ≤ θ ≤ 90 deg.

Units used:

Mg = 103 kg

Given:

M = 1.4 Mg

a = 0.4 m

g = 9.81m/s2

While slowly walking, a man having a total mass M places all his weight on one foot. Assuming that the normal force NC of the ground acts on his foot at C, determine the resultant vertical compressive force FB which the tibia T exerts on the astragalus B, and the vertical tension FA in the Achilles tendon A at the instant shown.

Units Used:

kN = 103 N

Given:

M = 80 kg

a = 15 mm

b = 5 mm

c = 20 mm

d = 100 mm

Determine the reactions at the roller A and pin B.

Given:

M = 800 lb ft c = 3 ft

F = 390 lb d = 5

a = 8 ft e = 12

b = 4 ft θ = 30 deg

The platform assembly has weight W1 and center of gravity at G1. If it is intended to support a maximum load W2 placed at point G2, determine the smallest counterweight W that should be placed at B in order to prevent the platform from tipping over.

Given:

W1 = 250 lb a = 1 ft c = 1 ft e = 6 ft

W2 = 400 lb b = 6 ft d = 8 ft f = 2 ft

The articulated crane boom has a weight W and mass center at G. If it supports a load L, determine the force acting at the pin A and the compression in the hydraulic cylinder BC when the boom is in the position shown.

Units Used:

kip = 103 lb

Given:

W = 125 lb

L = 600 lb

a = 4 ft

b = 1 ft

c = 1 ft

d = 8 ft

θ = 40 deg

The device is used to hold an elevator door open. If the spring has stiffness k and it is compressed a distance δ, determine the horizontal and vertical components of reaction at the pin A and the resultant force at the wheel bearing B.

Given:

k = 40N/m

b = 125 mm

δ = 0.2 m c = 100 mm

a = 150 mm θ = 30 deg

Determine the reactions on the bent rod which is supported by a smooth surface at B and by a collar at A, which is fixed to the rod and is free to slide over the fixed inclined rod.

Given:

F = 100 lb

M = 200 lb ft

a = 3 ft

b = 3 ft

c = 2ft

d = 3

e = 4

f = 12

g = 5

The cantilevered jib crane is used to support the load F. If the trolley T can be placed anywhere in the range x1 ≤ x ≤ x2, determine the maximum magnitude of reaction at the supports A and B.

Note that the supports are collars that allow the crane to rotate freely about the vertical axis. The collar at B supports a force in the vertical direction, whereas the one at A does not.

Units Used:

kip = 1000 lb

Given:

F = 780 lb

a = 4 ft

b = 8 ft

x1 = 1.5 ft

x2 = 7.5 ft

The uniform rod AB has weight W. Determine the force in the cable when the rod is in the position shown.

Given:

W = 15 lb

L = 5 ft

θ1 = 30 deg

θ2 = 10 deg

The power pole supports the three lines, each line exerting a vertical force on the pole due to its weight as shown. Determine the reactions at the fixed support D. If it is possible for wind or ice to snap the lines, determine which line(s) when removed create(s) a condition for the greatest moment reaction at D.

Units Used:

kip = 103 lb

Given:

W1 = 800 lb

W2 = 450 lb

W3 = 400 lb

a = 2ft

b = 4 ft

c = 3 ft

The picnic table has a weight WT and a center of gravity at GT . If a man weighing WM has a center of gravity at GM and sits down in the centered position shown, determine the vertical reaction at each of the two legs at B. Neglect the thickness of the legs. What can you conclude from the results?

Given:

WT = 50 lb

WM = 225 lb

a = 6 in

b = 20 in

c = 20 in

If the wheelbarrow and its contents have a mass of M and center of mass at G, determine the magnitude of the resultant force which the man must exert on each of the two handles in order to hold the wheelbarrow in equilibrium.

Given:

M = 60 kg

a = 0.6 m

b = 0.5 m

c = 0.9 m

d = 0.5 m

g = 9.81m/s2

The man has weight W and stands at the center of the plank. If the planes at A and B are smooth, determine the tension in the cord in terms of W and θ.

When no force is applied to the brake pedal of the lightweight truck, the retainer spring AB keeps the pedal in contact with the smooth brake light switch at C. If the force on the switch is F, determine the unstretched length of the spring if the stiffness of the spring is k.

Given:

F = 3 N

k = 80N/m

a = 100 mm

b = 50 mm

c = 40 mm

d = 10 mm

θ = 30 deg

The telephone pole of negligible thickness is subjected to the force F directed as shown. It is supported by the cable BCD and can be assumed pinned at its base A. In order to provide clearance for a sidewalk right of way, where D is located, the strut CE is attached at C, as shown by the dashed lines (cable segment CD is removed). If the tension in CD' is to be twice the tension in BCD, determine the height h for placement of the strut CE.

Given:

F = 80 lb

θ = 30 deg

a = 30 ft

b = 10 ft

The worker uses the hand truck to move material down the ramp. If the truck and its contents are held in the position shown and have weight W with center of gravity at G, determine the resultant normal force of both wheels on the ground A and the magnitude of the force required at the grip B.

Given:

W = 100 lb      e = 1.5 ft

a = 1 ft            f = 0.5 ft

b = 1.5 ft         θ = 60 deg

c = 2 ft            ϕ = 30 deg

d = 1.75 ft

The horizontal beam is supported by springs at its ends. If the stiffness of the spring at A is kA , determine the required stiffness of the spring at B so that if the beam is loaded with the force F, it remains in the horizontal position both before and after loading.

Units Used:

kN = 103 N

Given:

kA = 5kN/ma = 1 m

F = 800 N b = 2 m

The shelf supports the electric motor which has mass m1 and mass center at Gm. The platform upon which it rests has mass m2 and mass center at Gp. Assuming that a single bolt B holds the shelf up and the bracket bears against the smooth wall at A, determine this normal force at A and the horizontal and vertical components of reaction of the bolt B on the bracket.

Given:

m1 = 15 kg       c = 50 mm

m2 = 4 kg         d = 200 mm

a = 60 mm       e = 150 mm

b = 40 mm

g = 9.81m/s2

A cantilever beam, having an extended length L, is subjected to a vertical force F. Assuming that the wall resists this load with linearly varying distributed loads over the length a of the beam portion inside the wall, determine the intensities w1 and w2 for equilibrium.

Units Used:

kN = 103 N

Given:

F = 500 N

a = 0.15 m

L = 3 m

The upper portion of the crane boom consists of the jib AB, which is supported by the pin at A, the guy line BC, and the backstay CD, each cable being separately attached to the mast at C. If the load F is supported by the hoist line, which passes over the pulley at B, determine the magnitude of the resultant force the pin exerts on the jib at A for equilibrium, the tension in the guy line BC, and the tension T in the hoist line. Neglect the weight of the jib. The pulley at B has a radius of r.

Units Used:

kN = 103 N

Given:

F = 5 kN

r = 0.1 m

a =r

b = 1.5 m

c = 5 m

The mobile crane has weight W1 and center of gravity at G1; the boom has weight W2 and center of gravity at G2. Determine the smallest angle of tilt θ of the boom, without causing the crane to overturn if the suspended load has weight W.

Neglect the thickness of the tracks at A and B.

Given:

W1 = 120000 lb

W2 = 30000 lb

W = 40000 lb

a = 4 ft

b = 6 ft

c = 3 ft

d = 12 ft

e = 15 ft

The mobile crane has weight W1 and center of gravity at G1; the boom has weight W2 and center of gravity at G2. If the suspended load has weight W determine the normal reactions at the tracks A and B. For the calculation, neglect the thickness of the tracks.

Units Used:

kip = 103 lb

Given:

W1 = 120000 lb a = 4 ft

W2 = 30000 lb b = 6 ft

W = 16000 lb c = 3 ft

θ = 30 deg d = 12 ft

e = 15 ft

The man attempts to support the load of boards having a weight W and a center of gravity at G.

If he is standing on a smooth floor, determine the smallest angle θ at which he can hold them up in the position shown. Neglect his weight.

Given:

a = 0.5 ft

b = 3 ft

c = 4 ft

d = 4 ft

The motor has a weight W. Determine the force that each of the chains exerts on the supporting hooks at A, B, and C. Neglect the size of the hooks and the thickness of the beam.

Given:

W = 850 lb

a = 0.5 ft

b = 1 ft

c = 1.5 ft

θ1 = 10 deg

θ2 = 30 deg

θ3 = 10 deg

The boom supports the two vertical loads. Neglect the size of the collars at D and B and the thickness of the boom, and compute the horizontal and vertical components of force at the pin A and the force in cable CB.

Given:

F1 = 800 N

F2 = 350 N

a = 1.5 m

b = 1 m

c = 3

d = 4

θ = 30 deg

The boom is intended to support two vertical loads F1 and F2. If the cable CB can sustain a maximum load Tmax before it fails, determine the critical loads if F1 = 2F2. Also, what is the magnitude of the maximum reaction at pin A?

Units Used:

kN = 103 N

Given:

Tmax = 1500 N

a = 1.5 m

b = 1 m

c = 3

d = 4

θ = 30deg

The uniform rod of length L and weight W is supported on the smooth planes.

Determine its position θ for equilibrium. Neglect the thickness of the rod.

The toggle switch consists of a cocking lever that is pinned to a fixed frame at A and held in place by the spring which has unstretched length δ. Determine the magnitude of the resultant force at A and the normal force on the peg at B when the lever is in the position shown.

Given:

δ = 200 mm

k = 5N/m

a = 100 mm

b = 300 mm

c = 300 mm

θ = 30 deg

The rigid beam of negligible weight is supported horizontally by two springs and a pin. If the springs are uncompressed when the load is removed, determine the force in each spring when the load P is applied. Also, compute the vertical deflection of end C. Assume the spring stiffness k is large enough so that only small deflections occur.

The rod supports a weight W and is pinned at its end A. If it is also subjected to a couple moment of M, determine the angle θ for equilibrium. The spring has an unstretched length δ and a stiffness k.

Given:

W = 200 lb

M = 100 lb ft

δ = 2 ft

k = 50lb/ft

a = 3 ft

b = 3 ft

c = 2 ft

The smooth pipe rests against the wall at the points of contact A, B, and C.

Determine the reactions at these points needed to support the vertical force F.

Neglect the pipe's thickness in the calculation.

Given:

F = 45 lb

θ = 30 deg

a = 16 in

b = 20 in

c = 8 in

The rigid metal strip of negligible weight is used as part of an electromagnetic switch. If the stiffness of the springs at A and B is k, and the strip is originally horizontal when the springs are unstretched, determine the smallest force needed to close the contact gap at C.

Units Used:

mN 10−3 = N

Given:

a = 50 mm

b = 50 mm

c = 10 mm

k = 5N/m

The rigid metal strip of negligible weight is used as part of an electromagnetic switch. Determine the maximum stiffness k of the springs at A and B so that the contact at C closes when the vertical force developed there is F. Originally the strip is horizontal as shown.

Units Used:

mN 10− 3 = N

Given:

a = 50 mm

b = 50 mm

c = 10 mm

F = 0.5 N

Determine the distance d for placement of the load P for equilibrium of the smooth bar in the position θ as shown. Neglect the weight of the bar.

The wheelbarrow and its contents have mass m and center of mass at G. Determine the greatest angle of tilt θ without causing the wheelbarrow to tip over.

Determine the force P needed to pull the roller of mass M over the smooth step.

Given:

M = 50 kg

a = 0.6 m

b = 0.1 m

θ = 60 deg

θ1 = 20 deg

g = 9.81m/s2

Determine the magnitude and direction θ of the minimum force P needed to pull the roller of mass M over the smooth step.

Given:

a = 0.6 m

b = 0.1 m

θ1 = 20 deg

M = 50 kg

g = 9.81m/s2

A uniform glass rod having a length L is placed in the smooth hemispherical bowl having a radius r. Determine the angle of inclination θ for equilibrium.

The disk has mass M and is supported on the smooth cylindrical surface by a spring having stiffness k and unstretched length l0. The spring remains in the horizontal position since its end A is attached to the small roller guide which has negligible weight. Determine the angle θ to the nearest degree for equilibrium of the roller.

Given:

M = 20 kg

k = 400N/m

l0 = 1 m

r = 2 m

g = 9.81m/s2

a = 0.2 m

Guesses F = 10 N R = 10 N θ = 30 deg

Determine the x, y, z components of reaction at the fixed wall A. The force F2 is parallel to the z axis and the force F1 is parallel to the y axis.

Given:

a = 2 m d = 2 m

b = 1 m F1 = 200 N

c = 2.5 m F2 = 150 N

The wing of the jet aircraft is subjected to thrust T from its engine and the resultant lift force L. If the mass of the wing is M and the mass center is at G, determine the x, y, z components of reaction where the wing is fixed to the fuselage at A.

Units Used:

Mg = 103 kg

kN = 103 N

g = 9.81m/s2

Given:

T = 8 kN

L = 45 kN

M = 2.1 Mg

a = 2.5 m

b = 5 m

c = 3 m

d = 7 m

The uniform concrete slab has weight W. Determine the tension in each of the three parallel supporting cables when the slab is held in the horizontal plane as shown.

Units Used:

kip = 103 lb

Given:

W = 5500 lb

a = 6 ft

b = 3 ft

c = 3 ft

d = 6 ft

The air-conditioning unit is hoisted to the roof of a building using the three cables. If the tensions in the cables are TA, TB and TC, determine the weight of the unit and the location (x, y) of its center of gravity G.

Given:

TA = 250 lb

TB = 300 lb

TC = 200 lb

a = 5 ft

b = 4 ft

c = 3 ft

d = 7 ft

e = 6 ft

The platform truck supports the three loadings shown. Determine the normal reactions on each of its three wheels.

Given:

F1 = 380 lb b = 12 in

F2 = 500 lb c = 10 in

d = 5 in

F3 = 800 lb

e = 12 in

a = 8 in f = 12 in

Due to an unequal distribution of fuel in the wing tanks, the centers of gravity for the airplane fuselage A and wings B and C are located as shown. If these components have weights WA, WB and WC, determine the normal reactions of the wheels D, E, and F on the ground.

Units Used:

kip = 103 lb

Given:

WA = 45000 lb

WB = 8000 lb

WC = 6000 lb

a = 8 ft e = 20 ft

b = 6 ft f = 4 ft

c = 8 ft g = 3 ft

d = 6 ft

If the cable can be subjected to a maximum tension T, determine the maximum force F which may be applied to the plate. Compute the x, y, z components of reaction at the hinge A for this loading.

Given:

a = 3 ft

b = 2 ft

c = 1 ft

d = 3 ft

e = 9 ft

T = 300 lb

The boom AB is held in equilibrium by a ball-and-socket joint A and a pulley and cord system as shown. Determine the x, y, z components of reaction at A and the tension in cable DEC.

Given:

F = (0 0 -1500) lb

a = 5 ft

b = 4 ft

c = b

d = 5 ft

e = 5 ft

f = 2 ft

The cable CED can sustain a maximum tension Tmax before it fails. Determine the greatest vertical force F that can be applied to the boom. Also, what are the x, y, z components of reaction at the ball-and-socket joint A?

Given:

Tmax = 800 lb

a = 5 ft

b = 4 ft

c = b

d = 5 ft

e = 5 ft

f = 2 ft

The uniform table has a weight W and is supported by the framework shown. Determine the smallest vertical force P that can be applied to its surface that will cause it to tip over. Where should this force be applied?

Given:

W = 20 lb

a = 3.5 ft

b = 2.5 ft

c = 3 ft

e = 1.5 ft

f = 1 ft

The windlass is subjected to load W. Determine the horizontal force P needed to hold the handle in the position shown, and the components of reaction at the ball-and-socket joint A and the smooth journal bearing B. The bearing at B is in proper alignment and exerts only force reactions perpendicular to the shaft on the windlass.

Given:

W = 150 lb

a = 2 ft

b = 2 ft

c = 1 ft

d = 1 ft

e = 1 ft

f = 0.5 ft

A ball of mass M rests between the grooves A and B of the incline and against a vertical wall at C. If all three surfaces of contact are smooth, determine the reactions of the surfaces on the ball. Hint: Use the x, y, z axes, with origin at the center of the ball, and the z axis inclined as shown.

Given:

M = 2 kg

θ1 = 10 deg

θ2 = 45 deg

Member AB is supported by cable BC and at A by a square rod which fits loosely through the square hole at the end joint of the member as shown. Determine the components of reaction at A and the tension in the cable needed to hold the cylinder of weight W in equilibrium.

Units Used:

kip = 103 lb

Given:

W = 800 lb

a = 2 ft

b = 6 ft

c = 3 ft

The pipe assembly supports the vertical loads shown. Determine the components of reaction at the ball-and-socket joint A and the tension in the supporting cables BC and BD.

Units Used:

kN = 103 N

Given:

F1 = 3kN d = 2 m

F2 = 4kN e = 1.5 m

a = 1 m g = 1 m

b = 1.5 m h = 3 m

c = 3 m i = 2 m

f = c − e j = 2m

The hatch door has a weight W and center of gravity at G. If the force F applied to the handle at C has coordinate direction angles of α, β and γ, determine the magnitude of F needed to hold the door slightly open as shown. The hinges are in proper alignment and exert only force reactions on the door. Determine the components of these reactions if A exerts only x and z components of force and B exerts x, y, z force components.

Given:

W = 80 lb

α = 60 deg

β = 45 deg

γ = 60 deg

a = 3 ft

b = 2 ft

c = 4 ft

d = 3 ft

The hatch door has a weight W and center of gravity at G. If the force F applied to the handle at C has coordinate direction angles α, β, γ determine the magnitude of F needed to hold the door slightly open as shown. If the hinge at A becomes loose from its attachment and is ineffective, what are the x, y, z components of reaction at hinge B?

Given:

W = 80 lb

α = 60 deg

β = 45 deg

γ = 60 deg

a = 3 ft

b = 2 ft

c = 4 ft

d = 3 ft

The bent rod is supported at A, B, and C by smooth journal bearings. Compute the x, y, z components of reaction at the bearings if the rod is subjected to forces F1 and F2. F1 lies in the y-z plane. The bearings are in proper alignment and exert only force reactions on the rod.

Given:

F1 = 300 lb d = 3 ft

F2 = 250 lbe = 5 ft

a = 1 ft α = 30 deg

b = 4 ft β = 45 deg

c = 2 ft θ = 45 deg

The bent rod is supported at A, B, and C by smooth journal bearings. Determine the magnitude of F2 which will cause the reaction Cy at the bearing C to be equal to zero. The bearings are in proper alignment and exert only force reactions on the rod.

Given:

F1 = 300 lb d = 3 ft

Cy = 0 lb e = 5 ft

a = 1 ft α = 30 deg

b = 4 ft β = 45 deg

c = 2 ft θ = 45 deg

Determine the tension in cables BD and CD and the x, y, z components of reaction at the ball-and-socket joint at A.

Given:

F = 300 N

a = 3 m

b = 1 m

c = 0.5 m

d = 1.5 m

Determine the tensions in the cables and the components of reaction acting on the smooth collar at A necessary to hold the sign of weight W in equilibrium. The center of gravity for the sign is at G.

Given:

W = 50 lb f = 2.5 ft

a = 4 ft g = 1 ft

b = 3 ft h = 1 ft

c = 2 ft i = 2 ft

d = 2 ft j = 2 ft

e = 2.5 ft k = 3 ft

The member is supported by a pin at A and a cable BC. If the load at D is W, determine the x, y,

z components of reaction at these supports.

Units Used:

kip = 103 lb

Given:

W = 300 lb

a = 1 ft

b = 2 ft

c = 6 ft

d = 2 ft

e = 2 ft

f = 2 ft

Determine the x, y, z components of reaction at the pin A and the tension in the cable BC necessary for equilibrium of the rod.

Given:

F = 350 lb e = 12 ft

a = 4 ftf = 4 ft

b = 5 ft g = 10 ft

c = 4 ft h = 4 ft

d = 2 ft i = 10 ft

Rod AB is supported by a ball-and-socket joint at A and a cable at B. Determine the x, y, z components of reaction at these supports if the rod is subjected to a vertical force F as shown.

Given:

F = 50 lb

a = 2 ft c = 2 ft

b = 4 ft d = 2 ft

The member is supported by a square rod which fits loosely through a smooth square hole of the attached collar at A and by a roller at B. Determine the x, y, z components of reaction at these supports when the member is subjected to the loading shown.

Given:

M = 50 lb⋅ ft

F = (20 -40 -30) lb

a = 2 ft

b = 1 ft

c = 2 ft

The platform has mass M and center of mass located at G. If it is lifted using the three cables, determine the force in each of these cables.

Units Used:

Mg = 103 kg kN = 103 N g = 9.81m/s2

Given:

M = 3 Mg

a = 4 m

b = 3 m

c = 3 m

d = 4 m

e = 2 m

The platform has a mass of M and center of mass located at G. If it is lifted using the three cables, determine the force in each of the cables. Solve for each force by using a single moment equation of equilibrium.

Units Used:

Mg = 1000 kg

kN = 103 N

g = 9.81m/s2

Given:

M = 2 Mg c = 3 m

a = 4 m d = 4 m

b = 3 m e = 2 m

The cables exert the forces shown on the pole. Assuming the pole is supported by a ball-and-socket joint at its base determine the components of reaction at A.

The forces F1 and F2 lie in a horizontal plane.

Given:

F1 = 140 lb

F2 = 75 lb

θ = 30 deg

a = 5 ft

b = 10 ft

c = 15 ft

The silo has a weight W, a center of gravity at G and a radius r. Determine the vertical component of force that each of the three struts at A, B, and C exerts on the silo if it is subjected to a resultant wind loading of F which acts in the direction shown.

Given:

W = 3500 lb

F = 250 lb

θ1 = 30 deg

θ2 = 120 deg

θ3 = 30 deg

r = 5 ft

b = 12 ft

c = 15 ft

The shaft assembly is supported by two smooth journal bearings A and B and a short link DC. If a couple moment is applied to the shaft as shown, determine the components of force reaction at the bearings and the force in the link. The link lies in a plane parallel to the y-z plane and the bearings are properly aligned on the shaft.

Units Used:

kN = 103 N

Given:

M = 250 N ∙ m

a = 400 mm

b = 300 mm

c = 250 mm

d = 120 mm

θ = 30 deg

φ = 20 deg

If neither the pin at A nor the roller at B can support a load no greater than Fmax determine the maximum intensity of the distributed load w, so that failure of a support does not occur.

Units Used:

kN = 103 N

Given:

Fmax = 6kN

a = 3 m

b = 3 m

If the maximum intensity of the distributed load acting on the beam is w, determine the reactions at the pin A and roller B.

Units Used:

kN = 103 N

Given:

F = 6 kN

a = 3 m

b = 3 m

w = 4 kN/m

Determine the normal reaction at the roller A and horizontal and vertical components at pin B for equilibrium of the member.

Units Used:

kN = 103 N

Given:

F1 = 10kN

F2 = 6kN

a = 0.6 m

b = 0.6 m

c = 0.8 m

d = 0.4 m

θ = 60 deg

The symmetrical shelf is subjected to uniform pressure P. Support is provided by a bolt (or pin) located at each end A and A' and by the symmetrical brace arms, which bear against the smooth wall on both sides at B and B'. Determine the force resisted by each bolt at the wall and the normal force at B for equilibrium.

Units Used:

kPa = 103 Pa

Given:

P = 4 kPa

a = 0.15 m

b = 0.2 m

c = 1.5 m

A uniform beam having a weight W supports a vertical load F. If the ground pressure varies linearly as shown, determine the load intensities w1 and w2 measured in lb/ft, necessary for equilibrium.

Given:

W = 200 lb

F = 800 lb

a = 7 ft

b = 6 ft

The uniform ladder rests along the wall of a building at A and on the roof at B. If the ladder has a weight W and the surfaces at A and B are assumed smooth, determine the angle θ for equilibrium.

Given:

a = 18 ft

W = 25 lb

θ1 = 40 deg

Determine the x, y, z components of reaction at the ball supports B and C and the ball-and-socket A (not shown) for the uniformly loaded plate.

Given:

P = 2lb/ft2

a = 4 ft

b = 1 ft

c = 2 ft

d = 2 ft

A vertical force F acts on the crankshaft. Determine the horizontal equilibrium force P that must be applied to the handle and the x, y, z components of force at the smooth journal bearing A and the thrust bearing B. The bearings are properly aligned and exert the force reactions on the shaft.

Given:

F = 80 lb

a = 10 in

b = 14 in

c = 14 in

d = 8 in

e = 6 in

f = 4 in

Determine the force in members AB, AD, and AC of the space truss and state if the members are in tension or compression. The force F is vertical.

Units Used:

kip = 103 lb

Given:

F = 600 lb

a = 1.5 ft

b = 2 ft

c = 8 ft

Determine the force in each member of the truss and state if the members are in tension or compression.

Units Used:

kN = 103 N

Given:

P1 = 7kN

P2 = 7kN

Determine the force in each member of the truss and state if the members are in tension or compression.

Units Used:

kN = 103 N

Given:

P1 = 8kN

P2 = 10kN

The truss, used to support a balcony, is subjected to the loading shown.

Approximate each joint as a pin and determine the force in each Member State whether the members are in tension or compression.

Units Used:

kip = 103 lb

Given:

P1 = 600 lb

P2 = 400 lb

a = 4 ft

θ = 45 deg

The truss, used to support a balcony, is subjected to the loading shown.

Approximate each joint as a pin and determine the force in each member state whether the members are in tension or compression.

Units Used:

kip = 103 lb

Given:

P1 = 800 lb

P2 = 0 lb

a = 4 ft

θ = 45 deg

Determine the force in each member of the truss and state if the members are in tension or compression.

Units Used:

kN = 103 N

Given:

P1 = 20kN

P2 = 10kN

a = 1.5 m

e = 2m

Determine the force in each member of the truss and state if the members are in tension or compression.

Units Used:

kN = 103 N

Given:

P1 = 40kN

P2 = 20kN

a = 1.5 m

e = 2 m

Determine the force in each member of the truss and state if the members are in tension or compression.

Units Used:

kN = 103 N

Given:

F1 = 3kN

F2 = 8kN

F3 = 4kN

F4 = 10kN

a = 2 m

b = 1.5 m

Determine the force in each member of the truss in terms of the external loading and state if the members are in tension or compression.

The maximum allowable tensile force in the members of the truss is Tmax, and the maximum allowable compressive force is Cmax. Determine the maximum magnitude P of the two loads that can be applied to the truss.

Given:

Tmax = 1500 lb

Cmax = 800 lb

Determine the force in each member of the truss and state if the members are in tension or compression.

Given:

P1 = 0 lb

P2 = 1000 lb

a = 10 ft

b = 10 ft

Determine the force in each member of the truss and state if the members are in tension or compression.

Given:

P1 = 500 lb

P2 = 1500 lb

a = 10 ft

b = 10 ft

Determine the force in each member of the truss and state if the members are in tension or compression.

Units Used:

kN = 103 N

Given:

P1 = 10 kN

P2 = 15 kN

a = 2 m

b = 4 m

c = 4 m

Determine the force in each member of the truss and state if the members are in tension or compression.

Units Used:

kN = 103 N

Given:

P1 = 0kN

P2 = 20kN

a = 2 m

b = 4 m

c = 4 m

Determine the force in each member of the truss and state if the members are in tension or compression.

Given:

P1 = 100 lb

P2 = 200 lb

P3 = 300 lb

a = 10 ft

b = 10 ft

θ = 30 deg

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