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civil engineering

Engineering Mechanics Statics 11 Edition Russell C. Hibbeler - Solutions

The beam consists of three segments pin connected at B and E. Draw the shear and moment diagrams for the beam.Units Used: kN = 103 NGiven: MA = 8 kN ∙ m F = 15 kN w = 3 kN/m a = 3 m b = 2 mc = 2 md = 2 m e = 2 m f = 4 m
Draw the shear and moment diagrams for the beam.
Draw the shear and moment diagrams for the beam.Units Used:kip = 103 lbGiven:F = 2000 lbw = 500lb/fta = 9 ftb = 9 ft
Draw the shear and moment diagrams for the beam.Units Used:kN = 103 NGiven:w = 3kN/m a = 3 m b = 3 m
Draw the shear and moment diagrams for the beam. Units Used: kip = 103 lb Given: w = 100 lb/ftM0 = 9 kip⋅ ft a = 6 ft b = 6 ft c = 4 ft
Draw the shear and moment diagrams for the beam.
Draw the shear and moment diagrams for the beam.Units Used:kN = 103 NGiven: w = 2 kN/m a = 3 m b = 3 m
Draw the shear and moment diagrams for the beam.Units Used:kip = 103 lbGiven:w = 5kip/ftM1 = 15 kip⋅ ft M2 = 15 kip⋅ ft a = 6 ft b = 10 ft c = 6 ft
Draw the shear and moment diagrams for the beam.Units Used:kip = 103 lbGiven:w1 = 2kip/ftw2 = 1 kip/fta = 15 ft
Determine the force P needed to hold the cable in the position shown, i.e., so segment BC remains horizontal. Also, compute the sag yB and the maximum tension in the cable.Units Used:kN = 103 NGiven:F1 = 4kNF2 = 6kNa = 4 m b = 6 m c = 3 md = 2 me = 3 m
Cable ABCD supports the lamp of mass M1 and the lamp of mass M2. Determine the maximum tension in the cable and the sag of point B.Given:M1 = 10 kgM2 = 15 kga = 1 mb = 3 mc = 0.5 md = 2 m
The cable supports the three loads shown. Determine the sags yB and yD of points B and D.Given:a = 4 ft b = 12 ft c = 20 ft d = 15 ft e = 12 ftf = 14 ftP1 = 400 lbP2 = 250 lb
The cable supports the three loads shown. Determine the magnitude of P1 and find the sag yD for the given data.Given:P2 = 300 lb yB = 8 ft a = 4 ft b = 12 ft c = 20 ftd = 15 fte = 12 ftf = 14 ft
The cable supports the loading shown. Determine the distance xB the force at point B acts from A.Given:P = 40 lb F = 30 lb a = 5 ft b = 8 ft c = 2 ftd = 3 fte = 3f = 4
The cable supports the loading shown. Determine the magnitude of the horizontal force P.Given:F = 30 lb xB = 6 ft a = 5 ftb = 8 ft c = 2 ftd = 3 fte = 3f = 4
Determine the forces P1 and P2 needed to hold the cable in the position shown, i.e., so segment CD remains horizontal. Also, compute the maximum tension in the cable.Given: kN = 103 NF = 5kN a = 1.5 m b = 1 m c = 2 md = 4 me = 5 mf = 4 m
The cable supports the loading shown. Determine the distance xB from the wall to point B.Given:W1 = 8 lbW2 = 15 lba = 5 ftb = 8 ftc = 2 ftd = 3 ft
Determine the maximum uniform loading w, measured in lb/ft, that the cable can support if it is capable of sustaining a maximum tension Tmax before it will break.Given:Tmax = 3000 lba = 50 ftb = 6 ft
The cable is subjected to a uniform loading w. Determine the maximum and minimum tension in the cable.Units Used:kip = 103 lbGiven:w = 250lb/fta = 50 ftb = 6 ft
The cable is subjected to the triangular loading. If the slope of the cable at A is zero, determine the equation of the curve y = f(x) which defines the cable shape AB, and the maximum tension developed in the cable.Units Used:kip = 103 lbGiven:w = 250lb/fta = 20 ftb = 30 ft
The cable supports a girder which has weight density γ. Determine the tension in the cable at points A, B, and C.Units used:kip = 103 lbGiven:γ = 850lb/fta = 40 ftb = 100 ftc = 20 ft
The cable is subjected to the triangular loading. If the slope of the cable at point O is zero, determine the equation of the curve y = f(x) which defines the cable shape OB, and the maximum tension developed in the cable.Units used:kip = 103 lbGiven:w = 500lb/fta = 15 ftb = 8 ft
The cable is subjected to the parabolic loading w = w0 (1− (2x/a)2). Determine the equation y = f(x) which defines the cable shape AB and the maximum tension in the cable.Units Used:kip = 103 lbw = wo [1- (2x/a)2]a = 100 ft w0 = 150lb/ftb = 20 ft
The cable will break when the maximum tension reaches Tmax. Determine the minimum sag h if it supports the uniform distributed load w.Given: kN = 103 NTmax = 10 kNw = 600N/ma = 25 m
A fiber optic cable is suspended over the poles so that the angle at the supports is θ. Determine the minimum tension in the cable and the sag. The cable has a mass density ρ and the supports are at the same elevation.Given:θ = 22 degρ = 0.9kg/ma = 30 mg = 9.81m/s2
A cable has a weight density γ and is supported at points that are a distance d apart and at the same elevation. If it has a length L, determine the sag.Given:γ = 3lb/ft d = 500 ft L = 600 ft
Show that the deflection curve of the cable discussed in Example 7.15 reduces to Eq. (4) in Example 7.14 when the hyperbolic cosine function is expanded in terms of a series and only the first two terms are retained. (The answer indicates that the catenary’s may be replaced by a parabola in the
A uniform cord is suspended between two points having the same elevation. Determine the sag-to-span ratio so that the maximum tension in the cord equals the cord's total weight.
A cable has a weight density γ. If it can span a distance L and has a sag h determine the length of the cable. The ends of the cable are supported from the same elevation.Given:γ = 2lb/ft L = 100 ft h = 12 ft
The transmission cable having a weight density γ is strung across the river as shown. Determine the required force that must be applied to the cable at its points of attachment to the towers at B and C.Units Used:kip = 103 lbGiven:γ = 20lb/ft b = 75 fta = 50 ft c = 10 ft
Determine the maximum tension developed in the cable if it is subjected to a uniform load w.Units Used:MN = 106 NGiven:w = 600N/ma = 100 mb = 20 mθ = 10 deg
A chain of length L has a total mass M and is suspended between two points a distance d apart.Determine the maximum tension and the sag in the chain.Given:L = 40 m M = 100 kg d = 10 m g = 9.81m/s2
The cable has a mass density ρ and has length L. Determine the vertical and horizontal components of force it exerts on the top of the tower.Given:ρ = 0.5kg/mL = 25 mθ = 30 degd = 15 mg = 9.81m/s2
A cable of length L is suspended between two points a distance d apart and at the same elevation. If the minimum tension in the cable is Tmin, determine the total weight of the cable and the maximum tension developed in the cable.Units Used: kip = 103 lbGiven: L = 50 ft d = 15 ft Tmin = 200 lb
The chain of length L is fixed at its ends and hoisted at its midpoint B using a crane. If the chain has a weight density w, determine the minimum height h of the hook in order to lift the chain completely off the ground. What is the horizontal force at pin A or C when the chain is in this
A steel tape used for measurement in surveying has a length L and a total weight W. How much horizontal tension must be applied to the tape so that the distance marked on the ground is a? In practice the calculation should also include the effects of elastic stretching and temperature changes on
A cable of weight W is attached between two points that are a distance d apart, having equal elevations. If the maximum tension developed in the cable is Tmax determine the length L of the cable and the sag h. Given: W = 100 lb d = 50 ft Tmax = 75 lb
Determine the distance a between the supports in terms of the beam's length L so that the moment in the symmetric beam is zero at the beam's center.
Determine the internal normal force, shear force, and moment at point D.Given:w = 150N/ma = 4 mb = 4 mc = 3 m
The beam is supported by a pin at C and a rod AB. Determine the internal normal force, shear force, and moment at point D.Units Used:kN = 103 NGiven:F = 4kNa = 6 mb = 5 mc = 3 md = 6 mθ = 60 deg
Express the shear and moment acting in the pipe as a function of y, where 0 ≤ y ≤ b ft.Given:w = 4lb/fta = 2 ftb = 4 ft
Determine the normal force, shear force, and moment at points B and C of the beam.Given: kN = 103Na = 5 m F2 = 6 kNb = 5 m w1 = 2kN/mc = 1 m w2 = 1kN/md = 3 mF1 = 7.5kN M = 40kN ∙ m
The chain is suspended between points A and B. If it has a weight density w and the sag is h, determine the maximum tension in the chain.Given:w = 0.5lb/ftL = 60 fth = 3 ft
Draw the shear and moment diagrams for the beam.Units Used:kN = 103 NGiven:w = 2kN/m a = 5 m b = 5 mM = 50 kN ∙ m
The horizontal force is P. Determine the normal and frictional forces acting on the crate of weight W. The friction coefficients are μk and μs.Given:W = 300 lbP = 80 lbμs = 0.3μk = 0.2θ = 20 deg
Determine the magnitude of force P needed to start towing the crate of mass M. Also determine the location of the resultant normal force acting on the crate, measured from point A.Given:M = 40 kg c = 200 mmμ s = 0.3 d = 3a = 400 mm e = 4b = 800 mm
Determine the friction force on the crate of mass M, and the resultant normal force and its position x, measured from point A, if the force is P.Given:M = 40 kg μs = 0.5a = 400 mm μk = 0.2b = 800 mm d = 3c = 200 mme = 4P = 300 N
The loose-fitting collar is supported by the pipe for which the coefficient of static friction at the points of contact A and B is μs. Determine the smallest dimension d so the rod will not slip when the load P is applied.Given:μ s = 0.2
The spool of wire having a mass M rests on the ground at A and against the wall at B. Determine the force P required to begin pulling the wire horizontally off the spool. The coefficient of static friction between the spool and its points of contact is μs.Units Used:kN = 103 NGiven:M = 150 kgμ s
The spool of wire having a mass M rests on the ground at A and against the wall at B. Determine the force P required to begin pulling the wire horizontally off the spool. The coefficient of static friction between the spool and its points of contact is μs.Units Used:kN = 103 NGiven:M = 150 kgμ s
The spool of wire having a mass M rests on the ground at A and against the wall at B. Determine the forces acting on the spool at A and B for the given force P.The coefficient of static friction between the spool and the ground at point A is μs. The wall at B is smooth.Units Used:kN = 103 NGiven:P
The crate has a mass M and is subjected to a towing force P acting at an angle θ1 with the horizontal. If the coefficient of static friction is μs, determine the magnitude of P to just start the crate moving down the plane.Given:M = 350 kgθ1 = 20 degθ2 = 10 degμs = 0.5g = 9.81m/s2
The winch on the truck is used to hoist the garbage bin onto the bed of the truck. If the loaded bin has weight W and center of gravity at G, determine the force in the cable needed to begin the lift. The coefficients of static friction at A and B are μΑ and μB respectively. Neglect the height
The motorcyclist travels with constant velocity along a straight, horizontal, banked road. If he aligns his bike so that the tires are perpendicular to the road at A, determine the frictional force at A. The man has a mass MC and a mass center at GC, and the motorcycle has a mass Mm and a mass
The block brake is used to stop the wheel from rotating when the wheel is subjected to a couple moment M0 If the coefficient of static friction between the wheel and the block is μs, determine the smallest force P that should be applied.
The block brake is used to stop the wheel from rotating when the wheel is subjected to a couple moment M0 If the coefficient of static friction between the wheel and the block is μs , show that the brake is self locking, i. e., P ≤ 0 , provided b/c ≤ μ s.
The block brake is used to stop the wheel from rotating when the wheel is subjected to a couple moment M0 If the coefficient of static friction between the wheel and the block is μs , determine the smallest force P that should be applied if the couple moment MO is applied counterclockwise.
The block brake consists of a pin-connected lever and friction block at B. The coefficient of static friction between the wheel and the lever is μs and a torque M is applied to the wheel. Determine if the brake can hold the wheel stationary when the force applied to the lever is (a) P1 (b)
The block brake consists of a pin-connected lever and friction block at B. The coefficient of static friction between the wheel and the lever is μs and a torque M is applied to the wheel. Determine if the brake can hold the wheel stationary when the force applied to the lever is?(a) P1(b)
The doorstop of negligible weight is pin connected at A and the coefficient of static friction at B is μs. Determine the required distance s from A to the floor so that the stop will resist opening of the door for any force P applied to the handle.Given:μ s = 0.3a = 1.5 in
The chair has a weight W and center of gravity at G. It is propped against the door as shown. If the coefficient of static friction at A is μA, determine the smallest force P that must be applied to the handle to open the door.Given:μA = 0.3a = 1.20 ftb = 0.75 ftc = 3ftθ = 30 degW = 10 lb
The uniform hoop of weight W is suspended from the peg at A and a horizontal force P is slowly applied at B. If the hoop begins to slip at A when the angle is θ, determine the coefficient of static friction between the hoop and the peg.Given:θ = 30 deg
The uniform hoop of weight W is suspended from the peg at A and a horizontal force P is slowly applied at B. If the coefficient of static friction between the hoop and peg is μs, determine if it is possible for the hoop to reach an angle θ before the hoop begins to slip.Given:μs = 0.2θ = 30 deg
The coefficient of static friction between the shoes at A and B of the tongs and the pallet is μs1 and between the pallet and the floor μs2. If a horizontal towing force P is applied to the tongs, determine the largest mass that can be towed μs1 = 0.5 a = 75 mmμ s2 = 0.4 b = 20 mmP = 300 N c =
The pipe is hoisted using the tongs. If the coefficient of static friction at A and B is μ s, determine the smallest dimension b so that any pipe of inner diameter d can be lifted.
A very thin bookmark having a width a. is in the middle of a dictionary of weight W. If the pages are b by c, determine the force P needed to start to pull the bookmark out. The coefficient of static friction between the bookmark and the paper is μs. Assume the pressure on each page and the
The uniform dresser has weight W and rests on a tile floor for which the coefficient of friction is μs. If the man pushes on it in the direction θ, determine the smallest magnitude of force F needed to move the dresser. Also, if the man has a weight Wman, determine the smallest coefficient of
The uniform dresser has weight W and rests on a tile floor for which the coefficient of friction is μs. If the man pushes on it in the direction θ, determine the smallest magnitude of force F needed to move the dresser. Also, if the man has a weight Wman, determine the smallest coefficient of
The cam is subjected to a couple moment of M. Determine the minimum force P that should be applied to the follower in order to hold the cam in the position shown.The coefficient of static friction between the cam and the follower is μs. The guide at A is smooth.Given:a = 10 mmb = 60 mmM = 5 N ∙
The board can be adjusted vertically by tilting it up and sliding the smooth pin A along the vertical guide G. When placed horizontally, the bottom C then bears along the edge of the guide, where the coefficient of friction is μs. Determine the largest dimension d which will support any applied
The homogeneous semi cylinder has a mass m and mass center at G. Determine the largest angle θ of the inclined plane upon which it rests so that it does not slip down the plane. The coefficient of static friction between the plane and the cylinder is μs . Also, what is the angle φ for this
A chain having a length L and weight W rests on a street for which the coefficient of static friction is μs. If a crane is used to hoist the chain, determine the force P it applies to the chain if the length of chain remaining on the ground begins to slip when the horizontal component is Px. What
The fork lift has a weight W1 and center of gravity at G. If the rear wheels are powered, whereas the front wheels are free to roll, determine the maximum number of crates, each of weight W2 that the fork lift can push forward. The coefficient of static friction between the wheels and the ground is
The brake is to be designed to be self locking, that is, it will not rotate when no load P is applied to it when the disk is subjected to a clockwise couple moment MO. Determine the distance d of the lever that will allow this to happen. The coefficient of static friction at B is μs.Given:a = 1.5
The concrete pipe of weight W is being lowered from the truck bed when it is in the position shown. If the coefficient of static friction at the points of support A and B is μs determine where it begins to slip first: at A or B, or both at A and B.Given:W = 800 lb a = 30 inμ s = 0.4 b = 18 inθ =
A wedge of mass M is placed in the grooved slot of an inclined plane. Determine the maximum angle θ for the incline without causing the wedge to slip. The coefficient of static friction between the wedge and the surfaces of contact is μs.Given:M = 5 kgμs = 0.2φ = 60 degg = 9.81m/s2
A roll of paper has a uniform weight W and is suspended from the wire hanger so that it rests against the wall. If the hanger has a negligible weight and the bearing at O can be considered frictionless, determine the force P needed to start turning the roll. The coefficient of static friction
A roll of paper has a uniform weight W and is suspended from the wire hanger so that it rests against the wall. If the hanger has a negligible weight and the bearing at O can be considered frictionless, determine the minimum force P and the associated angle θ needed to start turning the roll. The
The door brace AB is to be designed to prevent opening the door. If the brace forms a pin connection under the doorknob and the coefficient of static friction with the floor is μs determine the largest length L the brace can have to prevent the door from being opened. Neglect the weight of the
The man has a weight W, and the coefficient of static friction between his shoes and the floor is μs. Determine where he should position his center of gravity G at d in order to exert the maximum horizontal force on the door. What is this force?Given:W = 200 lbμ s = 0.5h = 3 ft
In an effort to move the two crates, each of weight W, which are stacked on top of one another, the man pushes horizontally on them at the bottom of crate A as shown. Determine the smallest force P that must be applied in order to cause impending motion. Explain what happens. The coefficient of
The man having a weight of W1 pushes horizontally on the bottom of crate A, which is stacked on top of crate B. Each crate has a weight W2. If the coefficient of static friction between each crate is μs and between the bottom crate, his shoes, and the floor is μs, determine if he can cause
The crate has a weight W and a center of gravity at G. Determine the horizontal force P required to tow it. Also, determine the location of the resultant normal force measured from A.Given:a = 3.5 ftb = 3 ftc = 2 ftW = 200 lbh = 4 ftμ s = 0.4
The crate has a weight W and a center of gravity at G. Determine the height h of the tow rope so that the crate slips and tips at the same time. What horizontal force P is required to do this?Given:a = 3.5 ftb = 3 ftc = 2 ftW = 200 lbh = 4 ftμ s = 0.4
Determine the smallest force the man must exert on the rope in order to move the crate of mass M. Also, what is the angle θ at this moment? The coefficient of static friction between the crate and the floor is μs.Given:M = 80 kgμ s = 0.3α = 30 degβ = 45 degg = 9.81m/s2
The symmetrical crab hook is used to lift packages by means of friction developed between the shoes A and B and a package. Determine the smallest coefficient of static friction at the shoes so that the package of weight W can be lifted.Given:a = 1 ftb = 2 ftc = 0.8 ftd = 1 ftθ = 45 deg
The friction hook is made from a fixed frame which is shown colored and a cylinder of negligible weight. A piece of paper is placed between the smooth wall and the cylinder. Determine the smallest coefficient of static friction μ at all points of contact so that any weight W of paper p can be
The crate has a weight W1 and a center of gravity at G. If the coefficient of static friction between the crate and the floor is μs, determine if the man of weight W2 can push the crate to the left. The coefficient of static friction between his shoes and the floor is μs. Assume the man exerts
The crate has a weight W1 and a center of gravity at G. If the coefficient of static friction between the crate and the floor is μs , determine the smallest weight of the man so that he can push the crate to the left. The coefficient of static friction between his shoes and the floor is μs.
The wheel has weight WA and rests on a surface for which the coefficient of friction is μB. A cord wrapped around the wheel is attached to the top of the homogeneous block of weight WC. If the coefficient of static friction at D is μD determine the smallest vertical force that can be applied
Determine the smallest couple moment which can be applied to the wheel of weight W1 that will cause impending motion. The cord is attached to the block of weight W2, and the coefficients of static friction are μB and μD.Given:W1 = 20 lb a = 1.5 ftW2 = 30 lb b = 3 ftμ B = 0.2 c = 1.5 ftμD = 0.3
The beam AB has a negligible mass and thickness and is subjected to a triangular distributed loading. It is supported at one end by a pin and at the other end by a post having a mass mp and negligible thickness. Determine the minimum force P needed to move the post. The coefficients of static
The beam AB has a negligible mass and thickness and is subjected to a triangular distributed loading. It is supported at one end by a pin and at the other end by a post having a mass mp and negligible thickness. Determine the two coefficients of static friction at B and at C so that when the
The block of weight W is being pulled up the inclined plane of slope α using a force P. If P acts at the angle φ as shown, show that for slipping to occur, P = W sin(α + θ)/ cos(φ − θ) where θ is the angle of friction; θ = tan-1 μ..
Determine the angle φ at which P should act on the block so that the magnitude of P is as small as possible to begin pulling the block up the incline. What is the corresponding value of P? The block has weight W and the slope α is known.
Determine the angle φ at which P should act on the block so that the magnitude of P is as small as possible to begin pulling the block up the incline. What is the corresponding value of P? The block as weight W and the slope α is known.Given:M = 6 kgμs = 0.5θ1 = 30 degθ2 = 30 deg
Block C has a mass mc and is confined between two walls by smooth rollers. If the block rests on top of the spool of mass ms, determine the minimum cable force P needed to move the spool. The cable is wrapped around the spool's inner core the coefficients of static friction at μA and μB.Given:g =
A board of weight W1 is placed across the channel and a boy of weight W2 attempts to walk across. If the coefficient of static friction at A and B μs, determine if he can make the crossing; and if not, how far will he get from A before the board slips?Given:W1 = 50 lbW2 = 100 lbμs = 0.4a = 10 ftb
Determine the minimum force P needed to push the tube E up the incline. The tube has a mass of M1 and the roller D has a mass of M2. The force acts parallel to the plane, and the coefficients of static friction at the contacting surfaces are μA, μB and μC. Each cylinder has a radius of
The concrete pipe at A rests on top of B and C. If the coefficient of static friction between the pipes is μs and at the ground μ's, determine their smallest values so that the pipes will not slip. Each pipe has a radius r and weight W, and the angle between the centers as indicated is θ.

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