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physics
mechanics
Mechanics of Materials 7th edition James M. Gere, Barry J. Goodno - Solutions
A lifeboat hangs from two ship's davits, as shown in the figure. A pin of diameter d = 0.80 in. passes through each davit and supports two pulleys, one on each side of the davit.Cables attached to the lifeboat pass over the pulleys and wind around winches that raise and lower the lifeboat. The
A cable and pulley system in figure part (a) supports a cage of mass 300 kg at B. Assume that this includes the mass of the cables as well. The thickness of each the three steel pulleys is t = 40 mm. The pin diameters are dpA = 25 mm, dpB = 30 mm and dpC = 22 mm [see figure, parts (a) and part
A ship's spar is attached at the base of a mast by a pin connection (see figure). The spar is a steel tube of outer diameter d2 = 3.5 in. and inner diameter d1 = 2.8 in. The steel pin has diameter d = 1 in., and the two plates connecting the spar to the pin have thickness t = 0.5 in. The allowable
An aluminum tube is required to transmit an axial tensile force P = 33 k [see figure part (a)]. The thickness of the wall of the tube is to be 0.25 in.(a) What is the minimum required outer diameter dmin if the allowable tensile stress is 12,000 psi?(b) Repeat part (a) if the tube will have a hole
A tubular post of outer diameter d2 is guyed by two cables fitted with turnbuckles (see figure). The cables are tightened by rotating the turnbuckles, thus producing tension in the cables and compression in the post. Both cables are tightened to a tensile force of 110 kN. Also, the angle between
A large precast concrete panel for a warehouse is being raised to a vertical position using two sets of cables at two lift lines as shown in the figure part (a). Cable 1 has length L1 = 22 ft and distances along the panel (see figure part (b)) are a = L1/2 and b = L1/4. The cables are attached at
A steel column of hollow circular cross section is supported on a circular steel base plate and a concrete pedestal (see figure). The column has outside diameter d = 250 mm and supports a load P = 750 kN.(a) If the allowable stress in the column is 55 MPa, what is the minimum required thickness t?
An elevated jogging track is supported at intervals by a wood beam AB (L = 7.5 ft) which is pinned at A and supported by steel rod BC and a steel washer at B. Both the rod (dBC = 3/16 in.) and the washer (dB = 1.0 in.) were designed using a rod tension force of TBC = 425 lb. The rod was sized using
A flat bar of width b = 60 mm and thickness t = 10 mm is loaded in tension by a force P (see figure). The bar is attached to a support by a pin of diameter d that passes through a hole of the same size in the bar. The allowable tensile stress on the net cross section of the bar is σT =
Two bars AC and BC of the same material support a vertical load P (see figure). The length L of the horizontal bar is fixed, but the angle θ can be varied by moving support A vertically and changing the length of bar AC to correspond with the new position of support A. The allowable
A copper alloy pipe having yield stress σY = 290 MPa is to carry an axial tensile load P = 1500 kN [see figure part (a)]. A factor of safety of 1.8 against yielding is to be used.(a) If the thickness t of the pipe is to be one-eighth of its outer diameter, what is the minimum required
A horizontal beam AB with cross-sectional dimensions (b = 0.75 in.) × (h = 8.0 in.) is supported by an inclined strut CD and carries a load P = 2700 lb at joint B [see figure part (a)]. The strut, which consists of two bars each of thickness 5b/8, is connected to the beam by a bolt
Lateral bracing for an elevated pedestrian walkway is shown in the figure part (a). The thickness of the clevis plate tc = 16 mm and the thickness of the gusset plate tg = 20 mm [see figure part (b)]. The maximum force in the diagonal bracing is expected to be F = 190 kN.If the allowable shear
Forces P1 = 1500 lb and P2 = 2500 lb are applied at joint C of plane truss ABC shown in the figure part (a). Member AC has thickness tAC = 5/16 in. and member AB is composed of two bars each having thickness tAB / 2 = 3/16 in. [see figure part (b)]. Ignore the effect of the two plates which make up
The flat bars shown in parts (a) and (b) of the figure are subjected to tensile forces P = 3.0 k. Each bar has thickness t = 0.25 in.(a) For the bar with a circular hole, determine the maximum stresses for hole diameters d = 1 in. and d = 2 in. if the width b = 6.0 in.(b) For the stepped bar with
The flat bars shown in parts (a) and (b) of the figure are subjected to tensile forces P = 2.5 kN. Each bar has thickness t = 5.0 mm.(a) For the bar with a circular hole, determine the maximum stresses for hole diameters d = 12 mm and d = 20 mm if the width b = 60 mm.(b) For the stepped bar with
A flat bar of width b and thickness t has a hole of diameter d drilled through it (see figure). The hole may have any diameter that will fit within the bar.What is the maximum permissible tensile load Pmax if the allowable tensile stress in the material is σt?
A round brass bar of diameter d1 = 20 mm has upset ends of diameter d2 = 26 mm (see figure). The lengths of the segments of the bar are L1 = 0.3 m and L2 = 0.1 m. Quarter-circular fillets are used at the shoulders of the bar, and the modulus of elasticity of the brass is E = 100 GPa.If the bar
Solve the preceding problem for a bar of monel metal having the following properties: d1 = 1.0 in., d2 = 1.4 in., L1 = 20.0 in., L2 = 5.0 in., and E = 25 × 106 psi. Also, the bar lengthens by 0.0040 in. when the tensile load is applied.
A prismatic bar of diameter d0 = 20 mm is being compared with a stepped bar of the same diameter (d1 = 20 mm) that is enlarged in the middle region to a diameter d2 = 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm.(a) Does enlarging the bar in the middle region make it
A stepped bar with a hole (see figure) has widths b = 2.4 in. and c = 1.6 in. The fillets have radii equal to 0.2 in. What is the diameter dmax of the largest hole that can be drilled through the bar without reducing the load-carrying capacity?
A bar AB of length L and weight density γ hangs vertically under its own weight (see figure). The stress-strain relation for the material is given by the Ramberg-Osgood equation (Eq. 2-71):Derive the following formula for the elongation of the bar.
A prismatic bar of length L = 1.8 m and cross-sectional area A = 480 mm2 is loaded by forces P1 = 30 kN and P2 = 60 kN (see figure). The bar is constructed of magnesium alloy having a stress-strain curve described by the following Ramberg-Osgood equation:in which σ has units of
A circular bar of length L = 32 in. and diameter d = 0.75 in. is subjected to tension by forces P (see figure). The wire is made of a copper alloy having the following hyperbolic stress-strain relationship:(a) Draw a stress-strain diagram for the material. (b) If the elongation of the wire is
A prismatic bar in tension has length L = 2.0 m and cross-sectional area A = 249 mm2. The material of the bar has the stressstrain curve shown in the figure.Determine the elongation δ of the bar for each of the following axial loads: P = 10 kN, 20 kN, 30 kN, 40 kN, and 45 kN. From
An aluminum bar subjected to tensile forces P has length L = 150 in. and cross-sectional area A = 2.0 in.2 The stress-strain behavior of the aluminum may be represented approximately by the bilinear stress-strain diagram shown in the figure.Calculate the elongation δ of the bar for
A rigid bar AB, pinned at end A, is supported by a wire CD and loaded by a force P at end B (see figure). The wire is made of high-strength steel having modulus of elasticity E = 210 GPa and yield stress σY = 820 MPa. The length of the wire is L = 1.0 m and its diameter is d = 3 mm. The
Two identical bars AB and BC support a vertical load P (see figure). The bars are made of steel having a stress-strain curve that may be idealized as elastoplastic with yield stress σY. Each bar has cross-sectional area A.Determine the yield load PY and the plastic load PP.
Two cables, each having a length L of approximately 40 m, support a loaded container of weight W (see figure). The cables, which have effective cross-sectional area A = 48.0 mm2 and effective modulus of elasticity E = 160 GPa, are identical except that one cable is longer than the other when they
A hollow circular tube T of length L = 15 in. is uniformly compressed by a force P acting through a rigid plate (see figure). The outside and inside diameters of the tube are 3.0 and 2.75 in., repectively. A concentric solid circular bar B of 1.5 in. diameter is mounted inside the tube. When no
A stepped bar ACB with circular cross sections is held between rigid supports and loaded by an axial force P at midlength (see figure). The diameters for the two parts of the bar are d1 = 20 mm and d2 = 25 mm, and the material is elastoplastic with yield stress σY = 250 MPa.Determine the
A horizontal rigid bar AB supporting a load P is hung from five symmetrically placed wires, each of cross-sectional area A (see figure). The wires are fastened to a curved surface of radius R.(a) Determine the plastic load PP if the material of the wires is elastoplastic with yield stress
A load P acts on a horizontal beam that is supported by four rods arranged in the symmetrical pattern shown in the figure. Each rod has cross-sectional area A and the material is elastoplastic with yield stress σY. Determine the plastic load PP.
The symmetric truss ABCDE shown in the figure is constructed of four bars and supports a load P at joint E. Each of the two outer bars has a cross-sectional area of 0.307 in.2, and each of the two inner bars has an area of 0.601 in.2 The material is elastoplastic with yield stress σY =
Five bars, each having a diameter of 10 mm, support a load P as shown in the figure. Determine the plastic load PP if the material is elastoplastic with yield stress Y 250 MPa.
A circular steel rod AB of diameter d = 0.60 in. is stretched tightly between two supports so that initially the tensile stress in the rod is 10 ksi (see figure). An axial force P is then applied to the rod at an intermediate location C.(a) Determine the plastic load PP if the material is
A rigid bar ACB is supported on a fulcrum at C and loaded by a force P at end B (see figure). Three identical wires made of an elastoplastic material (yield stress σY and modulus of elasticity E) resist the load P. Each wire has cross-sectional area A and length L.(a) Determine the yield
The structure shown in the figure consists of a horizontal rigid bar ABCD supported by two steel wires, one of length L and the other of length 3L/4. Both wires have cross-sectional area A and are made of elastoplastic material with yield stress σY and modulus of elasticity E. A vertical
The L-shaped arm ABC shown in the figure lies in a vertical plane and pivots about a horizontal pin at A. The arm has constant cross-sectional area and total weight W. A vertical spring of stiffness k supports the arm at point B. Obtain a formula for the elongation of the spring due to the weight
A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has stiffness k1 = 300 N/m and natural length L1 = 250 mm. The corresponding quantities for the spring on the right are k2 = 400 N/m and L2 = 200 mm. The distance between the springs is L
A hollow, circular, cast-iron pipe (Ec = 12,000 ksi) supports a brass rod (Eb 14,000 ksi) and weight W = 2 kips, as shown. The outside diameter of the pipe is dc = 6 in.(a) If the allowable compressive stress in the pipe is 5000 psi and the allowable shortening of the pipe is 0.02 in., what is the
The horizontal rigid beam ABCD is supported by vertical bars BE and CF and is loaded by vertical forces P1 = 400 kN and P2 = 360 kN acting at points A and D, respectively (see figure). Bars BE and CF are made of steel (E = 200 GPa) and have cross-sectional areas ABE = 11,100 mm2 and ACF = 9,280
A framework ABC consists of two rigid bars AB and BC, each having length b (see the first part of the figure). The bars have pin connections at A, B, and C and are joined by a spring of stiffness k. The spring is attached at the midpoints of the bars. The framework has a pin support at A and a
A steel cable with nominal diameter 25 mm (see Table 2-1) is used in a construction yard to lift a bridge section weighing 38 kN, as shown in the figure. The cable has an effective modulus of elasticity E = 140 GPa.(a) If the cable is 14 m long, how much will it stretch when the load is picked
A steel wire and a copper wire have equal lengths and support equal loads P (see figure). The moduli of elasticity for the steel and copper are Es = 30,000 ksi and Ec = 18,000 ksi, respectively.(a) If the wires have the same diameters, what is the ratio of the elongation of the copper wire to the
By what distance h does the cage shown in the figure move downward when the weight W is placed inside it? Consider only the effects of the stretching of the cable, which has axial rigidity EA = 10,700 kN. The pulley at A has diameter dA = 300 mm and the pulley at B has diameter dB = 150 mm. Also,
A safety valve on the top of a tank containing steam under pressure p has a discharge hole of diameter d (see figure). The valve is designed to release the steam when the pressure reaches the value pmax.If the natural length of the spring is L and its stiffness is k, what should be the dimension h
The device shown in the figure consists of a pointer ABC supported by a spring of stiffness k = 800 N/m. The spring is positioned at distance b = 150 mm from the pinned end A of the pointer. The device is adjusted so that when there is no load P, the pointer reads zero on the angular scale.If the
Two rigid bars, AB and CD, rest on a smooth horizontal surface (see figure). Bar AB is pivoted end A, and bar CD is pivoted at end D. The bars are connected to each other by two linearly elastic springs of stiffness k. Before the load P is applied, the lengths of the springs are such that the bars
The three-bar truss ABC shown in the figure has a span L = 3 m and is constructed of steel pipes having cross-sectional area A = 3900 mm2 and modulus of elasticity E = 200 GPa. Identical loads P act both vertically and horizontally at joint C, as shown.(a) If P = 650 kN, what is the horizontal
An aluminum wire having a diameter d = 1/10 in. and length L = 12 ft is subjected to a tensile load P (see figure). The aluminum has modulus of elasticity E = 10,600 ksi If the maximum permissible elongation of the wire is 1/8 in. and the allowable stress in tension is 10 ksi, what is the allowable
Calculate the elongation of a copper bar of solid circular cross section with tapered ends when it is stretched by axial loads of magnitude 3.0 k (see figure).The length of the end segments is 20 in. and the length of the prismatic middle segment is 50 in. Also, the diameters at cross sections A,
Consider the copper tubes joined below using a "sweated" joint. Use the properties and dimensions given.(a) Find the total elongation of segment 2-3-4 (δ2-4) for an applied tensile force of P = 5 kN. Use Ec = 120 GPa.(b) If the yield strength in shear of the tin-lead solder is y = 30
The nonprismatic cantilever circular bar shown has an internal cylindrical hole of diameter d/2 from 0 to x, so the net area of the cross section for Segment 1 is (3/4)A. Load P is applied at x, and load P/2 is applied at x = L. Assume that E is constant.(a) Find reaction force R1.(b) Find internal
A prismatic bar AB of length L, cross-sectional area A, modulus of elasticity E, and weight W hangs vertically under its own weight (see figure).(a) Derive a formula for the downward displacement δC of point C, located at distance h from the lower end of the bar.(b) What is the
A flat bar of rectangular cross section, length L, and constant thickness t is subjected to tension by forces P (see figure). The width of the bar varies linearly from b1 at the smaller end to b2 at the larger end. Assume that the angle of taper is small.(a) Derive the following formula for the
A post AB supporting equipment in a laboratory is tapered uniformly throughout its height H (see figure). The cross sections of the post are square, with dimensions b × b at the top and 1.5b × 1.5b at the base.Derive a formula for the shortening δ of the post
A long, slender bar in the shape of a right circular cone with length L and base diameter d hangs vertically under the action of its own weight (see figure). The weight of the cone is W and the modulus of elasticity of the material is E.Derive a formula for the increase δ in the length
A uniformly tapered plastic tube AB of circular cross section and length L is shown in the figure. The average diameters at the ends are dA and dB = 2dA. Assume E is constant. Find the elongation δ of the tube when it is subjected to loads P acting at the ends. Use the following
The main cables of a suspension bridge [see part (a) of the figure] follow a curve that is nearly parabolic because the primary load on the cables is the weight of the bridge deck, which is uniform in intensity along the horizontal. Therefore, let us represent the central region AOB of one of the
A bar ABC revolves in a horizontal plane about a vertical axis at the midpoint C (see figure). The bar, which has length 2L and cross-sectional area A, revolves at constant angular speed w. Each half of the bar (AC and BC) has weight W1 and supports a weight W2 at its end.Derive the following
A long, rectangular copper bar under a tensile load P hangs from a pin that is supported by two steel posts (see figure). The copper bar has a length of 2.0 m, a cross-sectional area of 4800 mm2, and a modulus of elasticity Ec = 120 GPa. Each steel post has a height of 0.5 m, a cross-sectional area
A steel bar AD (see figure) has a cross-sectional area of 0.40 in.2 and is loaded by forces P1 = 2700 lb, P2 = 1800 lb, and P3 = 1300 lb. The lengths of the segments of the bar are a = 60 in., b = 24 in., and c = 36 in.(a) Assuming that the modulus of elasticity E = 30 × 106 psi,
A rectangular bar of length L has a slot in the middle half of its length (see figure). The bar has width b, thickness t, and modulus of elasticity E. The slot has width b/4.(a) Obtain a formula for the elongation δ of the bar due to the axial loads P.(b) Calculate the elongation of
Solve the preceding problem if the axial stress in the middle region is 24,000 psi, the length is 30 in., and the modulus of elasticity is 30 × 106 psi.
A two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load P1 equals 400 kN and the second-floor load P2 equals 720 kN. Each column has length L = 3.75 m. The cross-sectional areas of the first- and second-floor columns are 11,000
A steel bar 8.0 ft long has a circular cross section of diameter d1 = 0.75 in. over one-half of its length and diameter d2 = 0.5 in. over the other half (see figure). The modulus of elasticity E = 30 × 106 psi.(a) How much will the bar elongate under a tensile load P = 5000 lb?(b) If
A bar ABC of length L consists of two parts of equal lengths but different diameters. Segment AB has diameter d1 = 100 mm, and segment BC has diameter d2 = 60 mm. Both segments have length L/2 = 0.6 m.A longitudinal hole of diameter d is drilled through segment AB for one-half of its length
A wood pile, driven into the earth, supports a load P entirely by friction along its sides (see figure). The friction force f per unit length of pile is assumed to be uniformly distributed over the surface of the pile. The pile has length L, cross-sectional area A, and modulus of elasticity E.(a)
The assembly shown in the figure consists of a brass core (diameter d1 = 0.25 in.) surrounded by a steel shell (inner diameter d2 = 0.28 in., outer diameter d3 = 0.35 in.). A load P compresses the core and shell, which have length L = 4.0 in. The moduli of elasticity of the brass and steel are Eb =
A nonprismatic bar ABC is composed of two segments: AB of length L1 and cross-sectional area A1; and BC of length L2 and cross-sectional area A2.The modulus of elasticity E, mass density p, and acceleration of gravity g are constants. Initially, bar ABC is horizontal and then is restrained at A and
A bimetallic bar (or composite bar) of square cross section with dimensions 2b × 2b is constructed of two different metals having moduli of elasticity E1 and E2 (see figure). The two parts of the bar have the same cross-sectional dimensions. The bar is compressed by forces P acting
A rigid bar of weight W = 800 N hangs from three equally spaced vertical wires (length L = 150 mm, spacing a = 50 mm): two of steel and one of aluminum. The wires also support a load P acting on the bar. The diameter of the steel wires is ds = 2 mm, and the diameter of the aluminum wire is da = 4
A horizontal rigid bar of weight W = 7200 lb is supported by three slender circular rods that are equally spaced (see figure). The two outer rods are made of aluminum (E1 = 10 × 106 psi) with diameter d1 = 0.4 in. and length L1 = 40 in. The inner rod is magnesium (E2 = 6.5
A circular steel bar ABC (E = 200 GPa) has cross-sectional area A1 from A to B and cross-sectional area A2 from B to C (see figure). The bar is supported rigidly at end A and is subjected to a load P equal to 40 kN at end C. A circular steel collar BD having cross-sectional area A3 supports the bar
A rigid bar AB of length L = 66 in. is hinged to a support at A and supported by two vertical wires attached at points C and D (see figure). Both wires have the same cross-sectional area (A = 0.0272 in.2) and are made of the same material (modulus E = 30 × 106 psi). The wire at C has
A rigid bar ABCD is pinned at point B and supported by springs at A and D (see figure). The springs at A and D have stiffnesses k1 = 10 kN/m and k2 = 25 kN/m, respectively, and the dimensions a, b, and c are 250 mm, 500 mm, and 200 mm, respectively. A load P acts at point C.If the angle of rotation
A trimetallic bar is uniformly compressed by an axial force P = 9 kips applied through a rigid end plate (see figure). The bar consists of a circular steel core surrounded by brass and copper tubes. The steel core has diameter 1.25 in., the brass tube has outer diameter 1.75 in., and the copper
A cylindrical assembly consisting of a brass core and an aluminum collar is compressed by a load P (see figure). The length of the aluminum collar and brass core is 350 mm, the diameter of the core is 25 mm, and the outside diameter of the collar is 40 mm. Also, the moduli of elasticity of the
Three prismatic bars, two of material A and one of material B, transmit a tensile load P (see figure). The two outer bars (material A) are identical. The cross-sectional area of the middle bar (material B) is 50% larger than the cross-sectional area of one of the outer bars. Also, the modulus of
A circular bar ACB of diameter d having a cylindrical hole of length x and diameter d/2 from A to C is held between rigid supports at A and B. A load P acts at L/2 from ends A and B. Assume E is constant.(a) Obtain formulas for the reactions RA and RB at supports A and B, respectively, due to the
Three steel cables jointly support a load of 12 k (see figure). The diameter of the middle cable is ¾ in. and the diameter of each outer cable is ½ in. The tensions in the cables are adjusted so that each cable carries one-third of the load (i.e., 4 k). Later, the load is increased by
A plastic rod AB of length L = 0.5 m has a diameter d1 = 30 mm (see figure). A plastic sleeve CD of length c = 0.3 m and outer diameter d2 = 45 mm is securely bonded to the rod so that no slippage can occur between the rod and the sleeve. The rod is made of an acrylic with modulus of elasticity E1
The axially loaded bar ABCD shown in the figure is held between rigid supports. The bar has cross-sectional area A1 from A to C and 2A1 from C to D.(a) Derive formulas for the reactions RA and RD at the ends of the bar.(b) Determine the displacements δB and δC at points B
The fixed-end bar ABCD consists of three prismatic segments, as shown in the figure. The end segments have cross-sectional area A1 = 840 mm2 and length L1 = 200 mm. The middle segment has cross-sectional area A2 = 1260 mm2 and length L2 = 250 mm. Loads PB and PC are equal to 25.5 kN and 17.0 kN,
The aluminum and steel pipes shown in the figure are fastened to rigid supports at ends A and B and to a rigid plate C at their junction. The aluminum pipe is twice as long as the steel pipe. Two equal and symmetrically placed loads P act on the plate at C.(a) Obtain formulas for the axial stresses
The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress σ is produced in the rails when they are heated by the sun to 120°F if the coefficient of thermal
A rigid bar ABCD is pinned at end A and supported by two cables at points B and C (see figure). The cable at B has nominal diameter dB = 12 mm and the cable at C has nominal diameter dC = 20 mm. A load P acts at end D of the bar.What is the allowable load P if the temperature rises by 60°C and
A rigid triangular frame is pivoted at C and held by two identical horizontal wires at points A and B (see figure). Each wire has axial rigidity EA = 120 k and coefficient of thermal expansion α = 12.5 × 106 / °F.(a) If a vertical load P = 500 lb acts at point D, what
A steel wire AB is stretched between rigid supports (see figure). The initial prestress in the wire is 42 MPa when the temperature is 20°C.(a) What is the stress σ in the wire when the temperature drops to 0°C?(b) At what temperature T will the stress in the wire become zero?
A copper bar AB of length 25 in. and diameter 2 in. is placed in position at room temperature with a gap of 0.008 in. between end A and a rigid restraint (see figure). The bar is supported at end B by an elastic spring with spring constant k = 1.2 × 106 lb/in.(a) Calculate the axial
A bar AB having length L and axial rigidity EA is fixed at end A (see figure). At the other end a small gap of dimension s exists between the end of the bar and a rigid surface. A load P acts on the bar at point C, which is two-thirds of the length from the fixed end.If the support reactions
Pipe 2 has been inserted snugly into Pipe 1, but the holes for a connecting pin do not line up: there is a gap s. The user decides to apply either force P1 to Pipe 1 or force P2 to Pipe 2, whichever is smaller. Determine the following using the numerical properties in the box.(a) If only P1 is
A nonprismatic bar ABC made up of segments AB (length L1, cross-sectional area A1) and BC (length L2, cross-sectional area A2) is fixed at end A and free at end C (see figure). The modulus of elasticity of the bar is E. A small gap of dimension s exists between the end of the bar and an elastic
Wires B and C are attached to a support at the left-hand end and to a pin-supported rigid bar at the right-hand end (see figure). Each wire has cross-sectional area A = 0.03 in.2 and modulus of elasticity E = 30 × 106 psi. When the bar is in a vertical position, the length of each wire is L =
A rigid steel plate is supported by three posts of high-strength concrete each having an effective cross-sectional area A = 40,000 mm2 and length L = 2 m (see figure). Before the load P is applied, the middle post is shorter than the others by an amount s = 1.0 mm.Determine the maximum allowable
A capped cast-iron pipe is compressed by a brass rod, as shown. The nut is turned until it is just snug, then add an additional quarter turn to pre-compress the CI pipe. The pitch of the threads of the bolt is p = 52 mils (a mil is one-thousandth of an inch). Use the numerical properties
An aluminum pipe has a length of 60 m at a temperature of 10°C. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe. At what temperature (degrees Celsius) will the aluminum pipe be 15 mm longer than the steel pipe? (Assume that the coefficients of thermal expansion
A plastic cylinder is held snugly between a rigid plate and a foundation by two steel bolts (see figure).Determine the compressive stress σp in the plastic when the nuts on the steel bolts are tightened by one complete turn.Data for the assembly are as follows: length L = 200 mm, pitch
Solve the preceding problem if the data for the assembly are as follows: length L = 10 in., pitch of the bolt threads p = 0.058 in., modulus of elasticity for steel Es = 30 × 106 psi, modulus of elasticity for the plastic Ep = 500 ksi, cross-sectional area of one bolt As = 0.06 in.2,
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