Questions and Answers of Mechanics of Materials

The steel bar has the original dimensions shown in the figure. If it is subjected to an axial load of 50 kN, determine the change in its length and its new cross-sectional dimensions at section
Determine the relative displacement of one end of the tapered plate with respect to the other end when it is subjected to an axial load P. -dz- VP
The assembly consists of two rigid bars that are originally horizontal. They are supported by pins and 0.25-in.-diameter A-36 steel rods. If the vertical load of 5 kip is applied to the bottom bar
The truss consists of three members, each made from A-36 steel and having a cross-sectional area of 0.75 in2. Determine the greatest load P that can be applied so that the roller support at B is not
The truss consists of three members, each made from A-36 steel and having a cross-sectional area of 0.75 in2. Determine the greatest load P acts vertically downward at C. So that the roller support
The observation cage C has a weight of 250 kip and through a system of gears, travels upward at constant velocity along the A-36 steel column, which has a height of 200 ft. The column has an outer
Determine the elongation of the aluminum strap when it is subjected to an axial force of 30 kN. Eal= 70 GPa. 6 mm 15 mm 50 mm 15 mm 30 kN 30 kN -800 mm 250 mm 250 mm
The ball is truncated at its ends and is used to support the bearing load P. If the modulus of elasticity for the material is E, determine the decrease in the ball€™s height when the load
The column is constructed from high-strength concrete and eight A992 steel reinforcing rods. If the column is subjected to an axial force of 200 kip, determine the average normal stress in the
The column is constructed from high-strength concrete and eight A992 steel reinforcing rods. If the column is subjected to an axial force of 200 kip, determine the required diameter of each rod so
The A-36 steel pipe has a 6061-T6 aluminum core. It is subjected to a tensile force of 200 kN. Determine the average normal stress in the aluminum and the steel due to this loading. The pipe has an
If column AB is made from high strength precast concrete and reinforced with four 3/4 in. diameter A-36 steel rods, determine the average normal stress developed in the concrete and in each rod. Set
If column AB is made from high strength precast concrete and reinforced with four 3/4 in. diameter A-36 steel rods, determine the maximum allowable floor loadings P. The allowable normal stresses for
Determine the support reactions at the rigid supports A and C. The material has a modulus of elasticity of E. 'A |B 2a
If the supports at A and C are flexible and have a stiffness k, determine the support reactions at A and C. The material has a modulus of elasticity of E. P. 2a
The load of 2000 lb is to be supported by the two vertical steel wires for which ÏƒY= 70 ksi. Originally wire AB is 60 in. long and wire AC is 60.04 in. long. Determine the force developed
The load of 2000 lb is to be supported by the two vertical steel wires for which ÏƒY= 70 ksi. Originally wire AB is 60 in. long and wire AC is 60.04 in. long. Determine the cross-sectional
The A-36 steel pipe has an outer radius of 20 mm and an inner radius of 15 mm. If it fits snugly between the fixed walls before it is loaded, determine the reaction at the walls when it is subjected
The 10-mm-diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. If the yield stress for the steel is (ÏƒY)st=
The 10-mm-diameter steel bolt is surrounded by a bronze sleeve. The outer diameter of this sleeve is 20 mm, and its inner diameter is 10 mm. If the bolt is subjected to a compressive force of P = 20
The assembly consists of two red brass C83400 copper rods AB and CD of diameter 30 mm, a stainless 304 steel alloy rod EF of diameter 40 mm, and a rigid cap G. If the supports at A, C, and F are
The rigid beam is supported by the three suspender bars. Bars AB and EF are made of aluminum and bar CD is made of steel. If each bar has a cross-sectional area of 450 mm2, determine the maximum
The bolt AB has a diameter of 20 mm and passes through a sleeve that has an inner diameter of 40 mm and an outer diameter of 50 mm. The bolt and sleeve are made of A-36 steel and are secured to the
If the gap between C and the rigid wall at D is initially 0.15 mm, determine the support reactions at A and D when the force P = 200 kN is applied. The assembly is made of solid A-36 steel cylinders.
The support consists of a solid red brass C83400 copper post surrounded by a 304 stainless steel tube. Before the load is applied the gap between these two parts is 1 mm. Given the dimensions shown,
The specimen represents a filament-reinforced matrix system made from plastic (matrix) and glass (fiber). If there are n fibers, each having a cross-sectional area of Afand modulus of Ef, embedded in
The rigid bar is pinned at A and supported by two aluminum rods, each having a diameter of 1 in., a modulus of elasticity Eal= 10(103) ksi, and yield stress of (ÏƒY)al= 40 ksi. If the bar
An acetal polymer block is fixed to the rigid plates at its top and bottom surfaces. If the top plate displaces 2 mm horizontally when it is subjected to a horizontal force P = 2 kN, determine the
The 8-mm-diameter bolt is made of an aluminum alloy. It fits through a magnesium sleeve that has an inner diameter of 12 mm and an outer diameter of 20 mm. If the original lengths of the bolt and
The pipe with two rigid caps attached to its ends is subjected to an axial force P. If the pipe is made from a material having a modulus of elasticity E and Poisson€™s ratio v, determine
Determine the shear strain Î³xyat corners D and C if the plate distorts as shown by the dashed lines. 5 mm, 2 mm 4 mm IB 2 mm 300 mm T2 mm х 400 mm- 3 mm
Determine the shear strain Î³xyat corners A and B if the plate distorts as shown by the dashed lines. 5 mm, 2 mm 4 mm IB 2 mm 300 mm T2 mm -X- 400 mm 3 mm
A thin wire, lying along the x axis, is strained such that each point on the wire is displaced Î”x = kx2along the x axis. If k is constant, what is the normal strain at any point P along
The nylon cord has an original length L and is tied to a bolt at A and a roller at B. If a force P is applied to the roller, determine the normal strain in the cord when the roller is at C, and at D.
Part of a control linkage for an airplane consists of a rigid member CB and a flexible cable AB. If a force is applied to the end B of the member and causes a normal strain in the cable of 0.004
Part of a control linkage for an airplane consists of a rigid member CB and a flexible cable AB. If a force is applied to the end B of the member and causes it to rotate by Î¸ = 0.5°,
The material distorts into the dashed position shown. Determine the average normal strains along the diagonals AD and CF. 30 mm 15 mm 50 mm 200 mm | 50 mm A-150 mm-
The material distorts into the dashed position shown. Determine the average normal strains Îµx, Îµyand the shear strain Î³xyat A, and the average normal strain
Determine the shear strain Î³xyat corners D and C if the plastic distorts as shown by the dashed lines. y 12 mm 4 mm 8 mm IB 3 mm 300 mm 12 mm |A -400 mm- 5 mm
Determine the shear strain Î³xyat corners A and B if the plastic distorts as shown by the dashed lines. 12 mm 4 mm 8 mm 3 mm IB 300 mm 12 mm D. 400 mm- 5 mm
If a horizontal load applied to the bar AC causes point A to be displaced to the right by an amount L, determine the normal strain in the wire AB. Originally, Î¸ = 45°. -L-
The wire AB is unstretched when Î¸ = 45 °. If a load is applied to the bar AC, which causes u to become 47°, determine the normal strain in the wire. B -L-
The pin-connected rigid rods AB and BC are inclined at Î¸ = 30° when they are unloaded. When the force P is applied Î¸ becomes 30.2°. Determine the average normal
The square deforms into the position shown by the dashed lines. Determine the shear strain at each of its corners, A, B, C, and D, relative to the x, y axes. Side D' B' remains horizontal. 3 mm D' D
The rectangular plate is subjected to the deformation shown by the dashed line. Determine the average shear strain Î³xyin the plate. 150 mm 3 mm B I 200 mm х A. 3 mm
The force applied at the handle of the rigid lever causes the lever to rotate clockwise about the pin B through an angle of 2°. Determine the average normal strain in each wire. The wires are
If the load P on the beam causes the end C to be displaced 10 mm downward, determine the normal strain in wires CE and BD. 4 m -2 m-2m-| 3 m- Эи- Аапо
A thin strip of rubber has an unstretched length of 15 in. If it is stretched around a pipe having an outer diameter of 5 in., determine the average normal strain in the strip.
An air-filled rubber ball has a diameter of 6 in. If the air pressure within the ball is increased until the diameter becomes 7 in., determine the average normal strain in the rubber.
The cable has a specific weight g (weight/volume) and cross-sectional area A. Assuming the sag s is small, so that the cable€™s length is approximately L and its weight can be distributed
The yoke-and-rod connection is subjected to a tensile force of 5 kN. Determine the average normal stress in each rod and the average shear stress in the pin A between the members. 40 mm 5 kN. 30 mm
The 150 mm by 150 mm block of aluminum supports a compressive load of 6 kN. Determine the average normal and shear stress acting on the plane through section a€“a. Show the results on a
Determine the average punching shear stress the circular shaft creates in the metal plate through section AC and BD. Also, what is the average bearing stress developed on the surface of the plate
The circular punch B exerts a force of 2 kN on the top of the plate A. Determine the average shear stress in the plate due to this loading. 2 kN 4 mm | |2 mm
Determine the required thickness of member BC to the nearest 1/16 in., and the diameter of the pins at A and B if the allowable normal stress for member BC is Ïƒallow= 29 ksi and the
The long bolt passes through the 30-mm-thick plate. If the force in the bolt shank is 8 kN, determine the average normal stress in the shank, the average shear stress along the cylindrical area of
The beam AB is pin supported at A and supported by a cable BC. A separate cable CG is used to hold up the frame. If AB weighs 120 lb/ft and the column FC has a weight of 180 lb/ft, determine the
The bar is connected to the support using a pin having a diameter of d = 1 in. If the allowable tensile stress for the bar is (Ïƒt)allow= 20 ksi, and the allowable bearing stress between
If the allowable tensile stress for the bar is (Ïƒt)allow= 21 ksi, and the allowable shear stress for the pin is Ï„allow= 12 ksi, determine the diameter of the pin so that the
The aluminum bracket A is used to support the centrally applied load of 8 kip. If it has a thickness of 0.5 in., determine the smallest height h in order to prevent a shear failure. The failure shear
The rods AB and CD are made of steel. Determine their smallest diameter so that they can support the dead loads shown. The beam is assumed to be pin connected at A and C. Use the LRFD method, where
The hanger is supported using the rectangular pin. Determine the required thickness t of the hanger, and dimensions a and b if the suspended load is P = 60 kN. The allowable tensile stress is
The hanger is supported using the rectangular pin. Determine the magnitude of the allowable suspended load P if the allowable bearing stress is (Ïƒb)allow= 220 MPa, the allowable tensile
The compound wooden beam is connected together by a bolt at B. Assuming that the connections at A, B, C, and D exert only vertical forces on the beam, determine the required diameter of the bolt at B
Determine the maximum allowable load P that can be safely supported by the frame if t = 1.25 in. and b = 3.5 in. The wood has a normal failure stress of Ïƒfail= 6 ksi, and a shear failure
Determine the required minimum thickness t of member AB and edge distance b of the frame if P = 9 kip and the factor of safety against failure is 2. The wood has a normal failure stress of
The two aluminum rods AB and AC have diameters of 10 mm and 8 mm, respectively. Determine the largest vertical force P that can be supported. The allowable tensile stress for the aluminum is
The two aluminum rods support the vertical force of P = 20 kN. Determine their required diameters if the allowable tensile stress for the aluminum is Ïƒallow= 150 MPa. 45°
The bar has a cross-sectional area A and is subjected to the axial load P. Determine the average normal and average shear stresses acting over the shaded section, which is oriented at u from the
Determine the largest intensity w of the uniform loading that can be applied to the frame without causing either the average normal stress or the average shear stress at section b€“b to
Determine the average normal strain that occurs along the diagonals AC and DB. 5 mm, 2 mm 4 mm 2 mm 300 mm T2 mm 400 mm 3 mm
The stress€“strain diagram for polyethylene, which is used to sheath coaxial cables, is determined from testing a specimen that has a gage length of 10 in. If a load P on the specimen
The triangular plate is fixed at its base, and its apex A is given a horizontal displacement of 5 mm. Determine the average normal strain Îµxalong the x axis. 45° 800 mm 45° A' 5 mm 45%
The triangular plate is fixed at its base, and its apex A is given a horizontal displacement of 5 mm. Determine the average normal strain Îµx' along the x' axis. 45 800 mm 45° x' A' -5
If the normal strain is defined in reference to the final length ˆ†s', that is,instead of in reference to the original length, Eq. 2€“2, show that the difference in these strains
The head H is connected to the cylinder of a compressor using six 3/16-in. diameter steel bolts. If the clamping force in each bolt is 800 lb, determine the normal strain in the bolts. If
The wires each have a diameter of 1/2 in., length of 2 ft, and are made from 304 stainless steel. Determine the magnitude of force P so that the rigid beam tilts 0.015°. DO 2 ft 2 ft - -1 ft B A
The wires each have a diameter of 1/2 in., length of 2 ft, and are made from 304 stainless steel. If P = 6 kip, determine the angle of tilt of the rigid beam AB. D 2 ft 2 ft -1 ft-
The triangular plate is fixed at its base, and its apex A is given a horizontal displacement of 5 mm. Determine the shear strain, Î³xy, at A. 45° 800 mm 45 A' -5 mm 45% 800 mm
The corners of the square plate are given the displacements indicated. Determine the average normal strains Îµxand Îµyalong the x and y axes. 0.2 in. 10 in. -X- 0.3 in- 0.3
The assembly consists of three disks A, B, and C that are used to support the load of 140 kN. Determine the smallest diameter d1of the top disk, the largest diameter d2of the opening, and the largest
The boom is supported by the winch cable that has an allowable normal stress of Ïƒallow= 24 ksi. If it supports the 5000 lb crate when f = 20°, determine the smallest diameter of the
The boom is supported by the winch cable that has a diameter of 0.25 in. and an allowable normal stress of Ïƒallow= 24 ksi. Determine the greatest weight of the crate that can be supported
The steel pipe is supported on the circular base plate and concrete pedestal. If the thickness of the pipe is t = 5 mm and the base plate has a radius of 150 mm, determine the factors of safety
Determine the required diameter of the pins at A and B if the allowable shear stress for the material is Ï„allow= 100 MPa. Both pins are subjected to double shear. 2 kN/m A 3 m
The cotter is used to hold the two rods together. Determine the smallest thickness t of the cotter and the smallest diameter d of the rods. All parts are made of steel for which the failure normal
If the allowable tensile stress for wires AB and AC is Ïƒallow= 180 MPa, and wire AB has a diameter of 5 mm and AC has a diameter of 6 mm, determine the greatest force P that can be applied
If the allowable tensile stress for wires AB and AC is Ïƒallow= 200 MPa, determine the required diameter of each wire if the applied load is P = 6 kN. 45°
Determine the greatest constant angular velocity Ï‰ of the flywheel so that the average normal stress in its rim does not exceed Ïƒ = 15 MPa. Assume the rim is a thin ring having
The radius of the pedestal is defined by r = (0.5eˆ’0.08y2)m, where y is in meters. If the material has a density of 2.5 Mg/m3, determine the average normal stress at the support. Fr= 0.5e
If A and B are both made of wood and are 3/8 in. thick, determine to the nearest 1/4 in. the smallest dimension h of the vertical segment so that it does not fail in shear. The allowable shear stress
The lever is attached to the shaft A using a key that has a width d and length of 25 mm. If the shaft is fixed and a vertical force of 200 N is applied perpendicular to the handle, determine the
The connection is made using a bolt and nut and two washers. If the allowable bearing stress of the washers on the boards is (Ïƒb)allow= 2 ksi, and the allowable tensile stress within the
The tension member is fastened together using two bolts, one on each side of the member as shown. Each bolt has a diameter of 0.3 in. Determine the maximum load P that can be applied to the member if
The steel swivel bushing in the elevator control of an airplane is held in place using a nut and washer as shown in Fig. (a). Failure of the washer A can cause the push rod to separate as shown in
The spring mechanism is used as a shock absorber for a load applied to the drawbar AB. Determine the force in each spring when the 50-kN force is applied. Each spring is originally unstretched and
Determine the size of square bearing plates A€² and B€² required to support the loading. Take P = 1.5 kip. Dimension the plates to the nearest 1/2 in. The reactions at the
The bars of the truss each have a cross-sectional area of 1.25 in2. If the maximum average normal stress in any bar is not to exceed 20 ksi, determine the maximum magnitude P of the loads that can be
Determine the maximum load P that can be applied to the beam if the bearing plates A€² and B€² have square cross sections of 2 in. Ã— 2 in. and 4 in. Ã— 4
Determine the required diameter of the pins at A and B to the nearest 1/16 in. if the allowable shear stress for the material is Ï„allow= 6 ksi. Pin A is subjected to double shear, whereas

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