Questions and Answers of Mechanics of Materials

The prismatic bar has a cross-sectional area A. If it is subjected to a distributed axial loading that increases linearly from w = 0 at x = 0 to w = w0at x = a, and then decreases linearly to w = 0
The prismatic bar has a cross-sectional area A. If it is subjected to a distributed axial loading that increases linearly from w = 0 at x = 0 to w = w0at x = a, and then decreases linearly to w = 0
The bar has a cross-sectional area of 400(10ˆ’6) m2. If it is subjected to a uniform axial distributed loading along its length and to two concentrated loads, determine the average normal
The bar has a cross-sectional area of 400(10ˆ’6) m2. If it is subjected to a uniform axial distributed loading along its length and to two concentrated loads, determine the average normal
The uniform bar, having a cross-sectional area of A and mass per unit length of m, is pinned at its center. If it is rotating in the horizontal plane at a constant angular rate of Ï‰,
Rods AB and BC have diameters of 4 mm and 6 mm, respectively. If the 3 kN force is applied to the ring at B, determine the angle Î¸ so that the average normal stress in each rod is
The pier is made of material having a specific weight g. If it has a square cross section, determine its width w as a function of z so that the average normal stress in the pier remains constant. The
The 2-Mg concrete pipe has a center of mass at point G. If it is suspended from cables AB and AC, determine the diameter of cable AB so that the average normal stress in this cable is the same as in
The 2-Mg concrete pipe has a center of mass at point G. If it is suspended from cables AB and AC, determine the average normal stress in the cables. The diameters of AB and AC are 12 mm and 10 mm,
The two members used in the construction of an aircraft fuselage are joined together using a 30° fish-mouth weld. Determine the average normal and average shear stress on the plane of each weld.
The bar has a cross-sectional area of 400(10ˆ’6) m2. If it is subjected to a uniform axial distributed loading along its length of 9 kN/m, and to two concentrated loads as shown, determine
The bar has a cross-sectional area of 400(10ˆ’6) m2. If it is subjected to a triangular axial distributed loading along its length which is 0 at x = 0 and 9 kN/m at x = 1.5 m, and to two
If P = 15 kN, determine the average shear stress in the pins at A, B, and C. All pins are in double shear, and each has a diameter of 18 mm. 4P 4P 2P 0.5 m 0.5,m -1.5 m -1 m--1.5 m 307
If the average normal stress in each of the 20-mm-diameter bars is not allowed to exceed 150 MPa, determine the maximum force P that can be applied to joint C. 1.5 m 2 m –
Determine the average normal stress in each of the 20-mm-diameter bars of the truss. Set P = 40 kN. 1.5 m 2 m
The plate has a width of 0.5 m. If the stress distribution at the support varies as shown, determine the force P applied to the plate and the distance d to where it is applied. 4 m- (15x2) MPa- 30 MPa
If the block is subjected to a centrally applied force of P = 6 kip, determine the average normal stress in the material. Show the stress acting on a differential volume element of the material. 1
If the material fails when the average normal stress reaches 120 psi, determine the largest centrally applied vertical load P the block can support. 1 in. 1 in 4 in. 1 in. 12 in. in.
The small block has a thickness of 0.5 in. If the stress distribution at the support developed by the load varies as shown, determine the force F applied to the block, and the distance d to where it
A differential element taken from a curved bar is shown in the figure. Show that dN/dÎ¸ = V, dV/dÎ¸ = €“ N, dM/dÎ¸ = €“T, and
The brace and drill bit is used to drill a hole at O. If the drill bit jams when the brace is subjected to the forces shown, determine the resultant internal loadings acting on the cross section of
Determine the resultant internal loadings acting on the cross section of the frame at points F and G. The contact at E is smooth. 5 ft 30° 1.5 ft ,1.5 ft 2 ft B. -3 ft- 2 ft 80 lb 4 ft
Determine the resultant internal loadings acting on the cross section at point C. The cooling unit has a total weight of 52 kip and a center of gravity at G. 0.2 f в - 3 ft- - 3A- 3ft
The shaft is supported at its ends by two bearings A and B and is subjected to the forces applied to the pulleys fixed to the shaft. Determine the resultant internal loadings acting on the cross
The beam supports the distributed load shown. Determine the resultant internal loadings on the cross section at points D and E. Assume the reactions at the supports A and B are vertical. 800 lb/ft IB
The beam supports the triangular distributed load shown. Determine the resultant internal loadings on the cross section at point C. Assume the reactions at the supports A and B are vertical. 800
The blade of the hacksaw is subjected to a pretension force of F = 100 N. Determine the resultant internal loadings acting on section b€“b that passes through point D. 225 mm- 30°, b 150 mm
The blade of the hacksaw is subjected to a pretension force of F = 100 N. Determine the resultant internal loadings acting on section a€“a that passes through point D. -225 mm 30%,Ь D 150
Determine the resultant internal loadings acting on the cross sections at points F and G of the frame. 4 ft 75 Ib/ft B. -2 ft 1 ft -2 ft 1 ft 30° '1 ft 150 lb to
Determine the resultant internal loadings acting on the cross sections at points D and E of the frame. 4 ft 75 Ib/ft LA B. 2 ft 2 ft 1 ft 1 ft 30° 1 ft 150 lb
The beam supports the distributed load shown. Determine the resultant internal loadings acting on the cross section at point D. Assume the reactions at the supports A and B are vertical. 4 kN/m -1.5
The beam supports the distributed load shown. Determine the resultant internal loadings acting on the cross section at point C. Assume the reactions at the supports A and B are vertical. 4 kN/m A
Determine the resultant internal loadings at cross sections at points E and F on the assembly. 1.25 kN/m 1.5 m '0.5 m'0.5 m'0.5 m
Determine the resultant internal loadings on the cross section at point D. 1.25 kN/m 1.5 m '0.5 m' 0.5 m'0.5 m
The rods each have the same 25-mm diameter and 600-mm length. If they are made of A992 steel, determine the forces developed in each rod when the temperature increases by 50° C. -600 mm 60°
Two A992 steel pipes, each having a cross-sectional area of 0.32 in2, are screwed together using a union at B. Originally the assembly is adjusted so that no load is on the pipe. If the union is then
The force P is applied to the bar, which is made from an elastic perfectly plastic material. Construct a graph to show how the force in each section AB and BC (vertical axis) varies as P (horizontal
The 2014-T6 aluminum rod has a diameter of 0.5 in. and is lightly attached to the rigid supports at A and B when T1= 70°F. If the temperature becomes T2= €“ 10°F, and an axial force
The 2014-T6 aluminum rod has a diameter of 0.5 in. and is lightly attached to the rigid supports at A and B when T1= 70°F. Determine the force P that must be applied to the collar so that, when T
The rigid link is supported by a pin at A and two A-36 steel wires, each having an unstretched length of 12 in. and cross-sectional area of 0.0125 in2. Determine the force developed in the wires when
The joint is made from three A992 steel plates that are bonded together at their seams. Determine the displacement of end A with respect to end B when the joint is subjected to the axial loads. Each
The solid shaft of radius r is subjected to a torque T. Determine the radius r of the inner core of the shaft that resists one-half of the applied torque (T>2). Solve the problem two ways:
The solid shaft of radius r is subjected to a torque T. Determine the radius r' of the inner core of the shaft that resists one-quarter of the applied torque (T/4). Solve the problem two
A shaft is made of an aluminum alloy having an allowable shear stress of Ï„allow= 100 MPa. If the diameter of the shaft is 100 mm, determine the maximum torque T that can be transmitted.
The copper pipe has an outer diameter of 40 mm and an inner diameter of 37 mm. If it is tightly secured to the wall and three torques are applied to it, determine the absolute maximum shear stress
The copper pipe has an outer diameter of 2.50 in. and an inner diameter of 2.30 in. If it is tightly secured to the wall and three torques are applied to it, determine the shear stress developed at
The solid aluminum shaft has a diameter of 50 mm and an allowable shear stress of Ï„allow= 60 MPa. Determine the largest torque T1that can be applied to the shaft if it is also subjected to
The solid aluminum shaft has a diameter of 50 mm. Determine the absolute maximum shear stress in the shaft and sketch the shear-stress distribution along a radial line of the shaft where the shear
The solid 30-mm-diameter shaft is used to transmit the torques applied to the gears. Determine the absolute maximum shear stress in the shaft. 300 N-m 500 N-m 200 N-m 400 N-m 300 mm B. 400 mm 500 mm
The solid shaft is fixed to the support at C and subjected to the torsional loadings. Determine the shear stress at points A and B on the surface, and sketch the shear stress on volume elements
The link acts as part of the elevator control for a small airplane. If the attached aluminum tube has an inner diameter of 25 mm and a wall thickness of 5 mm, determine the maximum shear stress in
The assembly consists of two sections of galvanized steel pipe connected together using a reducing coupling at B. The smaller pipe has an outer diameter of 0.75 in. and an inner diameter of 0.68 in.,
The shaft has an outer diameter of 100 mm and an inner diameter of 80 mm. If it is subjected to the three torques, determine the absolute maximum shear stress in the shaft. The smooth bearings A and
The shaft has an outer diameter of 100 mm and an inner diameter of 80 mm. If it is subjected to the three torques, plot the shear stress distribution along a radial line for the cross section within
A steel tube having an outer diameter of 2.5 in. is used to transmit 9 hp when turning at 27 rev/min. Determine the inner diameter d of the tube to the nearest 18 in. if the allowable shear stress is
If the gears are subjected to the torques shown, determine the maximum shear stress in the segments AB and BC of the A-36 steel shaft. The shaft has a diameter of 40 mm. 300 N-m 100 N-m 200 N-m
If the gears are subjected to the torques shown, determine the required diameter of the A-36 steel shaft to the nearest mm if Ï„allow= 60 MPa. 300 N-m 100 N-m 200 N-m
The rod has a diameter of 1 in. and a weight of 10 lb/ft. Determine the maximum torsional stress in the rod at a section located at A due to the rod€™s weight. 4.5 ft 1.5 ft 1.5 ft B. 4 ft
The rod has a diameter of 1 in. and a weight of 15 lb/ft. Determine the maximum torsional stress in the rod at a section located at B due to the rod€™s weight. 4.5 ft -1.5 ft 1.5t B. 1.5 ft
The copper pipe has an outer diameter of 3 in. and an inner diameter of 2.5 in. If it is tightly secured to the wall at C and a uniformly distributed torque is applied to it as shown, determine the
The copper pipe has an outer diameter of 3 in. and an inner diameter of 2.50 in. If it is tightly secured to the wall at C and it is subjected to the uniformly distributed torque along its entire
The 60-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the shear stress at points A and B, and sketch the shear stress on volume elements
The 60-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimum shear stresses on the shaft€™s surface,
The solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the required diameter d of the shaft if the allowable shear stress for the material is
The 60-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimum shear stresses on the shaft's surface and specify
The solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the required diameter d of the shaft if the allowable shear stress for the material is Ï„allow=
When drilling a well at constant angular velocity, the bottom end of the drill pipe encounters a torsional resistance TA. Also, soil along the sides of the pipe creates a distributed frictional
The drive shaft AB of an automobile is made of a steel having an allowable shear stress of Ï„allow= 8 ksi. If the outer diameter of the shaft is 2.5 in. and the engine delivers 200 hp to
The drive shaft AB of an automobile is to be designed as a thin-walled tube. The engine delivers 150 hp when the shaft is turning at 1000 rev>min. Determine the minimum thickness of the
The shaft is subjected to a distributed torque along its length of t = (10x2) N ˆ™ m/m, where x is in meters. If the maximum stress in the shaft is to remain constant at 80 MPa, determine
The motor delivers 50 hp while turning at a constant rate of 1350 rpm at A. Using the belt and pulley system this loading is delivered to the steel blower shaft BC. Determine to the nearest 1/8 in.
The solid steel shaft AC has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at C, which delivers 3 kW of power to the shaft while it is turning at 50
The pump operates using the motor that has a power of 85 W. If the impeller at B is turning at 150 rev/min, determine the maximum shear stress in the 20-mm-diameter transmission shaft at A. 150
The gear motor can develop 1/10 hp when it turns at 300 rev/min. If the shaft has a diameter of 1/2 in., determine the maximum shear stress in the shaft. ニ川ニ川
The gear motor can develop 1/10 hp when it turns at 80 rev/min. If the allowable shear stress for the shaft is Ï„allow= 4 ksi, determine the smallest diameter of the shaft to the nearest
The gear motor can develop 1/4 hp when it turns at 600 rev/min. If the shaft has a diameter of 1/2 in., determine the maximum shear stress in the shaft.
The gear motor can develop 2 hp when it turns at 150 rev/min. If the allowable shear stress for the shaft is Ï„allow= 8 ksi, determine the smallest diameter of the shaft to the nearest 1/8
The 6-hp reducer motor can turn at 1200 rev/min. If the allowable shear stress for the shaft is Ï„allow= 6 ksi, determine the smallest diameter of the shaft to the nearest 1/16 in. that can
The 6-hp reducer motor can turn at 1200 rev/min. If the shaft has a diameter of 5/8 in., determine the maximum shear stress in the shaft.
The solid steel shaft DF has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 12 kW of power to the shaft while it is turning at 50
The solid steel shaft DF has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 12 kW of power to the shaft while it is turning at 50
The A-36 steel tubular shaft is 2 m long and has an outer diameter of 50 mm. When it is rotating at 40 rad/s, it transmits 25 kW of power from the motor M to the pump P. Determine the smallest
The A-36 solid steel shaft is 2 m long and has a diameter of 60 mm. It is required to transmit 60 kW of power from the moor M to the pump P. Determine the smallest angular velocity the shaft if the
The assembly consists of two posts AB and CD each made from material 1 having a modulus of elasticity of E1and a cross-sectional area A1, and a central post EF made from material 2 having a modulus
The wheel is subjected to a force of 18 kN from the axle. Determine the force in each of the three spokes. Assume the rim is rigid and the spokes are made of the same material, and each has the same
The C83400-red-brass rod AB and 2014-T6- aluminum rod BC are joined at the collar B and fixed connected at their ends. If there is no load in the members when T1= 50°F, determine the average
The assembly has the diameters and material indicated. If it fits securely between its fixed supports when the temperature is T1= 70Â°F, determine the average normal stress in each material when
The rod is made of A992 steel and has a diameter of 0.25 in. If the rod is 4 ft long when the springs are compressed 0.5 in. and the temperature of the rod is T = 40°F, determine the force in the
The two cylindrical rod segments are fixed to the rigid walls such that there is a gap of 0.01 in. between them when T1= 60°F. What larger temperature T2is required in order to just close the
The two cylindrical rod segments are fixed to the rigid walls such that there is a gap of 0.01 in. between them when T1= 60°F. Each rod has a diameter of 1.25 in. Determine the average normal
The pipe is made of A992 steel and is connected to the collars at A and B. When the temperature is 60°F, there is no axial load in the pipe. If hot gas traveling through the pipe causes its
The bronze C86100 pipe has an inner radius of 0.5 in. and a wall thickness of 0.2 in. If the gas flowing through it changes the temperature of the pipe uniformly from TA= 200€‘F at A to TB=
The 40-ft-long A-36 steel rails on a train track are laid with a small gap between them to allow for thermal expansion. Determine the required gap d so that the rails just touch one another when the
The device is used to measure a change in temperature. Bars AB and CD are made of A-36 steel and 2014-T6 aluminum alloy, respectively. When the temperature is at 75°F, ACE is in the horizontal
The bar has a cross-sectional area A, length L, modulus of elasticity E, and coefficient of thermal expansion a. The temperature of the bar changes uniformly along its length from TAat A to TBat B so
When the temperature is at 30°C, the A-36 steel pipe fits snugly between the two fuel tanks. When fuel flows through the pipe, the temperatures at ends A and B rise to 130°C and 80°C,
When the temperature is at 30°C, the A-36 steel pipe fits snugly between the two fuel tanks. When fuel flows through the pipe, the temperatures at ends A and B rise to 130°C and 80°C,
When the temperature is at 30°C, the A-36 steel pipe fits snugly between the two fuel tanks. When fuel flows through the pipe, it causes the temperature to vary along the pipe as T = (5/3 x2- 20x
The 50-mm-diameter cylinder is made from Am 1004-T61 magnesium and is placed in the clamp when the temperature is T1= 20° C. If the 304-stainless-steel carriage bolts of the clamp each have a
The 50-mm-diameter cylinder is made from Am 1004-T61 magnesium and is placed in the clamp when the temperature is T1= 15°C. If the two 304-stainless-steel carriage bolts of the clamp each have a

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