Questions and Answers of Mechanics of Materials

The coiled spring is subjected to a force P. If we assume the shear stress caused by the shear force at any vertical section of the coil wire to be uniform, show that the maximum shear stress in the
The frame supports a centrally applied distributed load of 1.8 kip>ft. Determine the state of stress at points A and B on member CD and indicate the results on a volume element located at each of
The 1-in.-diameter rod is subjected to the loads shown. Determine the state of stress at point A, and show the results on a differential volume element located at this point. y 9 in. 200 Ib 300 Ib
The 1-in.-diameter rod is subjected to the loads shown. Determine the state of stress at point B, and show the results on a differential volume element located at this point. 9 in. 200 lb B. 300 Ib
The sign is subjected to the uniform wind loading. Determine the stress components at points A and B on the 100-mm-diameter supporting post. Show the results on a volume element located at each of
The sign is subjected to the uniform wind loading. Determine the stress components at points C and D on the 100-mm-diameter supporting post. Show the results on a volume element located at each of
The bearing pin supports the load of 900 lb. Determine the stress components in the support member at point A. Represent the state of stress at point A with a differential element.
The bearing pin supports the load of 900 lb. Determine the stress components in the support member at point B. Represent the state of stress at point B with a differential element. 0.5 in. 0.25 in.
The C-frame is used in a riveting machine. If the force at the ram on the clamp at D is P = 8 kN, sketch the stress distribution acting over the section a€“a. -200 mm- 10 mm 40 mm -10 mm 60
Determine the maximum ram force P that can be applied to the clamp at D if the allowable normal stress for the material is Ïƒallow= 180 MPa. a D -200 mm-| 10 mm HTao mm 10 mm 60 mm
The uniform sign has a weight of 1500 lb and is supported by the pipe AB, which has an inner radius of 2.75 in. and an outer radius of 3.00 in. If the face of the sign is subjected to a uniformwind
The uniform sign has a weight of 1500 lb and is supported by the pipe AB, which has an inner radius of 2.75 in. and an outer radius of 3.00 in. If the face of the sign is subjected to a uniform wind
The pin support is made from a steel rod and has a diameter of 20 mm. Determine the stress components at points A and B and represent the results on a volume element located at each of these points.
The pin support is made from a steel rod and has a diameter of 20 mm. Determine the stress components at points C and D and represent the results on a volume element located at each of these points.
The handle of the press is subjected to a force of 20 lb. Due to internal gearing, this causes the block to be subjected to a compressive force of 80 lb. Determine the normal-stress acting in the
The bar has a diameter of 40 mm. Determine the state of stress at point A and show the results on a differential volume element located at this point. 200 mm y 200 mm 1200 N 15 800 N
The bar has a diameter of 40 mm. determine the state of stress at point B and show the results on a differential volume element located at this point. 200 mm y 200 mm 1200 N 15 800 N
The 3/4-in.-diameter shaft is subjected to the loading shown. Determine the stress components at point A. Sketch the results on a volume element located at this point. The journal bearing at C can
The 3/4-in.-diameter shaft is subjected to the loading shown. Determine the stress components at point B. Sketch the results on a volume element located at this point. The journal bearing at C can
The hook is subjected to the force of 80 lb. Determine the state of stress at point A at section a€“a. The cross section is circular and has a diameter of 0.5 in. Use the curved-beam
The hook is subjected to the force of 80 lb. Determine the state of stress at point B at section a€“a. The cross section has a diameter of 0.5 in. Use the curved-beam formula to calculate
The eye hook has the dimensions shown. If it supports a cable loading of 800 lb, determine the maximum normal stress at section a€“a and sketch the stress distribution acting over the cross
The 20-kg drum is suspended from the hook mounted on the wooden frame. Determine the state of stress at point E on the cross section of the frame at section a€“a. Indicate the results on an
The 20-kg drum is suspended from the hook mounted on the wooden frame. Determine the state of stress at point F on the cross section of the frame at section b€“b. Indicate the results on an
The gondola and passengers have a weight of 1500 lb and center of gravity at G. The suspender arm AE has a square cross-sectional area of 1.5 in. by 1.5 in., and is pin connected at its ends A and E.
If the cross section of the femur at section a€“a can be approximated as a circular tube as shown, determine the maximum normal stress developed on the cross section at section
A bar having a square cross section of 30 mm by 30 mm is 2 m long and is held upward. If it has a mass of 5 kg/m, determine the largest angle u, measured from the vertical, at which it can be
The wall hanger has a thickness of 0.25 in. and is used to support the vertical reactions of the beam that is loaded as shown. If the load is transferred uniformly to each strap of the hanger,
The wall hanger has a thickness of 0.25 in. and is used to support the vertical reactions of the beam that is loaded as shown. If the load is transferred uniformly to each strap of the hanger,
The H-beam is subjected to a shear of V = 80 kN. Determine the shear flow at point A. 250'mm 30 mm 300 mm -25 mm 50 mm -25 mm
The H-beam is subjected to a shear of V = 80 kN. Sketch the shear-stress distribution acting along one of its side segments. Indicate all peak values 250'mm 30 mm 25 mm 300 mm 50 mm -25 mm
The built-up beam is formed by welding together the thin plates of thickness 5 mm. Determine the location of the shear center O. -5 mm 200'mm 100 mm 100 mm 200 mm 300 mm
The assembly is subjected to a vertical shear of V = 7 kip. Determine the shear flow at points A and B and the maximum shear flow in the cross section A- 0.5 in. B- 6 in. 2 in 6 in.. 0.5 in. 0.5 in.
The box girder is subjected to a shear of V = 15 kN. Determine the shear flow at point B and the maximum shear flow in the girder€™s web AB. -15 mm 250 mm -15 mm 150 mm 25 mm 25 mm 150 mm
Determine the location e of the shear center, point O, for the thin-walled member having a slit along its section. -100 mm- 100 mm Fe- 100 mm
Determine the location e of the shear center, point O, for the thin-walled member. The member segments have the same thickness t. -Ь- IT
The beam supports a vertical shear of V = 7 kip. Determine the resultant force in segment AB of the beam. 0.5 in. 10 in. -0.5 in. IA 0.5 in. 5 in.
The stiffened beam is constructed from plates having a thickness of 0.25 in. If it is subjected to a shear of V = 8 kip, determine the shear-flow distribution in segments AB and CD. What is the
The pipe is subjected to a shear force of V = 8 kip. Determine the shear flow in the pipe at points A and B. 0.2 in. -6 in.
Determine the location e of the shear center, point O, for the thin-walled member. The member segments have the same thickness t. -p- -e-
A thin plate of thickness t is bent to form the beam having the cross section shown. Determine the location of the shear center O.
Determine the location e of the shear center, point O, for the tube having a slit along its length.
The beam is fabricated from four boards nailed together as shown. Determine the shear force each nail along the sides C and the top D must resist if the nails are uniformly spaced at s = 3 in. The
The T-beam is subjected to a shear of V = 150 kN. Determine the amount of this force that is supported by the web B. 200 mm 40 mm V= 150 kN 200 mm 40 mm
The member is subject to a shear force of V = 2 kN. Determine the shear flow at points A, B, and C. The thickness of each thin-walled segment is 15 mm. 200 mm 100 mm 300 mm V = 2 kN
Determine the shear stress at points B and C on the web of the beam located at section a€“a. 8000 lb 150 Ib/ft B. 4 ft -4 ft - 1.5 ftT1.5 ft
Determine the maximum shear stress acting at section a€“a in the beam. 8000 lb 150 lb/ft B. 4 ft 4 ft 1.5 ftT1.5 ft
A spherical gas tank has an inner radius of r = 1.5 m. If it is subjected to an internal pressure of p = 300 kPa, determine its required thickness if the maximum normal stress is not to exceed 12 MPa.
A pressurized spherical tank is made of 0.5-in.-thick steel. If it is subjected to an internal pressure of p = 200 psi, determine its outer radius if the maximum normal stress is not to exceed 15 ksi.
The thin-walled cylinder can be supported in one of two ways as shown. Determine the state of stress in the wall of the cylinder for both cases if the piston P causes the internal pressure to be 65
The tank of the air compressor is subjected to an internal pressure of 90 psi. If the inner diameter of the tank is 22 in., and the wall thickness is 0.25 in., determine the stress components acting
Air pressure in the cylinder is increased by exerting forces P = 2 kN on the two pistons, each having a radius of 45 mm. If the cylinder has a wall thickness of 2 mm, determine the state of stress in
Determine the maximum force P that can be exerted on each of the two pistons so that the circumferential stress in the cylinder does not exceed 3 MPa. Each piston has a radius of 45 mm and the
A boiler is constructed of 8-mm-thick steel plates that are fastened together at their ends using a butt joint consisting of two 8-mm cover plates and rivets having a diameter of 10 mm and spaced 50
The steel water pipe has an inner diameter of 12 in. and a wall thickness of 0.25 in. If the valve A is opened and the flowing water has a pressure of 250 psi as it passes point B, determine the
The steel water pipe has an inner diameter of 12 in. and a wall thickness of 0.25 in. If the valve A is closed and the water pressure is 300 psi, determine the longitudinal and hoop stress developed
The A-36-steel band is 2 in. wide and is secured around the smooth rigid cylinder. If the bolts are tightened so that the tension in them is 400 lb, determine the normal stress in the band, the
The gas pipe line is supported every 20 ft by concrete piers and also lays on the ground. If there are rigid retainers at the piers that hold the pipe fixed, determine the longitudinal and hoop
A pressure-vessel head is fabricated by welding the circular plate to the end of the vessel as shown. If the vessel sustains an internal pressure of 450 kPa, determine the average shear stress in the
An A-36-steel hoop has an inner diameter of 23.99 in., thickness of 0.25 in., and width of 1 in. If it and the 24-in.-diameter rigid cylinder have a temperature of 65° F, determine the
The ring, having the dimensions shown, is placed over a flexible membrane which is pumped up with a pressure p. Determine the change in the inner radius of the ring after this pressure is applied.
The inner ring A has an inner radius r1and outer radius r2. The outer ring B has an inner radius r3and an outer radius r4, and r2> r3. If the outer ring is heated and then fitted over the inner
Two hemispheres having an inner radius of 2 ft and wall thickness of 0.25 in. are fitted together, and the inside pressure is reduced to -10 psi. If the coefficient of static friction is µs=
In order to increase the strength of the pressure vessel, filament winding of the same material is wrapped around the circumference of the vessel as shown. If the pretension in the filament is T and
Determine the shortest distance d to the edge of the plate at which the force P can be applied so that it produces no compressive stresses in the plate at section a€“a. The plate has a
Determine the maximum distance d to the edge of the plate at which the force P can be applied so that it produces no compressive stresses on the plate at section a€“a. The plate has a
The plate has a thickness of 20 mm and the force P = 3 kN acts along the centerline of this thickness such that d = 150 mm. Plot the distribution of normal stress acting along section a€“a.
If the load has a weight of 600 lb, determine the maximum normal stress on the cross section of the supporting member at section a€“a. Also, plot the normal-stress distribution over the
The steel bracket is used to connect the ends of two cables. If the allowable normal stress for the steel is sallow = 30 ksi, determine the largest tensile force P that can be applied to the cables.
The steel bracket is used to connect the ends of two cables. If the applied force P = 1.50 kip, determine the maximum normal stress in the bracket. Assume the bracket is a rod having a diameter of
The column is built up by gluing the two boards together. Determine the maximum normal stress on the cross section when the eccentric force of P = 50 kN is applied. 150 mm 250 mm 75 mm 150 mm 50 mm
The column is built up by gluing the two boards together. If the wood has an allowable normal stress of Ïƒallow= 6 MPa, determine the maximum allowable eccentric force P that can be applied
The screw of the clamp exerts a compressive force of 500 lb on the wood blocks. Determine the maximum normal stress along section a€“a. The cross section is rectangular, 0.75 in. by 0.50
The beam is subjected to a shear force of V = 50 kip. Determine the maximum shear flow in the cross section. 1 in. 5 in. 1 in. 5 in. 1 in. 9 in. 12 in.
The beam is subjected to a shear force of V = 50 kip. Determine the shear flow at points A and B. 1 in. 5 in. 1 in. 5 in. 9 in. 1 in. B 12 in.
The aluminum strut is 10 mm thick and has the cross section shown. If it is subjected to a shear of V = 150 N, determine the maximum shear flow in the strut. 10 mm 40 mm в 10 mm tr-40 mm- 30 mm 30
The aluminum strut is 10 mm thick and has the cross section shown. If it is subjected to a shear of V = 150 N, determine the shear flow at points A and B. 10 mm 40 mm 10 mm t+-40 mm- 30 mm 30 mm 10
A shear force of V = 18 kN is applied to the box girder. Determine the shear flow at point C. 10 mm 30 mm 10 mm 100 mm B. 150 mm 100 mm 10 mm 30 mm 10 mm 150 mm 10 mm 125 mm 10 mm
A shear force of V = 18 kN is applied to the box girder. Determine the shear flow at points A and B. 10 mm 30 mm 10 mm 100 mm B 150 mm 100 mm 10 mm 30 mm 10 mm 150 mm 10 mm 125 mm 10 mm
A shear force of V = 450 kN is applied to the box girder. Determine the shear flow at points C and D. 90 mm 90 mm 100 mm 200 mm 190 mm -10 mm 200 mm I80 mm 10 mm
A shear force of V = 300 kN is applied to the box girder. Determine the shear flow at points A and B. 90 mm 90 mm 100 mm 200 mm 190 mm 10 mm 200 mm 180 mm 10 mm
The beam is made from three polystyrene strips that are glued together as shown. If the glue has shear strength of 80 kPa, determine the maximum load P that can be applied without causing the glue to
The beam is made from four boards nailed together as shown. If the nails can each support a shear force of 100 lb, determine their required spacing s¢ and s if the beam is subjected to
The member consists of two plastic channel strips 0.5 in. thick, glued together at A and B. If the glue can support an allowable shear stress of Ï„allow= 600 psi, determine the maximum
The member consists of two plastic channel strips 0.5 in. thick, glued together at A and B. If the distributed load has a maximum intensity of w0 = 3 kip>ft, determine the maximum shear stress
The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 in. If a force P = 2 kip is applied to the beam, determine the shear force resisted
The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 in. If each nail can resist a shear force of 50 lb, determine the largest force P
The T-beam is constructed as shown. If each nail can support a shear force of 950 lb, determine the maximum shear force V that the beam can support and the corresponding maximum nail spacing s to the
The simply supported beam is built up from three boards by nailing them together as shown. If P = 12 kN, determine the maximum allowable spacing s of the nails to support that load, if each nail can
The simply supported beam is built up from three boards by nailing them together as shown. The wood has an allowable shear stress of Ï„allow= 1.5 MPa, and an allowable bending stress of
A beam is constructed from three boards bolted together as shown. Determine the shear force in each bolt if the bolts are spaced s = 250 mm apart and the shear is V = 35 kN. 25 mm 25 mm 100 mm250 mm
The beam is constructed from three boards. Determine the maximum loads P that it can support if the allowable shear stress for the wood is Ï„allow= 400 psi. What is the maximum allowable
The double T-beam is fabricated by welding the three plates together as shown. If the weld can resist a shear stress tallow = 90 MPa, determine the maximum shear V that can be applied to the beam. 20
The double T-beam is fabricated by welding the three plates together as shown. Determine the shear stress in the weld necessary to support a sheer force of V = 80 kN. 20 mm 150 mm 50 mm 75 mm 50 mm
The beam is constructed from three boards. Determine the maximum shear V that it can support if the allowable shear stress for the wood is Ï„allow= 400 psi. What is the maximum allowable
The beam is constructed from three boards. If it is subjected to a shear of V = 5 kip, determine the maximum allowable spacing s of the nails used to hold the top and bottom flanges to the web. Each
The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in. If a sheer force of V = 900 lb is applied to the boards, determine the
The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in. If each nail can support a 400-lb shear force, determine the maximum shear
The beam in Fig. 6–48f is subjected to a fully plastic moment Mp. Prove that the longitudinal and transverse shear stresses in the beam are zero. Hint: Consider an element of the beam shown in Fig.
The beam has a rectangular cross section and is subjected to a load P that is just large enough to develop a fully plastic moment Mp= PL at the fixed support. If the material is elastic perfectly

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