Questions and Answers of Mechanics Of Materials

The beam has a square cross section and is made of wood having an allowable shear stress of τallow = 1.4 ksi. If it is subjected to a shear of V = 1.5 kip, determine the smallest dimension a of its
If the wide-ange beam is subjected to a shear of \(V=30 \mathrm{kN}\), determine the maximum shear stress in the beam. Set \(w=\) \(200 \mathrm{~mm}\). The neutral axis is located at \(\bar{y}=0.1747
If the wide-ange beam is subjected to a shear of \(V=30 \mathrm{kN}\), determine the shear force resisted by the web of the beam. Set \(w=200 \mathrm{~mm}\). The neutral axis is located at
Determine the shear stress at points \(C\) and \(D\) located on the web of the beam. 6ft- D:C 3 kip/ft 0.75 in. 6 ft. 6 ft .6 in.. 1 in. 4 in. D 4 in. '6 in.' 1 in.
Determine the maximum shear stress acting in the beam at the critical section where the internal shear force is maximum. 6 ft D:C 3 kip/ft -6 ft- .6 in.. 1 in. 0.75 in C [4 in. D [4 in. '6 in. 1 in.
The steel rod has a radius of 1.25 in. If it is subjected to a shear of \(V=5\) kip, determine the maximum shear stress. 1.25 in. V-5 kip
A member has a cross section in the form of an equilateral triangle. If it is subjected to a shear force \(\mathbf{V}\), determine the maximum average shear stress in the member using the shear
The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 8 in. If each nail can support a \(300-\) lb shear force, determine the maximum
The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every \(8 \mathrm{in}\). If an internal shear force of \(V=800 \mathrm{lb}\) is applied
The double-web girder is constructed from two plywood sheets that are secured to wood members at its top and bottom. If each fastener can support \(600 \mathrm{lb}\) in single shear, determine the
The double-web girder is constructed from two plywood sheets that are secured to wood members at its top and bottom. The allowable bending stress for the wood is \(\sigma_{\text {allow }}=\) \(8
The beam is fabricated from two equivalent structural tees and two plates. Each plate has a height of 6 in. and a thickness of 0.5 in. If a shear of \(V=50\) kip is applied to the cross section,
The beam is fabricated from two equivalent structural tees and two plates. Each plate has a height of 6 in. and a thickness of 0.5 in. If the bolts are spaced at \(s=8\) in., determine the maximum
Determine the average shear stress developed in the nails within region \(A B\) of the beam. The nails are located on each side of the beam and are spaced \(100 \mathrm{~mm}\) apart. Each nail has a
The nails are on both sides of the cantilever beam and each can resist a shear of \(2 \mathrm{kN}\). In addition to the distributed loading, determine the maximum load \(P\) that can be applied to
The beam is subjected to a shear of \(V=800 \mathrm{~N}\). Determine the average shear stress developed in the nails along the sides \(A\) and \(B\) if the nails are spaced \(s=100 \mathrm{~mm}\)
The timber T-beam is subjected to a load consisting of \(n\) concentrated forces, \(P_{n}\). If the allowable shear \(V_{\text {nail }}\) for each of the nails is known, write a computer program that
Determine the shear stress variation over the cross section of the thin-walled tube as a function of elevation y and show that \(\tau_{\max }=2 V / A\), where \(A=2 \pi r\). Choose a differential
The angle is subjected to a shear force of \(V=2\) kip. Sketch the distribution of shear flow along the leg \(A B\). Indicate numerical values at all peaks. 0.25 in. 5 in. 45 45 5 in.
Determine the location \(e\) of the shear center, point \(O\), for the thin-walled member having the cross section shown. a 60 a 60 a
Determine the location \(e\) of the shear center, point \(O\), for the beam having the cross section shown. The thickness is \(t\).
Determine the location \(e\) of the shear center, point \(O\), for the beam having the cross section shown. The thickness is \(t\). T
Determine the shear and moment in the shaft as functions of x within the region 125 mm x 725 mm, and then draw the shear and moment diagrams for the shaft. The bearings at A and B exert only vertical
Draw the shear and moment diagrams for the beam.The 20-kip load must be replaced by equivalent loadings at point C on the axis of the beam. A 15 kip 11 ft 20 kip 4 ft 4 ft 4 ft B
Draw the shear and moment diagrams for the compound beam. It is supported by a smooth plate at A which slides within the groove and so it cannot support a vertical force, although it can support a
The beam is subjected to the uniformly distributed moment m (moment/length). Draw the shear and moment diagrams for the beam. A L m
The ski supports the 180-lb weight of the man. If the snow loading on its bottom surface is trapezoidal as shown, determine the intensity w, and then draw the shear and moment diagrams for the ski. 3
The overhang beam has been fabricated with a projected arm BD on it. Draw the shear and moment diagrams for the beam ABC if it supports a load of 800 lb. The loading in the supporting strut DE must
The beam is subjected to the uniform distributed load shown. Draw the shear and moment diagrams for the beam. 1.5 m A 2 kN/m B -2 m 1 m
A member having the dimensions shown is used to resist an internal bending moment of M = 90 kN⋅m. Determine the maximum stress in the member if the moment is applied (a)about the z axis (as shown),
If the beam is subjected to an internal moment of M = 100kip•ft, determine the maximum tensile and compressive bending stress in the beam. 3 in. 3 in. 1.5 in. M 6 in. 2 in.
The channel strut is used as a guide rail for a trolley.If the maximum moment in the strut is M = 30N⋅m, determine the bending stress at points A, B, and C. -50 mm- C B 15 mm 15 mm 30 mm 15 mm +5
The channel strut is used as a guide rail for a trolley. If the allowable bending stress for the material is σallow = 175MPa, determine the maximum allowable bending moment in the strut. -50 mm- C B
Determine the dimension a of a beam having a square cross section in terms of the radius r of a beam with a circular cross section if both beams are subjected to the same internal moment which
The chair is supported by a fixed arm at A. If the load on the chair is 180 lb and the arm is a hollow tube section having the dimensions shown, determine the maximum bending stress at section a-a.
The man has a mass of 78 kg and stands motionless at the end of the diving board. If the board has the cross section shown, determine the maximum normal strain developed in the board. The modulus of
The steel rod having a diameter of 1 in. is subjected to an internal moment of M = 300lb•ft. Determine the stress created at points A and B. Also, sketch a three-dimensional view of the stress
The steel beam has the cross sectional area shown. Determine the largest intensity of distributed load w that it can support so that the bending stress does not exceed σmax = 22 ksi. 8 ft- 8 ft W -8
The steel beam has the cross-sectional area shown. If w=5 kip/ft, determine the absolute maximum bending stress in the beam. W 8 8 ft- 8 ft W ft- -8 ft- .8 in. 0.30 in. 0.3 in.- 10 in. 0.30 in.
Determine the largest intensity of distributed load w0 that the beam can support so that the maximum bending stress in the beam does not exceed σmax = 22ksi. Wo -12 ft. 12 ft- 8 in. 0.30 in. 0.3
If w0 = 0.5 kip/ft, determine the maximum bending stress in the beam. Wo 12 ft. 12 ft- 8 in. 0.30 in. 0.3 in.- 10 in. 0.30 in.
Determine the absolute maximum bending stress in the tubular shaft if di = 160 mm and do = 200 mm. A 15 kN/m 60 kNm 3 m 1 m- do
The tubular shaft is to have a cross section such that its inner diameter and outer diameter are related by di = 0.8do. Determine these required dimensions if the allowable bending stress is σallow
The wood beam has a rectangular cross section in the proportion shown. Determine its required dimension b if the allowable bending stress is σallow = 10 MPa. |A 500 N/m -2 m 2 m B 1.56
If the reaction of the ballast on the railway tie can be assumed uniformly distributed over cross section its length as shown, determine the maximum bending stress developed in the tie. The tie has
The reaction of the ballast on the railway tie can be assumed uniformly distributed over its length as shown. If the wood has an allowable bending stress of σallow = 1.5 ksi, determine the required
The two solid steel rods are bolted together along their length and support the loading shown. Assume the support at A is a pin and B is a roller. Determine the required diameter d of each of the
The member is subjected to the moment M = 850 N⋅m. Determine the stress at each corner and sketch the stress distribution. Set θ = 30. 250 mm D B 125 mm Z 125 mm E M = 850 N-m
The cantilever beam is made from the Z section having the cross section shown. If it supports the two loadings, determine the bending stress at the wall in the beam at point B. Use the result of
The cantilever wide-flange steel beam is subjected to the concentrated force P at its end. Determine the largest magnitude of this force so that the bending stress developed at A does not exceed
The cantilever wide-flange steel beam is subjected to the concentrated force of P = 600N at its end. Determine the maximum bending stress developed in the beam at section A. Z 10 mm: 150 mm 10 mm:
A white spruce beam is reinforced with A-36 steel straps at its top and bottom as shown. Determine the bending moment M it can support if (σst) allow = 22 ksi and ( σw) allow = 2.0 ksi. 3 in. 4 in.
The composite beam is made of 6061-T6 aluminum (A) and C83400 red brass (B). Determine the dimension h of the brass strip so that the neutral axis of the beam is located at the seam of the two
The composite beam is made of 6061-T6 aluminum (A) and C83400 red brass (B). If the height h = 40 mm, determine the maximum moment that can be applied to the beam if the allowable bending stress for
The low strength concrete floor slab is integrated with a wide-flange A-36 steel beam using shear studs (not shown) to form the composite beam. If the allowable bending stress for the concrete is
The top plate is made of 2014-T6 aluminum and is used to reinforce a Kevlar 49 plastic beam. Determine the maximum stress in the aluminum and in the Kevlar if the beam is subjected to a moment of M =
The top plate made of 2014-T6 aluminum is used to reinforce a Kevlar 49 plastic beam. If the allowable bending stress for the aluminum is (σallow) al = 40 ksi and for the Kevlar ( σallow)K = 8 ksi,
The curved beam is subjected to a bending moment of M=900 N⋅ m. Determine the stress at point C. 30 B 400 mm A C 15 mm 100 mm A. B M 20 mm 150 mm
While in flight, the curved rib on the jet plane is subjected to an anticipated moment of M = 16N ⋅ m at the section. Determine the maximum bending stress in the rib at this section, and sketch a
The circular spring clamp produces a compressive force of 3 N on the plates. Determine the maximum bending stress produced in the spring at A. The spring has a rectangular cross section as shown. 10
Determine the maximum compressive force the spring clamp can exert on the plates if the allowable bending stress for the clamp is σallow = 4MPa. The spring has a rectangular cross section as shown.
The ceiling-suspended C-arm is used to support the X-ray camera used for medical diagnoses. If the camera has a mass of 150 kg, with center of mass at G, determine the maximum bending stress at
Determine the greatest magnitude of the applied forces P if the allowable bending stress is (σc)allow = 50 MPa in compression and (σt) allow =120 MPa in tension. 250 mm 75 mm 10 mm 10 mm- 150 mm
If P = 6kN, determine the maximum tensile and compressive bending stresses in the beam. 250 mm 75 mm 10 mm 10 mm- 150 mm 160 mm 10 mm P 150 mm
The bar is subjected to a moment M = 40 N⋅m of Determine the smallest radius r of the fillets so that an allowable bending stress of σallow = 124MPa is not exceeded. M 20 mm 80 mm 7 mm M
The bar is subjected to a moment of M = 17.5 N ⋅ m. If r=5mm determine the maximum bending stress in the material. M 80 mm 7 mm 20 mm M
The simply supported notched bar is subjected to the two loads, each having a magnitude of P = 100 lb. Determine the maximum bending stress developed in the bar, and sketch the bending-stress
The wide-flange member is made from an elastic perfectly plastic material. Determine the shape factor for the beam. h
The beam is made from elastic perfectly plastic material. Determine the shape factor for the thick-walled tube.
The beam is made of an elastic perfectly plastic material for which σy = 200 MPa. Determine the magnitude of each force P that causes the maximum internal moment to be moment to be(a) the maximum
The beam has a rectangular cross section and is made of an elastic perfectly plastic material having a stress–strain diagram as shown. Determine the magnitude of the moment M that must be applied
The beam is made of a polyester that has the stress-strain curve shown. If the curve can be represented by the equation σ = [20 tan-1 (15ε)] ksi where tan-1 (15ε) is in radians, determine the
The beam is made of a material that can be assumed perfectly plastic in tension and elastic perfectly plastic in compression. Determine the maximum bending moment M that can be supported by the beam
The tube is subjected to a torque of 750 N. m. Determine the amount of this torque that is resisted by the gray shaded section. Solve the problem two ways:(a) by using the torsion formula,(b) by
The solid shaft has a diameter of 0.75 in. If it is subjected to the torques shown, determine the maximum shear stress developed in regions BC and DE of the shaft. The bearings at A and F allow free
The solid shaft has a diameter of 0.75 in. If it is subjected to the torques shown, determine the maximum shear stress developed in regions CD and EF of the shaft. The bearings at A and F allow free
The coupling is used to connect the two shafts together.Assuming that the shear stress in the bolts is uniform, determine the number of bolts necessary to make the maximum shear stress in the shaft
The aluminum tube has an inner diameter of 25 mm and a wall thickness of 5 mm. Determine the maximum shear stress in the fixed tube when the force of 600 N is applied to the cables. Also, sketch the
The solid shaft has a diameter of 2 in. If it is subjected to the torques shown, determine the maximum shear stress developed in regions CD and DE of the shaft. The bearings at A and F allow free
The solid shaft has a diameter of 2 in. If it is subjected to the torques shown, determine the absolute maximum shear stress developed in the shaft. The bearings at A and F allow free rotation of the
Two wrenches are used to tighten the pipe. If P = 300 N is applied to each wrench, determine the maximum torsional shear stress developed within regions AB and BC. The pipe has an outer diameter of
Two wrenches are used to tighten the pipe. If the pipe is made from a material having an allowable shear stress of τallow = 85 MPa, determine the maximum allowable force P that can be applied to
The motor delivers a torque of 50 N m to the shaft AB.This torque is transmitted to shaft CD using the gears at E and F. Determine the equilibrium torque T ′ on shaft CD and the maximum shear
If the applied torque on shaft CD is T' = 75 N m, determine the absolute maximum shear stress in each shaft. The journal bearings B, C, and D allow free rotation of the shafts, and the motor provides
If the tube is subjected to a uniform distributed torque of t0 = 1.2 kN ⋅ m/m, determine the shear stress developed at point C. The inner radius is 20 mm and the outer radius is 30 mm. 500 mm 500
If the tube is subjected to a uniform distributed torque of t0 = 1.2 kN . m m, determine the rod’s minimum required outer radius co and corresponding inner radius ci to the nearest mm if the
If the tube is made from a material having an allowable shear stress of τallow = 80 MPa, determine the maximum allowable intensity t0 of the uniform distributed torque. The inner radius is 26 mm and
The 160-mm-diameter solid shaft is supported by bearings at A and E. Determine the maximum shear stress developed in each segment of the shaft. B C D A 40 kNm 60 kNm F E 50 kNm 30 kNm
If the tubular shaft is made from material having an allowable shear stress of τallow = 90 MPa, determine the required minimum wall thickess of the shaft to the nearest millimeter. The shaft is
The motor M is connected to the speed reducer C by the tubular shaft and coupling. The shaft has an outer and inner diameter of 1 in. and 0.75 in., respectively, and is made from a material having an
The motor delivers 15 hp to the pulley at A while turning at a constant rate of 1800 rpm. Determine to the nearest 1/8 in. the smallest diameter of shaft BC if the allowable shear stress for steel is
A ship has a propeller drive shaft that is turning at 1500 rev/min while developing 1800 hp. If it is 8 ft long and has a diameter of 4 in., determine the maximum shear stress in the shaft caused by
The 20-mm-diameter shaft on the motor is made of a material having an allowable shear stress of τallow = 80 MPa.If the motor is operating at its maximum power of 6 kW, determine the minimum
The drive shaft of the motor is made of a material having an allowable shear stress of τallow = 80 MPa. If the motor is to deliver a power of 15 kW, determine the required minimum outer diameter and
The shaft is subjected to a torque T. Compare the effectiveness of using the tube with that of the solid section of radius c. To do this, calculate the percent increase in torsional stress and angle
The assembly is made of A-36 steel and consists of a solid rod 20 mm in diameter fixed to the inside of a tube using a rigid disk at B. Determine the angle of twist at D. The tube has an outer
The assembly is made of A-36 steel and consists of a solid rod 20 mm in diameter fixed to the inside of a tube using a rigid disk at B. Determine the angle of twist at C. The tube has an outer
The engine of a helicopter is delivering 600 hp to the rotor shaft AB when the blade is rotating at 1200 rev/min. Determine to the nearest in. the diameter of the shaft AB if the allowable shear
The engine of a helicopter is delivering 600 hp to the rotor shaft AB when the blade is rotating at 1200 rev min. Determine to the nearest 1/8 in.the diameter of the shaft AB if the allowable shear
The device serves as a compact torsional spring. It is made of A-36 steel and consists of a solid inner shaft CB which is surrounded by and attached to a tube AB using a rigid ring at B. The ring at

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