Questions and Answers of Mechanics Of Materials

Beam ABC with an overhang BC is subjected to a linearly varying distributed load on span AB with peak intensity q0 = 2500 N/m and a point load P = 1250 N applied at C. The beam has a width b =100 mm
A segment of a generator shaft is subjected to a torque T and an axial force P, as shown in the figure. The shaft is hollow (outer diameter d2 = 300 mm and inner diameter d1 =stress 250 mm) and
A cantilever wood beam with a width b =100 mm and depth h = 150 mm has a length L = 2 m and is subjected to point load P at mid-span and uniform load q =15 N/m. (a) If the normal stress σx = 0 at
The torsional pendulum shown in the figure consists of a horizontal circular disk of a mass M = 60 kg suspended by a vertical steel wire (G = 80 GPa) of a length L = 2 m and diameter d = 4 mm.
A cylindrical pressure vessel with flat ends is subjected to a torque T and a bending moment M (see figure). The outer radius is 12.0 in. and the wall thickness is 1.0 in. The loads are T = 800
A pressurized cylindrical tank with flat ends is loaded by torques T and tensile forces P (see figure). The tank has a radius of r = 125 mm and wall thickness t = 6.5 mm. The internal pressure p =
A cylindrical pressure vessel having a radius r =14 in. and wall thickness t = 0.5 in. is subjected to internal pressure p = 375 psi. In addition, a torque T = 90 kip-ft acts at each end of the
A cylindrical tank having a diameter d = 2.5 in. is subjected to internal gas pressure p = 600 psi and an external tensile load T = 1000 lb (see figure). Determine the minimum thickness t of the wall
Solve the preceding problem using transverse load V = 300 N and torque T = 3.5 Nm applied at point B. The bar has length L = 1.5 m and diameter d = 8 mm. Calculate the principal stresses and the
A cantilever beam with a width b =100 mm and depth h = 150 mm has a length L = 2 m and is subjected to a point load P = 500 N at B. Calculate the state of plane stress at point C located 50 mm below
A solid circular bar is fixed at point A. The bar is subjected to transverse load V = 70 lb and torque T = 300 lb-in. at point B. The bar has a length L = 60 in. and a diameter d = 3 in. Calculate
A scuba tank (see figure) is being designed for an internal pressure of 2640 psi with a factor of safety of 2.0 with respect to yield. The yield stress of the steel is 65,000 psi in tension and
A W 12 x 35 steel cantilever beam is subjected to an axial load P = 10 kips and a transverse load V = 15 kips. The beam has length L = 6 ft. (a) Calculate the principal normal stresses and the
A W 310 x 52 steel beam is subjected to a point load P = 45 kN and a transverse load V = 20 kN at B. The beam has a length L = 2 m. (a) Calculate the principal normal stresses and the maximum shear
Repeat Problem 8.3-1 for a fire extinguisher tank with an internal pressure of 1.8 MPa, a diameter of 130 mm, and thickness 1.5 mm.Problem 8.3-1A fire extinguisher tank is designed for an internal
A wood beam with a cross-section 4 x 6 in. is simply supported at A and B. The beam has a length of 9 ft and is subjected to point load P = 5 kips at mid-span. Calculate the state of stress at point
A fire extinguisher tank is designed for an internal pressure of 825 psi. The tank has an outer diameter of 4.5 in. and a thickness of 0.08 in. Calculate the longitudinal stress, the circumferential
Solve Problem 7.7-14 by using Mohr’s circle for plane strain.Solve the preceding problem for the following strains: Yxy &x=-1120 × 10-6, Ey = -430 × 10-6, = 780 x 10-6, and 0 = 45°.
Solve Problem 7.7-13 by using Mohr’s circle for plane strain.Problem 7.7-13An element of material in plane strain is subjected to strains. Ex 480 × 107 X Ey = = 70 × 10-6, and Y.xv = 420 ×
Solve Problem 7.7-12 by using Mohr’s circle for plane strain.Problem 7.7-12Solve the preceding problem for the following strains: Yxy & = 120 × 10-6, y E X =-360 × 10-6. =-450 × 10-6, and
Solve Problem 7.7-11 by using Mohr’s circle for plane strain.Problem 7.7-11The strains for an element of material in plane strain (see figure) are as follows:Determine the principal strains and
A simply supported wood beam is subjected to point load P at mid-span. The normal stress on the element C is known to be σx = 12 MPa. Find the maximum shear stress on the element and show the
A simply supported wood beam is subjected to point load P at mid-span. The stresses on element C are known to be σx = –92 psi and πxy = –7 psi. Find the principal stresses on the element and
Solve Problem 7.7-9 by using Mohr’s circle for plane strain.Problem 7.7-9An element of material subjected to plane strain (see figure) has strains ofCalculate the strains for an element oriented at
A square plate with side dimension of 2 in, is subjected to compressive stress σx and tensile stress σy. The stresses on element A oriented at angle u = 458 are σx = - 75 psi, σy = - 75 psi, and
An element in plane stress on the surface of an automobile drive shaft is subjected to stresses of σx = -45 MPa and πxy = 39 MPa. It is known that one of the principal stresses equals 41 MPa in
The stresses at a point on the down tube of a bicycle frame are σx = 4800 psi and πxy = –1950 psi. It is known that one of the principal stresses equals 6375 psi in tension.(a) Determine the
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x-axis. Show
The stresses acting on a stress element on the arm of a power excavator (see figure) are σx = 52 MPa and txy = 33 MPa. What is the allowable range of values for the stress σy if the maximum shear
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x-axis. Show
At a point on the web of a girder on a gantry crane, the stresses acting on the x face of a stress element are σx = 6250 psi and πxy = 1425 psi. What is the allowable range of values for the stress
An element in plane stress is subjected to stresses σx, σy, and πxy.(a) Determine the principal stresses and show them on a sketch of a properly oriented element.(b) Determine the maximum shear
The state of stress on an element along the hydraulic lift cylinder on a truck is σy = -5 MPa. Find the maximum shear stress on the element and show the state of stress on a sketch of a properly
An element in plane stress is subjected to stresses σx, σy, and πxy.(a) Determine the principal stresses and show them on a sketch of a properly oriented element.(b) Determine the maximum shear
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the-axis. Show
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the-axis. Show
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x-axis. Show
An element in plane stress is subjected to stresses σx, σy, and πxy.(a) Determine the principal stresses and show them on a sketch of a properly oriented element.(b) Determine the maximum shear
An element in plane stress is subjected to stresses σx, σy, and θxy. Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the -axiss. Show these stresses
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x-axis. Show
A rubber sheet in biaxial stress is subjected to tensile stresses σx = 270 Pa and σy = 144 Pa. The corresponding strains in the sheet are εx = 0.0002 and εy = 0.000015. Determine Poisson’s
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x-axis. Show
Repeat the preceding problem using σy = - 750 psi.
The normal stress on an elastomeric rubber pad in a test machine is σy = -100 psi (see figure). Assume E = 312 psi and shear modulus G =105 psi. (a) Calculate the strains in the pad in the
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x-axiss. Show
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x-axis. Show
An element in plane stress is subjected to stresses σx, σy, and θxy (see figure). Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from thex-axiss. Show
The T-beam shown in the figure is fabricated by welding together two steel plates. If the allowable load for each weld is 1.8 kips/in. in the longitudinal direction, what is the maximum allowable
A 4.0 in cube of concrete is compressed in biaxial stress by means of a framework that is loaded as shown in the figure. Assuming that each load F equals 25 kips, determine the change ΔV in the
A specimen used in a coupon test is shown in the figure. The stresses on element A are known to be σy = -1500 psi. Use Mohr’s circle to:(a) Find the stresses acting on the element oriented at an
A specimen used in a coupon test has normal stress σy =15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle u = 208 and show the full stress state on
An element on the surface of a drive shaft is in pure shear and is subjected to stresses πxy = 2700 psi, as shown in the figure. Using Mohr’s circle, determine the following.(a) The stresses
A cast-iron plate in biaxial stress is subjected to tensile stresses σx = 31MPa and σy = 17 MPa (see figure). The corresponding strains in the plate are Determine Poisson’s ratio n and the
An element of material in plain strain is subjected to strains εx = 0.0015, εy = 20.0002, and Yxy = 0.0003.(a) Determine the strains for an element oriented at an angle u = 2(b) Determine the
An element of a material is subjected to plane stresses as shown in the figure. The stresses σx, σy, and πxy are 10 MPa, –15 MPa, and 5 MPa, respectively. Assume E = 200 GPa and n = 0.3.(a)
The stresses on an element are known to be σx =120 MPa, σy =100 MPa, and σxy = 75 MPa. Find the stresses on an inclined section through the element at an angle u = 458. Ox 0 Tyx Txlyl et Oy 10x1 X
The state of stress on an element of material is shown in the figure. Calculate the unit volume change of the element if the stresses σx and σy are –20ksi and 10 ksi, respectively. Assume E =
The stresses acting on an element are σx = 750 psi, σy = 600 psi, and πxy = 400 psi. Determine the principal stresses and show them on a sketch of a properly oriented element.
An element of material in plain strain has the following strains: εx = 20.001 and εy = 0.0015.(a) Determine the strains for an element oriented at an angle θ = 258.(b) Find the principal strains
Repeat Problem 6.2-1 but now assume that the steel plate is smaller (0.5 in. × 5 in.) and is aligned with the top of the beam as shown in the figure.Problem 6.2-1 A composite beam is
A wood beam in a historic theater is reinforced with two angle sections at the outside lower corners (see figure). If the allowable stress in the wood is 12 MPa and that in the steel is 140 MPa, what
A footbridge on a hiking trail is constructed using two timber logs each having a diameter d = 0.5 m (see figure a). The bridge is simply supported and has a length of L = 4 m. The top of each log
A wood beam in a historic theater is reinforced with two angle sections at the outside lower corners (see figure). If the allowable stress in the wood is 12 MPa and that in the steel is 140 MPa, what
A reinforced concrete T-beam (see figure) is acted on by a positive bending moment of M = 175 kip-ft. Steel reinforcement consists of four bars of 1.41-inch diameter. The modulus of elasticity for
A cold-formed steel section is made by folding a steel plate to form a structural section such as that shown in the figure. This beam is subjected to bending moment M = 2 kip-in. at angle θ =
A cross-section in the shape of a circular arc of constant thickness is shown in the figure. Derive the following formula for the distance e from the center of the arc to the shear center S:in which
A wood beam AB with a rectangular cross-section (4 in. × 6 in.) serving as a roof purlin is simply supported by the top chords of two adjacent roof trusses. The beam is subjected to distributed load
A 2-m-long cantilever beam is constructed using a W 310 × 52 section. Load P acts in an inclined direction at the free end (see figure). Determine the allowable load P that can be carried by the
A composite beam consisting of fiberglass faces and a core of particle board has the cross-section shown in the figure. The width of the beam is 2.0in, the thickness of the faces is 0.10 in., and
Solve the preceding problem for the following data: b = 6 in., h =10 in., L = 12.0 ft, tan a = 1/3, and q = 325 lb/ft. n В A P E C B n a
A wood beam is strengthened using two steel plates as shown in Fig. a. The beam has simple supports and an overhang and is subjected to a point load and a uniform load as shown in Fig.b. Calculate
A sandwich beam having steel faces enclosing a plastic core is subjected to a bending moment M = 5 kN · m. The thickness of each steel face is t = 3 mm with a modulus of elasticity Es = 200 GPa. The
A composite beam is constructed using a steel plate (0.5 in X 6 in.) with two wood beams (3 in. X 6 in.) on either side. The wood and steel are securely fastened to act as a single beam. The beam is
Repeat Problems 6.2-17 but now use a transformed-section approach.Problem 6.2-17Repeat Problem 6.2-1 but now assume that the steel plate is smaller (0.5 in. × 5 in.) and is aligned with the top of
Beam ABCDE has a moment release just right of joint B and has concentrated moment loads at D and E. In addition, a cable with tension P is attached at F and runs over a pulley at C (Fig. a). The beam
Consider the compound beam with segments AB and BCD joined by a pin connection (moment release) just right of B (see figure part a). The beam cross-section is a double-T made up of three 50 mm 3150
A beam with a T-section is supported and loaded as shown in the figure. The cross-section has width b = 21/2 in, height h = 3 in., and thickness t = 3/8 in.(a) Determine the maximum tensile and
A simply supported beam is subjected to a linearly varying distributed load q(x) 0 maximum intensity q0 at B. The beam has a length L = 4 m and a rectangular cross-section with a width of 200 mm and
The T-beam shown in the figure has cross-sectional dimensions: b = 210 mm, t= 16 mm, h = 300 mm, and h1 = 280 mm. The beam is subjected to a shear force V = 68 kN. Determine the maximum shear stress
The three beams shown have approximately the same cross-sectional area. Beam 1 is a W14 x 82 with flange plates; beam 2 consists of a web plate with four angles; and beam 3 is constructed of 2 C
A steel bracket of the solid circular cross-section is subjected to two loads, each of which is P = 4.5 kN at D (see figure). Let the dimension variable be b = 240 mm.(a) Find the minimum permissible
A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide,
A cantilever beam is subjected to a concentrated moment at B. The length of the beam L = 3 m and the height h = 600 mm. The longitudinal strain at the top of the beam is 0.0005 and the distance from
simply supported beam with a length L =10 ft and height 7 in. is bent by couples M0 into a circular arc with downward deflection d at the midpoint. If the curvature of the beam is 0.003 ft21,
A simple beam ABC having rectangular cross sections with constant height h and varying width bx supports a concentrated load P acting at the midpoint (see figure). How should the width bx vary as a
A simple beam AB is loaded as shown in the figure.(a) Calculate the required section modulus S if sallow 518,000 psi, L = 32 ft, P = 2900 lb, and q = 450 lb/ft. Then select a suitable I-beam (S
A rigid frame ABC is formed by welding two steel pipes at B (see figure). Each pipe has a cross-sectional area A =11.31 X 103 mm2, a moment of inertia I = 46.37 3106 mm4, and an outside diameter d =
A steel pipe is subjected to a quadratic distributed load over its height with the peak intensity q0 at the base (see figure). Assume the following pipe properties and dimensions: height L, outside
A simple beam of length L = 5 m carries a uniform load of intensity q = 5.8 kN/m and a concentrated load 22.5 kN (see figure).(a) Assuming sallow = 110 MPa, calculate the required section modulus S.
Beam ABC has simple supports at A and B and an overhang from B to C. The beam is constructed from a steel W 16 X 31. The beam must carry its own weight in addition to uniform load q = 150 lb/ft.
Wide-flange shape, W18 x 71 ; V = 21 k.(see table F-1)See Table F-1 Z t- |v 0 |-b- ha h
A cantilever beam AB is loaded by a uniform load q and a concentrated load P, as shown in the figure.(a) Select the most economical steel C shape from Table F-3(a) in Appendix F; use q 5 20 lb/ft and
A circular pole is subjected to linearly varying distributed force with maximum intensity q0. Calculate the diameter d0 of the pole if the maximum allowable shear stress for the pole is 75 MPa. 90 =
Wide-flange shape, W 8 x 28 ; V =10 k(see Table F-1).Table F-1 N O -b- h₁ h
A vertical pole consisting of a circular tube of outer diameter 5 in. and inner diameter 4.5 in. is loaded by a linearly varying distributed force with a maximum intensity of q0. Find the maximum
A solid circular pole is subjected to linearly varying distributed force with maximum intensity q0 at the base and an axial compressive load P at the top (see figure). Find the required diameter d of
A simply supported beam (L = 4.5 m) must support mechanical equipment represented as a distributed load with intensity q =- 30 kN/m acting over the middle segment of the beam (see figure). Select
A pole is fixed at the base and is subjected to a linearly varying distributed force with the maximum intensity of q0 and an axial compressive load P = 20 kips at the top (see figure). The pole has a
A cable with force P is attached to a frame at A and runs over a frictionless pulley at D. Find expressions for shear force V and moment M at x = L/2 of beam BC. L/2 A B L/2 Cable V, M at
Cantilever beam AB carries an upward uniform load of intensity q1 from x = 0 to L/2 (see Figure) and a downward uniform load of intensity q from x = L/2 to L. (a) Find q1 in terms of q if the

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