Questions and Answers of Mechanics Of Materials

The anchor bolt was pulled out of the concrete wall and the failure surface formed part of a frustum and cylinder. This indicates a shear failure occurred along the cylinder BC and tension failure
If the shaft is subjected to an axial force of 5 kN, determine the bearing stress acting on the collar A. 5 kN 60 mm 100 mm 2.5 mm 15 mm 2.5 mm
If the 60-mm diameter shaft is subjected to an axial force of 5 kN, determine the average shear stress developed in the shear plane where the collar A and shaft are connected. 5 kN 60 mm 100 mm 2.5
The triangular blocks are glued along each side of the joint.A C-clamp placed between two of the blocks is used to draw the joint tight. If the glue can withstand a maximum average shear stress of
The triangular blocks are glued along each side of the joint. A C-clamp placed between two of the blocks is used to draw the joint tight. If the clamping force is F = 900N, determine the average
If P = 20 kN, determine the average shear stress developed in the pins at A and C. All pins are subjected to double shear as shown, and each has a diameter of 18 mm. A-2 m- m P 30 -2m- B
Determine the maximum magnitude P of the load the beam will support if the average shear stress in each pin is not allowed to exceed 60 MPa. All pins are subjected to double shear as shown, and each
The tapered rod has a radius of r = (2 − x/6) in.and is subjected to the distributed loading of w = (60 + 40x) lb/in. Determine the average normal stress at the center of the rod, B. w= (60+40x)
Consider the general problem of a bar made from m segments, each having a constant cross-sectional area Am and length Lm. If there are n loads on the bar as shown, write a computer program that can
The eye bolt is used to support the load of 5 kip. Determine its diameter d to the nearest 1/8 in. and the required thickness h to the nearest 1/8 in. of the support so that the washer will not
Determine the required cross-sectional area of member BC if the allowable normal stress is σallow = 24 ksi. 800 lb 400 lb 6 ft 6 ft B 60 6 ft 30 -45' D 6 ft
The hangers support the joist in such a way that the four nails on each hanger can be assumed to support an equal portion of the load. If the joist is subjected to the loading shown, determine the
The hangers support the joist in such a way that the four nails on each hanger can be assumed to support an equal portion of the load. Determine the smallest diameter of the nails at A and B to the
The 60 mm x 60 mm oak post is supported on the pine block. If the allowable bearing stresses for these materials are σoak = 43 MPa and σpine 25 MPa, determine the greatest load P that can be
If the allowable bearing stress for the plates under the supports at A and B is ( σb )allow =1.8 MPa, determine the size of square bearing plates A′ and B′ required to support the load.
If the allowable bearing stress for the plates under the supports at A and B is (σb )allow =1.8 MPa, determine the maximum load P that can be applied to the beam.The plates A′ and B′ have square
Member B is subjected to a compressive force of 910 lb. If A and B are both made of wood and are 1/2 in. thick, determine to the nearest 1/8 in. the smallest dimension b of the horizontal segment so
The beam is made from southern pine and is supported by base plates resting on brickwork. If the allowable bearing stresses for the materials are (σpine ) allow = 2.81 ksi and ( σbrick )allow =
The soft-ride suspension system of the mountain bike is pinned at C and supported by the shock absorber BD. If it is designed to support a load P = 1500 N, determine the required minimum diameter of
The soft-ride suspension system of the mountain bike is pinned at C and supported by the shock absorber BD. If it is designed to support a load of P = 1500 N, determine the factor of safety of pins B
The 60-kg flowerpot is suspended from wires AB and BC. If the wires have a failure normal stress of σfail = 380 MPa, determine the minimum diameter of each wire. Use a factor of safety of 2. A 60 45
The 60-kg flowerpot is suspended from wires AB and BC which have diameters of 1.75 mm and 1.5 mm, respectively.If the wires have a failure normal stress of σfail = 380 MPa, determine the factor of
The two wires are connected together at A. If the force P causes point A to be displaced horizontally 2 mm, determine the normal strain developed in each wire. C 300 mm 30 B 300 mm 30 A -P
The force P applied at joint D of the square frame causes the frame to sway and form the dashed rhombus. Determine the average normal strain developed in wire AC. Assume the three rods are rigid. P
The force P applied at joint D of the square frame causes the frame to sway and form the dashed rhombus. Determine the average normal strain developed in wire AE. Assume the three rods are rigid.
The rigid beam is supported by a pin at B and wires AD and CE. If the load P on the beam causes the end A to be displaced 6 mm downward, determine the normal strain developed in wires CE and AD. The
The piece of rubber is originally rectangular. Determine the average shear strain γxy at A if the corners B and D are subjected to the displacements that cause the rubber to distort as shown by the
The piece of rubber is originally rectangular and subjected to the deformation shown by the dashed lines. Determine the average normal strain along the diagonal DB and side AD. 3 mm- D 400 mm -x A
A thin wire, lying along the x axis, is strained such that each point on the wire is displaced Δx = kx2 along the x axis. If k is constant, what is the normal strain at any point P along the wire? x
The triangular plate ABC is deformed into the shape shown by the dashed lines. If at A, εAB = 0.0075, εAC = 0.01 and γxy = 0.005 rad, determine the average normal strain along edge BC. C y 300 mm
The plate is deformed uniformly into the shape shown by the dashed lines. If at A, γxy = 0.0075 rad., while εAB = εAF 0, determine the average shear strain at point G with respect to the x' and y'
If the force P causes point A to be displaced vertically by 2.2 mm, determine the normal strain developed in each wire. 600 mm B 30 P 600 mm 30 C
The square plate is deformed into the shape shown by the dashed lines. If DC has a normal strain εx= 0.004, DA has a normal strain εy = 0.005 and at D, Yxy = 0.02 rad, determine the average
The square plate ABCD is deformed into the shape shown by the dashed lines. If DC has a normal strain εx = 0.004, DA has a normal strain εx= 0.005, and at D, Yxy = 0.02 rad, determine the shear
The rubber block is fixed along edge AB, and edge CD is moved so that the vertical displacement of any point in the block is given by v(x) = (vo/b3)x3. Determine the shear strain Yxy = 0.02 at points
A concrete cylinder having a diameter of 6.00 in. and gauge length of 12 in. is tested in compression. The results of the test are reported in the table as load versus contraction. Draw the
A tension test was performed on a steel specimen having an original diameter of 12.5mm and gage length of 50mm. Using the data listed in the table, plot the stress-strain diagram, and determine
Determine the elongation of the square hollow bar when it is subjected to the axial force P = 100 kN. If this force is increased to P = 360 kN and released, find the permanent elongation of the bar.
A structural member in a nuclear reactor is made of a zirconium alloy. If an axial load of 4 kip is to be supported by the member, determine its required cross-sectional area. Use a factor of safety
A tension test was performed on a magnesium alloy specimen having a diameter 0.5 in. and gauge length 2 in. The resulting stress–strain diagram is shown in the figure. Determine the approximate
A tension test was performed on a magnesium alloy specimen having a diameter 0.5 in. and gauge length of 2 in.The resulting stress–strain diagram is shown in the figure. If the specimen is stressed
The σ - e diagram for a collagen fiber bundle from which a human tendon is composed is shown. If a segment of the Achilles tendon at A has a length of 6.5 in. and an approximate cross-sectional area
The stress-strain diagram for many metal alloys can be described analytically using the Ramberg-Osgood three parameter equation ε= σ/E + kon, where E, k, and n are determined from measurements
The acrylic plastic rod is 400 mm long and 20 mm in diameter. If an axial load of 500 N is applied to it, determine the change in its length and the change in its diameter.Ep = 1.85 GPa, vp = 0.45.
The elastic portion of the stress–strain diagram for a steel alloy is shown in the figure. The specimen from which it was obtained had an original diameter of 13 mm and a gauge length of 50 mm.
The aluminum block has a rectangular cross section and is subjected to an axial compressive force of 8 kip. If the 1.5-in. side changes its length to 1.500132 in., determine Poisson's ratio and the
The block is made of titanium Ti-6A1-4V and is subjected to a shortening of 0.06 in. along the y axis, and its shape is given a tilt of θ =89.7. Determine εx, εy, and Yxy. 4 in. 8 A 5 in.
The thin-walled tube is subjected to an axial force of 80 kN.If the tube elongates 6.08 mm and its circumference decreases 0.167 mm, determine the modulus of elasticity, Poisson’s ratio, and the
A cantilever beam has two triangular loads as shown in the figure.(a) Find an expression for beam deflection σC using superposition.(b) Find the required magnitude of load intensity q2 in terms of
Find required distance d (in terms of L) so that rotation B = 0 is due to M and q loadings applied at the same time. Also, what is the resulting net rotation θA at support A? Moment M is applied at
Find an expression for required moment MA (in terms of q and L) that will result in rotation θB = 0 due to MA and q loadings applied at the same time. Also, what is the resulting net rotation at
Find an expression for the required moment MA (in terms of q and L) that will result in rotation θB = 0 due to MA and q loadings applied at the same time. Also, what is the resulting net rotation at
The wing of a small plane is represented by a simplified prismatic cantilever beam model acted on by the distributed loads shown in the figure. Assume constant EI =1200 kN.m2. Find the tip deflection
The wing of a large commercial jet is represented by a simplified prismatic cantilever beam model with uniform load w and concentrated loads P at the two engine locations (see figure). Find
A framework ABCD is acted on by force P at 2L/3 from. Assume that EI is constant.(a) Find expressions for reactions at supports B and C.(b) Find expressions for angles of rotation at A, B, C, and
Compound beam ABC is loaded by point load P = 1.5 kips at a distance 2a/3 from point A and a triangularly distributed load on segment BC with peak intensity q0 = 0.5 kips/ft. If length a = ft and
Calculate the deflection at point C of a beam subjected to uniformly distributed load w = 275 N/m on span AB and point load P = 10 kN at C. Assume that L = 5 m and EI = 1.50 X 107 N.m2.
A steel beam ABC is simply supported at A and held by a high-strength steel wire at B. A load P = 240 lb acts at the free end C. The wire has axial rigidity EA = 1500 X 103 lb, and the beam has
A compound beam ABCDE (see figure) consists of two parts (ABC and CDE) connected by a hinge (i.e., moment release) at C. The elastic support at B has stiffness k = EI / b3. Determine the deflection
The compound beam ABC shown in the figure has a sliding support at A and a fixed support at C. The beam consists of two members joined by a pin connection (i.e., moment release) at B. Find the
A cantilever beam is subjected to a quadratic distributed load q(x) over the length of the beam (see figure). Find an expression for moment M in terms of the peak distributed load intensity q0 so
A simple beam with an overhang is subjected to a point load P = 6 kN. If the maximum allowable deflection at point C is 0.5 mm, select the lightest W 360 section from Table F-1(b) that can be used
Repeat Problem 9.5-15 for the anti-symmetric loading shown in the figure.Staticsso reactions at A and B are equal and opposite but neither is equal to P (unlike symmetnc load case)Problem 9.5-15Use
A cantilever beam has a length L = 12 ft and a rectangular cross-section (b = 16 in., h = 24 in.). A linearly varying distributed load with peak intensity q0 acts on the beam.(a) Find peak intensity
Use the method of superposition to find the angles of rotation θA and θB at the supports, and the maximum deflection θmax for a simply supported beam subjected to symmetric loads P at a
Derive the equation of the deflection curve for a cantilever beam AB when a couple of M0 acts counterclockwise at the free end (see figure). Also, determine the deflection σB and slope πB at the
A cantilever beam is subjected to load P at mid-span and counterclockwise moment M at B (see figure).(a) Find an expression for moment M in terms of the load P so that the reaction moment MA at A is
Beams AB and CDE are connected using rigid link DB with hinges (or moment releases) at ends D and B (see figure a). Beam AB is fixed at joint A and beam CDE is pin-supported at joint E. Load P =150
A cantilever beam carries a trapezoidal distributed load (see figure). Let wB = 2.5 kN/m, wA =.0 kN/m, and L = 2.5 m. The beam has a modulus E = 45GPa and a rectangular cross-section with
A cantilever beam ACB supports two concentrated loads P1 and P2, as shown in the figure. Determine the deflections dC and dB at points C and B, respectively. P₁ C P2 B
A beam ABC with simple supports at A and B and an overhang BC supports a concentrated load P at the free end C.(a) Determine the strain energy U stored in the beam due to the load P.(b) From the
Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of superposition, calculate the deflection at joint C. Assume that L = 4 m, a = 2 m, q = 15 kN/m, P = 7.5 kN, E =
Copper beam AB has a circular cross-section with a radius of 0.25 in. and length L = 3 ft. The beam is subjected to a uniformly distributed load w = 3.5 lb/ft. Calculate the required load P at joint
An overhanging beam ABC supports a concentrated load P at the end of the overhang. Span AB has length L, and the overhang has length a. Determine the deflection dC at the end of the overhang.
A simply supported beam (E = 12 GPa) carries a uniformly distributed load q = 125 N/m, and a point load P = 200 N at mid-span. The beam has a rectangular cross-section (b = 75 mm, h = 200 mm) and a
An object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). The beam has a rectangular cross-section of area A. Assuming that h is very large compared to the
A simply supported beam is loaded with a point load, as shown in the figure. The beam is a steel wide flange (W 12 X 35) in strong axis bending. Calculate the maximum deflection of the beam and the
A simply supported beam (E = 1600 ksi) is loaded by a triangular distributed load from A to C (see figure). The load has a peak intensity q0 = 10 lb/ ft, and the deflection is known to be 0.01 in. at
A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h. Obtain a formula for the maximum bending stress smax due to the falling weight in terms of h, σst, and
A simple beam AB of length L is loaded at the left-hand end by a couple of moments M0. Determine the angle of rotation uA at support A. Mo L B 30
A crank arm consists of a solid segment of length b1 and diameter d, a segment of length b2, and a segment of length b3, as shown in the figure. Two loads P act as shown: one parallel to -x and
An arm ABC lying in a horizontal plane and supported at A (see figure) is made of two identical solid steel bars AB and BC welded together at a right angle. Each bar is 22 in. long.(a) Knowing that
A horizontal bracket ABC consists of two perpendicular arms AB of a length 0.75 m and BC of a length 0.5 m. The bracket has a solid, circular cross section with a diameter equal to 65 mm. The bracket
An L-shaped bracket lying in a horizontal plane supports a load P = 150 lb (see figure). The bracket has a hollow rectangular cross section with thickness t = 0.125 in. and outer dimensions b = 2.0
A semicircular bar AB lying in a horizontal plane is supported at B (see figure part a). The bar has a centerline radius R and weight q per unit of length (total weight of the bar equals πqR). The
A double-decker bicycle rack made up of square steel tubing is fixed at A (figure a). The weight of a bicycle is represented as a point load applied at B on a plane frame model of the rack (figure
Beam ABCD has sliding support at A, roller supports at C and D, and a pin connection at B (see figure). Assume that the beam has a rectangular cross-section (b = 4 in., h = 12 in.). Uniform load q
Determine the maximum tensile, compressive, and shear stresses at points A and B on the bicycle pedal crank shown in the figure. The pedal and crank are in a horizontal plane and points A and B are
A gondola on a ski lift is supported by two bent arms, as shown in the figure. Each arm is offset by the distance b = 180 mm from the line of action of the weight force W. The allowable stresses in
A W 12 X 14 wide-f lange beam (see TableF-1(a), Appendix F) is simply supported with a span length of 120 in. (see figure). The beam supports two anti-symmetrically placed concentrated loads of
A W 360 X 79 steel beam is fixed at A. The beam has a length of 2.5 m and is subjected to a linearly varying distributed load with maximum intensity q0 = 500 N/m on segment AB and a uniformly
Repeat the preceding problem but now find the stress state on Element A at the base. Let WS = 240 N, WL = 250 N, t = 5 mm, d = 360 mm. See the figure for the locations of element A and all loads. 240
A W 12 X 35 steel beam is fixed at A. The beam has a length L = 6 ft and is subjected to a linearly varying distributed load with peak intensity q0 = 830 lb/ft. Calculate the state of plane stress at
A traffic light and signal pole is subjected to the weight of each traffic signal WS = 45 lb and the weight of the road lamp WL = 55 lb. The pole is fixed at the base. Find the principal normal
A sign is supported by a pipe having an outer diameter 110 mm and inner diameter 90mm. The dimensions of the sign are 2.0 m X 1.0 m, and its lower edge is 3.0 m above the base. Note that the center
A sign is supported by a pole of hollow circular cross section, as shown in the figure. The outer and inner diameters of the pole are 10.5 in. and 8.5 in., respectively. The pole is 42 ft high and
A post having a hollow, circular cross section supports a P = 3.2 kN load acting at the end of an arm that is b = 1.5 m long (see figure). The height of the post is L = 9 m, and its section modulus
A segment of a generator shaft with a hollow circular cross-section is subjected to a torque T = 240 kip-in. (see figure). The outer and inner diameters of the shaft are 8.0 in. and 6.25 in.,
A cantilever beam (width b = 3 in. and depth h = 6 in.) has a length L = 5 ft and is subjected to a point load P and a concentrated moment M = 20 kip-ft at end B. If normal stress σx = 0 at
The hollow drill pipe for an oil well (see figure) is 6.2 in. in outer diameter and 0.75 in. in thickness. Just above the bit, the compressive force in the pipe (due to the weight of the pipe) is 62

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