Questions and Answers of Mechanics Of Materials

Draw the shear-force and bending-moment diagrams for a simple beam AB supporting two equal concentrated loads P (see figure). Repeat if the left-hand load is upward and the right-hand load is
Two pipes (L1 = 2.5 m and L2 =1.5 m) are joined at B by flange plates (thickness tf =14 mm) with five bolts (dbf =13 mm) arranged in a circular pattern (see figure). Also, each pipe segment is
A steel tube (G =11.5 X 106 psi) has an outer diameter d2 = 2.0 in. and an inner diameter d1 = 1.5 in. When twisted by a torque T, the tube develops a maximum normal strain of 170 X 10-6. What is the
Two circular aluminum pipes of equal length L = 24 in. are loaded by torsional moments T. Pipe 1 has outside and inside diameters, d2 = 3 in. and d1 = 2.5 in, respectively. Pipe 2 has a constant
A circular tube AB is fixed at one end and free at the other. The tube is subjected to concentrated torques as shown in the figure. If the outer radius of the tube is 1.5 in. and the thickness is 3/4
Solve the preceding problem for the following data: b = 8.0 in., k =16 lb/in., a = 45, and P =10 lb.(a)(b) A 0000 T B k T I | C
A rigid bar of weight W = 800 N hangs from three equally spaced vertical wires (length L = 150 mm, spacing a = 50 mm): two of steel and one of aluminum. The wires also support a load P acting on the
Solve Prob. 2.8-1 if the collar has weight W = 50 lb, the height h = 2.0 in., the length L = 3.0 ft, the cross-sectional area A = 0.25 in2, and the modulus of elasticity E = 30,000 ksi. A k -10
An elliptical exerciser machine (see figure part a) is composed of front and back rails. A simplified plane-frame model of the back rail is shown in figure part b. Analyze the plane-frame model to
Find expressions for shear force V and moment M at x = 2L/3 of the beam (a) in terms of peak load intensity q0 and beam length variable L. Repeat for beam (b) but at x = L/2. A RA -X L % at L/2 V, M
Find expressions for shear force V and moment M at x = L/2 of beam BC. Express V and M in terms of peak load intensity q0 and beam length variable L. L/2 A B L/2 90 V, M at L/2 90 L/2 D L/2 C
Find expressions for shear force V and moment M at x = 2L/3 of beam (a) in terms of peak load intensity q0 and beam length variable L. Repeat for beam (b). A RA 9 at L/2 at L/2 ·X -L- Beam (a) V, M
Beam ABC has simple supports at A and B, an overhang BC and the distributed loading shown in the figure. Draw the shear-force and bending-moment diagrams for this beam. 25 lb/in. A -72 in.- 50
Find expressions for shear force V and moment M at x =x0 of beam AB in terms of peak load intensity q0 and beam length variable L. Let x0 = 2L/3. A X 90+² L 17 V, M at xo L 90 B
Find expressions for shear force V and moment M at x = x0 of beam AB in terms of peak load intensity q0 and beam length variable L. Let x0 = L/2. A q(x) = ·X X I% V, M at xo L 90 B
Find expressions for shear force V and moment M at x = L/2 of beam AB in structure(a). Express V and M in terms of peak load intensity q0 and beam length variable L. Repeat for structure (b) but
A cable with force P is attached to a frame at D and runs over a frictionless pulley at B. Find expressions for shear force V and moment M at x = L/3 of beam AB. C L/3 A L/3 L/3 D V, M at
Frame ABCD carries two concentrated loads (2P at C and P at D, see figure) and also a linearly varying distributed load on AB. Find expressions for shear force V and moment M at x = L/3 of beam AB in
First, solve for reactions using statics; then plot axial force (N) and shear force (V) diagrams. Confirm that the moment diagram is that shown below. Label all critical N, V, and M values and also
Frame ABC has a moment release just left of joint B. Find axial force N, shear force V, and moment M at the top of column AB. Write variables N, V, and M in terms of variables P and L.
A specimen of a methacrylate plastic is tested in tension at room temperature (see figure), producing the stress-strain data listed in the accompanying table. Plot the stress-strain curve and
Cable DB supports canopy beam OABC as shown in the figure. Find the required cross-sectional area of cable BD if the allowable normal stress is 125MPa. Determine the required diameter of the pins at
The data shown in the accompanying table are from a tensile test of high-strength steel. The test specimen has a diameter of 0.505 in. and a gage length of 2.00 in. At fracture, the elongation
A copper alloy pipe with a yield stress σ = 290 MPa is to carry an axial tensile load P =1500 kN. Use a factor of safety of 1.8 against yielding.(a) If the thickness t of the pipe is one-eighth of
A steel pad supporting heavy machinery rests on four short, hollow, cast iron piers. The ultimate strength of the cast iron in compression is 50 ksi. The outer diameter of the piers is d = 4.5 in.,
Segments AB and BCD of beam ABCD are pin connected at x =10 ft. The beam is supported by pin support at A and roller supports at C and D; the roller at D is rotated by 308 from the x axis (see
Consider the plane truss with a pin support at joint 3 and a vertical roller support at joint 5 (see figure).(a) Find reactions at support joints 3 and 5.(b) Find axial forces in truss members 11 and
A continuous cable (diameter 6 mm) with tension force T is attached to a horizontal frame member at B and C to support a sign structure. The cable passes over a small frictionless pulley at D. The
Continuous cable ADB runs over a small frictionless pulley at D to support beam OABC that is part of an entrance canopy for a building (see figure). Assume that the canopy segment has a weight of W =
Two steel wires support a moveable overhead camera weighing W = 2° lb (see fgure part a) used for close-up viewing of field action at sporting events. At some instant, wire 1 is at an angle a = 228
A plane truss has a pin support at A and a roller support at E (see figure).(a) Find reactions at all supports.(b) Find the axial force in truss member FE. A 4.5 m G 3 m B 9 kN 3 m C 6 kN E 3m D 13
Find support reactions at A and B and then use the method of joints to find all member forces. Let c = 8 ft and P = 20 kips.(a) Find reactions at both supports.(b) Find the axial force in truss
Find support reactions at A and B and then use the method of joints to find all member forces. Let b = 3 m and P = 80 kN. A b/2 2P D b/2 A = 60° 2P 8c = 80° a B = 40° B →X
Repeat 1.3-9 but use the method of sections to find member forces in AC and BD.Repeat 1.3-9Find support reactions at A and B and then use the method of joints to find all member forces. Let c = 8 ft
Find support reactions at A and B and then use the method of joints to find all member forces. Let c = 8 ft and P = 20 kips. y A A = 60° - c/2- P 2P 8c=80° a D 2P B = 40° B OB c/2- X
Repeat 1.3-10 but use the method of sections to find member forces in AB and DC.(a) Find reaction force components Bx, Bz, and Oz.(b) Find the axial force in truss member AC.Problem 1.3-10Find
A steel punch consists of two shafts: upper shaft and lower shaft. Assume that the upper shaft has a diameter d1 = 24 mm and the bottom shaft has a diameter d2 =16 mm. The punch is used to insert a
A space truss has three-dimensional pin supports at joints O, B, and C. Load P is applied at joint A and acts toward point Q. Coordinates of all joints are given in feet (see figure).(a) Find
A space truss is restrained at joints O, A, B and C, as shown in the figure. Load P is applied at joint A and load 2P acts downward at joint C.(a) Find reaction force components Ax, By, and Bz in
Solve the preceding problem if the mass of the tailgate is MT = 27 kg and that of the crate is MC = 68 kg. Use dimensions H = 305 m m, L = 406 mm, dC = 460 mm, and dT = 350 mm. The cable
A soccer goal is subjected to gravity loads (in the 2z direction, w = 73 N/m for DG, BG, and BC; w = 29 N/m for all other members; see figure) and a force F = 200 N applied eccentrically at the
A space truss is restrained at joints A, B and C, as shown in the figure. Load 2P is applied at in the 2x direction at joint A, load 3P acts in the 1z direction at joint B, and load P is applied in
Find support reactions at A and D and then calculate the axial force N, shear force V, and bending moment M at mid-span of AB. Let L = 14 ft, q0 =12 lb/ft, P = 50 lb, and M0 = 300 lb-ft.
Space frame ABCD is clamped at 3A, except it is free to translate in the x direction. There is also roller support at D, which is normal to line CDE. A triangularly distributed force with peak
Space frame ABC is clamped at A, except it is free to rotate at A about the x and y axes. Cables DC and EC support the frame at C. Force Py = − 50 lb is applied at the mid-span of AB, and a
A round brass bar of a diameter d1 = 20 mm has upset ends each with a diameter d2 = 26 mm (see figure). The lengths of the segments of the bar are L1 = 0.3 m and L2 = 0.1 m. Quarter-circular fillets
A circular steel tube with an outer diameter of 75mm and inner diameter of 65mm is subjected to torques T at its ends. Calculate the maximum permissible torque Tmax if the allowable normal strain is
A vertical steel bar ABC is pin-supported at its upper end and loaded by a force P1 at its lower end. A horizontal beam BDE is pinned to the vertical bar at joint B and supported at point D. Load
A solid steel bar of circular cross-section has diameter d = 2.5 in., L = 60 in., and shear modulus of elasticity G =11.5 X106 psi. The bar is subjected to torques T = 300 lb-ft at the ends.
Repeat Problem 3.3-1, but now use a circular tube with outer diameter do = 2.5 in. and inner diameter di = 1.5 in.Problem 3.3-1A solid steel bar of circular cross-section has diameter d = 2.5 in., L
A copper tube with a circular cross-section has a length L =1.25 m, thickness t = 2 mm, and shear modulus of elasticity G = 45 GPa. The bar is de signed to carry a 300 N ? m torque acting at the
A solid copper bar of circular cross-section has a length L = 1.25 m and shear modulus of elasticity G = 45 GPa. The bar is designed to carry a 250 N · m torque acting at the ends. If the allowable
A circular tube AB is fixed at one end and free at the other. The tube is subjected to concentrated torques as shown in the figure. If the outer radius of the tube is 1.5 in. and the thickness is 3/4
A solid steel shaft ABC with diameter d = 40 mm is driven at A by a motor that transmits 75kW to the shaft at 15 Hz. The gears at B and C drive machinery requiring power equal to 50 kW and 25 kW,
A square tube section has side dimension of 20 in. and a thickness of 0.5 in. If the section is used for a 10-ft-long beam subjected to 1250 kip-in. torque at both ends, calculate the maximum shear
An aluminum tube has an inside diameter d1 = 50 mm, shear modulus of elasticity G = 27 GPa, n = 0.33, and torque T = 4.0 kN ? m. The allowable shear stress in the aluminum is 50 MPa, and the
Find expressions for shear force V and moment M at mid-span of beam AB in terms of peak load intensity q0 and beam length variables a and L Let a = 5L/6. A V, M at L/2 a L- 90 C B DO
The simple beam AB supports a triangular load of maximum intensity q0 =10 lb/in. acting over one-half of the span and a concentrated load P = 80 lb acting at midspan (see figure). Draw the
Two tubes (AB, BC) of the same material are connected by three pins (pin diameter 5d p) just left of B as shown in the figure. The properties and dimensions for each tube are given in the figure.
A plane frame is restrained at joints A and D, as shown in the figure. Members AB and BCD are pin connected at B. A triangularly distributed lateral load with peak intensity of 80 N/m acts on CD. An
Find support reactions at A and D and then calculate the axial force N, shear force V, and bending moment M at the mid-span of column BD. Let L = 4 m, q0 =160 N/m, P = 200 N, and M0 = 380 N · m.
A 200-lb trap door (AB) is supported by a strut (BC) which is pin connected to the door at B(see figure).(a) Find reactions at supports A and C.(b) Find internal stress resultants N, V, and M on the
A plane frame is constructed by using a pin connection between segments ABC and CDE. The frame has pin supports at A and E and joint loads at B and D (see figure).(a) Find reactions at supports A and
A plane frame with pin supports at A and E has a cable attached at C, which runs over a frictionless pulley at F (see figure). The cable force is known to be 500 lb.(a) Find reactions at supports A
A plane frame with a pin support at A and roller supports at C and E has a cable attached at E, which runs over frictionless pulleys at D and B (see figure). The cable force is known to be 400 N.
A 150-lb rigid bar AB, with frictionless rollers at each end, is held in the position shown in the figure by a continuous cable CAD. The cable is pinned at C and D and runs over a pulley at A.(a)
A plane frame has a pin support at A and roller supports at C and E (see figure). Frame segments ABD and CDEF are joined just left of joint D by a pin connection.(a) Find reactions at supports A, C,
A plane frame has a pin support at A and roller supports at C and E (see figure). Frame segments ABD and CDEF are joined just left of joint D by a pin connection.(a) Find reactions at supports A, C,
A mountain bike is moving along a flat path at constant velocity. At some instant, the rider (weight = 670 N) applies pedal and hand forces, as shown in figure part a.(a) Find reaction forces at the
The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress s
A 10-ft rigid bar AB is supported with a vertical translational spring at A and a pin at B. The bar is subjected to a linearly varying distributed load with maximum intensity q0. Calculate the
A long, rectangular copper bar under a tensile load P hangs from a pin that is supported by two steel posts (see figure). The copper bar has a length of 2.0 m, a cross-sectional area of 4800 mm2, and
A steel bar with a uniform cross-section is fixed at both ends. A load P = 2.5 kips is applied at point C. The bar has a cross-sectional area of 8 in2. Calculate the reactions at joints A and B and
A round brass bar of a diameter d1 = 20 mm has upset ends each with a diameter d2 = 26 mm (see figure). The lengths of the segments of the bar are L1 = 0.3 m and L2 = 0.1 m. Quarter-circular fillets
A vertical bar consists of three prismatic segments A1, A2, and A3 with cross-sectional areas of 6000 mm2, 5000 mm2, and 4000 mm2, respectively. The bar is made of steel with E = 200 GPa. Calculate
A vertical bar is loaded with axial loads at points B, C, and D, as shown in the figure. The bar is made of steel with a modulus of elasticity E = 29,000 ksi. The bar has a cross-sectional area of
Repeat Problem 2.3-4, but now include the shortening dAC is not to exceed 4.0 mm? weight of the bar. See Table I-1 in Appendix I for the weight density of steel.Problem 2.3-4A vertical bar consists
Repeat Problem 2.3-5, but now include the weight of the bar. See Table I-1 in Appendix I for the weight density of steel.Problem 2.3-5A vertical bar is loaded with axial loads at points B, C, and D,
Bar ABC is fixed at both ends (see figure) and has load P applied at B. Find reactions at A and C and displacement dB if P = 200 kN, L = 2 m, t = 20 mm, b1 =100 mm, b2 =115 mm, and E = 96 GPa.
A device consists of a horizontal beam ABC supported by two vertical bars BD and CE. Bar CE is pinned at both ends but bar BD is fixed to the foundation at its lower end. The distance from A to B is
A flat aluminum alloy bar is fixed at both ends. Segment AB has a slight taper. If the temperature of the bar is raised uniformly by an amount ΔT = 20°F, find reactions at A and C. What is the
Repeat Problem 2.4-8, but assume that the bar is made of aluminum alloy and that BC is prismatic. Assume that P = 20 kips, L = 3 ft, t =1/4 in., b1 = 2 in., b2 = 2.5 in., and E =10,400 ksi.Problem
A prismatic bar with a length L = 3 ft and cross-sectional area A = 8 in2 is compressed by an axial centroidal load P =10 kips. Determine the complete state of stress acting on an inclined section pq
A hollow circular tube T of a length L =15 in. is uniformly compressed by a force P acting through a rigid plate. The outside and inside diameters of the tube are 3.0 and 2.75 in., respectively. A
Find support reactions at A and B and then calculate the axial force N, shear force V, and bending moment M at mid-span of AB. Let L = 14 ft, q0 = 12 lb/ft, P = 50 lb, and M0 = 300 lb-ft. Mo A
A circular tube AB is fixed at one end and free at the other end. The tube is subjected to axial force at joint B. If the outer diameter of the tube is 3 in. and the thickness is ¾ in., calculate
Segments AB and BCD of beam ABCD are pin connected at x = 4 m. The beam is supported by sliding support at A and roller supports at C and D (see figure). A triangularly distributed load with peak
A square plastic bar (length Lp, side dimension sp =193 mm) is inserted inside a hollow, square, cast iron tube (length Lc = 400 mm, side sc = 200 mm, and thickness tc = 3 mm). tc = 3 mm Cast iron
A space truss is restrained at joints A, B, and C, as shown in the figure. Load P acts in the 1z direction at joint B and in the 2z direction at joint C. Coordinates of all joints are given in terms
Two separate cables AC and BC support a sign structure of weight W =1575 lb attached to a building. The sign is also supported by a pin support at O and a lateral restraint in the z-direction at
A plane frame is restrained at joints A and C, as shown in the figure. Members AB and BC are pin connected at B. A triangularly distributed lateral load with a peak intensity of 90 lb/ft acts on AB.
Repeat Problems 2.3-18, but assume that the bar is made of copper alloy. Calculate the displacements SB and SC if P = 50 kips, L = 5 ft, t = 3 / 8 in., b1 = 2.75 in., b2 = 3 in., and E = 16,000
Two pipe columns (AB, FC) are pin connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1 or L2) and outer diameters (d1 or d2) are different for
Repeat Problems 2.3-18, but assume that the bar is made of aluminum alloy. If P2 =200 kN, what is P1 so that displacement dC = 0? What is displacement dB? Assume that L= 2 m, t = 20 mm, b1
Plastic bar AB of rectangular cross-section (b = 0.75 in. and h = 1.5 in.) and length L = 2 ft is fixed at A and has spring support (k = 18 kips/in.) at C. Initially, the bar and spring have no
Find expressions for all support reaction forces in the plane frame with load 2P applied at C, as shown in the figure. Joint A is sliding support, joint D is pinned, and joint F is roller support.
A compression bar having a square cross-section with sides b = 50 mm is subjected to load P. The bar is constructed from two pieces of wood that are connected by a glued joint along plane pq that is
A T-frame structure is composed of prismatic beam ABC and non prismatic column DBF that are joined at B by a frictionless pin connection. The beam has sliding support at A and the column is pin
Repeat Problem 2.3-29 if vertical load P at D is replaced by a horizontal load P at D (see figure).Problem 2.3-29A T-frame structure is composed of prismatic beam ABC and non prismatic column DBF
A circular copper bar with diameter d = 3 in. is subjected to torques T = 30 kip-in. at its ends. Find the maximum shear, tensile, and compressive stresses in the tube and their corresponding

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