Mechanics of Materials, SI Edition
9th Edition
ISBN: 9781337093354
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2, Problem 2.7.8P
The statically indeterminate structure shown in the figure consists of a horizontal rigid bar AB supported by five equally spaced springs. Springs l, 2, and 3 have stiff nesses 3k, 5k. and k, respectively. When unstressed, the lower ends of all Five springs lie along: a horizontal line. Bar AB. which has weight W, causes the springs to elongate by an amount S.
(a) Obtain a formula For the total strain energy of the springs in terms of the downward displacement d of the bar.
(b) Obtain a formula for the displacement S by equating the strain energy of the springs to the work done by the weight W.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Chapter 2 Solutions
Mechanics of Materials, SI Edition
Ch. 2 - A 10-ft rigid bar AB is supported with a vertical...Ch. 2 - Rigid bar ABC is supported with a pin at A and an...Ch. 2 - The L-shaped arm ABCD shown in the figure lies in...Ch. 2 - A steel cable with a nominal diameter of 25 mm...Ch. 2 - A steel wire- and an aluminum allay wire have...Ch. 2 - By what distance h does the cage shown in the...Ch. 2 - Rigid bar ACB is supported by an elastic circular...Ch. 2 - A plastic cylinder is held snugly between a rigid...Ch. 2 - A safety valve on the top of a tank containing...Ch. 2 - The device shown in the figure consists of a...
Ch. 2 - A small lab scale has a rigid L-shaped frame ABC...Ch. 2 - A small lab scale has a rigid L-shaped frame ABC...Ch. 2 - Two rigid bars are connected to each other by two...Ch. 2 - The three-bar truss ABC shown in the figure part a...Ch. 2 - An aluminum wire having a diameter d = 1/10 in....Ch. 2 - A uniform bar AB of weight W = 25 N is supported...Ch. 2 - A hollow, circular, cast-iron pipe (Ec =12,000...Ch. 2 - The horizon Lai rigid beam A BCD is supported by...Ch. 2 - Two pipe columns (AB, FC) are pin-connected to a...Ch. 2 - A framework ABC consists of two rigid bars AB and...Ch. 2 - Solve the preceding problem for the following...Ch. 2 - The length of the end segments of the bar (see...Ch. 2 - A long, rectangular copper bar under a tensile...Ch. 2 - An aluminum bar AD (see figure) has a...Ch. 2 - A vertical bar consists of three prismatic...Ch. 2 - A vertical bar is loaded with axial loads at...Ch. 2 - Repeat Problem 2.3-4, but now include the weight...Ch. 2 - -7 Repeat Problem 2.3-5, but n include the weight...Ch. 2 - A rectangular bar of length L has a slot in the...Ch. 2 - Solve the preceding problem if the axial stress in...Ch. 2 - A two-story building has steel columns AB in the...Ch. 2 - A steel bar is 8.0 Ft long and has a circular...Ch. 2 - A bar ABC of length L consists of two parts of...Ch. 2 - A woodpile, driven into the earth, supports a load...Ch. 2 - Consider the copper lubes joined in the strength...Ch. 2 - The nonprismalic cantilever circular bar shown has...Ch. 2 - *16 A prismatic bar AB of length L,...Ch. 2 - A flat bar of rectangular cross section, length L,...Ch. 2 - A flat brass bar has length L, constant thickness...Ch. 2 - Repeat Problem 2.3-18, but assume that the bar is...Ch. 2 - Repeat Problem 2.3-18, but assume that the bar is...Ch. 2 - A slightly tapered bar AB of solid circular crass...Ch. 2 - A circular aluminum alloy bar of length L = 1.8 m...Ch. 2 - A long, slender bar in the shape of a right...Ch. 2 - A post AB supporting equipment in a laboratory is...Ch. 2 - The main cables of a suspension bridge (see figure...Ch. 2 - A uniformly tapered lube AB of circular cross...Ch. 2 - A vertical steel bar ABC is pin-supported at its...Ch. 2 - A T-frame structure is torn posed of a prismatic...Ch. 2 - A T-frame structure is composed of prismatic beam...Ch. 2 - Repeat Problem 2.3-29 if vertical load P at D is...Ch. 2 - A bar ABC revolves in a horizontal plane about a...Ch. 2 - The assembly shown in the figure consists of a...Ch. 2 - A cylindrical assembly consisting of a brass core...Ch. 2 - A steel bar with a uniform cross section, is fixed...Ch. 2 - A horizontal rigid bar ABC is pinned at end A and...Ch. 2 - A solid circular steel cylinder S is encased in a...Ch. 2 - Three prismatic bars, two of material A and one of...Ch. 2 - A circular bar ACB of a diameter d having a...Ch. 2 - Bar ABC is fixed at both ends (see figure) and has...Ch. 2 - Repeat Problem 2.4-8, but assume that the bar is...Ch. 2 - A plastic rod AB of length L = 0.5 m has a...Ch. 2 - 2.4-11 Three steel cables jointly support a load...Ch. 2 - The fixed-end bar ABCD consists of three prismatic...Ch. 2 - A lube structure is acted on by loads at B and D,...Ch. 2 - A hollow circular pipe (see figure} support s a...Ch. 2 - The aluminum and steel pipes shown in the figure...Ch. 2 - A rigid bar of weight W = SOO N hangs from three...Ch. 2 - A bimetallic bar (or composite bar) of square...Ch. 2 - S Three-bar truss ABC (see figure) is constructed...Ch. 2 - A horizontal rigid bar of weight If' = 72001b is...Ch. 2 - A rigid bar ABCD is pinned at point B and...Ch. 2 - A rigid bar AB if of a length B = 66 in. is....Ch. 2 - Find expressions For all support reaction forces...Ch. 2 - A trimetallic bar is uniformly compressed by an...Ch. 2 - Find expressions for all support reaction Forces...Ch. 2 - The rails of a railroad track are welded together...Ch. 2 - A circular steel rod of diameter d is subjected to...Ch. 2 - A rigid bar of weight W = 750 lb hangs from three...Ch. 2 - A steel rod. of 15-mm diameter is held snugly (but...Ch. 2 - A bar AB of length L is held between rigid...Ch. 2 - A beam is constructed using two angle sections (L...Ch. 2 - A W 8 × 28 beam of a length 10 ft is held between...Ch. 2 - A plastic bar ACB having two different solid...Ch. 2 - ,5-9 A flat aluminum alloy bar is fixed at both...Ch. 2 - Repeat Problem 2.5-9 for the flat bar shown in the...Ch. 2 - A circular steel rod AB? (diameter d, = 1.0 in.,...Ch. 2 - A circular, aluminum alloy bar of a length L = 1.8...Ch. 2 - Rectangular bars of copper and aluminum are held...Ch. 2 - A brass sleeve S is fitted over a steel bolt B...Ch. 2 - A rigid triangular frame is pivoted at C and held...Ch. 2 - ,5-16 A rigid bar ABCD is pinned at end A and...Ch. 2 - A copper bar AB with a length 25 in. and diameter...Ch. 2 - A steel wire AB is stretched between rigid...Ch. 2 - -19 The mechanical assembly shown in the figure...Ch. 2 - A bar AB having a length L and axial rigidity EA...Ch. 2 - Pipe 2 has been inserted snugly into Pipe I. but...Ch. 2 - A non prism elk- bar ABC made up of segments...Ch. 2 - Wires B and C are attached to a support at the...Ch. 2 - A rigid steel plate is supported by three posts of...Ch. 2 - A capped cast-iron pipe is compressed by a brass...Ch. 2 - A plastic cylinder is held snugly between a rigid...Ch. 2 - Prob. 2.5.27PCh. 2 - Consider the sleeve made From two copper tubes...Ch. 2 - A polyethylene tube (length L) has a cap that when...Ch. 2 - Prestressed concrete beams are sometimes...Ch. 2 - Prob. 2.5.31PCh. 2 - A steel bar of rectangular cross section (1.5 in....Ch. 2 - A circular steel rod of diameter d is subjected to...Ch. 2 - A standard brick (dimensions 8 in. × 4 in. × 2.5...Ch. 2 - A brass wire of diameter d = 2.42 mm is stretched...Ch. 2 - Prob. 2.6.5PCh. 2 - A steel bar with a diameter d = 12 mm is subjected...Ch. 2 - During a tension lest of a mild-steel specimen...Ch. 2 - A copper bar with a rectangular cross section is...Ch. 2 - A prismatic bar with a length L = 3 ft and...Ch. 2 - A prismatic bar with a length L = 1 m and...Ch. 2 - The plane truss in the figure is assembled From...Ch. 2 - Plastic bar of diameter d = 32 mm is compressed in...Ch. 2 - A plastic bar of rectangular cross section (ft =...Ch. 2 - A copper bar of rectangular cross section (b = 18...Ch. 2 - A circular brass bar with a diameter J is member...Ch. 2 - Two boards are joined by gluing along a scarf...Ch. 2 - Acting on the sides of a stress element cut from a...Ch. 2 - A prismatic bar is subjected to an axial force...Ch. 2 - The normal stress on plane pq of a prismatic bar...Ch. 2 - A tension member is to be constructed of two...Ch. 2 - -21 Plastic bar AB of rectangular cross section (6...Ch. 2 - A compression bar having a square cross section...Ch. 2 - A prismatic bar AD of length L, cross-sectional...Ch. 2 - A bar with a circular cross section having two...Ch. 2 - A three-story steel column in a building supports...Ch. 2 - The bar ABC shown in the figure is loaded by a...Ch. 2 - Determine the strain energy per unit volume (units...Ch. 2 - The truss ABC shown in the Figure is subjected to...Ch. 2 - -7 The truss A BC Shawn in the figure supports a...Ch. 2 - The statically indeterminate structure shown in...Ch. 2 - A slightly tapered bar AB of rectangular cross...Ch. 2 - A compressive load P is transmitted through a...Ch. 2 - A block B is pushed against three springs by a...Ch. 2 - A bungee cord that behaves linearly elastically...Ch. 2 - A sliding collar of weight W = 150 lb falls From a...Ch. 2 - Solve the preceding problem if the collar has mass...Ch. 2 - Prob. 2.8.3PCh. 2 - A block weighing W = 5.0 N drops inside a cylinder...Ch. 2 - Solve the preceding problem for W = 1.0 lb. h = 12...Ch. 2 - Prob. 2.8.6PCh. 2 - A weight W = 4500 lb falls from a height h onto a...Ch. 2 - Prob. 2.8.8PCh. 2 - Prob. 2.8.9PCh. 2 - A bumping post at the end of a track in a railway...Ch. 2 - A bumper for a mine car is constructed with a...Ch. 2 - A bungee jumper having a mass of 55 kg leaps from...Ch. 2 - Prob. 2.8.13PCh. 2 - A rigid bar AB having a mass M = 1.0 kg and length...Ch. 2 - The flat bars shown in parts a and b of the figure...Ch. 2 - The flat bars shown in parts a and b of the figure...Ch. 2 - A flat bar of width b and thickness t has a hole...Ch. 2 - Around brass bar of a diameter d1= 20mm has upset...Ch. 2 - Prob. 2.10.5PCh. 2 - ,10-6 A prismatic bar with a diameter d0= 20 mm is...Ch. 2 - A stepped bar with a hole (see figure) has widths...Ch. 2 - A bar AB of length L and weight density y hangs...Ch. 2 - A prismatic bar of length L = 1.8 m and...Ch. 2 - Prob. 2.11.3PCh. 2 - A prismatic bar in tension has a length L = 2.0 m...Ch. 2 - An aluminum bar subjected to tensile Forces P has...Ch. 2 - A rigid bar AB is pinned al end A and is supported...Ch. 2 - Two identical bars AB and BC support a vertical...Ch. 2 - A stepped bar ACB with circular cross sections is...Ch. 2 - A horizontal rigid bar AB supporting a load P is...Ch. 2 - Prob. 2.12.4PCh. 2 - The symmetric truss ABCDE shown in the figure is...Ch. 2 - Five bars, each having a diameter of 10 mm....Ch. 2 - Prob. 2.12.7PCh. 2 - A rigid bar ACB is supported on a fulcrum at C and...Ch. 2 - The structure shown in the figure consists of a...Ch. 2 - Two cables, each having a length i. of...Ch. 2 - A hollow circular tube T of a length L = 15 in. is...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- A uniform bar AB of weight W = 25 N is supported by two springs, as shown in the figure. The spring on the left has a stiffness k[= 300 N/m and natural length Lt=250 mm. The corresponding quantities for the spring on the right are k2= 400 N/m and L^ = 200 mm. The distance between the springs is L = 350 mm, and the spring on the right is suspended from a support that is a distance it = SO mm below the point of support for the spring on the left. Neglect the weight of the springs. (a) At what distance x from the left-hand spring (figure part a) should a load P = 18 N be placed in order to bring the bar to a horizontal position? (b) If P is now removed, what new value of k{is required so that the bar (figure part a) will hang in a horizontal position underweight If? (c) If P is removed and kt= 300 N/m. what distance b should spring ktbe moved to the right so that the bar (figure part a) will hang in a horizontal position under weight II"? (d) If the spring on the left is now replaced by two springs in series (kt= 300 N/m, kt) with overall natural length Lt= 250 mm (see figure part b). what value of k; is required so that the bar will hang in a horizontal position under weight IF?arrow_forward-7 The truss A BC Shawn in the figure supports a horizontal load P1= 300 lb and a vertical load P2= 9001b. Both bars have a cross-sectional area A = 2.4 in2 and are made of steel with E = 30 X 106 psi. (a) Determine the strain energy U1of the truss when the load P1acts alone (P2= 0). (b) Determine the strain energy U2when the load P2acts alone (P1= 0). (c) Determine the strain energy U3when both loads act simultaneously.arrow_forwardA bungee cord that behaves linearly elastically has an unstressed length L0= 760 mm and a stiffness k = 140 N/m. The cord is attached to two pegs, distance/? = 380 mm apart, and is pulled at its midpoint by a Force P = 80 N (see figure). (a) How much strain energy U is stored in the cord? (b) What is the displacement Scof the point where the load is applied? (c) Compare the strain energy (with the quantity PSC12. Note: The elongation of the cord is not small compared lo its original length.arrow_forward
- Solve the preceding problem if the cube is granite (E = 80 GPa, v = 0.25) with dimensions E = 89 mm and compressive strains E = 690 X l0-6 and = = 255 X 10-6. For part (c) of Problem 7.6-5. find the maximum value of cr when the change in volume must be limited to 0.11%. For part. find the required value of when the strain energy must be 33 J.arrow_forwardA hollow circular pipe (see figure} support s a load P that is uniformly distributed around a cap plate at the top of the lower pipe. The inner and outer diameters of the upper and lower parts of the pipe are d1= 50 mm, d2= 60 mm, rf3 = 57 mm, and d1= 64 mm, respectively. Pipe lengths are Lt= 2 m and L, = 3 m. Neglect the self-weight of the pipes. Assume that cap plate thickness is small compared to I, and E,. Let E = 110 MPa. (a) If the tensile stress in the upper part is d = 10.5 MPa. what is load PI Also, what are reactions ft, at the upper support and R-, at the lower support? What is the stress ar(MPa) in the lower part? (b) Find displacement S(mm) at the cap plate. Plot the axial force diagram (AFD) [Ar(.f)] and axial displacement diagram (ADD)[5(.t)]. (c) Add the uniformly distributed load q along the censorial axis of pipe segment 2. Find q (kN/m) so that It, = 0. Assume that load P from part (a) is also applied.arrow_forwardBy what distance h does the cage shown in the figure move downward when the weight W is placed inside it? (See the figure.) Consider only the effects of the stretching of the cable, which has axial rigidity EA = 10,700 kN. The pulley at A has a diameter da= 300 mm and the pulley at B has a diameter dB= 150 mm. Also, the distance L1= 4.6 m, the distance L2=10.5 m, and the weight W = 22 kN. Note: When calculating the length of the cable. include the parts of the cable that go around the pulley sat A and B.arrow_forward
- A bimetallic bar (or composite bar) of square cross sec lion with dimensions 2b X lb is construe ted of two different metals having module of elasticity E2and E2(see figure). The two parts of the bar have the same cross-sectional dimensions. The bar is compressed by forces P acting through rigid end plates. T h e line of action of t he loads has an eccentricity e of such magnitude that each part of the bar is stressed uniformly in compression. (a) Determine the axial forces Ptand P2in the two parts of the bar. (b} Determine the eccentricity e of the loads. (c) Determine the ratio C|/tr2 of the stresses in the two parts of the bar.arrow_forward-11 A solid steel bar (G = 11.8 X 106 psi ) of diameter d = 2,0 in. is subjected to torques T = 8.0 kip-in. acting in the directions shown in the figure. Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements.arrow_forwardA three-story steel column in a building supports roof and floor loads as shown in the figure. The story height H is 10.5 ft. the cross-sectional area A of the column is 15.5 in2, and the modulus of elasticity E of the steel is 30 × 106 psi. Calculate the strain energy U of the column assuming P1= 40 kips and P2= P3= 60 kips.arrow_forward
- A bar with a circular cross section having two different diameters d and 2d is shown in the figure. The length of each segment of the bar is L/2T and the modulus of elasticity of the material is E. (a) Obtain a formula for the strain energy U of the bar due to the load P. (b) Calculate the strain energy if the load P = 27 kN, the length L = 600 mm, the diameter d = 40 mm, and the material is brass with E = 105 GPa.arrow_forwardA trimetallic bar is uniformly compressed by an axial force P = 9 kips applied through a rigid end plate (see figure}. The bar consists of a circular steel core surrounded by brass and copper tubes. The steel core has a diameter of L.25 i n., the brass tube has an outer diameter of 1.75 in., and the copper tube has an outer diameter of 2.25 in. The corresponding modulus of elasticity are f, = 30, 000 ksi, Eb= 16,000 ksi, and E = 18,000 ksi Calculate the compressive stresses ers, ab, and cin the steel, brass, and copper, respectively, due to the force P.arrow_forwardA circular aluminum tube of length L = 600 mm is loaded in compression by forces P (see figure). The outside and inside diameters are d2= 75 mm and d1= 63 mm, respectively. A strain gage is placed on the outside of the lube to measure normal strains in the longitudinal direction. Assume that E = 73 GPa and Poissons ratio is v = 0.33. (a) IF the compressive stress in the tube is 57 MPa, what is the load P? (b) If the measured strain is e = 78 J X 10-6, what is the shorteningarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Strain energy and strain energy density introduced; Author: Engineer4Free;https://www.youtube.com/watch?v=m14sqLGg4BQ;License: Standard youtube license