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 2.7.5P
Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit.
| DATA FOR PROBLEM 2.7-5 | |||
| Material | Weight Density (lb/in3) | Modulus of Elasticity (ksi) | Proportional Limit (psi) |
| Mild sleel | 0.284 | 30,000 | 36,000 |
| Tool steel | 0.284 | 30,000 | 75,000 |
| Aluminum | 0.0984 | 10,500 | 60,000 |
| Rubber (soft) | 0.0405 | 0.300 | 300 |
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Use the engineering stress strain diagram provided below to answer parts (A) to
(H) below (the stress-strain diagram bas already been drawn for you):
stress strain diagram
400
350 0
300 0
250 0
200 0
150.0
100.0
50.0
O 05
0 1
0.15
strain
A. Determine the tensile strength of this alloy.
B. show the elastic, plastic and total strain on the diagram
stress (Mpa)
2) Use the engineering stress strain diagram provided below to answer parts (A) to
(H) below (the stress-strain diagram has already been drawn for you):
stress strain diagram
400
350 0
300 0
250 0
200 0
150.0
100.0
50.0
00
0 05
01
0. 15
strain
A. Determine the tensile strength of this alloy.
B. show the clastic, plastic and total strain on the diagram
stress (Mpa)
Please annotate the attached to highlight the different phases of the stress/strain graph for 0.15% carbon steel.
From the attached graph, calculate the following:
1-modulus of elasticity
2-tensile strength
3-the ductility in % of elongation
4- yield strength at a strain offset of 0.002
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 wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?arrow_forwardPlease annotate the attached stress strain graph of 0.9% carbon steel to show the different phases. From the graph work out the following: 1) modulus of elasticity 2) tensile strength 3) the ductility in % elongation 4) yield strength at a strain offset of 0.002arrow_forwardStress Strain Diagram The Data shown in the table have been obtained from a tensile test conducted on a high-strength steel. The test specimen had a diameter of 0.505 inch and a gage length of 2.00 inch. Using software. plot the Stress-Strain Diagram for this steel and determine its: A= TTdT(050s A %3D 1. Proportional Limit, 2. Modulus of Elasticity, 3. Yield Strength (SY) at 0.2% Offset, 4. Ultimate Strength (Su), 5. Percent Elongation in 2.00 inch, 6. Percent Reduction in Area, 7. Present the results (for Steps 1-6) in a highly organized table. e Altac ie sheet (as problelle 4 A = 0.2.002 BEOINNING of the effort Elongation (in) Elongation (In) Load Load #: #3 (Ib) (Ib) 1 0.0170 15 12,300 0.0004 1,500 16 12,200 0.0200 0.0010 3. 3,100 17 12,000 0.0275 0.0016 4,700 18 13,000 0.0335 5. 6,300 0.0022 19 15,000 0.0400 0.0026 6. 8,000 20 16,200 0.055 0.0032 9,500 21 17,500 0.0680 0.0035 8. 11,000 22 18,800 0.1080 0.0041 11,800 23 19,600 0.1515 0.0051 24 20,100 0.2010 10 12,300 0.0071 25…arrow_forward
- The following data was obtained as a result of tensile testing of a standard 0.505 inch diameter test specimen of magnesium. After fracture, the gage length is 2.245 inch and the diameter is 0.466 inch. a). Calculate the engineering stress and strain values to fill in the blank boxes and plot the data. Load(lb) Gage Length (in) Stress (kpsi) Strain 0 2 1000 2.00154 2000 2.00308 3000 2.00462 4000 2.00615 5000 2.00769 5500 2.014 6000 2.05 6200 (max) 2.13 6000 (fracture) 2.255 b). Calculate the modulus of elasticity c). If another identical sample of the same material is pulled only to 6000 pounds and is unloaded from there, determine the gage length of the sample after unloading.arrow_forwardFrom the stress-strain data for poly(methyl methacrylate) shown in figure below, determine the modulus of elasticity in the elastic linear region and the tensile strength at 40 °C (104 °F). Stress (MPa) 80 70 60 30 20 10 4°C (40°F) ,20°C (68°F) 30°C (86°F) .40°C (104°F) 0.1 Strain 50°C (122°F) 60°C (140°F) 0.2 To 1.30 The modulus of elasticity is 2.3 GPa and the tensile strength is 49 MPa O The modulus of elasticity is 38 MPa and the tensile strength is 3.3 GPa The modulus of elasticity is 1.2 GPa and the tensile strength is 52 MPa The modulus of elasticity is 1.2 GPa and the tensile strength is 38 MPa T 12 10 8 2 0.3 Stress (10³ psi)arrow_forwardProblem 4 The attached figure shows, for a gray cast iron, the tensile engineering stress-strain curve in the elastic region. Determine (a) the tangent modulus at 25 MPa and (b) the secant modulus taken to 35 MPa. Stress (MPa) 60 50 40 30 20 10 0.0002 0.0004 Strain 0.0006 T 8 6 ★ 2 0.0008 Stress (10³ psi)arrow_forward
- The figure below shows the tensile engineering stress-strain behavior for a steel alloy. (a) What is the modulus of elasticity? (b) What is the yield strength at a strain offset of 0.002? (c) What is the tensile strength? Stress (MPa) 600 500 400 300 200 100 T I 0.00 Stress (MPa) 0.04 500 400 300 200 100 0.000 0.08 0.002 Strain 0.004 Strain 0.12 I 0.006 0.16 0.20 In the previous problem, A load of 85,000 N (19,100 lbf) is applied to a cylindrical specimen of the steel alloy that has a cross-sectional diameter of 15 mm (0.59 in.). (a) Will the specimen experience elastic and/or plastic deformation? Why? (b) If the original specimen length is 250 mm (10 in.), how much will it increase in length when this load is applied?arrow_forward1.7C1 1.4C1 ci 0.9C1 Uniform plastic elongation Necking Elastie 0 4 % 15% 35% Strain in % Stress-Strain diagram Stress in MPaarrow_forwardCalculate the Modulus of elasticity, Modulus of toughness and Modulus of Resilience for the material from stress-strain diagram below.arrow_forward
- Determine the tensile yield strength (0.2% offset) and the maximum strength of a metal alloy having the following tensile stress-strain diagram. 600 500 400 500 300 400 300E 200 3200 100 100E 0.000 0.002 0.004 0.006 Strain ol 0.00 0.16 0.20 0.08 Strain 0.04 0.12 Select one: O The tensile yield strength Sy = 290 Mpa and the maximum strength Smax = 500 Mpa. O The tensile yield strength Sy = 170 Mpa and the maximum strength Smax = 400 Mca. G The tensile yield strength Sy = 200 Mpa and the maximum strength Smax = 500 Moa. O Tne tensile yield strength Sy = 390 Mpa and the maximum strength Smax= 500 Mpa. The tensile yed strength Sy = 150 Mpa and the maximum strength Smax = 250 Mpa. Stress (MPa) Stress (MPa)arrow_forwardmaterial with a rectangular cross-section of 4 mm by 25 mm is loaded in tension with a force of 32 kN. A strain gauge bonded to the material measures a strain of 400 microstrain when the sample is loaded. culate Young's modulus of the material, measured to the nearest GPa (GN/m2) and enter your answer in the box below. ung's modulus: [ GPaarrow_forwardStrain of Silly Putty: Initial length (L0): 2.85 cm Final length (L): 8.50 cm Strain: % (show calculation below): (Please type answer no write by hend)arrow_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