
EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220102804487
Author: BEER
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 2.9, Problem 72P
For a member under axial loading, express the normal strain ∈' in a direction forming an angle of 45° with the axis of the load in terms of the axial strain ∈x by (a) comparing the hypotenuses of the triangles shown in Fig. 2.43, which represent respectively an element before and after deformation, (b) using the values of the corresponding stresses ϭ' and ϭx shown in Fig. 1.38, and the generalized Hooke’s law.
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Solve this problem and show all of the work
Solve this problem and show all of the work
Solve this problem and show all of the work
Chapter 2 Solutions
EBK MECHANICS OF MATERIALS
Ch. 2.1 - A nylon thread is subjected to a 8.5-N tension...Ch. 2.1 - A 4.8-ft-long steel wire of 14 -in.-diameter is...Ch. 2.1 - An 18-m-long steel wire of 5-mm diameter is to be...Ch. 2.1 - Two gage marks are placed exactly 250 mm apart on...Ch. 2.1 - An aluminum pipe must not stretch more than 0.05...Ch. 2.1 - A control rod made of yellow brass must not...Ch. 2.1 - A steel control rod is 5.5 ft long and must not...Ch. 2.1 - A cast-iron tube is used to support a compressive...Ch. 2.1 - A 4-m-long steel rod must not stretch more than 3...Ch. 2.1 - A nylon thread is to be subjected to a 10-N...
Ch. 2.1 - A block of 10-in. length and 1.8 1.6-in. cross...Ch. 2.1 - A square yellow-brass bar must not stretch more...Ch. 2.1 - Rod BD is made of steel (E = 29 106 psi) and is...Ch. 2.1 - The 4-mm-diameter cable BC is made of a steel with...Ch. 2.1 - A single axial load of magnitude P = 15 kips is...Ch. 2.1 - A 250-mm-long aluminum tube (E = 70 GPa) of 36-mm...Ch. 2.1 - The specimen shown has been cut from a...Ch. 2.1 - The brass tube AB (E = 105 GPa) has a...Ch. 2.1 - Both portions of the rod ABC are made of an...Ch. 2.1 - The rod ABC is made of an aluminum for which E =...Ch. 2.1 - For the steel truss (E = 200 GPa) and loading...Ch. 2.1 - For the steel truss (E = 29 106 psi) and loading...Ch. 2.1 - Members AB and BC are made of steel (E = 29 106...Ch. 2.1 - The steel frame (E = 200 GPa) shown has a diagonal...Ch. 2.1 - Link BD is made of brass (E = 105 GPa) and has a...Ch. 2.1 - Members ABC and DEF are joined with steel links (E...Ch. 2.1 - Each of the links AB and CD is made of aluminum (E...Ch. 2.1 - The length of the 332-in.-diameter steel wire CD...Ch. 2.1 - A homogenous cable of length L and uniform cross...Ch. 2.1 - The vertical load P is applied at the center A of...Ch. 2.1 - Denoting by the "engineering strain'' in a...Ch. 2.1 - The volume of a tensile specimen is essentially...Ch. 2.3 - An axial centric force of magnitude P = 450 kN is...Ch. 2.3 - An axial centric force of magnitude P = 450 kN is...Ch. 2.3 - The 4.5-ft concrete post is reinforced with six...Ch. 2.3 - The 4.5-ft concrete post is reinforced with six...Ch. 2.3 - An axial force of 200 kW is applied to the...Ch. 2.3 - The length of the assembly shown decreases by 0.40...Ch. 2.3 - A polystyrene rod consisting of two cylindrical...Ch. 2.3 - Three steel rods (E = 29 106 psi) support an...Ch. 2.3 - Fig. P2.41 2.41 Two cylindrical rods, one of steel...Ch. 2.3 - Solve Prob. 2.41, assuming that rod AC is made of...Ch. 2.3 - Each of the rods BD and CE is made of brass (E =...Ch. 2.3 - The rigid bar AD is supported by two steel wires...Ch. 2.3 - The rigid bar ABC is suspended from three wines of...Ch. 2.3 - The rigid bar AD is supported by two steel wires...Ch. 2.3 - The aluminum shell is fully bonded to the brass...Ch. 2.3 - The aluminum shell is fully bonded to the brass...Ch. 2.3 - The brass shell (b = 11.6 10-6/F) is fully bonded...Ch. 2.3 - The concrete post (Ec = 3.6 106) psi and c = 5.5 ...Ch. 2.3 - A rod consisting of two cylindrical portions AB...Ch. 2.3 - A rod consisting of two cylindrical portions AB...Ch. 2.3 - Fig. P2.52 2.52 A rod consisting of two...Ch. 2.3 - The steel rails of a railroad (rack (Es = 200GPa,...Ch. 2.3 - Two steel bars (Es = 200 GPa and s = 11.7 10-6/C)...Ch. 2.3 - Determine the maximum load P that can be applied...Ch. 2.3 - An aluminum rod (Ea = 70 GPa, a = 23.6 10-6/C)...Ch. 2.3 - Knowing that a 0.02-in. gap exists when the...Ch. 2.3 - Determine (a) the compressive force in the bars...Ch. 2.3 - At room temperature (20C) a 0.5-mm gap exists...Ch. 2.9 - A standard tension test is used to determine the...Ch. 2.9 - A 2-m length of an aluminum pipe of 240-nun outer...Ch. 2.9 - A line of slope 4:10 has been scribed on a...Ch. 2.9 - A 2.75-kN tensile load is applied to a test coupon...Ch. 2.9 - Fig. P2.65 2.65 In a standard tensile test a steel...Ch. 2.9 - The change in diameter of a large steel bolt is...Ch. 2.9 - The brass rod AD is fitted with a jacket that is...Ch. 2.9 - A fabric used in air-inflated structures is...Ch. 2.9 - A 1-in. square was scribed on the side of a large...Ch. 2.9 - The block shown is made of a magnesium alloy for...Ch. 2.9 - The homogeneous plate ABCD is subjected to a...Ch. 2.9 - For a member under axial loading, express the...Ch. 2.9 - In many situations it is known that the normal...Ch. 2.9 - In many situations physical constraints prevent...Ch. 2.9 - The plastic block shown is bonded to a rigid...Ch. 2.9 - The plastic block shown is bonded to a rigid...Ch. 2.9 - Two blocks of rubber with a modulus of rigidity G...Ch. 2.9 - Fig. P2.77 and P2.78 2.78 Two blocks of rubber...Ch. 2.9 - An elastomeric bearing (G = 130 psi) is used to...Ch. 2.9 - 2.80 For the elastomeric bearing In Prob. 2.79...Ch. 2.9 - A vibration isolation unit consists of two blocks...Ch. 2.9 - Prob. 82PCh. 2.9 - Prob. 83PCh. 2.9 - Prob. 84PCh. 2.9 - Prob. 85PCh. 2.9 - A 2.75-kN tensile load is applied to a test coupon...Ch. 2.9 - A vibration isolation support consists of a rod A...Ch. 2.9 - Prob. 88PCh. 2.9 - Prob. 89PCh. 2.9 - Show that for any given material, the ratio G/E of...Ch. 2.9 - Prob. 91PCh. 2.9 - Prob. 92PCh. 2.13 - Knowing that, for the plate shown, the allowable...Ch. 2.13 - Knowing that P = 38 kN, determine the maximum...Ch. 2.13 - A hole is to be drilled in the plate at A. The...Ch. 2.13 - Fig. P2.95 and P2.96 2.96 (a) For P = 13 kips and...Ch. 2.13 - 2.97 Knowing that the hole has a diameter of 9 mm,...Ch. 2.13 - For P = 100 kN, determine the minimum plate...Ch. 2.13 - Prob. 99PCh. 2.13 - A centric axial force is applied to the steel bar...Ch. 2.13 - The cylindrical rod AB has a length L = 5 ft and a...Ch. 2.13 - Fig. P2.101 and P.102 2.102 The cylindrical rod AB...Ch. 2.13 - Rod AB is made of a mild steel that is assumed to...Ch. 2.13 - Prob. 104PCh. 2.13 - Rod ABC consists of two cylindrical portions and...Ch. 2.13 - Prob. 106PCh. 2.13 - Prob. 107PCh. 2.13 - Prob. 108PCh. 2.13 - Each cable has a cross-sectional area of 100 mm2...Ch. 2.13 - Prob. 110PCh. 2.13 - Two tempered-steel bars, each 316 in. thick, are...Ch. 2.13 - Prob. 112PCh. 2.13 - Prob. 113PCh. 2.13 - Prob. 114PCh. 2.13 - Prob. 115PCh. 2.13 - Prob. 116PCh. 2.13 - Prob. 117PCh. 2.13 - Prob. 118PCh. 2.13 - Prob. 119PCh. 2.13 - For the composite bar in Prob. 2.111, determine...Ch. 2.13 - Prob. 121PCh. 2.13 - Bar AB has a cross-sectional area of 1200 mm2 and...Ch. 2.13 - Bar AB has a cross-sectional area of 1200 mm2 and...Ch. 2 - The uniform wire ABC, of unstretched length 2l, is...Ch. 2 - The aluminum rod ABC (E = 10.1 106 psi), which...Ch. 2 - Two solid cylindrical rods are joined at B and...Ch. 2 - Prob. 127RPCh. 2 - Prob. 128RPCh. 2 - Prob. 129RPCh. 2 - A 4-ft concrete post is reinforced with four steel...Ch. 2 - The steel rods BE and CD each have a 16-mm...Ch. 2 - Prob. 132RPCh. 2 - Prob. 133RPCh. 2 - The aluminum test specimen shown is subjected to...Ch. 2 - Prob. 135RP
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
- Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful! Please do not copy other's work,i will be very very grateful!!Please do not copy other's work,i will be very very grateful!!arrow_forward= The frame shown is fitted with three 50 cm diameter frictionless pulleys. A force of F = 630 N is applied to the rope at an angle ◊ 43°. Member ABCD is attached to the wall by a fixed support at A. Find the forces indicated below. Note: The rope is tangent to the pully (D) and not secured at the 3 o'clock position. a b •C *су G E e d BY NC SA 2013 Michael Swanbom Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 81 cm b 50 cm с 59 cm d 155 cm For all answers, take x as positive to the right and positive upward. At point A, the fixed support exerts a force of: A = + ĴN and a reaction couple of: →> ΜΑ Member CG is in Select an answer magnitude У as k N-m. and carries a force of N.arrow_forwardThe lower jaw AB [Purple 1] and the upper jaw-handle AD [Yellow 2] exert vertical clamping forces on the object at R. The hand squeezes the upper jaw-handle AD [2] and the lower handle BC [Orane 4] with forces F. (Member CD [Red 3] acts as if it is pinned at D, but, in a real vise-grips, its position is actually adjustable.) The clamping force, R, depends on the geometry and on the squeezing force F applied to the handles. Determine the proportionality between the clamping force, R, and the squeezing force F for the dimensions given. d3 d4 R 1 B d1 2 d2 D... d5 F 4 F Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value d1 65 mm d2 156 mm d3 50 mm 45 d4 d5 113 mm 30 mm R = Farrow_forward
- A triangular distributed load of max intensity w =460 N/m acts on beam AB. The beam is supported by a pin at A and member CD, which is connected by pins at C and D respectively. Determine the reaction forces at A and C. Enter your answers in Cartesian components. Assume the masses of both beam AB and member CD are negligible. cc 040 BY NC SA 2016 Eric Davishahl W A C D -a- B Ул -b- x Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value α 5.4 m b 8.64 m C 3.24 m The reaction at A is A = i+ ĴN. λ = i+ Ĵ N. The reaction at C is C =arrow_forward56 Clamps like the one shown are commonly used in woodworking applications. This clamp has the dimensions given in the table below the figure, and its jaws are mm thick (in the direction perpendicular to the plane of the picture). a.) The screws of the clamp are adjusted so that there is a uniform pressure of P = 150 kPa being applied to the workpieces by the jaws. Determine the force carried in each screw. Hint: the uniform pressure can be modeled in 2-D as a uniform distributed load with intensity w = Pt (units of N/m) acting over the length of contact between the jaw and the workpiece. b.) Determine the minimum vertical force (parallel to the jaws) required to pull either one of the workpieces out of the clamp jaws. Use a coefficient of static friction between all contacting surfaces of μs = 0.56 and the same clamping pressure given for part (a). 2013 Michael Swanbom A B C a Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.…arrow_forwardDetermine the force in each member of the space truss given F=5 kN. Use positive to indicate tension and negative to indicate compression. F E Z -2 m. B 3 m C 5 m 3 m A -4 m. AB = KN FAC = FAD = KN KN KN FBC = KN FBD FBE = = KN Farrow_forward
- A short brass cyclinder (denisty=8530 kg/m^3, cp=0.389 kJ/kgK, k=110 W/mK, and alpha=3.39*10^-5 m^2/s) of diameter 4 cm and height 20 cm is initially at uniform temperature of 150 degrees C. The cylinder is now placed in atmospheric air at 20 degrees C, where heat transfer takes place by convection with a heat transfer coefficent of 40 W/m^2K. Calculate (a) the center temp of the cylinder, (b) the center temp of the top surface of the cylinder, and (c) the total heat transfer from the cylinder 15 min after the start of the cooling. Solve this problem using the analytical one term approximation method. (Answer: (a) 45.7C, (b)45.3C, (c)87.2 kJ)arrow_forwardA short brass cyclinder (denisty=8530 kg/m^3, cp=0.389 kJ/kgK, k=110 W/mK, and alpha=3.39*10^-5 m^2/s) of diameter 4 cm and height 20 cm is initially at uniform temperature of 150 degrees C. The cylinder is now placed in atmospheric air at 20 degrees C, where heat transfer takes place by convection with a heat transfer coefficent of 40 W/m^2K. Calculate (a) the center temp of the cylinder, (b) the center temp of the top surface of the cylinder, and (c) the total heat transfer from the cylinder 15 min after the start of the cooling. Solve this problem using the analytical one term approximation method.arrow_forwardA 6 cm high rectangular ice block (k=2.22 W/mK, and alpha=0.124*10^-7 m^2/s) initially at -18 degrees C is placed on a table on its square base 4 cm by 4cm in size in a room at 18 degrees C. The heat transfer coefficent on the exposed surfaces of the ice block is 12 W/m^2K. Disregarding any heat transfer from the base to the table, determine how long it will be before the ice block starts melting. Where on the ice block will the first liquid droplets appear? Solve this problem using the analytical one-term approximation method.arrow_forward
- Consider a piece of steel undergoing a decarburization process at 925 degrees C. the mass diffusivity of carbon in steel at 925 degrees C is 1*10^-7 cm^2/s. Determine the depth below the surface of the steel at which the concentration of carbon is reduced to 40 percent from its initial value as a result of the decarburization process for (a) an hour and (b) 10 hours. Assume the concnetration of carbon at the surface is zero throughout the decarburization process.arrow_forwardPlease do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful! Please do not copy other's work,i will be very very grateful!!arrow_forwardMultiple Choice Circle the best answer to each statement. 1. Which geometry attribute deviation(s) can be limited with a profile of a surface tolerance? A. Location B. Orientation C. Form D. All of the above 2. A true profile may be defined with: A. Basic radii B. Basic angles C. Formulas D. All of the above 3. Which modifier may be applied to the profile tolerance value? A B C. D. All of the above 4. The default tolerance zone for a profile tolerance is: A. Non-uniform B. Unilateral C. Bilateral equal distribution D. Bilateral-unequal distribution 5. An advantage of using a profile tolerance in place of a coordinate tolerance is: A. A bonus tolerance is permitted. B. A datum feature sequence may be specified C. A profile tolerance always controls size D. All of the above 6. The shape of the tolerance zone for a profile tolerance is: A. Two parallel planes B. The same as the true profile of the toleranced surface C. Equal bilateral D. Cylindrical when the diameter symbol is speci- fied…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY

Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press

Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON

Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education

Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY

Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning

Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Lec21, Part 5, Strain transformation; Author: Mechanics of Materials (Libre);https://www.youtube.com/watch?v=sgJvz5j_ubM;License: Standard Youtube License