Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Question
Chapter 2.9, Problem 82P
To determine
Find the effective spring constant of the system.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Problem (2)
A vibration isolation unit consists of two blocks of
hard rubber bonded to a plate AB as shown. A force of
magnitude P = 24 kN causes a deflection ô = 1.5 mm
of the plate AB.
(a)
150 mm
J00 mm
Determine the modulus of rigidity (G)
of the rubber used.
If a rubber having G= 19 MPa is used
(b)
and denoting P the magnitude of the force
applied to AB and by ô the corresponding
deflection, determine the equivalent spring
constant k = P/d of the system.
30 mm
30 mm
Aluminum
L= 3 m
A = 500 mm²
E = 70 GPa
A
3.5 m
P
B
Steel
L = 4 m
A = 300 mm²
E = 200 GPa
2.5 m
с
# 3A. The rigid bar AB, attached to two vertical rods as shown, is horizontal before the load P is applied.
Determine the vertical movement of P if its magnitude is 50 kN.
#3B. A steel rod is stretched between two rigid walls and carries a tensile load of 5000 N at 20°C. If the
allowable stress is not to exceed 130 MPa at -20°C, what is the minimum diameter of the rod? Assume
a=11.7μm/(m-°C) and E=200 GPa.
Stiffness is the property that enables material to withstand high stress without great strain. it is a resistance to any sort of deformation and is a function of the modulus of elasticity, E of the material
True or false
Chapter 2 Solutions
Mechanics of Materials, 7th Edition
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
- A vibration isolation unit consists of two blocks of hard rubber with a modulus of rigidity G= 19 MPa bonded to a plate AB and to rigid supports as shown. Denoting by P the magnitude of the force applied to the plate and by δ the corresponding deflection, determine the effective spring constant, k 5 P/δ, of the system.arrow_forwardA vibration isolation unit consists of two blocks of hard rubber bonded to a plate AB and to rigid supports as shown. Knowing that a force of magnitude P= 25 kN causes a deflection δ= 1.5 mm of plate AB, determine the modulus of rigidity of the rubber used.arrow_forwardDetermine the horizontal displacement of joint C. The length, L, of trusses AC, BC is 1,300 mm. The applied force at joint C, is 5.0 kN. The cross-sectional area of both trusses, A, is 360 mm2. The elastic modulus of truss AC, E1, is 135 GPa. The elastic modulus of truss BC, E2, is 150 GPa.arrow_forward
- A 1.05-m-long rod of negligible weight is supported at its ends by wires A and B of equal length. The cross-sectional area of A is 1.80 mm^2 and that of B is 4.20 mm^2 . Young's modulus for wire A is 2.30×1011 Pa ; that for B is 1.20×1011 Pa . At what point along the rod should a weight w be suspended to produce equal stresses in A and B? (d=? m from wire A) At what point along the rod should a weight w be suspended to produce equal strains in A and B? (d=? m from wire A)arrow_forward1. The steel stepped rod carries the axial loads shown in Fig. Knowing that Aj=20 cm², A2=10 cm², E=200 GPa, [G]=160Mpa. Odraw the diagram of the axial force of the rod. check the strength of the rod. Odetermine the change in the length of the rod. - A1=20cm? A=10 cm 160KN 40KN 200KN B 400mm 400mmarrow_forwardFor the shown static system, determine the minimum diameter of cable BD to withstand the shown load, given that the maximum allowable stress for the cable is 90 MPа. 40° 32 kN D B 30° 1. [10] 1.2 m C 1.6 m 0.8 marrow_forward
- 100KN A force of 100 KN is applied on a column as shown. The column is made from two materials. [The top one is a functionally graded material with a linearly varying modulus and densities. Its length is 2 meter. The density and elastic modulus of the top material at point A are 2700 А kg m3 and 72 Gpa, respectively. The density and modulus of kg the top material at point B are 3000 and 100 Gpa. The m 3 В kg bottom material is made from steel (density =7800 and m2 modulus=200GPA). The length of the bottom material is 1m. The cross-sections of both materials comprising the column are cylindrical with a diameter of 0.5 m. C ID (oijj + bị = 0) and considering the weight and the applied force determine: Using equilibrium while The stress distribution in both membersarrow_forward2.59. Derive the following relations involving the elastic constants: 2 K = λ +23³ G G = E = V = X(1 — 2v) 2v 2G(1 + v) 3(1 – 2v) G(3λ + 2G) A + G X 2(X+G) 3K(1 – 2v) 2(1 + v) = E 2G E 3(1 – 2v) -1= 3KE 9K- - E 2G(1 + v) = 3K(1 – 2v) 3K-2G 2(3K+G) = 9KG 3K+ G 3K- E 6Karrow_forwardA vibration isolation unit consists of two blocks of hard rubber bonded to plate AB and to rigid supports as shown. For the type and grade of rubber used, τall= 220 psi and G= 1800 psi. Knowing that a centric vertical force of magnitude P=3.2 kips must cause a 0.1-in. vertical deflection of the plate AB, determine the smallest allowable dimensions a and b of the blockarrow_forward
- A rectangular steel block is 4 inches long in the x direction, 2 inches long in the y direction, and 3 inches long in the z direction. The block is subjected to a triaxial loading of three resultant forces as follows: 72 kips compression in the x direction, 60 kips tension in the y direction, and 56 kips tension in the z direction. If ν = 1/3 and E = 29 x 106 psi, ( a ) determine the single resultant load in the z direction that would produce the same deformation in x direction as the original loadings. ( b ) determine the single resultant load in the y direction that would produce the same deformation in x direction as the original loadings.arrow_forwardA rigid bar AN is hinged at A and is supported by a rod CD at C. The rod is pin connected at D. Assume E = 200GPa. Determine a. Displacement of the loaded end B of the bar. b. Tensile stress induced in rod CD by the 80kN load c. The value of W that can be safely applied if the allowable stress in the rod is 124MPa. 1.8 m 2 m 36 mmg. 1.2 m B 80kN¹arrow_forwardThe rigid bar AC is supported by two axial bars (1) and (2). Both axial bars are made of bronze [E = 100 GPa; a = 18 × 10-6 mm/mm/ °C). The cross-sectional area of bar (1) is A1 = 184 mm2 and the cross-sectional area of bar (2) is A2 = 380 mm2. After load P has been applied and the temperature of the entire assembly has increased by 38°C, the total strain in bar (2) is measured as 1240 µɛ (elongation). Assume L1 = 1290 mm, a = 590 mm, b = 820 mm, and L2 = 2000 mm. Determine: (a) the magnitude of load P. (b) the vertical displacement of pin A. L2 (1) L1 B a P Answers: (a) The magnitude of P = i kN. (b) The vertical displacement of pin A = i mm (down).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
An Introduction to Stress and Strain; Author: The Efficient Engineer;https://www.youtube.com/watch?v=aQf6Q8t1FQE;License: Standard YouTube License, CC-BY