Concept explainers
Rod AB is made of a steel for which the yield strength is σY = 450 MPa and E = 200 GPa; rod BC is made of an aluminum alloy for which σY = 280 MPa and E = 73 GPa. Determine the maximum strain energy that can be acquired by the composite rod ABC without causing any permanent deformations.
Fig. P11.123
Find the maximum strain energy that can be acquired by the composite rod ABC.
Answer to Problem 123RP
The maximum strain energy of the composite rod ABC is
Explanation of Solution
Given information:
The diameter of the composite rod AB is
The diameter of the composite rod BC is
The length of the rod AB is
The length of the rod BC is
The yield strength of the steel rod AB is
The modulus of elasticity of the steel rod is
The yield strength of the aluminum alloy BC is
The modulus of elasticity of the aluminum alloy is
Calculation:
Calculate the area of the rod (A) as shown below.
For the steel rod AB.
Substitute
For the aluminum alloy BC.
Substitute
Calculate the applied load
For the steel rod AB.
Substitute
For the aluminum alloy BC.
Substitute
Take the smaller value as the applied load,
Calculate the strain energy (U) as shown below.
Substitute
Therefore, the maximum strain energy of the composite rod ABC is
Want to see more full solutions like this?
Chapter 11 Solutions
Mechanics of Materials, 7th Edition
- Prob.8: [2.63] A standard tension test is used to determine the properties of an experimental plastic. The test specimen is a 16 mm diameter rod and it is subjected to a 3.2 kN tensile force. Knowing that an elongation of 11 mm and a decrease of diameter of 0.625 mm are observed in a 125 mm gage length, determine the modulus of elasticity, the modulus of rigidity, and Possion's ratio of the material. P 16 -mm diameter 125 mm P'arrow_forwardProve that the sum of the normal strains in perpendicular directions is constant, i.e., Px + Py = Px′ + Py′arrow_forward3) An eccentric force P is applied as shown in Fig. 2 to a steel bar of 25 x 90-mm cross section. The strains at A and B have been measured and found to be ƐA = + 400µ and be ЄB = - - 90μ. Knowing that E = 210 GPa, determine (a) the magnitude of force P, (b) the distance d, and (c) neatly draw the stress distribution diagrams of the system. 30 mm 25 mm- 90 mm A B Fig. 2 1 45 mm 15 mmarrow_forward
- A spherical gas container having an inner diameter of 5 m and a wall thickness of 24 mm is made of steel for which E = 200 GPa and v = 0.29. Knowing that the gage pressure in the container is increased from zero to 1.8 MPa, determine (a) the maximum normal stress in the container, (b) the corresponding increase in the diameter of the container. Hint: refer back to earlier notes for relationship between strain, Poisson's ratio, and stress in two directions Sm The unpressurized cylindrical storage tank shown has a 5-mm wall thickness and is made of steel having a 400-MPa ultimate strength in tension. Determine the maximum height h to which it can be filled with water if a factor of safety of 4.0 is desired. (Density of water = 1000 kg/m³.) 14.5 m Hint: recall pressure (p) due to a column of water is p = yharrow_forwardA uniform steel rod of cross-sectional area A is attached to rigid supports and is unstressed at a temperature of 8°C. The steel is assumed to be elastoplastic with yield stress=250 MPa and E =200 GPa. Knowing that α = 11.7×10^–6/°C, determine the stress in the bar when the temperature is raised to 165°C. (b)and after the temperature has returned to 8°C.arrow_forwardA steel rod is subjected to a gradually applied load (F) which gave a rise to a maximum stress of 200 MPa. The rod is 250 mm long and one part of its length is square and the remainder is circular with a diameter of 25 mm. If the total strain energy in the rod and modulus elasticity of the material is 1.3 J and 200 GPa, determine the following: LI The applied load F 2 The total extension of the bar 3 The length of the square portion of the bar 4 The suddenly applied load that will induce the same amount of energy 5 The load that falls from a height of 8 mm induces 1,3 J in the bar.arrow_forward
- A steel rod is subjected to a gradually applied load (F) which gave a rise to a maximum stress of 200 MPa. The rod is 250 mm long and one part of it's length is square and the remainder is circular with a diameter of 25 mm. If the total strain energy in the rod and modulus elasticity of the material is 1,3 J and 200 GPa, determine the following : 4.1.The applied load F and the total extension of the bar 4.2.The length of the square portion of the bar and the suddenly applied load that will induce the same amount of energy. 4.3.The load that falls from a height of 8 mm induces 1,3 J in the bararrow_forwardA solid 20-mm-diameter shaft is subjected to an axial load P. The shaft is made of aluminum [E = 70 GPa; v=0.33]. A strain gage is mounted on the shaft at the orientation shown in Fig. P13.77. (a) If P= 18.5 kN, determine the strain reading that would be expected from the gage. (b) If the gage indicates a strain value of ε = 950 ue, determine the axial force P applied to the shaft.arrow_forwardIn a standard tensile test, a steel rod of 25 mm diameter and 200 mm long exhibits a strain of 1.0186x 10³ upon application of an axial load of 220 kN. Knowing that v = 0.4 and E = 200 GPa, determine the change in diameter of the rod. Answer in millimeters.arrow_forward
- 2. A steel wire 30 ft long, hanging vertically, supports a load of 500 lbf. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 20,000 psi and the total elongation is not to exceed 0. in. Assume E = 29 × 106 psi.arrow_forwardTwo tempered-steel bars, each 316316 in. thick, are bonded to a 1212 -in. mild-steel bar. This composite bar is subjected as shown to a centric axial load of magnitude P. Both steels are elastoplastic with E = 29 × 106 psi and with yield strengths equal to 100 ksi and 50 ksi, respectively, for the tempered and mild steel. Determine the residual stresses in the tempered-steel bars if the load P is gradually increased from zero to 103 kips and then decreased back to zero. The residual stress in the tempered steel bars isarrow_forwardA composite rod of overall length of 200 mm comprised of a steel rod and brass rod attached rigidly to the end. The diameter and the length of the steel rod is 10 mm and 120 mm, respectively, the diameter and the length of the brass rod as 20 mm and 80 mm respectively. The rod is used as a tie in a link mechanism and the strain in the brass rod is limited to 0.0053. Given that the total extension of the composite rod must not exceed 0,1624 mm and E for steel is 200 GPa, respectively. Calculate : A) Strain in the steel rod B) Load carried by the steel and the brass rods C) Modulus of elasticity for the brass. Can you please resend that question as it appears to be blank??arrow_forward
- 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