Concept explainers
Bar AB has a cross-sectional area of 1200 mm2 and is made of a steel that is assumed to be elastoplastic with E = 200 GPa and σY = 250 MPa. Knowing that the force F increases from 0 to 520 kN and then decreases to zero, determine (a) the permanent deflection of point C, (b) the residual stress in the bar.
Fig. P2.122
*2.123 Solve Prob. 2.122, assuming that a = 180 mm.
(a)
The permanent deflection of point C.
Answer to Problem 123P
The permanent deflection of point C is
Explanation of Solution
Given information:
The distance between member AC (a) is
The cross sectional area A of section AB is
The modulus of elasticity E is
The yield stress
The force F is
Calculation:
Determine the force to yield portion AC using the relation:
Substitute
Sketch the bar ACB as shown in Figure 1.
Find the load
Substitute
Find the length
Refer to Figure 1.
Find the deflection at point C using the relation:
Here,
Substitute
Find the stress in rod along CB using the relation:
Substitute
Calculate the load
Here,
Substitute
Find the force
Substitute
Determine the deflection at point C
Substitute
Calculate the stress at along AC using the relation:
Substitute
Calculate the stress along BC using the relation:
Substitute
Determine the permanent deflection at point C using the relation:
Substitute
Thus, the permanent deflection of point C is
(b)
Find the residual stress in bar AC and CB.
The residual stress in bar AC is
The residual stress in bar CB is
Explanation of Solution
Calculation:
Find the residual stress in bar AC using the relation:
Substitute
Thus, the residual stress in bar AC is
Find the residual stress in bar BC using the relation:
Substitute
Thus, the residual stress in bar CB is
Want to see more full solutions like this?
Chapter 2 Solutions
Mechanics of Materials, 7th Edition
- = P2.39 Two cylindrical rods, AC made of aluminum and CD made of steel, are joined at C and restrained by rigid supports at A and D. For the loading shown and knowing that Ea 10.4 × 106 psi and Es = 29 × 106 psi, determine (a) the reactions at A and D, (b) the deflection of point C. -8 in.- E A 1-¹-in. diameter Fig. P2.39 10 in.-10 in.. B. 18 kips C D 14 kips 15-in. diameterarrow_forward2.75 The plastic block shown is bonded to a rigid support and to a vertical plate to which a 55-kip load P is applied. Knowing that for the plastic used G = 150 ksi, determine the deflection of the plate.2.76 What load P should be applied to the plate of Prob. 2.75 to produce a 116-in. deflection? Solve 2.76arrow_forwardTwo cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. The steel rod has a length of 300 mm while the brass rod has a length of 200 mm. The diameters of the rods are shown in the figure below. A force of 60 kN is applied at point B of the steel segment. For the loading shown and knowing that modulus of elasticity values for steel and brass are respectively Es = 200 GPa and Eb = 105 GPa, determine a.) The reactions at A and E: RA and RE. b.) The deflection of point C from its original location. how to doarrow_forward
- Problem 2.35 The 5-ft concrete post is reinforced with six steel bars, each with a 7/8-in. diameter. Knowing that E, = 29 x 106 psi and E.= 3.6 x 106 psi, determine the normal stresses in the steel and in the %3D concrete when a 200-kip axial centric force is applied to the post. 5 ft 10 in. 10 in. Flg. P2.35arrow_forward2.13 A steel plate, which is 1.5 m by 1.5 m and 30 mm thick, is lifted by four cables attached to its corners that meet at a point that is 2 m above the plate. Determine the required cross-sectional area of the cables if the stress in them is not to exceed 20 MPa. Steel plate Prob. 2.13 Cablesarrow_forward2.60 At room temperature (20°C) a 0.5-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 140°C, determine (a) the normal stress in the aluminum rod, (b) the change in length of the aluminum rod. 0.5 mm 300 mm 250 mm B Aluminum Stainless steel A = 2000 mm² E = 75 GPa a = 23 × 16-6/°C Fig. P2.60 A = 800 mm² E = 190 GPa a = 17.3 × 10-6/°Carrow_forward
- 2. The length of the 2-mm-diameter steel wire CD has been adjusted so that, with no load applied, a gap of 1.5 mm exists between the end Bof the rigid beam ACB and a contact point E. load should be applied to the beam to cause contact between B and E. Using E = 200 GPa, determine where a 225-N 250 mm 225 N 1.5 mm B C A 360 mm 90 mmarrow_forwardQ1. (A). A 25mm square cross-section bar of length 300mm carries an axial compressive load of 50kN. Determine the stress set up in the bar and its change of length when the load is applied. For the bar material E= 200 GN/m². Q2. A beam AB, 1.2 m long, is simply-supported at its ends A and B and carries two concentrated loads, one of 10 kN at C, the other 15 kN at D. Point C is 0.4 m from A, point D is 1 m from A. Draw the S.F. and B.M. diagrams for the beam. Q3. A solid steel shaft (A) of 50 mm diameter rotates at 250 rev/min. Find the greatest power that can be transmitted for a limiting shearing stress of 60 MN/m2 in the steel.arrow_forwardChapter 4 : Stresses & Strains in Statically Indeterminate Structures I 53 EXERCISE 4.1 1. An alloy bar 800 mm long and 200 mm in cross-section is held between two rigid plates and is subjected to an axial load of 200 kN as shown in Fig. 4.7. | A В C 200 kN 300 500 Fig. 4.7 Find the reactions at the two ends A and C as well as extension of the portion AB. [Ans. 125 kN ; 75 kN ; 0.094 mm] 2. A bar ABC fixed at both ends A and Cis loaded by an axial load (P) at C. If the distances AB and BC are equal to a and b respectively then find the reactions at the ends A and C. 3. An axial force of 20 kN is applied to a steel bar ABC which is fixed at both ends A and C as shown in Fig. 4.8. 2 A = 200 mm A = 100 mm 20 kN+ A В 2 m 1 m Fig. 4.8 Determine the reactions at both the supports and stresses developed in two parts of the bar. Take E = 200 GPa. [Ans. R = R = 10 kN; oAR = 50 MPa (C); oBC = 100 MPa (7)] %3D %3! %3D 4. A prismatic bar ABCD has built-in ends A and D. It is subjected to two point…arrow_forward
- A pin-connected structure is supported and loaded as shown. Member ABCD is rigid and is horizontal before the load P is applied. Bars (1) and (2) are both made from steel [E = 30,000 ksi] and both have a cross-sectional area of 1.25 in.?. If the normal stress in bar (1) must be limited to 23 ksi, determine the maximum load P that may be applied to the rigid bar. 120 in. 80 in. (2) (1) B C 54 in. 54 in. 24 in. O 40.7 kips O 60.3 kips 32.2 kips 43.1 kipsarrow_forwardA pin-connected structure is supported and loaded as shown. Member ABCD is rigid and is horizontal before the load P is applied. Bars (1) and (2) are both made from steel [E = 30,000 ksi] and both have a cross-sectional area of 1.25 in.?. If the normal stress in bar (1) must be limited to 31 ksi, determine the maximum load P that may be applied to the rigid bar. 120 in. 80 in. (2) (1) B D 54 in. 54 in. 24 in. Parrow_forwardProb.3: [2.26] The length of 2 mm diameter steel wire CD has been adjusted so that with no load is applied, a gap of 1.5 mm exists between the end B of the rigid beam ACB and a contact point E. Knowing that E = 200 GPa, determine where a 20 kg block should be placed on the beam in order to cause contact between B and E. 0.25 m CO 20 kg В A E 1.5 mm -0.32 m 0.08 marrow_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