Concept explainers
Determine the maximum load P that can be applied to the brass bar of Prob. 2.55 if the allowable stress in the steel bars is 30 MPa and the allowable stress in the brass bar is 25 MPa.
2.55 Two steel bars (Es = 200 GPa and αs = 11.7 × 10-6/°C) are used to reinforce a brass bar (Eb = 105 GPa, αb = 20.9 × 10-6/°C) that is subjected to a load P = 25 kN. When the steel bars were fabricated, the distance between the centers of the holes that were to fit on the pins was made 0.5 mm smaller than the 2 m needed. The steel bars were then placed in an oven to increase their length so that they would just fit on the pins. Following fabrication, the temperature in the steel bars dropped back to room temperature. Determine (a) the increase in temperature that was required to fit the steel bars on the pins, (b) the stress in the brass bar after the load is applied to it.
Fig. P2.55
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Mechanics of Materials, 7th Edition
- 1. A 60-mm diameter steel tube with a wall thickness of 3 mm just fits in a rigid hole. Determine the tangential stress developed if an axial compressive load of 12 kN is applied. Use v = 0.30 and E = 200 GPa. Answer: 0 = 6.37 MPa 2. A 200-mm long bronze tube closed at both ends fits without clearance in a 70-mm hole in a rigid block. It has a diameter of 70 mm and a wall thickness of 5 mm. The tube then sustained an internal pressure of 4.5 MPa. Use v = 0.33 and E= 83 GPa. Compute the tangential stress in the tube. Answer: Ot = 5.20 MPaarrow_forwardThe rigid beam BC is supported by rods (1) and (2). The cross-sectional area of rod (1) is 9 mm². The cross-sectional area of rod (2) is 14 mm². For a uniformly distributed load of w 4.0 kN/m, determine the length a so that the normal stress is the same in each rod. Assume L = 4.50 m. (1) Answer: a = L W a (2) marrow_forwardA 13-mm-diameter steel (E = 193 GPa) rod (2) is connected to a 27-mm-wide by 10-mm-thick rectangular aluminum (E = 72 GPa) bar (1), as shown. Assume L1 = 0.74 m and L2 = 1.38 m. Determine the force P (in kN rounded to the nearest tenths) required to stretch the assembly 8.1 mm.arrow_forward
- The rigid beam BC is supported by rods (1) and (2). The cross-sectional area of rod (1) is 11 mm². The cross-sectional area of rod (2) is 14 mm2. For a uniformly distributed load of w = 4.1 kN/m, determine the length a so that the normal stress is the same in each rod. Assume L = 5.35 m. A (1) (2) a L. Answer: a = i marrow_forwardRigid bar ABC supports a weight of W = 26 kN. Bar ABC is pinned at A and supported at B by rod (1), which has a circular cross section. If the normal stress in rod (1) must be limited to 110 MPa, determine the minimum diameter required for the rod. (1) B C 700 mm 350 mmarrow_forwardAxial loads are applied with rigid bearing plates to the solid cylindrical rods shown. The normal stress in aluminum rod (1) must be limited to 19 ksi, the normal stress in brass rod (2) must be limited to 24 ksi, and the normal stress in steel rod (3) must be limited to 12 ksi. Determine the minimum diameter required for each of the three rods. Assume P = 9 kips, Q = 4 kips, R = 18 kips and S = 21 kips. Calculate the internal force (positive if tensile, negative if compresive) in rod (1). Use a FBD cutting through the rod in the section that includes the free end A.Answer: F1 = ? kips.arrow_forward
- Axial loads are applied with rigid bearing plates to the solid cylindrical rods shown. The normal stress in aluminum rod (1) must be limited to 19 ksi, the normal stress in brass rod (2) must be limited to 24 ksi, and the normal stress in steel rod (3) must be limited to 12 ksi. Determine the minimum diameter required for each of the three rods. Assume P = 9 kips, Q = 4 kips, R = 18 kips and S = 21 kips.Calculate the internal force (positive if tensile, negative if compresive) in rod (1). Use a FBD cutting through the rod in the section that includes the free end A.arrow_forward4. A steel rod of 3 cm diameter is enclosed centrally in a hollow copper tube of external diameter 5 cm and internal diameter of 4 cm. The composite bar is then subjected to an axial pull of 45 000 N. If the length of each bar is equal to 150 mm. Determine (i) The stress in the rod and tube (ii) Load carried by each bararrow_forwardThe rigid beam BC is supported by rods (1) and (2). The cross-sectional area of rod (1) is 10 mm2. The cross-sectional area of rod (2) is 18 mm2. For a uniformly distributed load of w = 2.4 kN/m, determine the length a so that the normal stress is the same in each rod. Assume L = 5.25 m.arrow_forward
- P- 45° 45° Fig. 2-38arrow_forwardA 13-mm-diameter steel (E = 193 GPa) rod (2) is connected to a 27-mm-wide by 10-mm-thick rectangular aluminum (E = 72 GPa) bar (1), as shown. Assume L1 = 0.74 m and L2 = 1.38 m. Determine the force P (in kN rounded to the nearest tenths) required to stretch the assembly 8.1 mm. (1) L₁ B L2 C P ...arrow_forwardTwo solid cylindrical rods support a load of P = 25 kN as shown. Rod (1) has a diameter of 16 mm, and the diameter of rod (2) is 12 mm. Determine the axial stress in rod (1). 5.6 m 3.8 m (1) 91.1 MPa O 121.0 MPa 62.4 MPa 101.1 MPa O 75.5 MPa B 4.6 m 2 3.3 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