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Two tempered-steel bars, each
Fig. P2.111
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Mechanics of Materials, 7th Edition
- 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 22 ksi, and the normal stress in steel rod (3) must be limited to 14 ksi. Determine the minimum diameter required for each of the three rods. Assume P = 9 kips, Q = 5 kips, R = 20 kips and S = 30 kips. (1) VQ B (2) (3) D First: 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 = i kips.arrow_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 22 ksi, and the normal stress in steel rod (3) must be limited to 13 ksi. Determine the minimum diameter required for each of the three rods. Assume P = 7 kips, Q = 2 kips, R = 16 kips and S = 20 kips.arrow_forwardSolve correct pleasearrow_forward
- 1. A steel rod with a cross sectional area of 150 sq.mm is stretched between two fixed points. The tensile load at 20 deg C is 5000 N. At what temperature will the stress be zero. Assume a=11.7μm/m - degC and E=200GPaarrow_forwardPlease fastarrow_forwardA bronzebar 3 m long with a cross sectional area of 320 mm 2 is placed between two rigid walls. At atemperature of 20 C, the gap is 25 mm. Find the temperature at which the compressive stress in the barwill be 35 MPa. Use α = 18.0 × 10 6 C and E = 80 GPaarrow_forward
- Two vertical wires are suspended at 450 mm apart. Their lower ends support a rigid horizontal bar that carries a load F. The left-hand wire is made of copper and has a diameter of 3 mm. The right-hand wire is made of steel and has a diameter of 2 mm. Calculate: (a) The position of F if the elongation in both wires is the same. (b) The load carried by each wire and the total elongation if F = 350 N and both wires are initially 3,5 m long. (Esteel = 200 GPa and Ecopper = 100 GPa).arrow_forwardRigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod (1) has an elastic modulus of E₁ = 15,000 ksi and a diameter of d₁ = 0.45 in. Aluminum rod (2) has an elastic modulus of E₂ = 10,000 ksi and a diameter of d₂ = 0.70in. Aluminum rod (3) has a diameter of d3= 0.95in. The yield strength of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a = 2.5 ft, b = 1.5 ft, L₁= 6 ft, L₂= 8 ft, and L3= 3 ft. (a) Determine the magnitude of load P that can safely be applied to the structure if a minimum factor of safety of 2.0 is required. (b) Determine the deflection of point D for the load determined in part (a). (c) The pin used at B has an ultimate shear strength of 55 ksi. If a factor of safety of 2.5 is required for this double shear pin connection, determine the minimum pin diameter that can be used at B. 5 L₁ A₁ = A₂ = A A3 = i Bronze (1) i a B Aluminum (3)…arrow_forwardRigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod (1) has an elastic modulus of E1 = 15,000 ksi and a diameter of d1 = 0.40 in. Aluminum rod (2) has an elastic modulus of E2 = 10,000 ksi and a diameter of d2 = 0.70in. Aluminum rod (3) has a diameter of d3 = 1.00in. The yield strength of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a = 2.5 ft, b = 1.5 ft, L1 = 6 ft, L2 = 8 ft, and L3 = 3 ft.arrow_forward
- The blue bar is made from steel with the following mechanical properties: Young's Modulus, E = 17x10° psi; Poisson's Ratio v = 0.31. The bar has a circular cross-section with diameter d= 0.50 in. being the length of each side. 557 lb 557 Ib 60 in. - Determine the following under the action of the axial load (assume elastic behavior): a. The bar's axial deformation, ô, in in.: b. The average axial or longitudinal strain, ELong: c. The change in the bar's diameter, in in.:arrow_forwardRigid bar ABC is supported by bronze rod (1) and aluminum rod (2), as shown. A concentrated load P is applied to the free end of aluminum rod (3). Bronze rod (1) has an elastic modulus of E1 = 15,000 ksi and a diameter of d1 = 0.50 in. Aluminum rod (2) has an elastic modulus of E2 = 10,000 ksi and a diameter of d2 = 0.85in. Aluminum rod (3) has a diameter of d3 = 1.00in. The yield strength of the bronze is 48 ksi and the yield strength of the aluminum is 40 ksi. Assume a = 2.5 ft, b = 1.5 ft, L1 = 6 ft, L2 = 8 ft, and L3 = 3 ft. (A) Calculate the cross-sectional areas of the three rods. in in.2 (B) For a factor of safety of 2.1, calculate the allowable stresses in the bronze and the aluminum rods. IN KSI. (C) What is the magnitude of load P that can safely be applied to the structure for a minimum factor of safety of 2.1? in kips (D) The pin used at B has an ultimate shear strength of 58 ksi. If a factor of safety of 2.5 is required, determine the allowable shear stress in this pin.…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 cireular 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, detemine the following: 4.3 The length of the square portion of the bar The suddenly applied load that will induce the same amount of energy 4.4 4.5 The load that falls from a height of 8 mm induces 1,3 J in the bar.arrow_forward
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