6. Figure Q6 shows the assembly of two aluminium (E = 70 GPa) rods AB and CD having diameter of 20 mm, a stainless steel (E = 200 GPa) rod EF having a diameter of 30 mm and a rigid plate that connects those three rods at BED. The yield stresses for the aluminium and steel materials are 20 MPa and 250MPa, respectively. Factor of safety of each material is set to 2.5. a) Determine the maximum permissible value of P that can be applied on the structural assembly. b) Calculate the total displacement of point F due to the maximum permissible load obtained in a). 200mm 300mm A B 4P E F Rigid plate 2P C D 4P Figure Q6
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5 = 100 MPa. - Area of steel rod (d = 30 mm): A_ef = (π/4) d^2 = (π/4)(30 mm)^2 = 225π mm^2 = 706.8583 mm^2. - Given σ_s = 2P / A_ef, set 2P / A_ef = 100 MPa → P_s = (100 MPa)(A_ef)/2. P_s = (100 N/mm^2)(706.8583 mm^2)/2 = 35,342.9 N = 35.343 kN. Show more…
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An aluminium rod is rigidly attached between a steel rod and a bronze rod as shown in Figure 3. Axial loads are applied at the positions indicated: (a) Find the maximum value of P that will not exceed a stress in steel of 140 MPa, in aluminium of 90 MPa, or in bronze of 100 MPa. (b) Using the answer from question (a), determine the total elongation of the rods. Steel A = 500 mm² E = 200 GPa 2.5 m Aluminium A = 400 mm² E = 70 GPa 2.0 m Bronze A = 200 mm² E = 83 GPa 1.5 m 4P 2P Figure 3
Problem 5: The aluminum and steel pipes shown in the figure are fastened to rigid supports at ends A and B and to a rigid plate C at their junction. The aluminum pipe is twice as long as the steel pipe that has a length L = 400 mm. Two equal and symmetrically placed loads P = 30 kN act on the plate at C. (a) Determine the stresses σa and σs in the aluminum and steel pipes, respectively, and the movement of the rigid plate C. (b) If the temperature of both rods is raised by 40°C, determine the stresses σa and σs in the aluminum and steel pipes, respectively, and the movement of the rigid plate C. The cross-sectional area of the aluminum pipe Aa = 500 mm² and of the steel pipe As = 60 mm², modulus of elasticity of aluminum Eal = 70 GPa, and modulus of elasticity of steel Est = 210 GPa, coefficient of linear expansion of steel αst = 12(10^-6)/°C, and αal = 23(10^-6)/°C.
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