3 For a composite bar as shown below, what is the relation between axial deformation and thermal deformations in the bar? Cu tube (1) Steel bar (2) D d- Where, o,, o, = stresses in Cu and steel bar respectively. = Coefficient of thermal expansion for Cu and steel bar respectively.
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- A flat bar of aluminum alloy 25 mm wide and 5 mm thick is placed between two steel bars each 25 mm wide and 10 mm thick to form a composite bar 25 mm x 25 mm as shown. The three bars are fastened together at their ends when the temperature is 15℃. Find the stress in each of the materials when the temperature of the whole assembly is raised to 55 ℃.Steel: Es = 200 GPa; Coefficient of expansion = 1.2x10^-5/℃.Aluminum: Eal = 200/3 GPa; Coefficient of expansion = 2.3x10-5/℃.A composite beam is made of two brass [E = 120 GPa] bars bonded to two aluminum [E = 70 GPa] bars, as shown. The beam is subjected to a bending moment of 400 N-m acting about the z axis. Using a = 15 mm, b = 100 mm, c = 30 mm, and d = 65 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. Aluminum y Brass Aluminum b Brass C a dA composite beam is made of two brass [E = 110 GPa] bars bonded to two aluminum [E = 71 GPa] bars, as shown. The beam is subjected to a bending moment of 260 N-m acting about the z axis. Using a = 10 mm, b = 85 mm, c = 20 mm, and d = 55 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. Aluminum С Aluminum Answers: (a) Jal= Brass (b) Obr= i b Brass a MPa MPa
- A composite beam is made of two brass [E = 110 GPa] bars bonded to two aluminum [E = 71 GPa] bars, as shown. The beam is subjected to a bending moment of 260 N-m acting about the z axis. Using a = 10 mm, b = 85 mm, c = 20 mm, and d = 55 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. 2 Aluminum C Aluminum Answers: (a) Jal= Brass- (b) Obr= i i b Brass (2 (2 MPa O MPa EA steel bar is heated from room temperature to 800C while it is free to expand. The bar will therefore be subject to: O A. compression B. tension C. no stress D. shearA bar of solid circular cross section is loaded in tension by forces P (see figure). P L The bar has a length L = 14.0 in. and diameter d = 0.65 in. The material is a magnesium alloy having a modulus of elasticity E = 6.4 x 106 psi. The allowable stress in tension is allow = 17,300 psi, and the elongation of the bar must not exceed 0.04 in. What is the allowable value of the forces P (in lb)?
- A composite beam is made of two brass [E = 112 GPa] bars bonded to two aluminum [E = 69 GPa] bars, as shown. The beam is subjected to a bending moment of 350 N-m acting about the z axis. Using a = 15 mm, b = 115 mm, c = 25 mm, and d = 65 mm, calculate (a) the maximum bending stress in the aluminum bars. (b) the maximum bending stress in the brass bars. Z Aluminum с Aluminum Answers: (a) Jal= (b) Obr= Brass i y i b Brass a a MPa MPaSITUATION. As shown in the figure below, a rigid bar with negligible mass is pinned at O and attached to two vertical rods. Assume that the rods were initially stress-free. Allowable stress in steel is 120 MPa and in bronze is 60 MPa. For this problem, a = 1.8m; b = 1.3m; c= 1.7m. a b C P Steel: A-900 mm² Bronze: A=1200 mm² E = 83 GPa L=2.0 m E = 200 GPa L=1.5m What is the value of P without exceeding the allowable stress of bronze, in kN? O 161 O 174 O 145 124 4SITUATION. As shown in the figure below, a rigid bar with negligible mass is pinned at O and attached to two vertical rods. Assume that the rods were initially stress-free. Allowable stress in steel is 120 MPa and in bronze is 60 MPa. For this problem, a = 1.8m; b = 1.3m; c = 1.7m. b C NANTSELEINE Steel: A = 900 mm² E = 200 GPa L=1.5m Bronze: A=1200 mm² E=83 GPa L=2.0m What is the ratio of the elongation of steel to bronze? O 0.367 O 0.433 O 0.467 0.333
- Problem 2 For the beam shown in the figure A) Draw the shear-force and bending-moment diagrams for the beam shown in the figure. B) For the composite section, aluminium [E = 70 GPa] bonded to a steel [E = 210 GPa], located at the maximum bending moment, determine: (1) the maximum bending stresses in the aluminium and steel bars. (2) the stress in the two materials at the joint where they are bonded together. K4N/M 2m B 10kN/mm 4m 2m D Steel Aluminum 42mm 20 mm 13 mmEXAMPLE: 14. The composite bar in the figure is stress-free before the axial loads PI and P2 are applied. Assuming that the left wall is rigid, while the right wall yields 0.80mm. calculate the stress in each material if PI = 150 kN and P2 = 90 kN. Aluminum 150 kN 500 mm Steel Bronze 90 KN 250 mm 350 mm 0.8 mmSITUATION. As shown in the figure below, a rigid bar with negligible mass is pinned at O and attached to two vertical rods. Assume that the rods were initially stress-free. Allowable stress in steel is 120 MPa and in bronze is 60 MPa. For this problem, a = 1.8m; b = 1.3m; c= 1.7m. a b I Steel: A 900 mm Bronze: A E 200 GPa E 83 GPa L-2.0m L=1.5m What is the value of P without exceeding the allowable stress of steel, in KN? 230 250 280 340 1200 mm