A rod is composed of an aluminum section rigidly attached between steel and bronze sections, as shown in the figure. Axial loads are applied at the positions indicated. If P= 4000 Ib and the cross-sectional area of the rod is 1.0 sq.in. What is the stress in the bronze? (in ksi) Note: indicate sign (no sign means positive/tension) 4P Steel Bronze Aluminum 2 ft 3ft 2.5 ft
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- A tensile test was performed on a metal specimen with a diameter of 1 2 inch and a gage length (the length over which the elongation is measured) of 4 inches. The dam were plotted on a load-displacement graph. P vs. L. A best-fit line was drawn through the points, and the slope of the straight-line portion was calculated to be P/L =1392 kips/in. What is the modulus of elasticity?A tensile test was performed on a metal specimen having a circular cross section with a diameter 0. 510 inch. For each increment of load applied, the strain was directly determined by means of a strain gage attached to the specimen. The results are, shown in Table: 1.5.1. a. Prepare a table of stress and strain. b. Plot these data to obtain a stress-strain curve. Do not connect the data points; draw a best-fit straight line through them. c. Determine the modulus of elasticity as the slope of the best-fit line.A compressive load P is transmitted througha rigid plate to three magnesium-alloy bars that areidentical except that initially the middle bar is slightlyshorter than the other bars (see figure). The dimensionsand properties of the assembly are as follows:length L = 1.0 m, cross-sectional area of each barA = 3000mm2, modulus of elasticity E = 45 GPa,and the gap s = 1.0 mm.(a) Calculate the load P1 required to close the gap.(b) Calculate the downward displacement d of therigid plate when P = 400 kN.(c) Calculate the total strain energy U of the threebars when P = 400 kN.(d) Explain why the strain energy U is not equal toPδ / 2. Hint: Draw a load-displacement diagram.
- PROBLEM 1) An aluminum bar carries the axial loads at the positions shown. If E=70GPA, compute the total deformation of the bar. Assume that the bar is suitably braced to prevent buckling. 0.4m D 10KN 0.8m 0.4m B 5KN 0.6m AL 20KN What is the deformation &pE in mm? A=800 mm² A=1,200 mm²The light rigid bar ABCD shown is pinned at C and connected to two vertical rods. The bar was initially horizontal, and the rods were stress-free before the load P = 20 KN is applied. %3D Steel E200 GPa A-600mm L1 m 2.0 m 0.6 m 1.5 m Pa20 KN Aluminum E-70 GPa A=900mm L-1.5 m What is the ratio of the deformation of steel to deformation of aluminum?As shown in the figure below, a bronze bar is affixed between a steel bar and an aluminum bar. Axial loads are applied at the positions indicated. If the largest value of P that will not exceed an overall deformation of 4.0 mm, or the following stresses: 150 MPa in the steel, 130 MPa in the bronze, and 90 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa. determine the stress in the bronze, steel, and aluminum
- The length of the assembly shown below decreases by 0.5 mm when an axial force is applied by means of rigid end plates. Determine (a) the magnitude of the applied force, (b) the corresponding stress in the brass core.Situation No. 2 A bronze bar is fastened between a steel bar and an aluminum bar as shown below. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the steel, 120 MPa in the bronze, and 80 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa. Bronze Steel A = 480 mm? Aluminum A = 650 mm A = 320 mm 3P 4P 2P 1.0 m 2.0 m 1.5 m5. A bronze bar is fastened between a steel bar and an aluminum bar as shown in Figure 5. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the steel, 120 MPa in the bronze, and 80 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa. Steel A = 480 mm² 1.0 m Bronze A = 650 mm² 3P 4P 2.0 m FIGURE 5 Aluminum A = 320 mm² 1.5 m 2P
- The rubber band given below is subjected to the following tensile loading. Calculate the minimum thickness of the rubber (tr) and the minimum steel pin diameter (Dpin) so that the structure does not fail. Consider: Allowable tensile strength of the rubber= 20MPa Allowable shear strength of the steel = 200MPa Reflection: 1) How would you solve this problem if a Factor of Safety was given? 2) Are there any other dimensions worth calculating for the rubber belt?Problem 2: A bronze bar is fastened between a steel bar and an aluminum bar as shown. Axial loads are applied at the positions indicated. Find the largest value of P that will not exceed an overall deformation of 3.0 mm, or the following stresses: 140 MPa in the steel, 120 MPa in the bronze, and 80 MPa in the aluminum. Assume that the assembly is suitably braced to prevent buckling. Use Est = 200 GPa, Eal = 70 GPa, and Ebr = 83 GPa. Steel Bronze 480 mm² 650 mm² 3P 1.0 m 4P 2.0 m Aluminum 320 mm² 1.5 m 2PAn aluminum tube is fastened between a steel rod and a bronze rod as shown. Axial loads are applied at the positions indicated. For Bronze: Allowable stress = 120 MPa, EB = 83,000 MPa For Aluminum: Allowable stress = 120 Mpa, EA = 70,000 MPa For Steel: Allowable stress = 120 MPa, Es = 200,000 MPa Assume that the assembly is suitably braced to prevent buckling. Maximum overall deformation should not exceed 2mm. a) Give the value of the force acting on the bronze so as not to exceed allowable stresses and deformation. b) Give the value of the force acting on the aluminum so as not to exceed its allowable stresses and deformation. c) Give the value of the force acting on the steel so as not to exceed its allowable stresses and deformation.