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Topic: Generalized Hooke's Law
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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?Steel 1 m Aluminum T 0.75 m Determine the maximum permissible value of T subject to the following conditions: tt S 80 MPa, Tal 50 MPa, and the angle of rotation of the free end is limited to 0.1 radian. For T. Hollow Solid d= 30 mm D= 40 mm %3D steel, G = 82 GPa and for aluminum, G= 28 GPa. %3D d = 30 mm %3D10/10 FIND STRESS IN Aluminum. IF E st= .200000 MPa, Ealu.=70000 MPa 100 kN RALU.=30 MM Aluminum Steel 55 MPа 19 MPa 69 MPa 31 MPa no one ( 1m RST 20 MM
- 3) An bronze rod is rigidly attached between a aluminum rod and a steel rod as shown. Axial loads are applied at the positions indicated. Find the maximum allowable value of P that will not exceed a stress in steel of 140MPA, in aluminum of 90MPA or in bronze of 100MPа. Aluminum A = 500mm? Bronze A = 200mm? Steel A = 150mm2 2P ЗР L st = 1.2m L br = 2m Lal = 3.5m10/10 FIND STRESS IN Aluminum. IF E st= .200000 MPa, Ealu.=70000 MPa 100 kN RALU. 30 MM Aluminum Steel 1m RST 20 MMPROBLEM 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 5KN 0.6m A 20KN 3) What is the deformation &cn in mm? A=800 mm? A=1,200 mm²
- A hollow aluminum tube is rigidly attached between steel rod and a bronze rod as shown. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in aluminum of 80 MPa, in steel of 150 MPa or bronze of 100 MPa. Steel Aluminum Bronze А P> ЗР - 2P outside = 30 mm d inside = 20 mm d d = 16 mm d = 60 mm -100mm- -150mm- -125mm-Sample: Malleable Steel (AISI 4145) Original Diameter: 6.14mm Gauge Length: 55 mm Final Length: 68.12 mm Final Diameter: 3.54mm Load (kN) Deformation (mm) Stress (MPa) 12.95 Strain (%) 0.3838 0.54 0.7841 0.95 26.48 1.3899 1.63 1.9485 2.07 3.3090 3.10 4.5821 4.22 5.9359 5.03 7.0340 5.51 8.2413 6.22 10.9446 7.22 13.1951 8.18 12.8228 8.77 12.2583 9.11 12.5915 9.61 13.2536 10.33 13.6636 10.71 13.9772 11.35 14.5433 12.63 15.1155 13.88 15.4970 15.10 15.6484 17.09 15.4031 17.79 14.7655 18.73 13.6721 19.28 10.4617 19.88X Your answer is incorrect. Two polymer bars are connected to a rigid plate at B, as shown. Bar (1) has a cross-sectional area of 1.42 in.? and an elastic modulus of 2180 ksi. Bar (2) has a cross-sectional area of 1.139 in.? and an elastic modulus of 4150 ksi. Assume L;-23 in., L2-41 in., Q-6.7 kips, P-3.7 kips, and R-14.1 kips. Determine the horizontal deflection of end Crelative to end A. R (1) (2) P L1 L2 Answer: UCIA - i 0.0725 in.
- Two polymer bars are connected to a rigid plate at 8, as shown. Bar (1) has a cross-sectional area of 1.42 in.and an elastic modulus of 2180 ksi. Bar (2) hasa cross-sactional area of 1139 in.and anelastic modulus of 4150 ksi. Assume l-23 in., L-41 in, Q-6.7 kips, P-3.7 kips, and R-14.1 kips. Datermine the horizontal deflection of end Crelative to end A P R (1) (2) Answer: uga in.Steel, Brass, and Copper rods are connected as shown in the figure. Initially, the temperature was 15 degrees Celsius and the stress on the bars is zero. Eventually, the temperature increased to 25 degrees Celsius. Determine the total deformation on the steel. Steel Brass Copper Est = 200 GPa Ebr = 100 GPa Ecu = 120 GPa %3D ast = 12(10-6)/°C abr = 21(10¬6)/°C acu = 17(10-)/°C %3D Acu = 515 mm² |Ast = 200 mm? Abr = 450 mm² %3D 300 mm- 200 mm 100 mm O -0.0058mm O 0.0165mm O -0.0165mm O 0.0058mmThe 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?