natural strain at point B
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- A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?(a) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressureDetermine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit. DATA FOR PROBLEM 2.7-5 Material Weight Density (lb/in3) Modulus of Elasticity (ksi) Proportional Limit (psi) Mild sleel 0.284 30,000 36,000 Tool steel 0.284 30,000 75,000 Aluminum 0.0984 10,500 60,000 Rubber (soft) 0.0405 0.300 300
- A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?- A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle ? = 20° and show the full stress state on a sketch of a properly oriented element.The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress ?? =6.5×10-6 /? is produced in the rails when they are heated by the sun to 120"F if the coefficient of thermal expansion a = the modulus of elasticity E = 30 × 106 psi?
- The true stress (o), true strain (ɛ) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e. up to stress of 500 MPa and strain of 0.5. then from point A, there is unloading up to point B, i.e. to stress of 100 MPa, Given that the Young's modulus E = 200 GPa, the natural strain at point B (s,) (correct to two decimal places). (MPa) 500 100 C EB 0.5The true stress (6), true strain (ɛ) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e. up to stress of 500 MPa and strain of 0.5. then from point A, there is unloading up to point B, i.e. to stress of 100 MPa, Given that the Young's modulus E = 200 GPa, the natural strain at point B (§g) 1. (MPа) 500 100 Eg 0.5Question 4 At a point in a thin steel plate in plane stress (oz = Txz = Tyz = 0), Ex=800H, Ey= - 400, and Ky = 200. For the steel plate, G = 76.92 GPa and V= 0.30. (a) Determine the extensional strain &zat this point. (b) Determine the stresses Ox, Oy and Txy at this point. (c) Determine the change in volume or dilatation, &v, at this point.
- Question-1: The strain rosette shown in the figure was used to obtain normal strain data at a point on the free surface of a machine part. (a) Determine the strain components &, S, and %, at the point. (b) Determine the principal strains and the maximum in-plane shear strain at the point. (c) Draw a sketch showing the angle 6, the principal strain deformations, and the maximum in-plane shear strain distortions. (d) Determine the magnitude of the absolute maximum shear strain. 45 45 &- 50 με, 8--730 με , ε375 με, ν-0.30Part (1): A 30 ?? square plate is subjected to uniform pressure as shown in Figure.1. The 2D loading stresses are described. If the modulus of elasticity is 200 ??? and the lateral constant (Poisson's ratio ? = 0.3). Estimate the change in length in the vertical, horizontal and diagonal sides as well as determine the volumetric strain. Illustrate the effect of two-dimensionalstrain by constructing appropriate sketches (before and after deformation).Repeat the analysis for lower value of pressure and higher value in the range of [20 -100 MPa] and comment on the overall resultsA 30 ?? square plate is subjected to uniform pressure as shown in Figure.1. The 2D loading stressesare described. If the modulus of elasticity is 200 ??? and the lateral constant (Poisson's ratio ? = 0.3). Estimatethe change in length in the vertical, horizontal and diagonal sides as well as determine the volumetric strain.Illustrate the effect of two-dimensionalstrain by constructing appropriate sketches (before and after deformation).Repeat the analysis for lower value of pressure and higher value in the range of [20 -100 MPa] and comment onthe overall results.