Determine shear yield stress using Von Mises
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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?Determine 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 300A brittle material made of ASTM grade 30 cast iron has ultimate strength in tension of 31 kpsi and ultimate strength in compression of 109 kpsi and undergoes the following plane of stress state: o, = 20 kpsi and Tyy = 10 kpsi (CW). a) using the 3D Mohr's circle, find all three principal normal stresses. b) using the Brittle-Coulomb-Mohr theory and Modified-Mohr theory, find the factors of safety for the given plane of stress state.
- 1. A circular rod of diameter 20mm and 500mm long is subjected to atensile force 50kN. The modulus elasticity for steel may be taken as 200kN/??2. Find stress and strain due to applied load.2. In the stress-strain curve for steel shown below, identify following stresses in ksi and write their values in the space below: 2.1. Yield Point: ksi 2.2. Ultimate Tensile Strength: ksi 60- 400 350 50 300 E 40 250 30 200 150 20 100- 10 50 0. Strain, in/in or m/m J stv A Aa Stress, MPa Stress, ksi1.7C1 1.4C1 ci 0.9C1 Uniform plastic elongation Necking Elastie 0 4 % 15% 35% Strain in % Stress-Strain diagram Stress in MPa
- A certain high tensile strength steel has a modulus of elasticity of 2 x 106 kg/cm² and a yield point stress of 6,000 kg/cm². Find the minimum limiting value of the slenderness ratio for which Euler's equation is valid.Consider the material Al-$456 It has the following physical ploperties Syleld = 230mPA %3D s-72GPA (modulos elasticity) Oultimate=315 mPA G- 28GPA Cmad vlus rigidity) Tuield =130 mPA Joltimate=185 mPA A Calculate Poisson's ratio B) If we have a following dimensions And Forces 3-0 block of Al-5456 with the Ex =800N X= Bcm Fy=1000N ) Is Our block Safes (consider only plane stes) Dset up the 3 eqetions to find the strains (Ex Ey E2) in each directian E Solve the 3exuations to find the Einal dimensions of our block1.6-7 A wire 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 mathemat- ically by %3| 18,000ɛ 0 < 8< 0.03 (ơ = ksi) = 1+ 300ɛ in which e is nondimensional and o has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (b) 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?
- 3. Find the young's modulus of a bars a rod of diameter 25 mm and of length 250 mm which is subjected to a tensile load of 50 kN when the extension of the rod is equal to 0.3 mm. And if the modulus of elasticity of the material of the rod is 2x105 N/mm² determine stress, strain and % elongation of the rod.1.6-7 A wire of length L = 2.5 m and diameter d = 1.6 mm is stretched by tensile forces P = 600 N. The wire is made of a copper alloy having a stress- strain relationship that may be described mathemat- ically by 124,020ɛ 0 s8s 0.03 (o = MPa) 1+ 300ɛ in which e is nondimensional and o has units of MPa. (a) Construct a stress-strain diagram for the material. (b) 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?1. A part made of Aluminum 6061-T6 has a yield strength = 400 MPa. For each stress state below, draw all 3 Mohr's circles, find the principal stresses, and calculate the safety factor against yield using both the distortion-energy (von Mises) and maximum shear stress (Tresca) criterions. (If relevant) A clearly labeled diagram (or diagrams) clearly pertaining to your analysis with a coordinate system and relevant labels. Final answer with appropriate units and significant figures. You can use the fprintf() command in MATLAB to format numerical results A 2-3 sentence reflection on your answer. Does it make sense? Why or why not? What are some implications?