1. We can visualize the factor of safety for an arbitrary stress using a surface in principal stress space. For a ductile material that yields according to a von Mises criterion with a yield stress σy, sketch the von Mises surface in σ₁ - 02 space and sketch the stress surface that corresponds to a factor of safety FoS = 2. For a brittle material that yields according to a max normal (Rankine) criterion with a tensile strength Gyt and a compressive strength σvc = 20yt, sketch the yield surface and the surface that corresponds to a factor of safety FoS = 2.

A 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.

In the picture there is a sketch of a socket wrench. Assume the wrench is held at a fixed point “A”. The yield stress of the material is known to be 400 MPa. Answer the questions below Describe the stresses at point “A” and their causes and calculate the stresses. Determine the factor of safety against yield assuming the Tresca yield criteria. Determine the factor of safety against yield assuming the von Mises yield criteria using both principal stresses and “Cartesian” stresses. Do your values match or not, and is this expected? Explain. Do the calculated values make sense with the respect to the Tresca value? Explain, why or why not?

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In the attached picture there is a sketch of a socket wrench. Assume the wrench is held at a fixed point “A”. The yield stress of the material is known to be 500 MPa. Answer the questions below Describe the stresses at point “A” and their causes and calculate the stresses. Determine the factor of safety against yield assuming the Tresca yield criteria. Determine the factor of safety against yield assuming the von Mises yield criteria using both principal stresses and “Cartesian” stresses. Do your values match or not, and is this expected? Explain. Do the calculated values make sense with the respect to the Tresca value? Explain, why or why not?

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?

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The data shown in the accompanying table are From a tensile test of high-strength steel. The test specimen has a diameter of 0.505 in. and a gage length of 2.00 in. (see figure for Prob. 1.5-3). At fracture, the elongation between the gage marks is 0.12 in. and the minimum diameter is 0.42 in. Plot the conventional stress-strain curve for the steel and determine the proportional limit, modulus of elasticity (the slope of the initial part of thestress-strain curve), yield stress at 0.1% offset, ultimate stress, percent elongation in 2.00 in., and percent reduction in area. TENSILE-TEST DATA FOR PROB. L.5-7 Laid (lb) Elongation (in) 1000 0.0002 2000 0.0006 6000 0.0019 10,000 0.0033 12,000 0.0039 12,900 0.0041 13,400 0.0047 13,600 0.0054 13,800 0.0063 14,000 0.0090 14,400 0.0102 15,200 0.0130 16,800 0.0230 18,400 0.0336 20,000 0.0507 22,400 0.1108 22,600 Fracture

The stresses on the surface of a ductile alloy component 50 MPa are as pictured. The yield strength of the alloy is oy = 190MPA. 100 MPa Find Principal Stresses: Отах MPa Omin MPа 50 MPa Calculate Mises equivalent stress for the given state of plane stress: OM MPa Calculate Factor of Safety predicted by the maximum-distortion-energy theory using Mises stress: FS Does the component fail according to this theory? Yes or No Calculate Factor of Safety predicted by the maximum-shear-stress theory of failure: FS Does the component fail according to this theory? Yes or No