A thin-walled spherical shell made of a high-strength steel, whose forming-limit diagram is as shown, is being expanded by internal pressure. If the original shell diameter is 250 mm, what is the maximum diameter to which it can safely be expanded? Major strain (%) 140 120 100 80 60 40 20 O280 mm 0 -60 -40 O 350 mm Pure shear 367.5 mm Simple tension (For R = 1) O None of the above -20 Plane strain Failure zone Equal (balanced) biaxial Low-carbon steel Brass High-strength steel Aluminum alloy Safe zone 0 Minor strain (%) I 1 20 40 60 80

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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?

The principal plane stresses and associated strains in a 35 ksi, 02 = 15 ksi, plane at a point are 01 1 €1 = 1.02(10-3), 2 = 0.180(10-³). ▼ Determine the modulus of elasticity. Express your answer using three significant figures and include the appropriate units. E= Submit Part B V= μA Value Request Answer Submit Determine the Poisson's ratio. Express your answer using three significant figures. ΠΑΠΙ ΑΣΦ | Η VE Units Request Answer ? vec POSSIA space ?

The tube has a length of 2 m and is made of the material with the properties provided in the following figure. (a) Determine the torque needed to just cause the maximum strain to reach 0.015. (b) What is the permanent angle of twist of the tube when this torque is removed?

The stresses on the surface of a hard bronze component are shown in the figure below. The yield strength of the bronze is σY = 345 MPa.a) What is the factor of safety predicted by the maximum-shear-stress theory of failure for the stress state shown? Does the component fail according to this theory?b) What is the value of the Mises equivalent stress for the given state of plane stress?c) What is the factor of safety predicted by the failure criterion of the maximum-distortion energy theory of failure? Does the component fail according to this theory?

Derive the following equation for computing shear stress in a solid bar along an oblique plane with angle B with respect to the vertical plane. The bar is subjected to centric axial loading. sin 0 cos 0 T = Ao

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(30%) A circular aluminum tube subjected to T pure torsion by torques T has an outer radius r2 equal to 2 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 500x10-6 rad, what is the shear strain y1 at the inner surface? (b) If the maximum allowable rate of twist (0) is 0.15°/m and the maximum shear strain is to be kept at 500x10-6 rad by adjusting the torque T, what is the minimum required outer radius (r2 )min?

5. Consider a cylindrical specimen of a steel alloy (Figure 6.22) 10 mm in diameter and 75 mm long that is pulled in tension. Determine its elongation when a load of 20,000 N is applied. Stress (MPa) 600 500 400 300 200 100 0 0.00 0.04 Stress (MPa) 500 400 300 200 100 0.000 0.002 0.004 0.006 0.08 Strain Strain 0.12 0.16 0.20 Figure 6.22 Tensile stress-strain behavior for a steel alloy.