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For the case of plane stress, show that Hooke’s law can be written as
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Mechanics of Materials
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- Your answer is partially correct. On the free surface of an aluminum [E=10100 ksi; v = 0.35] component, the strain rosette shown was used to obtain the following normal strain data: a=-425 με, ε = -200 με, and ε & εν +575 μɛ. Determine the normal stress that acts along an axis that is rotated at an angle of 0 = 60° counterclockwise from the positive x axis. 60° 60° b a 60° x Determine the normal strains at the point associated with the x and y axes. Answers: Ex = -425 με, ε, Ξ i με.arrow_forwardThe state of stress at a point in a member is shown on the rectangular stress element; the magnitudes of the stresses are |σx|=66 MPa, |σy|=39 MPa|, and |τxy|=71 MPa. Using the stress-transformation equations, determine the state of stress on the inclined plane AB.arrow_forwardThe state of plane strain on an element is represented by the following components: Ex =D340 x 10-6, ɛ, = , yxy Ey =D110 x 10-6, 3D180 x10-6 ху Draw Mohr's circle to represent this state of strain. Use Mohrs circle to obtain the principal strains and principal plane.arrow_forward
- A 23 mm diameter bronze bar 2.8 m long is placed between two rigid walls. At a temperature of -3°C, the gap Δ = 4.6 mm. Find the temperature(at degree-Celsius) at which the compressive stress in the bar will be 34 MPa. Use α = 18.09 × 10-6 m/(m·°C) and E = 82 GPa. Answer in two decimal places. Numerical values only. Don't indicate units here, just on the submitted solution.arrow_forwardDetermine the maximum normal stress on a transverse plane in the straight portion of the structure shown below and clearly indicate where it occurs. The member is braced in the plane perpendicular to the plane of symmetry. Consider (a) Section B-B shown below at the left (symmetric section).(b) Section B-B shown below (unsymmetric).arrow_forwardThe solid 1.25-in.-diameter rod is subjected to a uniform axial distributed loading along its length of w = 825 lb/ft. Two concentrated loads also act on the rod: P = 1700 lb and Q = 1400 lb. Assume a = 15 in. and b = 30 in. Determine the normal stress in the rod at the following locations: (a) x = 10 in. (b) x = 30 in. → → → → - → · В A C a b Answer: Ox=10in. = psi Ox=30in. = psi Save for Later Attempts: 0 of 1 used Submit Answerarrow_forward
- Can you please explain why the question above is true and if not kindly explain why is False.arrow_forward4. For a state of biaxial strain (ε biax) in a linear-elastic isotropic material, what are the corresponding stresses? How would this change if the Poisson's ratio was zero? Briefly explain why. Assume standard material constants E, v, λ, etc. Γε Ebiax=0 01 bod 000 0 LO 0 0arrow_forward8000 mm3 aluminium cube is stressed in 3 mutually perpendicular direction x,y and z. The stresses in these directions are σx = 50 kPaσy = 80 kPaσz = -100 kPaDetermine the volumetric strain and change in volume. ν is 0.34 and E is 71 GPaarrow_forward
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