&=0.004, & = -0.003, & = 0.002, at angles 0 = 0, 0 = 60°, 0 = 120° С a) Calculate the component strains: &, &, and Ky. b) Calculate the principal strains.
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The strains measured by a rosette strain gauge are
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- Q3)The following strains were recorded E₁ 450*10", &, 230x10 and £, = 0, determine: BUR on (1 rectangular strain a)The principal strains and the directions of the principal strain axes. b)The principal stresses if E-200GPa and v0.3. Using graphical Mohr's circles. rosetteFind strainProblem 3. Strains are measured on the surface of a structural component as &A = = 1200 x 10-6. EB = 500 x 10-6, &c = 300 × 10-6. E = 200 GPa and v = 0.3. b) a) Find the principal stresses and show these on a sketch of a properly oriented element. Use Mohr's Circle to find the stresses at 0 = 30° counterclockwise from the x axis and show these on a sketch of a properly oriented element. y 60° C B A X
- A point On a free surface of a machine point (E = 214Gpa, G= 83Gpa) the stress state is shown on the diagram below e) Find the three principle strains, absolute max shear strain and the max in plane shear strain f) Determine the principle strains (Ep1,Ep2) and the max in the plane shear strain in the correct schematic4. Show that Cp = as +45°. principal strain and shear strainThe plate distorts as shown by the dashed lines. The dimensions are L= 410 mmmm, H= 320 mm, d1= 3 mm, d2= 5 mm, d3= 12 mm, d4= 9 mm, d5= 3 mm, and d6= 7 mm. A) Determine the shear strain γxy at corner C. B) Determine the shear strain γxy at corner D.
- 2) The state of stesss at a point in a body relative to the xyz coordinate system is: 2 3 -5 [o]= 3 2 kpsi 6. %3D -5 2 -4 a) Determine the principle stresses and the direction cosines corresponding to each principle stress. b) Draw the 3D Mohr's circles. c) Determine the maximum shear stress. d) Find the orientation of the plane containing the maximum shear stress relative to the original axis system 3) For the stress tensor in problem 2: a) Determine the normal and shear stress on a surface intersecting a plane defined by 3 points (0,0,0); (2,-1,3); (-2,0,1) b) Give the magnitudes of these stresses and the direction cosines defining their directions.Draw Mohr's circle for the following plane strain state. Then compute (or extract from your drawing) the principal strains and max shear strain. (Positive sign convention for each is shown on the figure.) Ex = 200μ, Ey=-200μ, Yxy = 50μ (rad) You For the previous problem, compute the following six stress quantities: d. dy, dz. Txy, Tyz. Tzx. Assume this is an aluminum alloy (E = 10,000 ksi, G = 3800 ksi, v = 0.33). Do not forget units! ExThe area of the upper face of a rectangular block is .5mx.5m The lower face is fixed. The height of the block is 1cm. A shearing force applied to the top face produces a displacement of 0.015mm. Find the strain, stress and shearing force. Modulus of rigidity 4.5 x 10¹0 N/m². **Need asap pls. Thank you.
- 1.40 Given a major principal strain of 600µ and strain invariants I, = 400µ and I, = - 4800µ, find the remaining principal strains. Find, in magnitude and direction, the octahedral normal and shear strains. Answer: (1u = 1 x 10 ) 200p.- 400u. 133µ, 822uA material is subjected to the following strain system,ex=200x10-6, ey=-56x10-6,yxy=230x10-6. Using graphical method, determine A. The principal strains B. The directions of principal strain axes C. The linear strain on an axis inclined at 50o counter clockwise to the direction of ex Given that young's modulus for the material is 207GN/m2 and the poisson's ratio is 0.27, determine the principal stressesAn 6 mm diameter aluminum rod has lines scribed on it that are exactly 10 cm apart. After a 2.08 kN force has been applied, the separation between the lines has increased to l' = 10.009 cm. 30 cm 10 cm -F l' a. Calculate the stress and strain in the rod. (Express your answer for stress using two significant figures.) |MPa (Express your answer for strain using four decimal spaces.) E = b. To what total length has the rod stretched? (Express your answer using three decimal places.) L final cm