[Problem 4]Show that the following strain components are the solutions of a problem in elasticity.E, = 2.xy',E, = -6.xy', E, = 2.x' +x'y-yWhere & is defined as the small strain component.urgent solution.please explain properly.will surely upvote

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Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.19P: During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as...

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Question-1: The strain rosette shown in the figure was used to obtain normal strain data at a point on the free surface of a machine part. (a) Determine the strain components &, S, and %, at the point. (b) Determine the principal strains and the maximum in-plane shear strain at the point. (c) Draw a sketch showing the angle 6, the principal strain deformations, and the maximum in-plane shear strain distortions. (d) Determine the magnitude of the absolute maximum shear strain. 45 45 &- 50 με, 8--730 με , ε375 με, ν-0.30
Tensile test specimens are extracted from the "X" and "y" directions of a rolled sheet of metal. "x" is the rolling direction, "y" is transverse to the rolling direction, and "z" is in the thickness direction. Both specimens were pulled to a longitudinal strain = 0.15 strain. For the sample in the x-direction, the width strain was measured to be ew= -0.0923 at that instant. For the sample in the y-direction, the width strain was measured to be gw=-0.1000 at that instant. The yield strength of the x-direction specimen was 50 kpsi and the yield strength of the y-direction specimen was 52 kpsi. Determine the strain ratio for the x direction tensile test specimen. Determine the strain ratio for the y-direction tensile test specimen. Determine the expected yield strength in the z-direction. Give your answer in units of kpsi (just the number). If the sheet is plastically deformed in equal biaxial tension (a, = 0, to the point where & = 0.15, calculate the strain, 6, that would be expected.
Q4. The triangular plate ABC is deformed into the shape shown by the dashed lines. If at A, EAB = 0.007, EAC = 0.015, and xy = 0.006 rad, determine the average normal strain along edge BC. 350 mm y A -Yxy 1 450 mm 1 B X (Note: Work show the SI units throughout the solution and the final result should be in SI units)
3.For a body under three dimensional stress state, describe the procedure for obtaining the absolute maximum shearing stress at a given point. What is meant by strain transformation? Describe two procedures for obtaining stress form Mohr’s circle for strain.
Example 1: (i) Find the compatibility condition for the strain tensor e; if e1 , e22 , e12 are independent of x3 and e31 = e32 = e33 = 0. (ii) Find the condition under which the following are possible strain components. eii = k(x,? – x2), e12 = k' x1 x2 , e22 = k x1 X2 , %3D e31 = e32 = e33 = 0, k & k' are constants (iii) when eij given above are possible strain components corresponding displacements , given that u; = 0. find the
Find strain
The strain components, ex= 940 micro strain, ey= -360 micro strain and yxy=830micro strain are given for a point in body subjected to plane strain. Determine; a. Magnitude of the principal strains b. The direction of the principal strain axes c. The maximum in-plane shear strain. Confirm your answer by means of Mohr's circle of strain and determine the linear strain on an axis inclined at 20 degrees clockwise to the direction of ey
Problem 2 refers to the following: a load P is applied to the cantilever beam shown which causes it to bend and deflect elastically: 2. a. b. 6 C. Gage 1 2 3 4 5 6 5 3 4 on bottom Strain (ue) A student group recorded the following strains from the loaded beam but failed to record which gages (1-6) the strain recordings came from (all strains are in microstrain): -154, 318, -23, 555,-323, 81. 2 1 Write the correct strain readings in the table above. Note gages 1, 3, 4, and 5 are longitudinal gages, and gages 2 and 6 are transverse gages. Gage 4 is on the bottom of the beam and is the same distance from the load as gage 3. Calculate an estimate of Poisson's ratio for this material. If the elastic modulus for this material is 10 Mpsi, calculate the uniaxial stress at the location of gages 5 & 6.
Q. // (A) - An element of bone in plane strain where the state of strain are (Ex = 8 × 10¬4, €y = 5 × 10¬4, Yxy = 12 × 10-4). Find (a) the stresses at orientation a counterclockwise angle (40 deg.) from the x-axis, b) the strain energy and (c) the failure stress by Von Misses criteria. Known Modulus of elasticity = 2 × 10° N /m² and Poisson's ratio = 0.3
Question 5: (8 marks) The 45° strain rosette shown in Figure 5 is mounted on a machine element. The following readings are obtained from each gauge: Ea = 650 x 106, : b = -300 x 106, and : &c = 480 x 10°. Determine (a) the in-plane principal strains, and (b) the maximum in-plane shear strain and the associated average normal strain. a Figure 5 45° 45°
Exercise 3 If the displacement field is given by Ux = kxy, uy = kxy, uz = 2k(x + y)z where k is a constant small enough to ensure applicability of the small deformation theory, (a) write down the strain matrix (b) what is the strain in the direction nx = ny = n, =1//3 ?
Solid mechanic 2 Sketch the strain element that experiences a negative shear strain only on x-y plane.