9. An initially rectangular element of material is deformed as sh in the figure (deformation shown below is greatly exaggerated). Calculate the normal strains in the x and y axis. +1.5x 104in. 1.2 x 104 in. L. В Undeformed Deformed 0.25 in. 1.8 x 10 in. 0.7 x 104 in.
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MECH OF DEFORM BODIES
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- During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.- 7.2-26 The strains on the surface of an experiment al device made of pure aluminum (E = 70 GPa. v = 0.33) and tested in a space shuttle were measured by means of strain gages. The gages were oriented as shown in the figure. and the measured strains were = 1100 X 106, h = 1496 X 10.6, and = 39.44 X l0_. What is the stress o in the x direction?A 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 stresses
- 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 eyThe figure below shows a hollow circular beam with an outside diameter of 100 mm and a wall thickness of 40 mm loaded in bending with force F = 200 kN. F Ra Rb 1m 1 m Young's modulus of the beam is 80 GPa. Calculate the second moment of area, I, in m* in the form a x 10 0 where the number a is correct to two decimal places. I: x10 m4 Calculate the maximum bending moment, M, in kilonewtonmetres (kNm): M: kNm Calculate the maximum bending stress, o, in megapascals (MPa) correct to two decimal places. MPaQuestion 2 A 60° strain rosette is installed on the traction-free surface of a component with one of the strain gages aligned along the y-axis, as illustrated in Figure Q2. The gages show the following strain readings upon loading the structure: E, = 925 x10“ ; &, = 740 x10“ ; ɛ. = -555 ×106 (a) Determine the strains in the x-y directions and show the corresponding strain element. (b) Calculate the principal in-plane strains and the corresponding principal directions. Show the principal strain element. (c) Calculate the in-plane maximum shear strain and show the corresponding strain element. (d) If the structure is made of steel with elastic modulus and Poisson's ratio of 220 GPa and 0.30, respectively, calculate the principal stresses. Show the principal stress element. (e) Determine the normal strain in the n-direction. & Ea
- 2) Find the strains in the 1-2 coordinate system (local axes) in a unidirectional boron/epoxy lamina with 50% fiber volume fraction, if the stresses in the 1-2 coordinate system applied to are ơ1 = 6 MPa, ơ2 =2 MPa, and T12 = -4 MPa. Use the properties of the given unidirectional lamina in the book and assume plane stress conditions for the lamina.Question: The stress components at point O of a part made of steel material (E = 210 GPa and v= 0.3) are given below. 25 40 - 20 40 30 35| MPа - 20 35 -10 a) Calculate the strain components (Exx, Eyy, Ezz, Yxy, Yxz and Yyz). b) Calculate the principal strain components (E,, E2, and E3) and the maximum shear stress (max). c) Draw the 3-D Mohr circle for the strain components.Question 3: Please refer to the metal bar and its cross-section shown below. Two strain gages a and and b are attached to the bar as shown; note that 3 is the angle of their orientation with the x-axis. Assume: the Young's modulus of the metal = 16, 500 ksi; the Poisson's ratio of the metal = 0.33; P, = 13 kips; P, = 20 kips; d = 4.0 in.; t = 0.75 in.; L = 18 in.; and B = 40°. Determine the strains expected in the strain gages. 가 2 B b a H Ps N H y d
- Part 1 A thin square plate PQRS is symmetrically deformed into the shape shown by the dashed lines in the figure. Assume d = 255 mm, d₁ = 256.1 mm, and d₂ = 253.6 mm. For the deformed plate, determine (a) the normal strain of diagonal QS. (b) the shear strain Yxy at corner P. d₂ Answer: dos d = i d₁ Undeformed Calculate the deformation of diagonal QS. R Deformed X mmPROBLEM 4. A piece of rubber, which was originally a square shape, has been deformed into a shape shown with the dashed lines in the figure. After the deformation, the CD line remained parallel to the direction before the deformation. (a) Calculate the average normal strains along AB and diagonal AD. (b) Calculate the average shear strain yxy at point A. 6 mm 84 mm 4 mm 80 mm 2 mm 80 mm mmTensile 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.