A sheet of copper is stretched bi-axially in the xy-plane. If the strains in the sheet are x = 0.40 x 103 and Ey = 0.30 x 103, determine ox and oy, Use E = 1.595 x 107 psi and v=0.33.
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- Compare the engineering and true secant elastic moduli for the natural rubber in Example Problem 6.2 at an engineering strain of 6.0. Assume that the deformation is all elastic.3. A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are ex = 0:40 103 and €y = 0:30 103, determine Oz and oy. Use E = 110 GPa and v = 0:35.1.A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are € E =0.40x10-3 and ɛ =0.3 x 10- determine O and o. Use E = 110 GPa and v=0.35. y y. = Blank 1 MPa Answer in 1 decimal place = Blank 2 MPa Answer in 1 decimal place
- A steel bar, whose cross section is 0.60 inch by 4.10 inches, was tested in tension. An axial load of P = 31,025 lb. produced a deformation of 0.115 inch over a gauge length of 2.10 inches and a decrease of 0.0080 inch in the 0.60-inch thickness of the bar. a. Determine the lateral strain. b. Determine the axial strain. c. Determine the Poisson’s ratio v. d. Determine the decrease in the 4.05-in. cross-sectional dimension (in inches).30. An aluminum alloy rod has a circular cross section with a diameter of 8mm. The rod is subjected to a tensile load of 5kN. Assume that the material is in the elastic region and E = 69 GPa. If Poisson's Ratio is 0.33, what will be the lateral strain? E= 6/8 v = -E(lateral)/(axial)A square plate O-P-Q-R of a linear elastic material with sides 1.0 m is loaded in a state of plane stress. Under a given stress condition, the plate deforms to a new configuration O-P'-Q'-R' as shown in figure (not to scale). Under the given deformation the edges of the plate remain straight. 10 mm y4 R'. Q' 10 mm R Q 10 mm P 20 mm The horizontal displacement of the point (0.5 m, 0.5 mm) in the plate O-P-Q-R (in mm, round off to one decimal place) is
- 30. An aluminum alloy rod has a circular cross section with a diameter of 8mm. The rod is subjected to a tensile load of 5kN. Assume that the material is in the elastic region and E=69 GPa If Poisson's Ratio is 0.33, what will be the lateral strain? E=68 v=-e(lateral) e(axial)X Your answer is incorrect. Two polymer bars are connected to a rigid plate at B, as shown. Bar (1) has a cross-sectional area of 1.42 in.? and an elastic modulus of 2180 ksi. Bar (2) has a cross-sectional area of 1.139 in.? and an elastic modulus of 4150 ksi. Assume L;-23 in., L2-41 in., Q-6.7 kips, P-3.7 kips, and R-14.1 kips. Determine the horizontal deflection of end Crelative to end A. R (1) (2) P L1 L2 Answer: UCIA - i 0.0725 in.3. The distribution of stress in an aluminum machine component is given (in megapascals) by Ox = y + z? Oy = x + z Oz = 3x + y Txy = 3z2 Tyz = x Txz = %3D Calculate the state of strain at a point positioned at (1,2,4). Use E=70 GPa and v = 0.3
- 1.17 Figure P1.17 shows the stress-strain relations of metals A and B during tension tests until fracture. Determine the following for the two metals (show all calcu- lations and units): a. Proportional limit b. Yield stress at an offset strain of 0.002 in./in. 150 - - Metal A 100 • Metal B 50 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Strain, in./in. FIGURE P1.17 c. Ultimate strength d. Modulus of resilience e. Toughness f. Which metal is more ductile? Why? Stress, ksi(a) 128.5 GPa circular rod of diameter 30 mm and length 200 mm is subjected to a tensile force. The axtension of rod is 0.09 mm and change in diameter is 0.0045 mm. What is the Poisson's ratio of the material of the rod? (a) 0.35 (b) 0.33 (c) 0.32 (d) 0.30A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are ϵx = 0.40 x10-3 and ϵy = 0.30 x10-3, determine σx and σy. Use E = 110 GPa and v = 0.35.