Problem 8. Re-write the strain compatibility condition in the engineering notation. e22,33 +€33,22 = 2 €23,23
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- On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses on sketches of properly oriented elements.A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?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.
- An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy = 0.0003. (a) Determine the strains for an element oriented at an angle = 20°. (b) Determine the principal strains of the element. Confirm the solution using Mohr’s circle for plane strain.A strain rosette (see figure) mounted on the surface of an automobile frame gives the following readings: gage A,310 × 10-6:gage B,180 × l0-6; and gage C. -160 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.On the free surface of a component, a strain rosette was used to obtain the following normal strain data: €a = 300µɛ, ɛp = 400µs, and Ec = 200µe. Calculate the normal and shear strains in the x-y plane.
- 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 theTensile 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.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.
- Problem F2 stress (ksi) 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 strain (in/in) Above you will find the experimental stress-strain diagram of 1045 steel. Calculate the permanent set if a cylindrical specimen with a diameter of 2 in is loaded to the ultimate stress and then unloaded. Provide your answer in units of in/in with 3 significant figures after the decimal. The elastic modulus of 1045 steel is 29,000 ksi.In our previous topic regarding strain, repeat the problem on the strain using thefollowing parameters:F = 150000 +/- 150 lbfSide length = 1.2 +/- 0.025 inModulus of Elasticity = 25000 +/- 11.5 ksiDetermine the relative error. Is it above or below the accepted 5% error?A bar BD is held in a horizontal position when there is no load by the steel wire AB. When a weight Wis added at C, also hanging from a steel wire CE, then point C is displace down by 0.025in. The cross-sectional area of the wires is 0.002in². The wires are made of a steel alloy with E = 29000ksi and σy = 70ksi. Calculate the strain in both wires, and the weight W. B A N E Parameter ft L_1 4 L_2 1 L_3 2 L_4 4 The strain in AB is € AB = The strain in CE is ECE = The weight W = 30 W cc 080 BY NO SA 2021 Cathy Zupke Xlb D in./in. in./in.