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- 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.A uniaxial force was applied on the shown coupon during an experiment. The thickness, width and length of the coupon are 1mm, 20mm and 100 mm, respectively. the force applied had a magnitude of 1000N. A strain rosette was applied to the sample as shown. Strain gages a and c are perpendicular to each other. On the other hand, the angle between strain gages b and a is 30°. The strain gages reported the following strains Ea = -0.2x10-3 Ep = 0.667x10-3 Determine the elastic properties of the isotropic coupon. 30 aThe rectangular plate ABCD undergoes deformation as shown with the dashed lines. Find the average shear strain Yay at A with respect to the x and y axes. The values for the parameters are given here: parameter mm LAB 300 LAD 200 δι 2 бг 5 B y δη C LAB BY NO SA 2021 Cathy Zupke At A Yay = A LAD ↑ 82
- 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 stressesQ4 A three strain gages have been attached directly to a piston used to raise a medical chair, the strain gages give strains as Ea = 80 µ , Eb = 60 µ and Ec = 20 u . Determine the principal strains and the principal strain directions for the given set of strains. And Compute the strain in a direction -30° (clockwise) with the x axis. 45 PumpQ1 The 45° strain rosette is mounted on a steel robotic am as shown in Figure Ql. The robotic arm is made from steel with Esel = 200 GRA and poison ratio, v= 0.3. The following readings are obtained for each gauge: E=[Y+Z](10“) E = -250(10-) E= -200(10) Here the value of Y and Z depends on the 5th digit and 6th digit of your matric number as shown in Table 1. For example, if your matrix number is DD 070112 gives the value of Y=300 and Z-60: Table 1 5 digit of matric 6* digit of matric number number 250 300 350 30 2 60 3 400 3 90 4 450 120 5 500 150 6. 550 180 7 600 7 210 650 700 240 270 (a) Prove that &= E, and E, = E. Determine the shear strain, yand the normal strain, E, and &. (b) Estimate the in-plane principal strains and the angle associated with the principal strains, and (c) Calculate the principal stress associated with the prihcipal strains in (c). (d)
- The 45° strain rosette shown in figure below is mounted on the surface of a thin shell. The following readings are obtained for each gage: ea, eb, and ec. Note that e, is negative. Determine: • Shear strain yay • Principal strains e1 and e2 • The rotation angle (magnitude and direction) from x-axis to reach the principal orientation. Indicate direction as clockwise or counter-clockwise. epsilon_a = 4.50E-04 epsilon_b = 2.00E-04 epsilon_c = -1.00E-04 y а b 45° 45°The 45° strain rosette shown in figure below is mounted on the surface of a thin shell. The following readings are obtained for each gage: ea, eb, and ec .Note that Be is negative. Determine: • Shear strain yxy • Principal strains e1 and e2 · The rotation angle (magnitude and direction) from x-axis to reach the principal orientation. Indicate direction as clockwise or counter-clockwise. epsilon a = 4.50E-04 epsilon k= 2.00E-04 epsilons = -1.00E-04 %3D y а b 45° 45°5. Please calculate the strain and stress in the following two prompts a. A 1 cm long section of tendon stretches to 1.011 cm when it is subjected to a tensile force of 40,000 N. What is the strain in this segment of tendon? @? 17 b. The section of the patellar ligament in the previous question is 0.02 m² in the cross section. What is the stress in this section of ligament as a result of 50,000 N tensile force? E = Δι 19 0 = A 1.011 cm 50000 0,02 Scoco 40000 1.25 = T % 2500000 strain N/m² on trito flox your wrist, you may notice that your
- The shear stress-shear strain diagram for a material is shown. The bolt used to hold the lap joint is made of this material and has a diameter of 0.35 in. The material has a Poisson's Ratio of 0.2. T (ksi) F T1 G = Values for the figure are given in the following table. Note the figure may not be to scale. Variable T1 Y1 Value 40 ksi 0.003 rad 71 -7 (rad) a. Determine the Shear Modulus of the allow, G. b. Determine the Elastic Modulus of the allow, E. c. Determine the force required to cause the material to yield, F. Round your final answers to 3 significant digits/figures. ksiLearning Goal: To analyze an axially loaded cable on a suspension bridge and when given a specific deformation, find the normal strain in the cable and determine the shear strain at a corner of a loaded pillar when given the displacement of that corner. A tractor trailer is loaded to capacity and weighs 330 kN . Along its route, the tractor trailer travels over a suspension bridge's roadway that is supported by two pillars of height a = 16 m and numerous cables as shown below. As the fully loaded tractor trailer crosses the bridge, the cables extend slightly to caryy the load and the roadway drops Δr = 0.4 cm along the y-axis.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.