4. For a state of biaxial strain (ε biax) in a linear-elastic isotropic material, what are the corresponding stresses? How would this change if the Poisson's ratio was zero? Briefly explain why. Assume standard material constants E, v, λ, etc. Γε Ebiax=0 01 bod 000 0 LO 0 0
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- Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight (units of in ) that can be stored in each or the materials listed in the accompanying table, assuming that the material is stressed to the proportional limit. DATA FOR PROBLEM 2.7-5 Material Weight Density (lb/in3) Modulus of Elasticity (ksi) Proportional Limit (psi) Mild sleel 0.284 30,000 36,000 Tool steel 0.284 30,000 75,000 Aluminum 0.0984 10,500 60,000 Rubber (soft) 0.0405 0.300 300In 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?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.
- Exercise 2 : For the constant strain triangular shown in figure 2. Determine the strain-displacement matrix [B]. Take t=20 mm, E=2x10° N/mm2 K(200,400) I(100,100) J(400,100) Fig.2Gerilme-Şekil Değiştirme Diyagramı = Stress-Strain DiagramThe diameter (d) of a solid rod (i.e., with a circular cross-section) is 16 mm and is made from a homogeneous material. The length (L) of the rod is 1.75 m and Young’s Modulus for the material (E) is 250 GPa. When the rod is placed under tension it experiences deformation and a stress (?) of 650 MPa. Calculate the following:(1) Strain energy (U) to 2 decimal places in Joules.(2) Strain energy per unit volume (U/V) in J/m3(3) The change in length ∆L to 2 decimal places in mm.(4) The strain (?) due to deformation to 2 significant figures. (show all work)
- The relationship between true strain (ɛ-) and engineering strain (ɛ) in a uniaxial tension test is given as (a) & = In (1 + &7) (c) &7= In (1+ E) (b) ɛg = In (1- E) (d)= in (1- E) %3D %3DProblem 4 The attached figure shows, for a gray cast iron, the tensile engineering stress-strain curve in the elastic region. Determine (a) the tangent modulus at 25 MPa and (b) the secant modulus taken to 35 MPa. Stress (MPa) 60 50 40 30 20 10 0.0002 0.0004 Strain 0.0006 T 8 6 ★ 2 0.0008 Stress (10³ psi)You must perform mechanical tests with a linear elastic material (the material follows Hooke's law) applying forces (tension) in the range 0 to Fmax/2 for Sample A and between 0 to Fmax for Sample B. The samples are made of same material but have different geometries (see illustration). (a) Which of the two samples receives the maximum stress (σmax)? (b) Which of the two samples will have the larger length change (ΔLmax)? (c) Plot the expected curves for the two samples in the force-length and stress-strain planes. (d) Clearly indicate the values that the variables force, length, stress, and strain take at the beginning and end of each curve.
- material with a rectangular cross-section of 4 mm by 25 mm is loaded in tension with a force of 32 kN. A strain gauge bonded to the material measures a strain of 400 microstrain when the sample is loaded. culate Young's modulus of the material, measured to the nearest GPa (GN/m2) and enter your answer in the box below. ung's modulus: [ GPaA body is subjected to uniaxial tensile stress of 20 MPa in the y-direction as well as a temperature decrease of 10 degrees K. The material's elastic modulus is 90 GPa, the Poisson's ratio is 0.20, and the coefficient of thermal expansion is 12E-6 per degree K. What are the normal strains in the x, y, and z directions (microstrain units) ? Exx –102, ɛyy = 51, Ezz 82 -164, ɛ yy -164, Exx %3D Ezz -164 -164, E yy 102, Exx = Ezz = -164 164, E yy - -102, ExxQuestion 2 A material with the given stress-strain curves is loaded in tension. Loading process COMPLETELY STOPS at B. When stress is 700 MPa and during the Re-load process, Find: 1. The longitudinal and lateral strain 2. Change in diameter a (MPa) 1000 800 dy= 600 300 150 D. 0.02 0.03 0.04 0.023 e(mm/mm) 0.01 €y = 0.006 7 MPa 90 80 70 60 50 40 30 20 10 T = 73 Oy =0.0013 = 0.54 0.73 Y (rad) Yu