A 5-mm-thick rectangular alloy bar is subjected to ajtensile load P by pins at A and B, as shown in the figure. The width of the bar is 33 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: €, = He and e, - - 255 µe. (a) Determine Poisson's ratio for this specimen. (b) If the measured strains were produced by an axial load of P = 24 kN, what is the modulus of elasticity for this specimen? B Answers: (a) v= (b) E= GPa
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- Consider a cylindrical metal 6 mm in diameter and 50 mm long ispulled in tension. It is known that yield strength and elastic (Young’s) Modulus of thematerial are 200 MPa and 100 GPa, respectively, and its Poisson’s Ratio is 0.3.(a) Determine whether the deformation is elastic or plastic when 6000 N is applied.(b) Calculate specimen elongation (∆l) and reduction in diameter (∆d) when 5000 N isapplied? What are the values ∆l and ∆d when the load is released?(c) If necking occurs at a load of 8850 N, determine the UTS of the metal.(d) Calculate the ductility in terms of % E.L. if the length of the specimen at fracturepoint is 56.0 mm.The (G-E) diagram obtained in the tensile test performed on a metal sample with a diameter of 16 mm is as follows. The loads at points A, B and C and the elongation measured on l. 16 cm gauge length were determined as follows: B A B C Load (kgf) 4800 8400 7200 Elongation (mm) 0.192 28.8 38.4 c) Calculate the fracture work and the maximum elastic energy the metal rod can store. d) Find the cross-sectional area of a 6 m long rod made of this metal such that it can carry 12 tons of load with 2 times the safety of yield strength. How long does the rod extend under this load?An aluminium specimen with an initial gauge diameter d, = 10 mm and gauge length, 1, = 100 mm is %3D subjected to tension test. A tensile force P= 50 kN is applied at the ends of the specimen as shown, resulting in an elongation of 1 mm in gauge length. The Poisson's ratio (µ) of the specimen is Take shear modulus of material, G = 25 GPa. Consider engineering stress-strain conditions. P
- The elastic portion of the tension stress-strain diagram for an aluminum alloy is shown in the figure. The specimen used for the test has a gauge length of 2 in. and a diameter of 0.5 in. If the applied load is 10 kip, determine the new diameter of the specimen. The shear modulus is G al =3.811032 ksi1.14 The stress-strain relation shown in Figure P1.14 was obtained during the ten- sile test of an aluminum alloy specimen. 60,000 40,000 20,000 0.002 0.004 0.006 0.008 Strain, in./in. FIGURE P1.14 Determine the following: a. Young's modulus within the linear portion b. Tangent modulus at a stress of 45,000 psi c. Yield stress using an offset of 0.002 strain d. If the yield stress in part c is considered failure stress, what is the maximum working stress to be applied to this material if a factor of safety of 1.5 is used? Stress, psiIn a tensile test on a metal specimen having a cross section 20 mm by 10 mm elastic breakdown occurred at a load of 70 000 N. A thin plate madec from the same material is to be subjected to loading such that at a certain point in the plate the stresses are o,=-70 N/mm², 7.y= 60 N/mm² and o. Determine the maximum allowable values of o, using the Tresca and von Mises theories of elastic breakdown. Ans. 259 N/mm² (Tresca), 294 N/mm² (von Mises).
- A metal sample on a tension in the test ,296MPa , a tensile true strain 0.08, and true stress 356 MPa when the strain is 0.27. Determine the strength coefficient and strain hardening exponent in the flow curve equation.Q.1 The yield stresses (oy) have been measured using steel and aluminum specimens of various grain sizes, as follows: Material D (µm) σΥ (MPa) Steel 60.5 160 136 128 Aluminum 11.1 235 100 223 (a) Determine the coefficients o and kỵ in the Hall- Petch for these two materials. (b) Determine the yield stress in each material for a grain size of d=26 um.The specimen shown is made from a 25 mm diameter cylindrical steel rod with two 38 mm outer-diameter sleeves bonded to the rod as shown. Knowing that E = 200 GPa, determine (a) the load P so that the total deformation is 0.05 mm, (b) the corresponding deformation of the central portion BC. 38 mm diameter P' 25 mm diameter B 38 mm diameter C 50 mm 75 mm 50 mm
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