The rectangular block shown in Figure is subjected to tension within the elastic range. The increase in the length of a is 2 * 10-3in. and the contraction of b is 3.25 * 10-4 in. If the original lengths of a and b were 2 in. and 1 in., respectively, what is Poisson’s ratio for the material of the specimen?

The rectangular block shown in Figure is subjected to tension within the elastic range. The increase in the length of a is 2 * 10-3in. and the contraction of b is 3.25 * 10-4 in. If the original lengths of a and b were 2 in. and 1 in., respectively, what is Poisson’s ratio for the material of the specimen?

Steel Design (Activate Learning with these NEW titles from Engineering!)

6th Edition

ISBN:9781337094740

Author:Segui, William T.

Publisher:Segui, William T.

Chapter1: Introduction

Section: Chapter Questions

Problem 1.5.5P: The results of a tensile test are shown in Table 1.5.2. The test was performed on a metal specimen...

See similar textbooks

Similar questions

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 w = 33 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: €, =710 με and ε,--255 με (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? Answers: (a) v= (b) E= GPa
1.16 The stress-strain relationship shown in Figure P1.16 was obtained during the tensile test of an aluminum alloy specimen. 60,000 H Stress, psi 40,000 20,000 0 Figure P1.16 0.002 0.004 0.006 0.008 Strain, in./in. 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? 4
During a tension test, measurements for the applied load and the corresponding elongation are taken at frequent intervals. These data points are then used to: a. calculate the stress caused by the applied load at each data point. b. calculate the strain in the specimen induced by the applied load at each data point. c. plot a stress-strain diagram. d. all of the above
1.14 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, psi
An applied torque results in a shear strain (y) of 3.75 x 103 in a solid circular steel shaft. At this strain, a portion of the shaft cross- section yields as shown in Figure 2. Determine the magnitude of the applied torque. Take G = 80 GPa and yy = 2.8125 x %3D 10-3 FIGURE 2: Plastic zone 50 mm 200 mm Elastic core
A steel alloy specimen having a rectangular cross section of dimensions 19.1 mm x 3.1 mm (0.7520 in. × 0.1220 in.) has the stress-strain behavior shown in the Animated Figure 6.22b. If this specimen is subjected to a tensile force of 98290 N (22100 Ib;) then (a) Determine the amount of elastic strain induced. (b) Determine the amount of plastic strain induced. (c) If its original length is 610 mm, what will be its final length after this force is applied and then released? The elastic modulus for steel is 207 GPa. (a) i (b) i (c) i mm
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
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 tension test performed on a metal specimen to fracture produced the stress- strain relationship shown in Figure P1.14. Graphically determine the following (show units and all work): a. Modulus of elasticity within the linear portion. b. Yield stress at an offset strain of 0.002 in./in. c. Yield stress at an extension strain of 0.005 in/in. d. Secant modulus at a stress of 525MPA.
A tension test performed on a metal specimen to fracture produced the stress– strain relationship shown in Figure P1.14. Graphically determine the following (show units and all work): a. Modulus of elasticity within the linear portion. b. Yield stress at an offset strain of 0.002 m/m. c. Yield stress at an extension strain of 0.005 m/m. d. Secant modulus at a stress of 525 MPa. e. Tangent modulus at a stress of 525 MPa.
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.
2. A steel bar, whose cross section is 0.55 inch by 4.05 inches, was tested in tension. An axial load of P = 30,500 lb. produced a deformation of 0.105 inch over a gauge length of 2.05 inches and a decrease of 0.0075 inch in the 0.55-inch thickness of the bar. * Determine the lateral strain. Your answer Determine the axial strain. Your answer Determine the Poisson's rati v. Your answer Determine the decrease in the 4.05-in. cross-sectional dimension (in inches). * Your answer