In the case of plane stress, where the in-plane principal strains are given by
where v is Poisson’s ratio for the material.
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Statics and Mechanics of Materials (5th Edition)
- 2. A sheet of copper is stretched biaxially in the xy-plane. If the strains in the sheet are 0.40 x 10 - in the x direction and 0.30 x 10 in the y direction, determine the stresses in the x and y direction. Also, determine the strain in the z direction. The modulus of elastic and Poisson's ratio of copper is 110 GPa and 0.35 respectively. 3. If the copper in no. 2 is changed into steel with the same dimensions and with a modulus of elasticity of 200 GPa and a Poisson's ratio of 0.30, determine the strains in all direction if the same stresses in no. 2 where to be applied to the steel. €, E,arrow_forwardThe state of plane strain on an element is represented by the following components: Ex =D340 x 10-6, ɛ, = , yxy Ey =D110 x 10-6, 3D180 x10-6 ху Draw Mohr's circle to represent this state of strain. Use Mohrs circle to obtain the principal strains and principal plane.arrow_forward1. Find the relationships between strain components in the polar coordinate and strain components in the rectangular coordinate.arrow_forward
- The rigid bar AB is supported by a pin at A and by the wire BD. 2,5 m If the load P causes point C to move 8 mm to the left, determine the normal strain in the wire. 3,5 m D 4.0 marrow_forwardIf the in-plane principal strains are of opposite signs, then theabsolute maximum shear strain equals the maximum in-plane. True or false?arrow_forwardQ.4) By using the strain rosette shown in figure below, we obtained the following normal strain data at a point on the surface of a machine part made of steel [E = 207 GPa, v= 0.29]: ε-770 μ, E = 520 µ, & = - 435 µ (a) Determine the strain components &, &, and %y at the point. (b) Determine the principal strains and the maximum in-plane shear strain at the point using Mohr's circle. (c) Draw a sketch showing the angle Op, the principal strain deformations, and the maximum in-plane shear strain distortions. (d) Determine the magnitude of the absolute maximum shear strain. b ' 60°| 60°arrow_forward
- Your answer is partially correct. The strain components for a point in a body subjected to plane strain are ɛ, = -890 µɛ, ɛ, = -690µɛ and yy = -682 prad. Using Mohr's circle, determine the principal strains (ɛp1 > Ep2), the maximum inplane shear strain yip, and the absolute maximum shear strain ymax at the point. Show the angle 0, (counterclockwise is positive, clockwise is negative), the principal strain deformations, and the maximum in-plane shear strain distortion in a sketch. Answers: Ep1 = 927.99 με. Ep2 = 1116.0 PE. Vip = 188.01 prad. Ymax = -188.01 prad. Op = 36.82arrow_forwardThe strain at point A on the bracket has components P x = 300(10-6 ), Py = 550(10-6 ), gxy = -650(10-6 ), P z = 0. Determine (a) the principal strains at A in the x9y plane, (b) the maximum shear strain in the x–y plane, and (c) the absolute maximum shear strain.arrow_forwardAsaparrow_forward
- 1. The following state of strain has been determined on the surface of a cast-iron machine part: =- 720, =- 400, = 660 Knowing that E = 69 GPa and G = 28 GPa, determine the principal stresses using the following approaches: by determining the corresponding state of plane stress, and further using Mohr's circle for stress ii. by using Mohr's circle for strain to determine the orientation and magnitude of the principal strains, and further define the corresponding stressesarrow_forwardThe rigid body ABC is connected by two links and is exerted by force P as shown aside. If the normal strain in link BE is 0.5x10°, the normal strain in link AD is: -3 D E A 2 m PV 1 m Select one: -3 a. 4.5×10 b. 1.5x10° c. 1.0×10 -3 d. 3.0×10 -3 e. 0.75x10 f. None 3 m 1.5 m.arrow_forwardA sheet of steel is stretched biaxially in the xy-plane. The strains in the sheet are described below. Determine the stresses along the x and y axes. Use E=200 GPa and v=0.28 Ex = 0.4 x 10‐³ Ey = 0.3 x 10‐³arrow_forward
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning