Consider the plane stress element shown inrepresenting the state of stress at a materialpoint. If the magnitudes of the stresses aresuch that ox210 Pa, oy = 110 Pa, and= -Txy = 70 Pa, calculate the magnitudes ofprincipal stresses oj and 02, and themaximum shear stress, Tmax, generated at%3Dthis material point. (a) Record here the thepositive of the two principle stresses.(b) Record here the the negative of the twoprinciple stresses.(c) Record here the the maximum shearstress.TyzOy

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Consider the plane stress element shown in representing the state of stress at a material point. If the magnitudes of the stresses are such that ox = - 210 Pa, oy = 110 Pa, and Txy = 70 Pa, calculate the magnitudes of principal stresses ơ1 and o2, and the

Consider the plane stress element shown in representing the state of stress at a material point. If the magnitudes of the stresses are such that ox = - 210 Pa, oy = 110 Pa, and Txy = 70 Pa, calculate the magnitudes of principal stresses ơ1 and o2, and the

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.15P: A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded...

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A brass plate with a modulus of elastici ty E = 16 X 106 psi and Poisson’s ratio a = 0.34 is loaded in biaxial stress by normal stresses r and cry. (sec figure). A strain gage is bonded to the plate at an angle 4 = 350 If the stress o is 10,700 psi and the strain means used by the gageise = 390 X 106.whatisthcmax- imum in-plane shear stress (Tr, ),. and shear strain (>‘ ).? What is the maximum shear strain (y ) in the x-: plane? What is the maximum shear strain (y ).. in the y-r plane?
At a point in a stressed body, the cartesian components of stress are Oxx = 60 MPa, Guy = -40 MPa, Ozz = 20 MPa, Txy = -40 MPa, Tyz = 20 MPa, and Txz = 30 MPa. Determine: (a) The principle stresses and their direction cosines. (b) The normal and shear stresses on a plane whose outer normal has the following direction cosines: cos (n,x) = 0.429; cos (n, y) = 0.514; cos (n, z) = 0.743
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are S,-21 ksi, Sy=9 ksi, and Swy= 24 ksi. (a) Draw Mohr's circle for this state of stress. (b) Determine the principal stresses (op > op2) and the maximum in-plane shear stress Tmax acting at the point. (c) Find the smallest rotation angle 0, (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g, see Figure 12.15 or Figure 12.16) S. Answers: Opl = ksi. Op2 = ksi. Tmax = ksi. %3D
Consider the following plane stress state: Ox= -4 MPa, oy= 12 MPa, Txy=7 MPa ccw Calculate the following: 1. The coordinates of the center of the Mohr's circle C The location of the center of the Mohr's circle Cis MPа, MPa). 2. Principal normal stresses (01, 02) The principal normal stresses are o1 = MPa and o2 = MPа. 3. Maximum shear stress (T) The maximum shear stress is MPа. 4. The angle from the x axis to o1 (Pp) The angle from the x axis to o1 (Pp) is (Click to select) v 5. The angle from the x axis to 7 (s) The angle from the x axis to 7 (Ps) is (Click to select) v 6. The radius of the Mohr's circle The radius of the Mohr's circle is MPa. Prev 1 of 2 Next >
Q. 1 Find minimum and maximum normal and normal stresses for the plane stress systems as shown below, (a) Using analytical method, (b) using Mohr's circle method and depict the planes on which these stresses act. [Ans. 1,2 = 53.23N/mm², -73.2N/mm², 18.4°, 198.4⁰] 50 70 70 20 50
Consider the 2-D state of stress shown below. Using the provided scales graph the Mohr's Circle for the 2-D state of stress with "full' details Draw the Planes of Principal and Maximum Shear Stresses Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw → S Txy= -5 ksi Ox = 10 Ksi Tyx = 5 Ksi 10 5 -20 -10 5 10 15 20 5 10 Tccw → S'
(4) Construct Mohr's Circle for the state of stress at Point B. Use the Mohr's Circle to construct a stress element (rotated properly) that illustrates the principal stresses at Point B. Ans. ₁16.4 ksi; o₂ = -0.061 ksi ау 2 in bi 5'-0" (5) Check your work on the prior problem by plugging into the stress transformation equations. Remember: these are best done as one, fluid calculator operation. Did you get the same answer? 0 30 x 180 kip 10 in. Oy² (0x,Oy, Txy, 6) = 0x + Oy 2 6 in. . У 0₂-Oy cos 20 2 10 in. B O₂² (√x,Oy,Txy,0) = 0x10 + 0x-O cos 20 + Txy sin 20 2 2 Txy sin 20 - Z - Txy³ (0x, Oy, Txy,0) = − (Ox-Oy) sin 20 + Txy cos 20 2
Consider the following plane stress state: Ox=30 MPa, y= -60 MPa, Txy= 30 MPa cw Calculate the following: 1. The coordinates of the center of the Mohr's circle C The location of the center of the Mohr's circle Cis ( 2. Principal normal stresses (01, 02) The principal normal stresses are σ₁ = 39.08 3. Maximum shear stress (7) The maximum shear stress is 54.08 MPa. 4. The angle from the x axis to 0₁ (p) The angle from the x axis to 0₁ (p) is -16.85 5. The angle from the x axis to 7 (s) The angle from the x axis to T (s) is 28.15 6. The radius of the Mohr's circle The radius of the Mohr's circle is 54.08. ✰ MPa. MPa and 02 = -69.08 MPa. O -15 MPa, CW CCW O MPa).
Consider the 2-D state of stress shown below. Using the provided scales graph the Mohr's Circle for the 2-D state of stress with “full" details II-Obtain the Principal Stresses, the Maximum Shear Stress, and complete the table below III- Draw the Planes of Principal and Maximum Shear Stresses in the space provided below Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw > S y Ox =10 Ksi Тух 5 Ksi 10 5 -20 -15 -10 5 10 15 20 5 10 Tccw > S' O Avg. TMax. 01 02 Op1
Q-1 Figure Q-1, below, shows Mohr's cirde for a point in a physical object that is subjected to plane stress. (a) Determine the stresses Ox, Oy, and Txy, and show them on a stress element, properly orientedwith reference tox-y axes. (b) Determine the principal stresses o1, 02, and Tmax and show them on a stress element properly rotated with respect to the x-y element (c) Determine the stresses ơn, Ot and Trt, and show them on a stress element that is properly rotated with respect to the x-y element The sketches must indude the magnitude of the angles w.rt. positive x-axis as well as the angle between the x and n axes, and an indication of the direction of rotations (1.e., either clockwise (c.w.) or counterdockwise (c.C.w.)). 1 grid square 3 MPa
2. At a point in a brocket, the stresses on two mutually perpendicular planes are 180 MN/m? (tensile) and 70 MN/m2 (Compressive). The shear stress across the planes is 65 MN/m2. Find the following by Mohr's Circle method and compare with Analytical solutions: (i)The Normal stress on a plane making an angle of 50° with the plane of first stress. (ii)Shear stress on the plane (iii) Maximum shear stress (iv) Resultant stress and it's direction. (v) Major and minor principal stresses.
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx= 39 MPa, S, = 56 MPa, and Sy = 41 MPa. (a) Draw Mohr's circle for this state of stress. (b) Determine the principal stresses (op1 > op2) and the maximum in-plane shear stress Tmax acting at the point. (c) Find the smallest rotation angle 0, (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16) Sy Sx Answers: Opl = i MPa. On2 = i MPа. Tmax = i MPa. Op i