The state of stress at a point is σ = -4.00 kpsi, σy = 16.00 kpsi, σ = -14.00 kpsi, Try = 11.00 kpsi,Tyz = 8.000 kpsi, and T = -14.00 kpsi.Determine the principal stresses.The principal normal stress σ₁ is determined to be [The principal normal stress σ2 is determined to be [The principal normal stress σ3 is determined to bekpsi.kpsi.The principal shear stress 71/2 is determined to be [The principal shear stress 7½ is determined to be [The principal shear stress T₁/, is determined to be [kpsi.kpsi.kpsi.kpsi.

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Answered: The state of stress at a point is σ =…

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 7.2.21P: An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec...

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For each of the plane stress states listed below, draw a Mohr's circle. Find the principal normal and shear stresses and determine the angle from the x-axis to σ1. = (a) σx -8 MPa, σy = 7 MPa, Txy = 6 MPa cw (b) σx = 9 MPa, σy = −6 MPa, Txy = 3 MPa cw (c) σx = −4 MPa, σy = 12 MPa, Txy = 7 MPa ccw
A state of stress at a point A is given by σx = -75 MPa, σy = 122 MPa, and τxy = -3.75 MPa. Which of the following is one of the principal stresses for the point A.
At a point in the cross-section of an engineering component an element is subject to the following stresses: σx =100MPa σy =45MPa τxy = -50MPa Construct a Mohr’s Stress Circle and hence determine: (a) The Principal Stresses (σ1 & σ2) and the Directions of the Principal Planes (φ1 & φ2) (b) The Maximum Shear Stress (τmax) (c) Find the Normal Stress (σn) acting on a plane at 40 degs anticlockwise from the y-axis
A plane stress state is given by the principal stresses σx =25 MPa and σy= -11 MPa. Determine σx' in the case that the system is inclined by 30 degrees (counter-clockwise). Give your answer in MPa to the nearest whole number.
A point on a thin plate is subjected to two successive states of stress. The stresses have magnitude σx | = 31.5 MPa, |σy' | = 45.5 MPa, and |Tx'y' | = 20.5 MPa. 0x , Oy, Txy || = Determine the resulting state of stress on the element on the right. The rotation angles on the left-hand side of the figure are in relation to the orientation of the element on the right. Express your answers, separated by commas, to three significant figures. View Available Hint(s) 1977| ΑΣΦ | 11 VE 60° vec 220% ? Txy MPa, MPa, MPa ·0x
For the plane-stress condition given below: σx = 400 MPa σy = 500 MPa τxy = - 30 MPa Construct a Mohr’s circle of stress, find: (a) the principal stresses and the orientation of the principal axes relative to the x,y axes (b) determine the stresses on an element, rotated in the x-y plane 60° counter?clockwise from its original position ; Show these stresses on a sketch of an element oriented at this angle (c) Also, using the matrix transformation law to compare the solutions with Mohr’s circle
The state of plane stress at a point is represented on the element shown in the figure below. (a) Determine the principal stresses acting on this point, and the corresponding orientation (angle). (b) Determine the maximum in-plane shear stress, and the corresponding orientation (angle). Also determine the associated average normal stress. Draw Mohr's circle and show the stresses on the circle. 15 ksi 23 ksi 14 ksi
Problem 2: For the plane stress state listed below, draw a Mohr's circle diagram properly labeled. Keep in mind that the principal stress is that stress state where the shear stress is zero. That means it is the stress state along the normal stress line in Mohr's space. So, use your Mohr's circle to find the principal normal and shear stresses, and determine the angle from the x axis to o1. 0x = 20 kpsi, oy =-10 kpsi, Txy = 8 kpsi cw
Problem 3: For the plane stress state listed below, draw a Mohr's circle diagram properly labeled. Keep in mind that the principal stress is that stress state where the shear stress is zero. That means it is the stress state along the normal stress line in Mohr's space. So, use your Mohr's circle to find the principal normal and shear stresses, and determine the angle from the x axis to o1. 0x = 16 kpsi, oy = 9 kpsi, Ty = 5 kpsi ccw
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1) Determine the principal stresses. 2) Specify the orientation of the element
At a point in a stressed body, the cartesian components of stress are sigma xx = 60 MPa, sigma yy= -40 MPa, sigma zz = 20 MPa, tau xy = -40 MPa, tau yz = 20 MPa, and tau zx= 30 MPa. Determine: (a) 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

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