2.28 For the plane stress state shown:(a) Determine the principal stresses and show them on a properly orientedelement. For this part, use the transformation equations only and notMohr's circle(b) Repeat part (a) using Mohr's circle.(c) Determine the maximum shear stress and show the complete state ofstress on a properly oriented element containing this maximum shearstress.y25 kpsi15 kpsi12 kpsi1Problem 2.28 08CHAPTER 2STRESS AND STRAIN2.29 For Problem 2.28 determine the directional cosines for the surfaces contain-ing the maximum and minimum shear stresses.

a) Calculate the principle stress using stress transformation equation:

Answered: 2.28 For the plane stress state shown:…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The state of stress in a machine element is illustrated in the stress element as shown in Figure 4: (a) (b) 250 MPa Figure 4 By calculations ie using equations or formulae find the following: The principal stress. 400 MPa 560 MPa The normal and shear stresses on a plane inclined at 30° CW. L.
The stresses at a given point in a stressed body relative to rectangular axes are ox=20, y = -40, o₂ = 30 Txy = 15, Txx = -32, Tyz = 24 (in units of ksi) Compute the normal and maximum shear stresses on a plane through the point whose normal makes angles 45° with the x-axis and 72° with the y-axis.
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=600 psi, Sy = 2900 psi, and S 790 psi. (a) Draw Mohr's circle for this state of stress. (b) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (c) Show these stresses on an appropriate sketch (e.g, see Fig. 12.15 or Fig. 12.16) (d) Determine the absolute maximum shear stress at the point. Sy Part 1 Calculate the average normal stress and determine the radius of Mohr's Circle. Then draw Mohr's Circle for this state of stress. Answer: psi R = psi
Please show all steps
Q5: At a point in a strained material the stresses acting on planes at right angles to each other are o, 30, MN/m² tensile, together with associated shear stresses which assumed clockwise in effect on oy plane. If the maximum principal stress is limited to 1002 MN/m² tensile, and xy-60 MN/m², calculate: (a) the magnitude of the o, and oy; (b) the values of the maximum and minimum principal stresses; (c) the directions of the principal planes; (d) the maximum shear stress.
(a) Figure 1.1 shows a thick cylinder with inside radius of r;=94 mm and outside radius ro =136 mm was pressurized internally Pi = 56 MPa and externally Po= 26 MPa. Analyse: i. The hoop stress and radial stress on internal and external surface of the cylinder. ii. The hoop stress and radial stress at r= 115 mm. iii. The maximum and minimum shearing stress. iv. Sketch the distribution of hoop stress and radial stress along the cylinder wall. Po Figure 1.1 The thick cylinder
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The state of stress at a point in a structural member is given by = 0x = Ax² + By², ay = Cy² + Dz², oz Ez² + Fx² Txy = Gy + Hz, Txz = Iz + Jx, Tyz = Kx + Ly where A, B,..., L are constants. Find expressions of the body forces to ensure the equi- librium. Units of the stresses are MPa.
Calculate the principal stresses to the given state. Calculate the angle of rotation in the x-y plane. Calculate the extreme shear stresses. Are the extreme shear stresses the maximum shear stresses? Explain, Why or why not?
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1. For the two cases i.e. (a) 2D and (b) 3D shown below, find the principal stresses, maximum shear stresses and directions by using Mohr’s circle. Support your answers with diagrams. 41 GOMPa 60MPR Txy=40MPA 40MPA (a) (b)

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