(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. 0₁ = 16.4 ksi; o₂ = -0.061 ksi 2 in b b •B 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? 30⁰ x 180 kip 10 in. 6 in. . У 10 in. - B 0₂² (0x‚Oy,Txy, 6) = Ox+y + Ox-by cos 20 + Txy sin 20 2 2 Txy sin 20 2 Oy² (0x,Oy, Txy> 0) = 0x + Oyu Ox-y cos 20 Txy' (Ox, Oy, Try, Ⓒ) = − (Ox-Oy) sin sin 20 + 2 Z xy cos 20

(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. 0₁ = 16.4 ksi; o₂ = -0.061 ksi 2 in b b •B 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? 30⁰ x 180 kip 10 in. 6 in. . У 10 in. - B 0₂² (0x‚Oy,Txy, 6) = Ox+y + Ox-by cos 20 + Txy sin 20 2 2 Txy sin 20 2 Oy² (0x,Oy, Txy> 0) = 0x + Oyu Ox-y cos 20 Txy' (Ox, Oy, Try, Ⓒ) = − (Ox-Oy) sin sin 20 + 2 Z xy cos 20

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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Angle 1 Tyx Tyx Figure 1 Point A- x-direction stress 60MPA(compression), y-direction stress 40MPA(tension), negative shear stress 30MPA Using your assigned point determine the following for the yz-plane: a) From basic priciples determine the stresses on the plane of the indicated angle 1-30°, Show al calculations. Draw the orientation of the stress block for this scenario. b) Repeat question (a) using a Mohr circle. c) Using a Mohr circle, determine and draw the maximum stress block of the in-plane maximum shear and principle stresses. d) Determine the stresses and orientation of the stress block where the normal stress is zero. Make use of the stress transformation equations. e) Determine the values of absolute maximum shear stress and corresponding normal stress.
Given a stress state of ø, = -4 MPa, øy = 12 MPa, ty = 7 MPa ccw 1) Draw a properly oriented stress element illustrating this state of stress 2) Using Mohr's circle, find the principal stresses and directions, and show these on a stress element correctly aligned with respect to the xy coordinates. Draw another stress element to show zi and 72, find the corresponding normal stresses, and label the drawing completely. 3) Use the plane-stress transformation equations to validate your answers in part 2
Q2 The state of stress at a point of an elastic solid is given in the x-yz coordinates by: (a) Using the matrix transformation law, determine the state of stress at the same point for an element rotated about the x-axis 60° clockwise from its original position;(b) Calculate the stress invariants and write the characteristic equation for the originalstate of stress;(c) Calculate the deviatoric invariants for the original state of stress;(d) Calculate the principal stresses and the absolute maximum shear stress at the point;(e) What are the stress invariants and the characteristic equation for the transformed state of stress.
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1. This question relates to stresses due to combined loading. A shaft subjected to combined torsion and axial thrust is designed to resist a shear stress and a compressive stress as shown in Figure Q1. Using the information provided in Table Q1: Figure Q1 Txy 90 mpa ox 130 mpa a) Determine the principal stresses and show them on a sketch of a properly oriented element. b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. c) Calculate the safety factors according to the three theories (Rankine, Tresca, and Von- Mises). Take the yield strength of the material as, Oyield = 250 MPa. d) Sketch the Mohr's circle for the stressed component location and indicate the stress states, principal stresses, and maximum shear stress.
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