2.2. The stress at a point is defined by the components Oxy =7 ksi, oyy=10 ksi, Ory =-20 ksi. Sketch the corresponding Mohr's circle and hence find the maximum n-plane shear stress and the orientation of the planes on which it acts. Illustrate your answer with a sketch of an appropriately rotated rectangular element, taking care to ndicate the correct direction for the shear stress on these planes.

2.2. The stress at a point is defined by the components Oxy =7 ksi, oyy=10 ksi, Ory =-20 ksi. Sketch the corresponding Mohr's circle and hence find the maximum n-plane shear stress and the orientation of the planes on which it acts. Illustrate your answer with a sketch of an appropriately rotated rectangular element, taking care to ndicate the correct direction for the shear stress on these planes.

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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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

Question

2.2. The stress at a point is defined by the components Ox=7 ksi, Oyy=10 ksi, ơxy
-20 ksi. Sketch the corresponding Mohr's circle and hence find the maximum
Oyx
in-plane shear stress and the orientation of the planes on which it acts. Illustrate your
answer with a sketch of an appropriately rotated rectangular element, taking care to
indicate the correct direction for the shear stress on these planes.

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4. For an element subjected to stresses of x= 70 ksi y=-15 ksi xy=30 ksi SAH: (a) Draw Mohr's circle (b) Calculate the value of the principal stresses
I have been having trouble on this problem for a while how do I solve it?
For the stress state: Oz = 30 ksi, oy = 40 ksi, Try = -10 ksi a. Find the principal stresses and draw the stress element in the principal orientation. b. Find the maximum in plane shear stress and draw the stress element in the maximum in plane shear orientation.
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A state of plane stress is illustrated in the stress element in Figure 3. (a) (b) 30 MPa Figure 3. 40 MPa 60 MPa y X Find the center, X and Y of the Mohr circle. Plot the Mohr circle using these points. From the Mohr circle, find the principal stress and the maximum shear stress. Indicate on the Mohr circle where these values are found.
Using Mohr's Circle, solve Review problem R9-5 in the 10th Ed. of the text. Plot your solution along with notation of the axes and all the values below on graph paper. Show your calculation for the values below. 1. Find the Principal Stresses, and the orientation of the element at the those stresses 2. Find the maximum in plane shear stress, and the orientation of the element at that stress 3. Find the absolute maximum in plane shear stress 4. Find the normal stresses and shear stress when the element is rotated 30 degrees counterclockwise 30 ksi 10 ksi R9-5
a. At a point in a given material the three dimensional state of stress is given by ox = oy oz = 10 MPa ,Txy F 20 MPa, tyz = 10 MPa. Compute the principle planes if the 37.3 MPa, o2 %3D TXZ %3D corresponding principles stresses are, ol 10MPA, o3 = 2.7 MPa %3D %3D
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2.7. The principal stresses at a given point are ơj =10 MPa, ơ2=-100 MPa. Sketch Mohr's circle for this state of stress and determine the normal stress on a plane in- clined at an angle 0 to the principal plane 1. Hence find the range of values of 0 for which the normal stress is tensile.
Q-1 Figure Q-1, below, shows Mohr’s circle for a point in a physical object that is subjected to plane stress. Determine the stresses σx, σy, and τxy, and show them on a stress element, properly oriented with reference to x-y axes. Determine the principal stresses σ1, σ2, and τmax and show them on a stress element properly rotated with respect to the x–y element Determine the stresses σn, σt, and τnt, and show them on a stress element that is properly rotated with respect to the x–y The sketches must include the magnitude of the angles w.r.t. positive x-axis as well as the angle between the x and n axes, and an indication of the direction of rotations (i.e., either clockwise (c.w.) or counterclockwise (c.c.w.)).
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).