Example 4 If ox 80 MPa, oy = 0 MPa, and Txy = 50 MPa (cw), a) 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 T₁ and T₂, find the corresponding normal stresses, and label the drawing completely b) Repeat part a using the transformation equations only =

Example 4 If ox 80 MPa, oy = 0 MPa, and Txy = 50 MPa (cw), a) 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 T₁ and T₂, find the corresponding normal stresses, and label the drawing completely b) Repeat part a using the transformation equations only =

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 7.5.5P: Assume that the normal strains x and y , for an clement in plane stress (see figure) are measured...

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During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa and txy= 33 MPa (sec figure). What is the allowable range of values for the stress if the maximum shear stress is limited to = 37 MPa?
The normal and shear stresses acting on element A are 6500 psi, 17,300 psi, and 2900 psi (see the figure b for Problem 7.2-5). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element.
Assume that the normal strains x and y , for an clement in plane stress (see figure) are measured with strain gages. (a) Obtain a formula for the normal strain x in the : direction in terms x , y and Poisson’s ratio v. (b) Obtain a formula for the dilatation L’ in terms of x , y and Poisson’s ratio v.
For each of the plane stress states listed below, draw a Mohr's circle diagram properly labeled, find the principal normal and shear stresses, and determine the angle from the r axis to of. Draw stress elements as in Figure 3-11c and d and label all details. a.) sigma,x = - 12 kpsi, sigma,y = 22 kpsi, txy = 12 kpsi cw b.) sigma,x = 30 kpsi, sigma,y = -10 kpsi, txy = 10 kpsi ccw c.) sigma,x = -10 kpsi, sigma,y = 18 kpsi, txy = 9 kpsi cw Attached is an image of Figure 3-11c and d for example. THIS IS THE ONLY INFORMATION I AM PROVIDED WITH! Thank you for the help in advance!
What are the equation used for part a)? for the axial stress, why do we not use Axial Stress = Pr/(2t)? Also, the math for the pricipal stresses is incorrect.
For the flat stress state shown in the figure. Use Mohr's circle to determine (show the procedure only with the use of geometry): a. Draw Mohr's circle indicating coordinates of the points that represent the given stress state, center, radius, coordinates of the points that represent the state the maximum and minimum normal stresses, coordinates of the maximum shear and angle of rotation from the stress given to the plane principal. b. Use the results of literal a to draw the element subjected to main forces and the element subjected to maximum shear. 12 MPa 19 MPа y 19 MPа 46 MPа 46 MPа 19 MPа 19 MPа 12 MPa
.An element in the boiler is triaxially stressed, the stresses distribution is given by (see Figure 1). Oxx = 75 MPa; on = 60 MPa; 0 = 50 MPa; Try = 25 MPa; tyz = - 25 MPa; ta = 0 MPa. determine the components of this stress state on a x'y' z' coordinate axes system described by the following direction cosines. y 2/3 -2/3 -1/3 2/3 1/3 2/3 -1/3 -2/3 2/3 y' Compute also the magnitudes and directions of the principal stresses. 60 MPa 25 MPа 75 MPa 50 MPa 25 MPа Figure 1
P4 p 11:17 3G A1ZM.pdf > Q)The state of plane stress at a point is represented by the stress element below: A. Draw the Mohr's Circle. B. Determine the principle stresses and draw the corresponding stress elements. C. Determine the maximum shear stress and draw the corresponding stress element. D. Find the stresses on an element inclined at 30° clockwise and draw the corresponding stress element. E. Provide a table illustrating the stress values as well as the inclination angles and compare the obtained values from Mohr's Circle with those obtained from equations 60 MPa 50 MPa 30 МРа ...
At point O of a part subjected to plane stress made of steel material (E = 210 GPa and %3D ww v= 0.3) The tensile components are given below. 240 %3D - 30 MPa *yz yz a) The principal stress components (01, 02 and o3) and their angles with respect to the x-y-z axes of the planes where they are formed calculate b) Calculate the maximum shear stress (tmax) and the angles of the plane in which it is formed with respect to the x-y-z axes. c) Drawthe 2-D and 3-D Mohr circles for the stress components. d) At point O in a section plane passing through point O and having an angle of 30° counterclockwise with the +x-axis Calculate the resulting stress components. e) Calculate the strain components (Exx, EW, Ezz, YXV, YXz and Yyz) and draw the 2-D and 3-D Mohr circles for the strain components.
1. Given a combination of stresses on an element shown in the figure, (a) draw a Mohr's circle representing the complete state of stress of the element, i.e. show prinicpal stresses (01,02), maximum shear stresses (Tmax), principal direction (0p), original orientation, and original stresses (Ox, Oy, Txy). (b) draw three-dimensional Mohr's circles showing the three principal stresses and absolute maximum shear stress. Oy = -50 MPa Txy 20 MPa Ox = -150 MPa
The state of stress at a point in a loaded solid is given as [5 0 2 [0]=|0 0 0 MPa 20 -5 (a) Calculate the principal stresses (b) Plot the Mohr's circles for this point and calculate the maximum shear stress (c) Determine the principal directions only for the largest principal stress.