For the flat stress state shown in the figure.Use Mohr's circle to determine (show theprocedure only with the use of geometry):a. Draw Mohr's circle indicating coordinates ofthe points that represent the given stressstate, center, radius, coordinates of the pointsthatrepresent the state the maximum andminimum normal stresses, coordinates of themaximum shear and angle of rotation fromthe stress given to the plane principal.b. Use the results of literal a to draw theelement subjected to main forces and theelement subjected to maximum shear.12 MPa19 MPаy19 MPа46 MPа46 MPа19 MPа19 MPа12 MPa

Answered: Image /qna-images/answer/dca7b1a5-e2bc-4c19-b992-8dc9c918a957.jpg

Answered: For the flat stress state shown in the…

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 7.2.19P: At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with...

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The stresses acting on an element are x= 750 psi, y= 600 psi, and xy = 400 psi. Determine the principal stresses and show them on a sketch of a properly oriented element.
-18 through 7.4-25 An clement in plane stress is subjected to stresses sx,,sy., andtxy(see figure). Using Mohr’s circle, determine (a) the principal stresses and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.
-26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and compressive stress a. If it is known that the normal stress along the diagonal t—t is ??t= -6.57 kPa, find stress ??y on element A. a
At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with t = 1400 psi and trv = —900 psi, as shown in the figure part a. The figure part b shows an inclined plane aa cut through the same point in the material but oriented at an angle ft Determine the value of the angle 6 between zero and 90° such that no normal stress acts on plane aa. Sketch a stress clement having plane aa as one of its sides and show all stresses acting on the clement
(a) Construct Mohr's circle for an element in a uniaxial state of stress (b) Use this Mohr's circle to derive the equation for the normal stress On and shear stress En on the n-face. The equations should depend on Ox and θ (c) Use the Mohr's circle to determine the planes on which the maximum shear stress acts. Sketch a properly oriented maximum-shear-stress element and indicate the normal and shear stresses acting on its faces. Ơn nt o, Note: for (b), the angle θ is between 0 and 90° and is positive
Considering the original state of stress as shown in figure below and recalling the already developed equations for normal and shear stress at an angle Ɵ c.c.w from x-axis, mathematically prove that the planes of maximum in-plane shear stress are inclined at 45o to the principal planes.
State of stress at the wall and the roof of the following circular opening bafore the excavation is (a] = |0 4. Find the induced stress components at point a. R W with respect to the given x-y coordinate systerm, and expresst them in the matrix form. b. Find the total stresses at point W, and give them in matrix form. c. Repeat (a) and (b) for the roof. d. Find the stresses oy, Ciy, and tyy at point A which is located at a radial distance twice the radius of the tunnel.
Problem 2: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 18 ksi, oy = 24 ksi, and Txy = 15 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 24 ksi бу 18 ksi 15 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the stress components Ox, Oy, and Txy on an element rotated 25° counter-clockwise from the original element shown. Label all of these quantities on the circle. (c) Show all stresses from part (b) on a properly oriented stress element. Be sure to include all stress components acting on the element.
Consider the general case of plane stress as shown. Write a computer program that will show a plot of the three Mohr’s circles for the element, and will also determine the maximum in-plane shear stress and the absolute maximumshear stress.
Assume the plane stress element shown in Fig. E3-a represents the stress a geosynthetic membrane used in a mechanically stabilized earth wall. If the reference state of stress for this element results in the Mohr’s circle plot shown in Fig. E3-b, determine: The principal stresses. The principal directions (angles to the principal planes). The maximum in-plane shear stress. It is known that the seam, which is rotated 45 deg from the vertical as shown in Fig. E3-c, will fail if subjected to a tensile stress of 25 kPa or a shear stress of 1 kPa. Determine the normal stress and shear stress acting on the seam, and state if the seam will fail due to the loading indicated.
Mohr's circle is shown for a point in a physical object that is subjected to plane stress. Each grid square is 1 MPa in size. (a) Determine the stresses o, o, and the magnitude of Tyand show them on a stress element. (b) Determine the stresses o,, Og and the magnitude of Tht and show them on a stress element that is properly rotated with respect to thex-y element. The sketch must include the magnitude of the angle between thexand n axes and an indication of the rotation direction (i.e., either clockwise or counterclockwise). Answer: (a) Ox= MPа MPa Oy= MPa Txy = (b) On= MPa MPa Ot = MPa Tnt =
Problem 1: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 25 ksi, oy = 12 ksi, and Txy = 10 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 12 ksi 5 25 ksi 10 ksi (a) Draw a complete Mohr's circle for this stress state. Clearly label the X and Y faces, the center C, and the radius R. (b) Using Mohr's circle, determine the principal stresses, the maximum in-plane shear stress, and the normal stress that acts on the maximum shear stress plane. Label all of these quantities on the circle. (c) Calculate the orientation of the principal planes and the planes of maximum shear stress. Label all of these quantities on the circle. (d) Show all stresses from part (b) on properly oriented stress element(s). Be sure to include all stress components acting on the elements(s).

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