The state of stress shown to the left was produced by a combination of loadings on a body that is not shown. Determine the following via Mohr's circle: A) Draw Mohr's Circle for the x-y plane. B) Determine the principal stresses - All 3. C) Sketch a properly oriented differential element showing the principal stresses in the x-y plane. D) Determine the magnitude of the maximum shear stress in the x-y plane. E) Sketch a properly oriented differential element showing the maximum shear stress state in the

The state of stress shown to the left was produced by a combination of loadings on a body that is not shown. Determine the following via Mohr's circle: A) Draw Mohr's Circle for the x-y plane. B) Determine the principal stresses - All 3. C) Sketch a properly oriented differential element showing the principal stresses in the x-y plane. D) Determine the magnitude of the maximum shear stress in the x-y plane. E) Sketch a properly oriented differential element showing the maximum shear stress state 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 7.4.21P: -18 through 7.4-25 An clement in plane stress is subjected to stresses a,, ay., and axy. (see...

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-18 through 7.4-25 An clement in plane stress is subjected to stresses a,, ay., and axy. (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.
Question 2: An element in plane stress is subjected to stresses, ox = 16000 MPa, o, = 6000 MPa, and Txy = Tyx = 4000 MPa (as shown in figure below). Using the Mohr's circle, determine the following: A) The stress components with respect to ab axes which are inclined at 0 = 45° to the xy аxes. B) Locate the principal axes and evaluate principal stresses. C) Locate the axes of Maximum shear stress and evaluate the corresponding stress components. yt -9000 MPa a 5000 MPa 30° 12000 MPa Fig. Q1: An element in plane stress If the values of txy = Tyx = 0 and the element is subjected only to stresses, ox = 16000 MPa, Oy = -6000 MPa D) What are the differences of the results of A, B, and C above ? E) Discuss the differences.
The stresses acting on element A in the web of a train rail are found to be 'X (MPa)' tension in the horizontal x-direction and 'Y (MPa)' compression in the vertical y-direction. Also, shear stresses of magnitude 'S (MPa)' act in the directions shown in the figure. Draw Mohr's circle for the state of stress. Determine the stresses (Ox', Oy' and Txy') acting on an element oriented at an angle 'D' from the horizontal Show these stresses on a sketch of an element oriented at this angle X=45MPA,Y=150MPA,S=52MPA,D=-40 Degree
Determine the state of stress at point A of the rectangular post shown loaded with concentrated forces directed along the y axis equal to 75kN and along the x axis equal to 15kN. 1)Determine the total normal stress along the x and y axes at point A (include if tensile or compressive in your final solutions) 75 kN 50 mm 200 mm- 150 mm OAx= 15 kN OAy= 2) Draw the state of stress of point A 800 mm A 50 mm
2. At a point in a brocket, the stresses on two mutually perpendicular planes are 180 MN/m? (tensile) and 70 MN/m2 (Compressive). The shear stress across the planes is 65 MN/m2. Find the following by Mohr's Circle method and compare with Analytical solutions: (i)The Normal stress on a plane making an angle of 50° with the plane of first stress. (ii)Shear stress on the plane (iii) Maximum shear stress (iv) Resultant stress and it's direction. (v) Major and minor principal stresses.
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).
you can provide handwritten solution also. At a point in a material under stress, the intensity of the resultant stress on a certain plane is 60 N/mm2 (tensile) inclined 30o to normal of that plane. The stress on a plane at right angle to this has a normal tensile component ofintensity 40 N/mm2.Using the Mohr’s circle calculate, resultant stress on the second plane, the principal planes and stress, plane of maximum shear and its intensity.
(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
The state of plane stress at a point on the surface of the airplane fuselage is represented by the stress element shown in the figure. Using Mohr's Circle, determine a) the principal stresses and the maximum in-plane shear stress specifying the orientation of the element in each case. b) The equivalent state of stress at the point on the element that is oriented {a} clockwise from this position Draw all the corresponding stress elements. Given x = {x} MPa; y = {y} MPa and xy = {xy} MPa xy MPa y y MPa 10000 x MPa →→→→x Solve in terms of variables
2. The Principal stresses at a point across two perpendicular planes are 90MN/m² (tensile) and 40MN/m² (compressive). The shear stress across these planes is 25 MN/m² (counter clockwise). Find the normal, tangential and the resultant stress & its inclination on a plane making an angle of 35° with the plane of first stress.
Two forces are applied on the beam shown below. (a) Determine the normal and shear stresses at point B on the shown cross-section. (b) Show the state of stress at the point B on a volume element. 400 lb B 1 in. 2 in. 500 Ib 2 in 10 in. 1.5 in. 1.5 in. Show your steps and highlight the following answers please I =
The state of stress at a point in a soil beneath a level ground surface consists of a major principal stress of 70 kPa and a minor principal stress of 25 kPa. The major principal stress acts in the vertical direction. (a) Draw the Mohr's circle of stress and show the pole point (origin of planes). (b) Determine the maximum shear stress and calculate the orientation angle (relative to horizontal) of the plane of positive maximum shear stress. (c) Determine the normal stress and shear stress on a plane that makes an angle of -20° (i.e., 20° clockwise) relative to the horizontal plane.