4 ksi The state of plane stress at a point is shown on the element. (a) Draw Mohr's circle neatly to scale, and use it to complete parts (b) and (c). -20 ksi (b) Determine the principal stresses, and sketch them on a prop- erly oriented element. 9 ksi (c) Determine the maximum in-plane shear stress and average normal stress, and sketch them on a properly oriented element. -20 -10 o (ksi) -30 -20 -10 10 20 30 10 20 T (ksi)

4 ksi The state of plane stress at a point is shown on the element. (a) Draw Mohr's circle neatly to scale, and use it to complete parts (b) and (c). -20 ksi (b) Determine the principal stresses, and sketch them on a prop- erly oriented element. 9 ksi (c) Determine the maximum in-plane shear stress and average normal stress, and sketch them on a properly oriented element. -20 -10 o (ksi) -30 -20 -10 10 20 30 10 20 T (ksi)

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 7.2.26P: -26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and...

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A structural member is subjected to the plane stress condition. The state of stress at a point of the member is shown in the figure. 45 MP (1) Draw the Mohr's circle for this 2D state of stress. (2) Determine the principal stresses, the maximum in-plane shear stresses and associated normal stresses acting at this point, (3) Represent these critical stresses on new stress elements, and indicate the angles of rotation of the new stress elements with respect to the original stress elements. 25 MP
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.
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.
4 ksi The state of plane stress at a point is shown on the element. (a) Draw Mohr's circle neatly to scale, and use it to complete part (b). (b) Determine the state of stress on an element rotated 35° counterclock- 20 ksi wise from the given element. Sketch the state of stress on the rotated element element. 9 ksi -20 -10 o (ksi) -30 -20 -10 10 20 30 10 20 T (ksi)
(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 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.
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
Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are S, 2750 psi, S, = 1100 psi, and Sy 1950 psi. Assume ß - 53°. (a) Draw Mohr's circle for this state of stress. %3D (b) Determine the principal stresses and the maximum in-plane shear stress acting at the point. Show these stresses on an appropriate sketch (e.g., see Fig. 12.15 or Fig. 12.16). (c) Determine the normal and shear stresses on the indicated plane and show these stresses on a sketch. (d) Determine the absolute maximum shear stress at the point. Sxy Answer: (a) Draw Mohr's Circle for this state of stress. (b) op1- psi Op2 - psi Tmax in-plane psi (c) on psi Tnt psi (d) Tabs max psi eTextbook and Media
(b) Mohr's circle, invented by Christian Otto Mohr, is a graphical representation of the transformation law for the stress system. Use Mohr's circle to determine the stresses on an element inclined at 30° clockwise to the state of plane stress system as shown in Figure 1 and show the corresponding stress elements. Q2 (a) It is important im 80 MPa 50 MPa Ľ 50 MPa Figure 1 80 MPa 25 MPa
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
Q-1 Figure Q-1, below, shows Mohr's cirde for a point in a physical object that is subjected to plane stress. (a) Determine the stresses Ox, Oy, and Txy, and show them on a stress element, properly orientedwith reference tox-y axes. (b) Determine the principal stresses o1, 02, and Tmax and show them on a stress element properly rotated with respect to the x-y element (c) Determine the stresses ơn, Ot and Trt, and show them on a stress element that is properly rotated with respect to the x-y element The sketches must indude the magnitude of the angles w.rt. positive x-axis as well as the angle between the x and n axes, and an indication of the direction of rotations (1.e., either clockwise (c.w.) or counterdockwise (c.C.w.)). 1 grid square 3 MPa
Consider the plane stress element shown in representing the state of stress at a material point. If the magnitudes of the stresses are such that ox 210 Pa, oy = 110 Pa, and = - Txy = 70 Pa, calculate the magnitudes of principal stresses oj and 02, and the maximum shear stress, Tmax, generated at %3D this material point. (a) Record here the the positive of the two principle stresses. (b) Record here the the negative of the two principle stresses. (c) Record here the the maximum shear stress. Tyz Oy