A plane stress state is given as follows (50MPa in the bottom right corner denotes the shear component, and others denote the normal components). 1) Please draw the Mohr's circle of this plane stress state. Indicate the center of the circle, the radius of the circle, and the point that corresponds to x-plane (the normal of the plane is x axis) 2) Determine the principal stresses and directions of this stress state using Mohr's circle. 3) Draw the stress element to show maximum shear stress T₁, T2, and the corresponding normal stress. 50 MPa 75 MPa 50 MPa

A plane stress state is given as follows (50MPa in the bottom right corner denotes the shear component, and others denote the normal components). 1) Please draw the Mohr's circle of this plane stress state. Indicate the center of the circle, the radius of the circle, and the point that corresponds to x-plane (the normal of the plane is x axis) 2) Determine the principal stresses and directions of this stress state using Mohr's circle. 3) Draw the stress element to show maximum shear stress T₁, T2, and the corresponding normal stress. 50 MPa 75 MPa 50 MPa

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 7.2.27P: -27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile...

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An element in plane stress on the fuselage of an airplane (figure part a) is subjected to compressive stresses with a magnitude of 42 MPa in the horizontal direction and tensile stresses with a magnitude of 9.5 MPa in the vertical direction (sec figure part b). Also, shear stresses with a magnitude of 15.5 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 40g from the horizontal. Show these stresses on a sketch of an element oriented at this angle.
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.
A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the figure. The width of the plate is h = 12.0 in. Measurements show that the normal strains in the x and v directions are s = 427 × 10-6 and s = 113 × l0-6, respectively. With reference to part b of the figure. which shows a Iwo-dimensional view of the plate. determine the following quantities. (a) The increase .d in the length of diagonal Oil. (b) The change . in the angle between diagonal Oti and the x axis, (c) The shear strain y associated with diagonals Oil and cf(that is. find the decrease in angle ced).
-27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile stress The stresses on element A oriented at angle ?? x1=45° aresy1= 75 psi. tx1y1= 275 psi. . Find the state of stress on the element lilt is rotated clockwise to align the x3 axis with the horizontal x axis.
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).
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
(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
Problem 2: For the plane stress state listed below, draw a Mohr's circle diagram properly labeled. Keep in mind that the principal stress is that stress state where the shear stress is zero. That means it is the stress state along the normal stress line in Mohr's space. So, use your Mohr's circle to find the principal normal and shear stresses, and determine the angle from the x axis to o1. 0x = 20 kpsi, oy =-10 kpsi, Txy = 8 kpsi cw
The state of stress at a point on a thin plate is as shown in the left side of the Figure below. Determine the state of stress (ox, oy, txy) represented on the element oriented as shown on the right. 120 Sigma_x^prime (MPa) 200 Sigma_y^prime (MPa) 60 Tau_xy^prime (MPa) 30 Alpha (degrees) O x' Oy Txy' Txy Ox
Consider the 2-D state of stress shown below. Using the provided scales graph the Mohr's Circle for the 2-D state of stress with "full' details Draw the Planes of Principal and Maximum Shear Stresses Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw → S Txy= -5 ksi Ox = 10 Ksi Tyx = 5 Ksi 10 5 -20 -10 5 10 15 20 5 10 Tccw → S'
(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
Given a stress state of ø, = -4 MPa, øy = 12 MPa, ty = 7 MPa ccw 1) Draw a properly oriented stress element illustrating this state of stress 2) 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 zi and 72, find the corresponding normal stresses, and label the drawing completely. 3) Use the plane-stress transformation equations to validate your answers in part 2