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. 75 MPa 50 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. 75 MPa 50 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 7.2.21P: An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec...

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-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.
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.
On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses on sketches of properly oriented elements.
An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec figure). On this inclined clement, the normal and shear stresses have the magnitudes and directions shown in the figure. Determine the normal and shear stresses acting on an clement whose sides are parallel to the \y axes, that is, determine crv, tr(_, and t, Show the results on a sketch of an clement oriented at B .
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).
A plane stress state is given as follows (50MP 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 71, T2, and the corresponding normal stress. 75 MPa 50 MPa 50 MPa
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).
(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
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 II-Obtain the Principal Stresses, the Maximum Shear Stress, and complete the table below III- Draw the Planes of Principal and Maximum Shear Stresses in the space provided below Provide "full" details and Use 3 Sig. Fig. in this problem Oy = 15 Ksi Tcw > S y Ox =10 Ksi Тух 5 Ksi 10 5 -20 -15 -10 5 10 15 20 5 10 Tccw > S' O Avg. TMax. 01 02 Op1
Q. 1 Find minimum and maximum normal and normal stresses for the plane stress systems as shown below, (a) Using analytical method, (b) using Mohr's circle method and depict the planes on which these stresses act. [Ans. 1,2 = 53.23N/mm², -73.2N/mm², 18.4°, 198.4⁰] 50 70 70 20 50
1. For the two cases i.e. (a) 2D and (b) 3D shown below, find the principal stresses, maximum shear stresses and directions by using Mohr’s circle. Support your answers with diagrams. 41 GOMPa 60MPR Txy=40MPA 40MPA (a) (b)