Here, we don't have 3rd component in the direction of z axis, so we won't be having principle stress in the same direction.
Now, applying 2D principle stress equation.
1. Principle Stresses
Here, -ve sign shows compressive stress in nature.
So, as per question, and
2. Maximum Shear Stress
3. Octahedral Shear Stress
4. Angle
1. The nonzero stress components relative to axes (x, y, z) are Oxx = -90 MPa,...
6. The components of stress within a structure are oxx 90 MPa, oxy -30 MPa, oxz = ayz = 0 50 MPa, oyy -60 MPa, ozz (4 poin Draw 3D Mohr's circle and locate the principal stresses 01, 02 and a3 as well as the maximum shear stress a. b. Calculate the angle required to rotate the x-y plane to the principal frame and locate that angle on the cirlce (4 poir c. Draw the rotated 3D stress element
Question 3 68 MPa 56 MPa 12 MPa Figure 3. Stress components acting on an element. Figure 3 shows an element experiencing several stress components. Determine the following: 1. The stress components oxx, y, and Tyyacting on the element oriented at a counter clockwise angle 0 = 30° from the horizontal x axis 2. The principal stresses, the maximum shear stress and their associated angles Show all results on sketches of properly oriented elements. Note: Solutions MUST be obtained using...
1. Given a plane element in a body is subjected to a normal tensile stress in the x-direction of 120 MPa, a normal stress in the y-direction of-75 MPa and shear stresses of 50 MPa, as shown. Determing a. What is the maximum principal stress? b. What is the minimum principal stress? 75 MPa What is the maximum shear stress? 50 MPa c. d. what is the angle to the principal plane, θ e. What is the angle to the...
The state of stress at a point on a body is given by the following stress components: 0 = 15 MPa, Oy = -22 MPa and Try = 9 MPa Matlab input: sx = 15; sy = -22; txy = 9; 1) Determine the principal stresses 01 and 02. 1 = MPa 02= MPa 2) Sketch the principal stress element, defined by the rotation @pl. y Enter the rotation @pi (-360º < Opl < 360°): Opl = Add stress components:...
For the 3-D stress element below the normal stress in the z-direction is a principal stress. 1) Sketch the 3-D Mohr's Circles and calculate the three Principal Stresses 01, 02, and 03 2) Calculate and show on the circles the Maximum Absolute Shear Stress Tabs,max Note: since the normal stress in the z-direction is a principal stress, you just need to find out if it is 01, 02, or 03 N 5 MPa 10 MPa x -5 MPa 5 MPa...
50 MPa 3. For the shown stress block: a) b) Find the Principal Stresses Find the angle of the Principal Stresses from the given orientation (Ans: 18.43" and 108.4 (+90* from the first angle) Find the maximum shear stress and the corresponding average normal stress (Partial Ans: maximum shear stress 25 MPa) Find the angle θ,of the maximum shear stress from the given orientation. 15 MPa 10 MPa c) d) 50 MPa 3. For the shown stress block: a) b)...
Consider the following stress state in plane stress: Qx = 120 MPa Qy = -30 MPa Txy = 70 MPa a) Calculate the two in-plane principal stresses and show the principal stress state on a properly oriented stress element. b) Calculate the maximum in-plane shear stress. c) Calculate the maximum out-of-plane shear stress. On what plane (x-z or y-z) does this shear stress occur?
There is one force element in xy-axes, with Sigma (x) = 30 MPa, Sigma (y) = 60 MPa, and Tao (xy) = 40 MPa. (Sigma for normal stress and Tao for shear stress) (1) Draw a force element with all above stresses labeled in xy-axes and translate the information on a Mohr's circle; (2) Rotate the force element 30 degree (counterclockwise). Use Mohr's circle to derive the stresses in this new element; (3) Use Mohr's circle to determine the principal...
Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude 0,1 = 35 MPa, oyl = 57 MPa, and Tryl = 41 MPa Oy Txy Determine the principal normal stresses 01 and 02, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle...
Let x-y-z be the principal axes. When rotating around y axis, what is the maximum shear stress encountered, and what is the corresponding rotation angle? Show the derivation.