Problem 9. Determine the equivalent state of stress if an element is oriented 30° clockwise from the element shown using both stress transformation equations and Mohr's circle. Sketch the result on an element. 9 MPa 4 MPa 6 MPa
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- The state of plane stress at a point is shown on the element in Figure below. Represent this state of stress on an element oriented 20° clockwise from the position shown by using Mohr's Circle. 16 ksi 10 ksi ksiSTRESS TRANSFORMATION EQUATIONAt a point on the surface of a pressurized cylinder, the material element is subjected to stresses; σx = 60 MPa, σy = - 40 MPa, and τxy = - 30 MPa. Construct Mohr’s circle, then use it to determine the following: Do not use the equations of transformations.1- The principal stresses and the maximum shear stress.2- Show these stresses on sketches of properly stress elements.3- A point on the circle where the element is only subjected to pure shear stress. Calculate the value of that pure shear stress.
- Problem 2: A state of plane stress at a point on the surface of a structure consists of the following stress components: Ox = 18 ksi, oy = 24 ksi, and Txy = 15 ksi. Note that the stress components act in the directions shown on the element below. Ox Txy 24 ksi бу 18 ksi 15 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 stress components Ox, Oy, and Txy on an element rotated 25° counter-clockwise from the original element shown. Label all of these quantities on the circle. (c) Show all stresses from part (b) on a properly oriented stress element. Be sure to include all stress components acting on the element.The state of plane stress at a point is represented on the element shown in the figure below. (a) Determine the principal stresses acting on this point, and the corresponding orientation (angle). (b) Determine the maximum in-plane shear stress, and the corresponding orientation (angle). Also determine the associated average normal stress. Draw Mohr's circle and show the stresses on the circle. 15 ksi 23 ksi 14 ksiSolve the following question
- 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).Determine the resulting maximum value of the normal stress. Specify the orientation of the plane on which these maximum values occur. **The answer is tensile stress is 0 ksi at 90 degrees. **The answer is compressive stress is 7 ksi at 0 degrees. Can you explain how that is? This was my thought process: I know that tensile would be zero because the force P is actually going inwards and not outwards. I know that means that there would be a compressive force. I am confused on the angles, how is a tensile force going 90 degress if there technically is no force in the tensile direction. And how is there a compressive force at 90 degrees if there is a stress? thank you!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
- The state of plane stress at a point with respect to the xy-axes is shown in Fig. (a). Using Mohr's circle, determine (1) the principal stresses and principal planes; (2) the maximum in-plane shear stress; and (3) the equivalent state of stress with respect to the x'y'-axes. Show all results on sketches of properly oriented elements. y20 MPa 50° 40 MPa 16 MPa (a)Problem 3: 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 = 16 kpsi, oy = 9 kpsi, Ty = 5 kpsi ccwDetermine the equivalent state of stress on an element if it is oriented 30° clockwise from the element shown. Use the stress-transformation equations. 300 MPa 950 MP