3. (a) Using Stress transformation equations, determine the principal planes, the principal stresses, the maximum in-nlano chear ctress and the corresponding normal stress. 100 MPa 75 MPa 150 MPa

(c) An element is subject to the stresses shown below in Figure 5 Calculate the centre and radius of the Mohr's stress circle and sketch the circle (1) (ii) Calculate the values of principal stresses and show them on the circle (ii) Determine the direction of the larger principal stress relative to the 75 N/mm. 30 N/mm A 14 Nmm 75 N/mm2 30 N/mm Figure 5

2) The state of stesss at a point in a body relative to the xyz coordinate system is: 2 3 -5 [o]= 3 2 kpsi 6. %3D -5 2 -4 a) Determine the principle stresses and the direction cosines corresponding to each principle stress. b) Draw the 3D Mohr's circles. c) Determine the maximum shear stress. d) Find the orientation of the plane containing the maximum shear stress relative to the original axis system 3) For the stress tensor in problem 2: a) Determine the normal and shear stress on a surface intersecting a plane defined by 3 points (0,0,0); (2,-1,3); (-2,0,1) b) Give the magnitudes of these stresses and the direction cosines defining their directions.

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I need help with the last 4 boxes.

An element is subject to the stresses shown below in Figure 5 (i) Calculate the centre and radius of the Mohr's stress circle and sketch the circle (ii) Calculate the values of principal stresses and show them on the circle (iii) Determine the direction of the larger principal stress relative to the 75 N/mm?. 30 N/mm? 14 N/mm? 75 N/mm? 75 N/mm? 30 N/mm2 Figure 5

(Solid Mechanics) Explain how to construct the upper right corner (red boundary indicated below) of the envelope for the maximum shear stress criterion.

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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

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