1. Fig. 1 shows the state of stress at point P on the surface of a...

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1. Fig. 1 shows the state of stress at point P on the surface of a cloth under the action of wringing. Obtain the equivalent state of stress on an element at the point which represents: (a) the principal stresses and the planes on which they act, and (b) the maximum in-plane shear stress and the corresponding plane. Also, determine the corresponding orientation of the element with respect to the element shown and sketch the results on the element. What is the average axial stress? 50 MPa 15 MPa Figure 1 2. Consider a stress field in a body described in the basis e, {e, ea, es): [0] = [421230-22] 01 2 -22 2 3 MPa where the constants have consistent units given that the coordinates (z,) are in meters. (a) Is this stress field in equilibrium in the absence of body and inertial forces? Support your answer. (b) Find the traction vector at x=2e;+es+es on a plane defined by the equation 1+2+3 = 2. (c) Find the magnitude of the normal and shear traction on this plane. (d) Use your favorite software (e.g.. MATLAB) to obtain the principal stresses and principal planes. 1. Fig. 1 shows the state of stress at point P on the surface of a cloth under the action of wringing. Obtain the equivalent state of stress on an element at the point which represents: (a) the principal stresses and the planes on which they act, and (b) the maximum in-plane shear stress and the corresponding plane. Also, determine the corresponding orientation of the element with respect to the element shown and sketch the results on the element. What is the average axial stress? 50 MPa 15 MPa Figure 1 2. Consider a stress field in a body described in the basis e, {e, ea, es): [0] = [421230-22] 01 2 -22 2 3 MPa where the constants have consistent units given that the coordinates (z,) are in meters. (a) Is this stress field in equilibrium in the absence of body and inertial forces? Support your answer. (b) Find the traction vector at x=2e;+es+es on a plane defined by the equation 1+2+3 = 2. (c) Find the magnitude of the normal and shear traction on this plane. (d) Use your favorite software (e.g.. MATLAB) to obtain the principal stresses and principal planes.