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The following list gives a summary of the techniques pre-sented in this section; it also outlines the general procedure for applying the techniques to a given stress analysis problem.➭Angle for Principal Stress Elementuni03D5σ=12arctan [2τxy/(σx-σy)](4–3)The angle uni03D5σis measured from the positive x-axis of the original stress element to the maximum principal stress, σ1. Then the minimum principal stress, σ2, is on the plane 90° from σ1.When the stress element is oriented as discussed so that the principal stresses are acting on it, the shear stress is zero. The resulting stress element is shown in Figure 4–4.Maximum Shear StressOn a different orientation of the stress element, the maxi-mum shear stress will occur. Its magnitude can be computed from➭Maximum shear stressτmax =Caσx-σy2b2+τxy2(4–4)The angle of inclination of the element on which the maxi-mum shear stress occurs is computed as follows:➭Angle for Maximum Shear Stress Elementuni03D5τ=12arctan [-(σx-σy)/2τxy](4–5)The angle between the principal stress element and the max-imum shear stress element is always 45°.On the maximum shear stress element, there will be normal stresses of equal magnitude acting perpendicular to the planes on which the maximum shear stresses are acting. These normal stresses have the value➭Average Normal Stressσavg=(σx+σy)/2(4–6)Note that this is the averageof the two applied normal stresses. The resulting maximum shear stress element is shown in Figure 4–5. Note, as stated above, that the angle between the principal stress element and the maximum shear stress element is always 45°.FIGURE 4–4 Principal stress elementyxH9268avgH9268avgH9268avgH9268avgH9270max–H9270maxH9270max–H9270maxH9278H9270FIGURE 4–5 Maximum shear stress elementGENERAL PROCEDURE FOR COMPUTING PRINCIPAL STRESSES AND MAXIMUM SHEAR STRESSES1. Decide for which point you want to compute the stresses.2. Clearly specify the coordinate system for the object, the free-body diagram, and the magnitude and direction of forces.3. Compute the stresses on the selected point due to the applied forces, and show the stresses acting on a stress element at the desired point with careful attention to directions. Figure 4–3 is a model for how to show these stresses.4. Compute the principal stresses on the point and the di-rections in which they act. Use Equations (4–1), (4–2), and (4–3).5. Draw the stress element on which the principal stresses act, and show its orientation relative to the original x-axis. It is recommended that the principal stress element be drawn beside the original stress element to illustrate the relationship between them.6. Compute the maximum shear stress on the element and the orientation of the plane on which it acts. Also, com-pute the normal stress that acts on the maximum shear stress element. Use Equations (4–4), (4–5), and (4–6).