Problem 4-29* In Section 4.6, we studied the strip loading (Fig. 4-40). (a) Find the princ...

Problem 4-29^* In Section 4.6, we studied the strip loading (Fig. 4-40). (a) Find the principal stresses σ₁ and σ₃ acting on principal planes π₁ and π₃ at point P with coordinates θ₁ and θ₂. Express the results for σ₁ and σ₃ in terms of α. (b) Show that the points belonging to a circle passing through P and through the two edges P₁ and P₂ of the strip load have the same state of stress as P. Write the equation for the maximum shear stress for this circle. (c) Sketch the trajectories of σ₁ and σ₃. (d) Using the equation for the maximum shear stress you obtained in (b), find the maximum shear stress for a given loading and the circle corresponding to it (that is, the value of α corresponding to maximum shear stress). The equations derived in Section 4.6 for σ₁₁, σ₃₃, and σ₁₃ are repeated below for convenience: