A two-dimensional state of stress at a point in a loaded material in the direction defmed by the x-y coordinate system is defined by three components of stress σxx σyy, and τxy. The stresses at the point in the direction defined by the x'- y' coordinate systems are calculated by the stress transformation equations:

where e is the angle shown in the figure. Write a user defined MATLAB function that determines the stresses σx'x, σy'y, and τx'y' given the stresses σxx, σYY, τxy, and the angle θ. For the function name and arguments, use [Stran] =StressTrans (S, th). The input argument S is a vector with the values of the three stress components σxx, σYY, and τxy, and the input argument this a scalar with the value of e. The output argument Stran is a vector with the values of the three stress components σx'x', σy'y', and τx'y'.
Use the function to determine the stresses transformation for the following cases:

(a) σxx = 160 MPa, σyy = -40 MPa, and Ï„xy = 60 MPa, θ = 20°
(b) σxx = -18ksi, σyy = 10ksi, and Ï„xy = -8ksi, θ = 65°.

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