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For an element that experiences the following stress conditions, without the aid of Mohr's circle, find the principal stresses, maximum shear stress, the direction in which maximum principal stress acts, the direction of the element on which the maximum shear stress acts, the direction of the element on which no shear stress acts, and the direction of element on which normal stress acts that is equal to average normal stress. Show all these four elements by drawing their directions compared to the original given element. Given, \sigma _(x)=8500\psi ;\sigma _(y)= -4100\psi ;\tau _(xy)=2000\psi.If an element made of 80002 Pearlitic malleable iron (ASTM A220) is subjected to the stress condition described in Problem 6, draw safe zones on the same graphing paper, as per the maximum normal stress theory (MNST), Coulomb-Mohr theory (CMT) and modified Mohr theory (MMT). Calculate the design factor of this element, as per all these three theories.