## egr 7

• Anonymous commented

i think u forgot to rate the answer.pls rate as soon as possible

• from the mohr circle formula,

σ1 ,σ2 are the principal stresses.

σ1 = (σx + σy)/2 + √[{(σxy)/2}2 + τxy2] = σmax

σ2 = (σx + σy)/2 - √[{(σxy)/2}2 + τxy2] = σmin

τmax = √[{(σxy)/2}2 + τxy2]

angle that the plane of maximum normal stress, σmax  makes with the x-axis, φ = tan-1(2τxy/(σx - σy))

angle that the direction that the plane of maximum shear stress makes with the x-axis = tan-1(-(σx - σy)/2τxy)

here, σx = -15 ksi

σy = 10 ksi

τxy = 8 ksi

put all values in the formula, we get;

σ1 = (-15 + 10)/2 + √[{(-15-10)/2}2 + 82] = 12.341 ksi

σ2 =  (-15 + 10)/2 - √[{(-15-10)/2}2 + 82] = 17.341 ksi

τmax =√[{(-15-10)/2}2 + 8214.841 ksi

angle that the plane of maximum normal stress, σmax  makes with the x-axis, φ = tan-1(2τxy/(σx - σy)) = tan-1(2*8/(-15 - 10)) = -32.620

angle that the direction that the plane of maximum shear stress makes with the x-axis = tan-1(-(σx - σy)/2τxy) = tan-1(-(-15 - 10)/2*8) = 57.380

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