At a critical point on the free surface of a loaded beam, the strains are measured in three directions at theta_a, -0, theta_b = 45, theta_c = 90 (see fig. i). they are found to be -l0^-4, 5 times l0^-5, +10^-4, respectively. calculate the magnitude and orientation of the principal strains x the point. if e = 120 gpa, v =0.3, find the magnitude of the principal stresses. determine the directions of the principal planes. a sheet of material is subjected to a two-dimensional stress system m the x-y plane. at a given point, an element with its sides parallel to x and y axes is found to have a shear strain of l times l0^-4, while an element at 45 degree to die first hot a shear strain of 4 times 10^-4 (fig. 2). calculate the maximum shear strain at this point. if the shear modulus 100 mpa, find the deference between the two principal stresses.