In this problem, you will construct the 2D Mohr's circle for two plane stress states defined in terms of the Cartesian components of the stress tensor in the x,y reference frame: [ σx,σy,τxy].
For each of these stress states, you must construct and use the Mohr's circle to obtain the numerical values of:
The normal and shear stresses (in units of MPa) acting on the faces of an an element oriented at 45∘ with respect to the x,y reference frame: these are the components [σx1, σy1, τx1y1] of the stress tensor in the reference frame (x1,y1) defined, as indicated in the figure below, with the coordinate axis x1 rotated by 45∘ CCW from the x-axis. Notice that in the figure we indicate the stress directions for positive values of the components.
The maximum and minimum principal stresses, σ1 and σ2, and the maximum shear stress, τmax, in units of MPa.
The angle ΘP (in degrees) that takes you from the x,y reference frame to the 1,2 principal frame. As shown in the figure below, take ΘP as the angle from the x-axis to the 1-axis, positive CCW, with −90∘≤ΘP ≤90∘.
For [σx=10MPa,σy=0MPa,τxy=0MPa], obtain:
σx1=
σy1=
τx1y1=
σ1=
σ2=
τmax=
ΘP=
For [σx=−11MPa,σy=1MPa,τxy=8MPa], obtain:
σx1=
σy1=
τx1y1=
σ1=
σ2=
τmax=
ΘP=
4 answers