Problems 1-4: For the problems below: (a) draw the Mohr's circle, (b) find the principal stresses and show them on a properly oriented element, and (c) find the maximum in-plane shear stress (the radius of the circle), (d) find the maximum shear stress (which is the larger of the maximum in-plane shear or half of the larger of the two principal stresses), and finally (e) the shear and normal stresses on a properly oriented element.
1. $\sigma_{xx} = 80$ (all ksi), $\sigma_{yy} = -20$, $\tau_{xy} = 40$, cut plane is 40 degrees cw from the top horizontal line of the stress element.
2. $\sigma_{xx} = -12$ (all ksi), $\sigma_{yy} = -8$, $\tau_{xy} = 4$, cut plane is 10 degrees ccw from the bottom horizontal line of the stress element.
3. $\sigma_{xx} = -10$ (all ksi), $\sigma_{yy} = -30$, $\tau_{xy} = -4$, cut plane is 30 degrees ccw from the top horizontal line of the stress element.
4. $\sigma_{xx} = 8$ (all ksi), $\sigma_{yy} = -2$, $\tau_{xy} = -6$, cut plane is 30 degrees cw from the right face of the stress element.
