Mohr's Circle for Plane Stress

R = (\frac{σ _{x} - σ _{y}}{2})^{2} + τ_{x y}^{2} σ_{1, 2} = σ_{avg} \pm R

Mohr's circle plots (σ, τ) with center at σavg = (σx+σy)/2 and radius R. Principal stresses are the σ-intercepts. The rotation on the circle is 2θ. Sign convention: the Handbook's τ positive direction must be followed consistently.

$R$ (MPa): Radius of Mohr's circle
$σ_{1, 2}$ (MPa): Principal stresses

Step-by-step solved example

σx=80 MPa, σy=20 MPa, τxy=30 MPa. σ1 and σ2?

Mohr's circle in σ–τ axes. Principal stresses at the horizontal intercepts.

1. Center and R
σavg=50. R=√(30²+30²)=√1800=42.4 MPa.
2. Principals
σ1=92.4 MPa, σ2=7.6 MPa.
$σ_{1} = 92.4 MPa$

Answer: σ1=92.4 MPa, σ2=7.6 MPa

10 practice questions

0/10 correct

1.Center of Mohr's circle is at

2.If τxy=0 and σx>σy, then σ1=

3.Max in-plane shear is

4.A 2θ rotation on Mohr is

5.Pure shear σx=σy=0, τ=τ0: principals are

6.σ1+σ2 equals

7.The point (σx, τxy) and (σy, −τxy) are

8.If R=0 the state is

9.σavg=40, R=10. σ2=

10.3-D principals need