Mohr’s Circle Calculator for Plane Stress and Plane Strain | Bending Moment and Shear Force Diagram Calculator

Mohr's circle is an easy way of visualizing the state of stress at a point in a loaded material.
This calculator is currently in BETA testing mode. Currently only 2D Plane Stress is available, however 2D Plane Strain and 3D Plane Stress/Strain will be added later.

Mohr's Circle for Plane Stress

0,0

σ (MPa)

τ (MPa)

τ_max (2, 11.7)

σ₂(-9.66,0)

σ₁(13.7,0)

C (2, 0)

(-8, 6)

(12, -6)

2θ_p2 = 31°

Add or Edit Mohr's Circle Parameters

Please fill in all fields.

Type:

Stress/Pressure Units:

Normal Stress along X-axis (σ_x)

MPa

Normal Stress along Y-axis (σ_y)

MPa

Shear Stress in XY-plane (τ_xy)

MPa

Rotation Angle: 00

0,0

σ_x = 8

σ_y = 12

τ_xy = 6

Element

Description	Symbol	Value	Formula
Normal Stress along X-axis	$\sigma_{x}$	-8 MPa	-
Normal Stress along Y-axis	$\sigma_{y}$	12 MPa	-
Shear Stress in XY-plane	$\tau_{xy}$	6 MPa	-
Rotated Element Normal Stress along X-axis	$\sigma_{x'}$	-8 MPa	$\sigma_{x'} = \frac{\sigma_{x} + \sigma_{y}}{2} + \frac{\sigma_{x} - \sigma_{y}}{2} \cos(2 \theta) + \tau_{xy} \sin(2 \theta)$
Rotated Element Normal Stress along Y-axis	$\sigma_{y'}$	12 MPa	$\sigma_{y'} = \sigma_{x} + \sigma_{y} - \sigma_{x'}$
Rotated Element Shear Stress in XY-plane	$\tau_{x'y'}$	6 MPa	$\tau_{x'y'} = - \frac{\sigma_{x} - \sigma_{y}}{2} \sin(2 \theta) + \tau_{xy} \cos(2 \theta)$
Mean Normal Stress	$\sigma_{avg}\textup{ or C}$	2 MPa	$\frac{\sigma_{x}+\sigma_{y}}{2}$
Maximum Shear Stress (Tresca)	$\tau_{max}\textup{ or R}$	11.662 MPa	$\sqrt{\left ({\frac{\sigma_{x}-\sigma_{y}}{2}}\right )^{2}+{\tau_{xy}}^{2}}$
Maximum Principal Stress (1)	$\sigma_{1}$	13.662 MPa	$\sigma_{avg}+\tau_{max}$
Minimum Principal Stress (2)	$\sigma_{2}$	-9.6619 MPa	$\sigma_{avg}-\tau_{max}$
Von-Mises Stress	$\sigma_{VM}$	20.298 MPa	$\sqrt{\frac{\left ({\sigma_{1}-\sigma_{2}}\right )^{2} + \left ({\sigma_{2}}\right )^{2} + \left ({-\sigma_{1}}\right )^{2}}{2}}$
Rotation of Max Principal Normal Stress Plane (1) (Angle between x-axis and σ₁)	$\theta_{p1}$	74.518°	${90}^{\circ}+\theta_{p2}$
Rotation of Min Principal Normal Stress Plane (2) (Angle between x-axis and σ₂)	$\theta_{p2}$	-15.482°	$\frac{\tan^{-1}\left ({\frac{2\tau_{xy}}{\sigma_{x} - \sigma_{y}}}\right )}{2}$
Rotation of Max Principal Shear Stress Plane (1) (Angle between x-axis and σ_avg,x)	$\theta_{s1}$	119.518°	${90}^{\circ}+\theta_{s2}$
Rotation of Min Principal Shear Stress Plane (2) (Angle between x-axis and σ_avg,y)	$\theta_{s2}$	29.518°	$\frac{\tan^{-1}\left ({\frac{-\left (\sigma_{x} - \sigma_{y}\right )}{2\tau_{xy}}}\right )}{2}$

Unrotated Element

0,0

σ₁ = 8

σ₂ = 12

τ_xy = 6

Element

Rotated Element (00 deg)

0,0

σ₁ = 8

σ₂ = 12

τ_xy = 6

Element

Element Rotated to Max Principal Stress (74.52 deg)

0,0

σ₁ = 13.7

σ₂ = 9.66

τ_xy = 0

Element

Element Rotated to Max Shear Stress (119.52 deg)

0,0

σ₁ = 2

σ₂ = 2

τ_xy = 11.66

Element

If you notice any bugs or have any suggestions please mention them in the comments below.

17 thoughts on “Mohr’s Circle Calculator for Plane Stress and Plane Strain”

Abdul wahab on February 5, 2017 at 8:38 pm said:

awesome work dude thanks alot for such a helping tool
jose on November 9, 2016 at 12:30 am said:

Excellent…
kemo on March 25, 2016 at 2:56 pm said:

This is very helpful. It would be way better if we can add up an angle.
jeff on March 5, 2016 at 10:11 am said:

PLEASE MAKE THE STRAIN MOHR’S CIRCLE WORK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Nicole on December 8, 2015 at 10:54 am said:

Hello,

This is amazing and so helpful!! Only bug for me is that text is overlapping in the Mohr Circle graph. It would be awesome for it not to overlap so I could screenshot the image or if I could download an image of it, that would be also very helpful.
- Nicole on December 8, 2015 at 11:00 am said:
  
  Found that I can rearrange the text on the graph.
Nisarg on October 25, 2015 at 3:44 pm said:

Hi,

Its helpful but for Mohrs circle what is the scale used for drawing it, like is it 1 cm=1psi or something like that, if we want to draw it graphically
- Paul Comino on October 25, 2015 at 7:08 pm said:
  
  Hi Nisarg. The scale is not that simple – the calculator’s scale will always change to fit in the mohr’s circle and so the scale could really be anything depending on the numbers.
Daniel Sullivan on May 2, 2015 at 10:31 am said:

Would I be correct in assuming that there are plans to show the correct orientation of the element – at present this feature does not appear to be working.
- Paul Comino on May 4, 2015 at 7:19 pm said:
  
  Yes that will be done later. We’ve been working a lot on SkyCiv but these calculators need love too.
James on April 27, 2015 at 8:33 am said:

If we could go on rotating a certain degree angle in the Mohr Circle from the point decided by the parameters of the right side in a given element, it will be much powerful.
??
- Paul Comino on May 4, 2015 at 7:20 pm said:
  
  Yes hopefully we can add something like this in future. Thanks for the suggestion.
  - Matthew on November 13, 2015 at 8:14 am said:
    
    I agree with that very, very much.
necati ataberk on February 23, 2015 at 6:37 am said:

There is a syntax error in maximum shear stress formula. It should be the square root of that.
- Paul Comino on February 23, 2015 at 12:24 pm said:
  
  Thank you for letting us know. It should be fixed now
Zhaoshuo on November 23, 2014 at 4:48 pm said:

It will be great to have the capacity to find the stresses after rotating certain degree.
deepak on October 22, 2014 at 12:54 am said:

very good

Comments are closed.