Created By : Abhinandan Kumar

Reviewed By : Phani Ponnapalli

Last Updated : May 17, 2023

The major stresses can be calculated using Mohr's circle calculator based on a 2D stress state. The calculator will return the principal stress of the system based on the values of normal and shear stresses on a body. One of the most essential parts of constructing any body or system is stress The calculator uses Mohr's circle equations to do this.

Normal Stresses
Normal stress in X direction (σ_xx)
Normal stress in Y direction (σ_yy)

Shear Stresses
shear stress (τ_xy)
shear stress (τ_yx)

Principal stresses
Maximum principal stress (σ_1)
Minimum principal stress (σ_2)

Other results
Maximum shear stress (𝛕_max)
von Mises stress (σ_mises)
Angle of orientation (θ)
Mean stress (σ_m)

### What is Mohr's Circle?

Mohr's circle is a two-dimensional graphical depiction of the stress state that can be used to transform stress.

What is the difference between a stress state and primary stress?

A body's stress state is the result of a combination of strains in all three directions, i.e., X, Y, and Z or 1, 2, and 3. There are three normal stresses (acting perpendicular to the face): σ11, σ22, and σ33, as well as six shear stresses (acting parallel to the plane): ≡¥¢ò12, ≡¥¢ò23, ≡¥¢ò13, ≡¥¢ò21, ≡¥¢ò32, and ≡¥¢ò31. The stresses that the body is subjected to that are depicted in the diagram below.

The shear stresses can be reduced to three values when considering equilibrium operating on the body, namely ≡¥¢ò12 =≡¥¢ò 21, ≡¥¢ò13 = ≡¥¢ò31, and ≡¥¢ò32 = ≡¥¢ò23. As a result, six stresses can be used to characterise a stress state: three normal stresses and three shear stresses. If just in-plane orientations are taken into account, the resultant stress state can be achieved by lowering the stresses, ≡¥¢ò13 = ≡¥¢ò31 = 0, and ≡¥¢ò32 = ≡¥¢ò23 = 0. Three stresses may now be used to characterise the 2D stress state: two normal stresses (σ11 and σ22) and shear stress (≡¥¢ò12 = ≡¥¢ò21). This can also be depicted as indicated in the diagram below (with 1 and 2 directions as x and y).

### What is Principal Stress and How do you Calculate it?

Consider a situation in which the plane is just subjected to normal stress. Principal stresses are the tensions that exist at that point. This is accomplished by decreasing the shear stresses to zero and then converting the existing stress state.

The principal stresses can be written mathematically using the principal stress equation:

σ1 = ((σxx + σyy) / 2) + √(((σxx - σyy) / 2)2 + τxy2)

σ2 = ((σxx + σyy) / 2) - √(((σxx - σyy) / 2)2 + τxy2)

Where, σ1 and σ2 = minimum and maximum principal stresses.

Similarly, the state's maximum shear stress (max) can be calculated using the equation:

τmax = √(((σxx - σyy) / 2)2 + τxy2)

Maximum shear stress can also be calculated using the major stresses as follows:

τmax = (σ1 - σ2) / 2

while the maximum stress (max) is written as:

σmean = (σxx + σyy) / 2

The angle of orientation is calculated as follows:

2θ = tan-1(2*τxy/(σxx - σyy))

The equations above will assist you in sketching Mohr's circle and vice versa. The preceding equations can also be deduced or acquired using the geometrical approach described in the section below.

### Estimating Primary Stress using Mohr's Circle

To use Mohr's circle to estimate principle stress, you must first grasp what Mohr's circle is and how to draw a Mohr's circle. A stress transformation is performed using a Mohr's circle, which is a graphical depiction of a stress condition. For a given 2D stress state with normal stresses (σxx and σyy) and shear stresses (τxy and τyx), design a Mohr's circle as follows:

• Step 1: Plot the coordinates (σyy,τxy) and (σxx,-τxy) as points A and B, with as the X-axis and as the Y-axis, respectively.
• Step 2: To get the diameter AB, join the points A and B.
• Step 3: Find the circle's centre, O, which is the place where line AB intersects the X-axis.
• Step 4: Draw a circle with O as the central point.
• Step 5: The principal stresses are the spots where the circle contacts the X-axis.

### Mohr's Circle Calculator: How to use it?

To use the principal stress formula and Mohr's circle calculator, follow the instructions below.

• Step 1: σxx place the typical tension in the X-direction.
• Step 2: σyy place the typical tension in the Y-direction.
• Step 3: τxy please fill in the shear stress.
• Step 4: Mohr's circle calculator will now calculate maximum and minimum principal stresses, maximum shear stress, angle of orientation, von Mises, and mean stress using the primary stress equations.

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### FAQs on Mohr's Circle Calculator

1. What is the significance of von Mises's stress?

Before the distortional energy reaches its yielding point, the von Mises stress (VM) indicates the comparable stress condition of the material. It is worth noting that the von Mises stress only includes distortion energy (shape change), not dilational energy (change in volume).

2. Mohr's circle has what radius?

The value of maximum in-plane shear stress determines the diameter of the Mohr's circle. On planes of zero shearing stress, the maximum and minimum normal stresses are found. The major stresses and the planes on which they act are referred to as the maximum and minimum normal stresses, respectively.

3. What is the purpose of using Mohr's circle?

Mohr's circle is a graphical representation of the plane stress transformation equations. It's handy for showing the relationships between normal and shear stresses acting on a stress element at any angle.

4. Is there a stress scalar in von Mises' theory?

The stresses estimated at any site can be written theoretically into a scalar number known as von Mises stress, which can be compared to yield points seen experimentally.

5. In the Mohr circle, what is the pole?

For the two-dimensional instance, the pole of a Mohr diagram is a single point on the Mohr circle that allows any point on the Mohr circle to be connected to the actual plane direction associated with that location. Any second rank tensor can be represented by a Mohr diagram.