2D Mohr’s Circle Plotter for Strain

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Mohr’s Circle for Stress (2D)

Mohr’s Circle for 2D Planar Stress

Mohr’s Circle is a graphical representation used in 2D planar stress analysis to determine principal stresses, maximum shear stresses, and stress orientations. For a given state of stress on a 2D plane, Mohr’s Circle provides a visual way to understand how normal and shear stresses transform as the orientation of the plane changes. By plotting the normal stress (σ) on the x-axis and shear stress (τ) on the y-axis, the circle allows engineers to quickly find principal stresses (the maximum and minimum normal stresses with zero shear) and the maximum shear stress, along with their respective orientations.

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Bolt in Shear Load Calculator

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Bolt Centroid and Shear Force/Stress Calculator

Bolts

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Bolt and Member Stiffness Calculator

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Bolt Stiffness

Effective Bolt Stiffness Calculator
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Member Stiffness

Member Stiffness Calculator
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Stiffness

Is defined by Hook's Law,

k = F/d

Wit the F is tension force, and d is the displacement.

Bolt Stiffness

Bolt stiffness is crucial in bolted joint design, as it affects how the load is shared between the bolt and the clamped components. For optimal performance the bolt stiffness should be lower than the member stiffness to ensure that the joint remains tight and the load is distributed effectively.

Member Stiffness

Refers to the components being clamped (e.g., plates, beams) and their ability to resist deformation.

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Yielding And Failure Criteria Calculator

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Von Mises Ellipse and Tresca Hexagon Plotter

Results

Criteria Equivalent Stress (MPa) Safety Factor
Von Mises
Tresca
Maximum Principal Stress
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Torque and Shear Stress Calculator

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Shear Stress Calculator

Shear Stress Calculator

τ_max: –
Torque Calculator

Torque Calculator

T: –
Radius Calculator

Radius Calculator

r: –

τmax​ = T⋅r/J

where T is torque, r is the radius, and J is the polar moment of inertia, which reflects the object’s resistance to twisting. Together, torque and shear stress calculations help engineers design components that withstand rotational forces without deforming or failing.
 

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Stress From Bending Moment Calculator

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Calculate Stress

Bending Stress Calculator

Bending Stress Calculator

σ: –

Calculate Bending Moment

Bending Moment Calculator

Bending Moment Calculator

M: –

Calculate Moment Inertia of area

Moment of Inertia Calculator

Moment of Inertia Calculator

I: –

Bending Moment Stress

The equation for bending stress (σ) is derived from the bending moment (M) and is given by:

σ = M⋅y / I​

where:

  • σ = Bending stress
  • M = Bending moment
  • y = Distance from the neutral axis to the point where stress is calculated
  • I = Moment of inertia of the cross-sectional area

This equation shows that bending stress is directly proportional to both the bending moment and the distance from the neutral axis, and inversely proportional to the moment of inertia.

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Bolt Strength Standards Filter

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Metric

Metric Bolt Properties Lookup

Properties:

Minimum Proof Strength: MPa

Minimum Tensile Strength: MPa

Minimum Yield Strength: MPa

SAE

SAE Grade Strength Lookup

Strength Properties:

Minimum Proof Strength: kpsi

Minimum Tensile Strength: kpsi

Minimum Yield Strength: kpsi

ASTM

ASTM Bolt Properties Lookup

Properties:

Minimum Proof Strength: kpsi

Minimum Tensile Strength: kpsi

Minimum Yield Strength: kpsi

About the Bolts data

The data used here are publicly available or typical size of the standard bolts and washer, which is okay for initial design calculation. For more detailed and exact selection, please use actual vendor database.

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BOLT AND MEMBER STIFFNESS CALCULATORS

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Bolt Stiffness Calculator

Effective Bolt Stiffness Calculator
>>
>>
>>
>>

Member Stiffness Calculator

Member Stiffness Calculator
>>

Stiffness

Is defined by Hook's Law,

k = F/d

Wit the F is tension force, and d is the displacement.

Bolt Stiffness

Bolt stiffness is crucial in bolted joint design, as it affects how the load is shared between the bolt and the clamped components. For optimal performance the bolt stiffness should be lower than the member stiffness to ensure that the joint remains tight and the load is distributed effectively.

Member Stiffness

Refers to the components being clamped (e.g., plates, beams) and their ability to resist deformation.

Mohr’s Circle For 3D Stress Calculator

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Mohr’s Circle for Strain

What is Mohr’s Circle for Stress?

Mohr’s Circle is a graphical representation used in engineering to visualize and analyze stress states at a point in a material. It provides insights into the normal and shear stresses on various planes passing through that point. Mohr’s Circle helps identify principal stresses (maximum and minimum normal stresses) and maximum shear stress, which are critical in assessing material strength and failure.

Stress Tensor

\[ \bar{\sigma} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\ \sigma_{xy} & \sigma_{yy} & \sigma_{yz} \\ \sigma_{xz} & \sigma_{yz} & \sigma_{zz} \end{bmatrix} \]

Some notes on Stress Tensor

A stress tensor is a mathematical representation of the internal forces within a material. It captures the intensity and direction of stress acting on different planes within a solid object. For a 3D object, the stress tensor is typically represented as a 3×3 matrix with normal stresses (σxx, σyy, σzz) along the diagonal and shear stresses (τxy, τxz, τyz) on the off-diagonals.

Due to the equilibrium, the stress tensor matrix is symmetry. If you put non-symmetry matrix in the calculator, the result will be unphysical!

Other Stress Analysis Modules

Material Selection Filter (Ashby Plot) Plotter

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Design Limits

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Material Density (Min/Max) Young’s Modulus (Min/Max) Yield Strength (Min/Max) Actions
Ultimate Strength (Min/Max) Specific Cost (Min/Max) Max Service Temp (Min/Max)

How to Use This materialSelectionFilter Module:

Select Axes:

    • Choose the properties for the X-axis and Y-axis (e.g., Density, Young’s Modulus) from the dropdowns.
    • Select the scale (Linear or Logarithmic) for each axis.

Set Design Limits:

      • You can learn how to make the equations in the above “>>” button, or watch the tutorial video.
      • Enter minimum and maximum values for the design limits on both the X-axis and Y-axis. These limits will be shown as dashed lines on the plot.
      • If you have design equation, you can input it in these formats:
        • multiplication: x * 2
        • power: x ** 2
        • trigonimetry: Math.sin(x)
        • exponential: Math.exp(x)
        • logaritmic: Math.log(x)

Plot the Materials:

    • Click the “Plot” button to generate a scatter plot of materials with the chosen axes and scales. The plot displays each material’s properties as colored circles.

Manage Materials:

    • To add a new material, click “Add Material” and fill in its properties in the table.
    • To remove a material, click the “Remove” button next to the material in the table.

Edit Material Properties:

    • Use the table to enter or modify each material’s minimum and maximum values for properties like Density, Young’s Modulus, Yield Strength, etc.

Save and Open Materials

    • You can save and open your edited materials data or your custom materials. If you refresh or close the page, the data will be reset.

The plot dynamically updates each time you add, edit, or remove materials, allowing you to compare their properties visually based on your selected parameters.