CAD Forum

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In an industry which is so closely regulated, engineers use MathCAD to design calculations, re-use intellectual properties and ensure compliance with regulatory standards. MathCAD also has the versatility to integrate with other programs such as FEA analysis or CAD modeling tools such as PTC Pro/ENGINEER Wildfire but also integrates with other third party applications such as SolidWorks. This allows work to be shared between different application spaces.

MathCAD is especially useful when data needs to be analysed, interpreted and reported on especially with the additional libraries already included such as Signal Processing, Image Processing and Wavelet Processing extension packs. It provides an excellent platform for algorithmic development.
 
Here we have a typical example of having to calculate the normal and shear distribution for the cross section of a rectangular beam:


Question
The bending moment and shear stress at a point on a rectangular beam are denoted as M and V, respectively. The beam width and depth are b and h, respectively. Calculate the normal and shear stress at a number, n, of points along the centre line of the beam cross section.

Parameters
 
 
Solution using MathCAD
Define a range variable i,

 
and calculate the distance, y, from the centroid to the point of interest on the cross- section.

 
The moment of inertia I, of a rectangular beam is given by the following formula:
 
 
Therefore:

 
The flexure formula calculates the normal stress σx, at distance y, from the centroid. The flexure formula equals the product of the moment M, and the distance y, divided by the moment of inertia I.


 
The shear stress is given by the product of shear V, and the first moment of inertia Q, of the cross –sectional area above the point, divided by the product of inertia I of the beam, and the cross-sectional width b of the beam at the point.
 
First moment of inertia Q is given by the formula:


Shear stress formula:

 
We can now graph both normal and shear stress:


Double clicking on your graph in MathCAD will allow access the graph editing functions where you can include legends, change symbols or to add in grid lines. This allows for better presentation of the final results and can make distinguishing between two different variables much easier:


Conclusion
MathCAD can be used to make engineering problems just that little bit easier, faster and more efficient. It allows engineers to perform, document and share calculation and design work and also makes compliance, reporting, verification and troubleshooting that much simpler.

For more information in Australia about Mathcad software, please contact us HERE. A free demo of Mathcad can be requested HERE.
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Mathcad Software Support
CADDIT Australia