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Concurrent Engineering Blog

6 Mathcad features to help calculate shear and bending moments

Posted by Concurrent Engineering on 29-Mar-2023 09:16:00

Mathcad is here to make some of the most complex and time-consuming calculations a breeze. Let’s find out more.




Mathcad is the choice of product design engineers who want precise and accurate calculations but also need traceability, security and simplicity. It’s excellent at completing complex yet essential mathematical tasks for engineers, so they can focus on what they do best.


In this article, we’ll look deeper at how Mathcad calculates and plots shear and bending moments. Let’s get started.


The challenge


When a vehicle travels across a bridge, it places stress on the bridge’s supporting beams, causing them to deflect. This deflection results from loading. Loading is a product of the bending moment, shear, the beam slope and the beam deflection itself. Mathcad helps you accurately calculate these numbers, so you can model how supporting beams in any project (it doesn’t have to be a bridge) react to loading.


Reusable functions


The great thing about Mathcad is that you can create functions to use and reuse. That way, one function can solve multiple problems rather than just one. Here are six features related to shear and bending and how they work in Mathcad.


  • Functions – Mathcad has a broad range of functions that help calculate loading-related figures. For example, you can calculate left and right reaction by summing the moment at a certain point and then summing the vertical loads. Mathcad will test these functions. A clockwise moment is considered positive. Mathcad is unit aware, so it can work with any units of length and force for the span and load


  • Symbolic evaluation – Mathcad’s Symbolic Evaluation Operator provides symbolic solutions rather than numeric solutions


  • PowerPoint compatibility – Mathcad plays nicely with Microsoft PowerPoint, so you can use the calculations you perform in Mathcad to make graphics in PowerPoint


  • X and Y plots – Once you have your equations in Mathcad, you can calculate and plot your shear and moments in diagrams using Mathcad’s X and Y features. 


  • Defining range variables – When creating plots, specify the values for span and load. Then, create a range variable for your diagram by laying down a starting point and step size. You can evaluate your range variables to create a vector of values


  • Vectorisation – Mathcad’s Vectorization Operator allows you to break your calculations down into individual elements 


Easy does it


When you combine functions in Mathcad, essential but complex and time-consuming calculations suddenly become quick and easy. Solving problems involving load (uniform, triangular or point) and plotting reaction, shear and bending moments has never been simpler.


If you’re an engineer regularly working on these types of mathematical tasks, Mathcad can make your work more efficient and accurate.


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