We’ll base our code development on the example structure shown in Fig. But once you’ve understood what’s going on for point loads, the process to implement applied moments and distributed loads only required incremental additions (which we’ll walk through in detail in the video series). We’ll walk through the calculation and coding process for point loads in detail here.
But after completing the project, you’ll be more than capable of expanding your calculator to other forms of loading. This should represent the most common forms of beam loading. Distributed loads of linearly varying magnitude (triangular loads).We’ll build in the ability for our code to calculate the reactions and internal shear forces and bending moments across our structure in response to: Again, we’ll use superposition to layer together the influence of multiple external forces/moments acting simultaneously. By calling this function within a loop for each x-coordinate, we’ll build up a range of shear and moment values along the length of our beam. We’ll then write a function to calculate the shear force and bending moment at some distance along our beam. We’ll start by constructing a vector of x-coordinates along our beam. We’ll take the same approach when it comes to calculating the shear force and bending moment at each point along our beam. If we record the reactions from each point load, we can use the Principle of Superposition to add them all together and find the reactions assuming that all of the point loads were acting simultaneously. Then we’ll construct a ‘for loop’ that cycles through each of the point loads we’ve specified and calls our function to determine the reactions from each point load acting individually.
So for example, we’ll write a function that calculates the reactions from a single point load located at meters from the left side of our beam. Provided we’re satisfied that the behaviour remains linear, we can use this principle to layer the resulting influences of as many actions as we like. If any of the loads on our structure induce non-linear plastic behaviour, application of the superposition principle is no-longer valid. It’s important to note that we can only use the Principle of Superposition when our structural behaviour can be assumed to be linear. We used the Principle of Superposition when we were calculating beam deflections from first principles here. In the context of our simply supported beam, this simply means that we can determine the influence of multiple loads acting simultaneously by adding together the influences of the same loads acting individually. We’re going to make use of the Principle of Superposition to build our calculator. The Principle of Superposition and our approach to the build
If you need help getting your coding environment setup, check out this video (part of another course but covers what you need to get up and running). If you need a refresher on the basics of shear forces and bending moments, check out my Ultimate Guide to Shear and Moment Diagrams.Īs I always say at the start of a new DegreeTutors project or course – you don’t need to be a Python programmer to complete this project! Complete beginners can work through this project and pick up the programming basics along the way. 🚨 For this project I’m working on the assumption that you’re familiar with the concepts of internal shear force and bending moment as stress resultants that arise within a structure due to external loading.
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