In this tutorial, we’ll take a first look at OpenSeesPy, a Python library for performing finite element analysis based on the OpenSees framework. By the end of this tutorial, you’ll be able to perform 2D truss analysis using OpenSeesPy. I suspect you’ll also be very keen to explore OpenSeesPy further after you see how powerful it is! OpenSees, and by extension OpenSeesPy can be tricky to get started with. The learning curve is relatively steep, but there is a huge amount of functionality packed into the library, so it’s worth persevering with.
Arches are one of the most efficient and elegant structural forms. Their efficiency has seen them selected throughout history as the go-to form for spanning large distances. In this tutorial, we’ll explore the different methods for analysing both determinate 3-hinge arches and indeterminate 2-hinge and fixed arches. Through worked examples, we’ll develop the various methods, with particular attention paid to how Virtual Work can help us unlock indeterminate arches. After completing this tutorial, you’ll have a better appreciation for the structural behaviour of arches, and you’ll be confident in analysing arch structures by hand!
In this tutorial on influence lines, we will explore influence lines and the techniques that can be used to construct influence line diagrams for determinate and indeterminate beam structures. By the end of this tutorial, you will be confident in drawing and formulating influence lines for determinate structures. You will also develop an appreciation of how we can implement more advanced structural analysis techniques to construct influence lines for indeterminate structures. Along the way, we’ll touch on Maxwell’s Reciprocal Theorem and the Müller-Breslau Principle.
In the second part of this series on plastic collapse analysis, we explore how what we learned in part one can be applied the frames. Plastic analysis methods are particularly useful in the analysis of indeterminate steel portal frames as it allows us to efficiently achieve relatively large spans by allowing for the formation of plastic hinges and moment redistribution within the frame. By the end of this tutorial, you will be confident applying plastic analysis methods to very common single and double-bay frame structures.
Often in structural analysis, linear-elastic analysis is used, predicting failure when structural members reach their yield stress. This method, while effective, ignores the plasticity that some structural materials experience beyond their yield limit. This can lead to an underestimate of the structures safe working capacity. In part one of this tutorial series on plastic analysis, we explore the analytical methods used to evaluate the ultimate capacity of a structure, the so-called plastic limit or plastic collapse limit.
This tutorial focussed on the second moment of area, also known as the moment of inertia. By the end of this tutorial, you should be comfortable explaining what the second moment of area is, why it’s important to engineers, how to calculate it and how to interpret the values in the context of civil and structural engineering. We’ll cover how to identify the location of the centroid of a cross-section shape, how to calculate the different moments of inertia and how to use the parallel axis theorem to compute second moments of area for compound cross-section shapes.
In this tutorial, we’ll discuss moment redistribution in reinforced concrete and how we can use it to our advantage to achieve more efficient designs. When designing any structural element, our first pass usually involves an elastic analysis. However, this approach can leave some structural capacity untapped. We’ll see how we can use the plastic behaviour of reinforced concrete at the ultimate limit state to develop more efficient designs by redistributing moments within the structure. We’ll do this by first explaining the moment redistribution behaviour in a statically indeterminate structure and then exploring what it means for the design of reinforced concrete sections.
In this tutorial, we’ll introduce the role of steel reinforcement in reinforced concrete design. We’ll see that steel plays a critical role in developing an internal moment of resistance and compensates for concrete’s inherent brittleness and weakness in tension. We’ll explore the fundamental mechanical model used to describe the behaviour of the cross-section under load. We’ll also see that to avoid a brittle failure, we must limit the depth of the neutral axis at the ultimate limit state. After reading this tutorial, you’ll have a good understanding of how to perform concrete section analysis and basic design.
In this post, guest author Vittorio Lora talks us through how he developed the idea for and ultimately built Beamsolver.com. A structural engineer by training, Vittorio has pivoted in his career to focus more on software development. But he couldn’t shake the desire to build the analytical beam calculator that he would have found so helpful as a student. Parameterised structural analysis problems are notoriously difficult to solve algorithmically. Unlike numerical problems, solution techniques based on linear algebra just don’t scale well. Vittorio explains how it was actually the simple techniques we all learn first that ultimately unlocked the problem.
Concrete is one of the most important and ubiquitous materials in the construction industry globally. Twice as much concrete is used (by weight) as steel, wood, plastics and aluminium combined. Its global usage is estimated at 10 billion tons per year. Fundamentally, concrete is simply a mixture of cement, water, aggregate and sand. When mixed, they form a slurry that undergoes a chemical reaction called hydration and gains strength slowly in a process called curing. In this article, we’ll discuss the properties of concrete, its constituents and what makes it such a versatile construction material.