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.
Welcome to this quick start guide on how to use the 3D truss analysis toolbox. In this tutorial, we’ll work through the solution of a sample 3D space frame (pin-jointed) structure. We’ll determine reaction forces, axial forces and nodal displacements. By the end of this tutorial, you’ll be comfortable using the toolbox to analyse your own structures. In the video accompanying this tutorial, we’ll also use the Blender modelling template file provided to model and analyse a structure from scratch. Like the 2D toolbox, students in particular, should find it helpful as a quick and easy tool for generating structural response data.
In this tutorial, we introduce torsion. This is simply a bending moment applied about the longitudinal axis. Torsion will cause twisting about the longitudinal axis and is a very common form of loading. Our starting point will be to explore the concept of strain as it applies to circular bars and to derive an equation that relates the strain to the angle of twist in the bar. Next, we’ll tie shear stress into the story and see how it relates to applied torque and torsional deformation. Finally, we’ll bring everything together with some numerical examples to demonstrate how to deploy the equations we’ve developed.
In this tutorial we’ll explore the moment distribution method. This is an excellent technique for quickly determining the shear force and bending moment diagrams for indeterminate beam and frame structures. In this tutorial, we’ll focus on applying the moment distribution method to beams. We’ll start by getting a clear understanding of the steps in the procedure before applying what we’ve learned to a more challenging worked example at the end.
In this tutorial, you’ll learn how to use the virtual work method to analyse trusses and calculate truss deflections. The virtual work method is based upon the Principle of Virtual Work which underpins many elegant and versatile analysis procedures. We’ll focus here on how it can be applied to trusses. This tutorial will initially develop the underlying theory, starting with the concept of strain energy. This will make the jump to virtual work much easier to understand. We’ll bring it all together with a thorough worked example at the end.
In this tutorial, we’ll cover free body diagrams and how to use them to evaluate the forces acting on a structure in equilibrium. A free body diagram is a diagram in which only the forces imposed on an object are shown. Free body diagrams are a simple tool to help us identify all of the forces that influence an object or structure. Typically, one of the first steps in analysing a structure is to sketch out its free body diagram, identifying all of the forces that must be considered in the analysis.