# Structural Analysis

## An Introduction to OpenSees and OpenSeesPy for 2D Truss Analysis

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.

## Arch Analysis – How to Analyse Determinate and Indeterminate Arches

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!

## Influence Lines: A Complete Introduction for Civil and Structural Engineers

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.

## Plastic Analysis of Frames – A Complete Guide – Part 2

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.

## Plastic Analysis and Plastic Collapse – A Complete Guide – Part 1

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.

## How moment redistribution leads to more efficient designs

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.

## How I Coded an Analytical Beam Calculator

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.

## 3D Truss Calculator – Quick Start Guide

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.

## How to Analyse Indeterminate Beams using the Moment Distribution Method

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.

## How to Apply the Virtual Work Method to Trusses

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.