In this project we’re going to build a Shear Force and Bending Moment Diagram calculator using Python in the Jupyter Notebook development environment. Generating the shear force and bending moment diagram for a simple beam with anything other than basic loading can be a tedious and time-consuming process. Once you finish this project, you’ll have a calculator that can produce shear force and bending moment diagrams at the push of a button.
In this Python project we’re going to build a Mohr’s Circle calculator. By the end of this project, you will have built your own stress analysis Python code. Along the way we’ll cover all of the fundamental topics that lead up to Mohr’s circle of stress. You will learn about how we use the 2D stress element to represent the state of stress at a point, the purpose of stress transformation equations, principal stresses and principal planes planes and of course Mohr’s circle!
In this tutorial we’re going to focus on trusses, also known as pin-jointed structures. We’ll briefly discuss their key features and methods of analysis. We’re going to start at the very beginning by briefly considering what exactly a truss is – but we’ll very quickly move on to truss analysis and demonstrate the joint resolution method and method of sections with some worked examples.
In this post we will use the Tintagel footbridge as a case study to explore structural behaviour and show how we can build up an understanding of the structure through analysis of increasingly refined finite element models models. We’ll apply this iterative approach by starting with a simple beam model and incrementally working towards a full 3D finite element model. Throughout this post we’ll make use of finite element analysis codes developed in DegreeTutors courses.
In this tutorial we’re going to explore beam deflection and see how we can calculate the deflection of any beam from first principles using the differential equation of the deflection curve. We’ll work our way through a numerical example before discussing how we can use superposition along with tabulated formulae to speed up the process of calculating beam deflection.
In this tutorial we examine the Direct Stiffness Method and work our way through a detailed truss analysis. By the end of this complete introduction, you should understand the basic ideas behind why the method works, how to implement it for truss analysis and you should understand the power and scalability of the technique. Once understood, the direct stiffness method opens the door to structural analysis of large scale complex structures.
By the end of this post you’ll understand when and why a dynamic analysis is performed instead of a (usually more straightforward) static analysis. Although we typically encounter static loading, dynamic loads occur with sufficient frequency that we need to understand how to assess their influence on a structure. Typical forms of dynamic loading can include loading due to earthquakes, wind, vehicle or pedestrian traffic or wave loading on coastal or offshore structures.
Shear force and bending moment diagrams tell us about the underlying state of stress in the structure. Determining shear and moment diagrams is an essential skill for any engineer. Unfortunately it’s probably the one structural analysis skill most students struggle with most. So in this post we’ll give you a thorough introduction to shear forces, bending moments and how to draw shear and moment diagrams. By the end of this post you’ll know a lot more about shear forces and moment moments then when you started.
In this tutorial, we’re going to work out exactly how to determine the plastic moment capacity of a cross-section. We’ll also explore the concept of moment redistribution with an illustrative example. By the end of this post you’ll be able to calculate the plastic moment capacity of any cross-section and understand in detail how moment redistribution occurs in a structure and ultimately how collapse can occur as a result of hinge formation.
So why is plastic behaviour so important to understand? It’s probably fair to say that most of our engineering analysis assumes linearly elastic behaviour. But in reality, if we limit our designs to purely elastic behaviour, we’re leaving a lot of structural capacity untapped. Structures very often have more load carrying capacity than a linearly elastic analysis suggests. In this post we’ll explore this reserve capacity.
In part two of this tutorial series we’ll consider how to analyse the lateral stability of a multi-storey structure with an asymmetrical arrangement of stabilising elements. Asymmetrically propped structures undergo twisting or rotation about the centre of stiffness in addition to direct lateral translation. We will consider how to determine the additional forces induced by this twisting. Finally we’ll compare our hand analysis results to a simple finite element analysis model.
All structures typically experience some form of lateral loading during their design life. Typical sources of lateral loading include forces due to wind blowing against the structure, hydrostatic forces due to groundwater (acting against basement walls for example) or inertia forces due to ground motion (earthquakes). In this, the first of a two-part series on structural stability, we will introduce common lateral stability schemes before diving into some numerical examples in this and the next post.
In this final post in this series on Column Buckling, we’ll look at more realistic buckling behaviour you’re likely to observe in reality. In particular we’ll explore the behaviour of columns subject to eccentric axial load and columns with an initial deformation, i.e. columns that don’t start out straight. It’s important to recognise that for a column with these characteristics, we do not observe the strict mathematical behaviour predicted for perfectly loaded perfectly straight columns
In this post we’ll start to consider more realistic column structures. In particular we’ll determine an expression for the critical load for an axially loaded column with pinned ends. Then we’ll explore other support conditions. We’ll also introduce some other key concepts such as buckling modes and effective length.
Long slender structural elements under the action of an axial load may fail due to buckling rather than direct compression. Buckling failure occurs when axial load induces a lateral deflection leading to a bending type failure. Buckling can also occur in plate and shell structures and is a relatively common cause of structural collapse. Depending on the geometry of the structural element, buckling can occur long before the material yields.
Structural analysis is the process of using mathematical and mechanical principles to determine the magnitude of internal forces in a structure. One of the main roles of a civil or structural engineer is carrying out structural analysis as the first step to designing a safe structure. In this tutorial we’ll demonstrate exactly how this process works for a real world structure.
A truss is a structure that consists of a collection of elements connected at pin joints or nodes. In theory, the pin joints provide no rotational resistance and behave as hinges. In practice this is not always the case.
In this tutorial, we’ll discuss common forms of truss, their features, approximate methods of analysis and the key assumptions that relate to our analysis.