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.
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.