Welcome to the DegreeTutors Blogtorial.
As the name suggests, these posts will be a mixture of the traditional blog post and an engineering tutorial. The hope is that I can give you some useful engineering information in a reasonably interesting way, or at least not in a formal lecture style. The first topic I’ll dive into is the concept of load paths. I’ll break this topic into 4 discrete posts, released over the next 4 weeks or so. We’ll build the discussion around pin-jointed trusses and in particular, a real world truss bridge. If you would like a typeset pdf version of this and future blogtorials, just sign up to my mailing list at the bottom of the page. Ok, lets crack on with the blogtorial #1!
1 What is a Load Path?
One of the first thing to wrap your head around as an engineer is the concept of a load path. This is basically the idea that any structure acts like a conduit through which ‘loading’ or force will travel. As force is transmitted through parts of a structure, stresses are induced within each element. As the engineer, your job is to ensure that the stresses stay within acceptable limits.
In the context of civil or structural engineering, the structure in question may be a building, a bridge or even a construction crane. The loading will typically be derived from people, or occupancy more generally. Loading may well be derived from environmental sources such as wind, snow, groundwater or perhaps dynamic loading due to earthquakes. Of course there is also the self-weight of the structure to consider. When loading is imposed on the structure, through our design, we need to ensure it’s transmitted safely (without structural failure) back down to the ground via the foundations of the structure. So, understanding how to track loads through a structure is a key skill. In this four post series I’ll explain how this is done using a case study structure.
2 Pin-jointed Trusses
One of the first ways engineering students are introduced to load paths is through the analysis of pin-jointed trusses. There is a couple of reasons for this; firstly, the truss is a very simple structure, easy to understand and analyse. Through some simple analysis we can quite easily trace the load path through a truss and visualise how the force is being transmitted (as you’ll see in an upcoming post).
The other reason we introduce pin-jointed trusses early on is because they are so ubiquitous. We see them all around the built environment. Their simplicity belies their exceptional ability to span very large distances with great efficiency. It’s this efficiency that makes them well suited as roof and bridge structures.
2.1 Structural Models versus Real World Structures
Before we can charge into the analysis of pin-jointed trusses, it’s important to understand some assumptions we make to facilitate the analysis. In fact, these assumptions speak to a more fundamental point which applies to structural analysis generally and in particular ‘by-hand’ methods of analysis as-opposed to computer-based analysis. The point is this…when we set about analysing a truss we first have to construct a model on which to base our analysis. That model might simply be a line-diagram drawn on a page. But we must always remember that the model is an imperfect representation of the real world structure. It’s our approximation of the actual structure and will almost never capture 100% of the detail of the real-world structure.
Sometimes the differences between model and structure are quite small, in which case we can have more confidence in our analysis. However if we’re not careful the simplifying assumptions that facilitate the hand analysis can be so limiting that the model behaviour is not a good representation of the structure. Having an appreciation for the impact of how your assumptions degrade the accuracy of your model is crucially important.
So, back to the task at hand, what assumptions apply to the analysis of our pin-jointed trusses? The first is that the nodes or joints that connect members behave as pins. In other words, if we consider two members meeting at a joint, they would be free to rotate relative to each other. Now, the implication of this is that no bending moments can be transmitted through a joint, only force. This leads to the second assumption; the members within a truss are subject to axial load only, tension or compression. Provided all external loads are applied at joints, then no bending will be induced within any of the members. Of course if an external force was applied to a member between joints, normal stresses due to bending would be induced in that member, but we typical try to avoid this ‘inter-nodal’ loading in trusses if possible.
The obvious question is how valid are these assumptions? Well, regarding the pinned joints, in reality true pins, allowing free rotation are very rarely provided. This is mainly driven by the relatively high cost of fabricating such joint. In a steel truss, the joints are almost always bolted or welded. As such, bending moments will be transmitted to some degree through joints and therefore within the structure. However, the geometry of the joints is usually such that their ability to transmit moment is quite limited. So our assumption usually causes model behaviour to deviate relatively little from the actual structural behaviour. With reference to the members developing only axial loads, it follows from our discussion of joints, that if inter-nodal loading is minimised, the predominant action experienced by the members will be axial force. So, all-in-all our truss models are pretty reasonable approximations of real truss structures.
In the next instalment, I’ll introduce our case study structure and we can start to get into some structural engineering. I’ll start to identify the load transmission path so we can unpick how the structure actually stands up. Remember to sign up to receive your typeset PDF copy of this and future posts.