Tag Archives: Structures

Classic question about the use of a Cantilever beam for designing vehicle structures

Good afternoon everyone! I know it’s been a while since the last post but I’ve been (and still am) very busy with all kind of simulations, tests and writing papers and my doctoral thesis. Hopefully, I’ll manage to write some more articles during the summer! I recently had a conversation with some senior engineers from a F1 team regarding Cantilever beams and some erroneous assumptions which are commonly made, so I wanted to discuss it with you! Hope you enjoy this brief post!


A few weeks ago, I had the chance to speak with three top F1 designers and we had a chat about a certain question regarding the use of the Cantilever beam as a tool to design some vehicle structural components. First of all, let’s remind what this type of configuration is. A Cantilever beam is a structure which is fully constrained at one end, having a vertical load applied at the other end of the beam to study the effect of bending, as illustrated in Fig. 1.

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Figure 1. Schematic of a Cantilever beam

This type of structure is very useful when designing certain components, since they can be simplified to this well-known beam, reducing the number of variables and being able to define simpler design targets. The thing is that usually, in reality, the components usually have some part of its length reinforced (e.g. thicker walls), so two questions arise: why is this non-homogeneous beam common and where should that reinforcement be placed?

We agreed that a lot of people answer very quickly that it should be placed at the free end of the beam, i.e. where the load is applied. According to these people, the reason for this is pretty obvious, since that end will suffer the greatest deflection (I will write another post soon where I derive this and discuss some ways to calculate it by hand!). Hence, if that region was reinforced, the deflection would be smaller and the structure would be better in terms of bending performance. But, is this true? Let’s have a thought.

Consider the structure from Fig.1 and try to analyse it with simple structural mechanics. Firstly, we need to determine the reaction forces and moment at the fixed end caused by load P. Applying equilibrium as shown in Fig.2, the following results are found:

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Figure 2. Equilibrium applied to the Cantilever beam

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Then, applying equilibrium to a portion “x” of the beam from the fixed end (see Fig. 3), the stress distribution can be easily calculated by applying, once again, equilibrium:

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Figure 3. Equilibrium applied to a section of the Cantilever beam

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While the axial stress is null and the shear stress is constant along the length of the beam, the bending moment depends on the position. This means that the maximum moment that the structure experiences is located precisely at the fixed end, rather than at the loaded point! Therefore, the fixed end is the region which suffers the most, resulting in designers adding extra material or other types of reinforcements in that area, in opposition to what other people mights have thought! If you don’t believe this, you can always hold a small stick in one had and apply a vertical displacement on the free end with your other hand: the stick will bend and break at the end that you’re holding!

My point with this post is that this simple question can be asked to you in an interview, and you should not jump into the first “logical” response that comes into your mind. Just spend some time thinking about the problem and you’ll see how basic structural mechanics can help you! And you thought you would never use all these basic theories you were taught at university…

What is the aim of the front wing in a F1 car?

Have you ever wondered why Formula 1 cars have those extremely complex front wings? Some people may think that these structures are only there for producing downforce, but in reality their function goes beyond that. Do you want to find out more? Well, here’s your chance!


A few years ago I had the opportunity to meet Craig Scarborough during one of his pesentations about Formula 1 at Cranfield University (United Kingdom). For those who are not familiar with that name, Mr Scarborough is a well known expert in motorsport and, just so you know, he’s quite a celebrity on social media (Twitter, LinkedIn…), where he usually shares top quality information about racing and the engineering behind it.

Yesterday, I contacted him after watching his latest video for motorsport.com in which he discusses the function of a front wing with Willem Toet, one of the best aerdynamicist in the world. They use a 3D airflow animation in order to illustrate how the wing of the McLaren MCL-32 works. After asking for his approval, Mr Scarborough was kind enough to give me permission to share the video with the audience of Engineering Breakdown, so here it is! I hope you enjoy it!

(Please note that in order to watch the videos, you need to reproduce them on Youtube, following the instructions).

How to solve a Finite Element problem using hand calculations

Basically, when we want to determine the forces and displacements in a certain structure using Finite Element Analysis (FEA), what we are doing is creating a system of equations that relates the stiffness of the elements to the displacements and forces in each node. When we run a simulation, we do not see all the calculations. For that reason, today I want to illustrate a simple case that can be easily solved by hand applying that methodology.


Before getting started, just think of a spring. Everyone has come across the Hooke’s law at a certain point during school. It states that the force in the spring is proportional to a constant “k” multiplied by the variation in length of the spring. FEA follows the same principle, but in this case the “k” constant is the stiffness matrix and the variation in length is a vector of displacements and rotations, depending on the case.

Let’s study a simple static case. Our structure consists of two bar elements connected at a common node, where a load “P” is applied. The other two nodes have both horizontal and vertical displacements constrained (see the boundary conditions). For this particular case, the reactions in nodes 1 and 3 and the displacements of node 2 are requested. I have solved the problem by hand following a few steps that, based on my experience, can be generalised for more complex problems. Pretty much, the summary of the methodology is: Read more

Things to take into account when making your own convertible car

Last February I participated in the Young Persons’ Lecture Competition, organised by IOM3. In particular, the local heat took place at the University of Surrey. I want to share with you the transcript of my presentation. I have to say that I tried to present a quite complex topic in a very simple way so that anybody without  an engineering background could follow it. Hope you enjoy it!


Abstract: What would happen if you removed the roof of your car? First of all, you would have a convertble vehicle to enjoy that one sunny day we have in England. Second and most importantly, you would probably be the bravest person on earth. Driving on a bad road or even going over a speed bump could have dramatic results. Using simple engineering concepts, logic and a shoe box you will be able to understand why that could happen ad how automotive companies overcome this issue.

Let’s start from the beginning. What is Strength of Materials? It is the science that studies the behaviour of solid objects when they are subjected to stresses and strains. So, first question: what kind of objects? Basically we can have 1D, 2D and… Exactly! 3D elements! Some examples could be a bar (1D), a shell or a plate (2D) and a hexaedron (3D). For this particular topic, I’m going to focus on 2D elements, since the body panels of a car can be considered as very thin shells assembled together.

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What’s the best way to go over a speed bump?

I’ve noticed that a lot of people try to avoid using the four wheels of the car when they go over a speed bump. Out of curiosity, I asked some of those drivers and all of them gave me the exact same answer: “Because if you only hit the obstacle  with the wheels of one side of the car, you will cause less damage to the vehicle and, besides, it is less uncomfortable for occupants”. Is that true? Let’s find out.


Let´s start from the beginning. The first thing we need to know is that cars have two axles (i.e.front and rear) and each of them has two wheels (i.e. right and left). On the other hand, speed bumpers are road obstacles which are designed to make drivers reduce the speed in certain areas and they are usually as wide as the lane. Why is that? Well, basically bumps are thought to be encountered by the two wheels of each axle simultaneously, creating a scenario known as “vertical symmetric load case”. This situation causes results in a bending moment which is applied to the structure of the car.

However, sometimes we can find some bumps which present a smaller width or even gaps. These are the situations where some drivers decide to vary the direction of the car so that the wheels of one of the sides avoid the contact with the obstacle. Therefore, only one wheel goes over the bump. Hence, the vehicle will suffer an “asymmetric vertical load case”. In other words, the automotive structure will be subjected to a torsional load, which is a worse scenario than the one introduced above since it can cause one of the wheels to lift off. I will show you how a relatively simple approach can be used to prove this statement.

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