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.

Now a second question arises: what types of loads can 2D elements resist? Well, generally speaking, we could classify them as follows:

- Tensile loads: when we pull the structure.
- Compression loads: they can be thought as a negative tensile load.
- Shear loads: when we have two forces acting in different directions applied at two parallel edges.
- Bending moments
- Torsion moments.

Once I’ve introduced these concepts, I must say that in order to perform in an efficient manner, a structure needs to be in equilibrium. If we have a quick look at the image above, we can extract the following conclusions:

**Tension/compression****:**we have two vertical loads acting in opposite directions. Under that loading case, the structure will not experience any rigid body motion. Therefore, the element is in equilibrium.**Bending:**we have a moment applied on the right edge that will make the element rotate anticlockwise. However, on the other edge there is another moment that will create a clockwise rotation. Therefore, the body is balanced.**Torsion:**same case as before, on one edge we have a moment which will twist the element in one direction, whereas on the other edge there is another moment balancing that rotation.

In case you havn’t noticed, I didn’t say anything about shear. If we look at that case very carefully, we can see how, even though the forces are balanced in terms of one going up and the other one going down, the body will suffer a clockwise rotation. That is due to the fact that the forces are creating a moment with respect to its centre of mass. Thus, the element will experience rigid body motion and, therefore, it can be said that it is not in equilibrium. In order to solve this problem, the only thing we need to do is add another pair of shear forces to balance that rotation. This concept is known as **complementary shear** and it is extremely important for automotive companies, since it is a key factor for transferring loads between the different panels of the body.

After all this theory, I’m just going to introduce a particular loading case by asking the following question: what happens when you go over a speed bump just with the wheels of one side of your car? Pretty much, you will be creating so called **asymmetric loading case**. In other words, your vehicle will suffer torsion. As I explained last year, this is the worst loading case for your car.

But, why is this related to complementary shear? Let’s think of our car as a shoe box, as presented in the figure below.

Then, applying the **Simple Structural Surfaces (SSS) **method (thanks to Jason Brown and his amazing book “Motor Vehicle Structures”!) we can see how al the surfaces are perfectly balanced, allowing the transmission of all loads between the different panels. Therefore, the shoe box can resist the asymmetric load case. Please note that the process to obtain this distribution of loads takes a bit of time, but it is quite simple and it is based almost exclusively on complementary shear. I would recommend you to try to get this same diagram and if you have any problem, just comment this post or send me an e-mail and I will be more than happy to explain it in further detail.

Okay, now we know the very basics of how the loads are distributed in a standard saloon car (i.e. our fantastic shoe box). Now, think of a convertible car. Basically, most convertibles look like the standard model without the roof, so… why not create our own covertible car by simply removing the roof panel of our vehicle?

Considering the same torsion case and our fancy shoe box, we can see what happens if we remove the roof panel…

Ladies and gentlemen, the structure would not be able to transfer any load! This means that the vehicle would suffer excessive deformations and rotations which could cause the structural failure of the car! Now you can see why at the beginning I said that if you decided to make a homemade convertible car, you would probably be the bravest person in the world.

To overcome this big issue, automotive companies apply soe engineering solutions to design convertible versions of existing models. Two widely used methods are:

- Adding a torsionally stiff
**grillage**type structure into the vehicle floor.

- Finding areas within the vehicle body which can be
**“boxed in”**to give torsionally stiff elements. Potential areas can be: the luggage or the engine compartment; the region near the A-pillar inside the car (using a ring frame); the region under the rear seat or near the fuel tank (there is usually a step in the floor). In the image which is illustrated below, the torsion box is highlighted by the arrow. Another old school partial solution to add extra stiffness could be a**T-roof**.

To sum up, I would like to go through the main things that we can extract from this post:

- A good vehicle structure must be in equilibrium, i.e. it must be able to transfer loads.
- Complementary shear is an “impact player” for studying load distribution in automotive structures and we should never neglect it.
- Removing the roof would also remove the capability of the structure to resist stresses, resulting in huge deformations.
- Some engineering solutions which are currently used in the automotve industry for adding resistance to toesion in convertible cars have been introduced.

If you still don’t believe me, I encourage you to play with a real shoe box and see what happens when you remove some of its panels while applying different loads!