**Lesson 1:**

## The difference between structure and mechanism.

Let’s start from the beginning… What is it exactly a structure? **A structure is a set of fixed elements that is able to resist the forces that act on it.**

Based on that definition, there’s no doubt that a **bridge **or a **building **(such as the museum of the image on the right) are examples of structures. After all, they are constructions made up of different elements (bricks, columns, beams, cables …) that are somehow fixed and designed to resist the forces that may act on them.

But this definition also includes other objects of our daily life as simple as a chair, a table, a bed frame … Those are also examples of structures, as they are objects made up of elements suchs as wooden legs, metal bars, boards… that must be properly assembled to resist some forces without breaking.

*(Guggenheim Museum of Bilbao, original image)*

## The three conditions that every structure must meet:

Any structure, to be considered as such, must meet the following conditions:

The **stability **of a structure depends on the **location of its center of gravity**. The center of gravity of a body is an imaginary point that is very easy to calculate in simple pieces, but it is not when the object has an irregular shape. For example, the center of gravity of a rectangular object is the point where its two diagonals meet. And the center of gravity of a triangle is the point at which all its medians meet (what in mathematics is called the **barycenter **or centroid):

But then … what is the relationship between the stability of a structure and its center of gravity? The answer is simple, a structure will be stable as long as its center of gravity falls (in a vertical line) within its base. Let’s see it with an example. Imagine that a car is parked on a slanted road. How can we know if the car will overturn o not? In this case, calculating the center of gravity exactly is not easy, however, it can be found approximately as it has been done in the image:

As you can see, in the first two cases the center of gravity falls within the base (represented by a blue line) and therefore the car will not overturn. In the third case, the center of gravity falls just at the limit of the base and therefore is in danger of overturning. In the last example the car will overturn for sure.

Perhaps the best known example of an unstable structure is the **Leaning Tower of Pisa**. Since the beginning of its construction in 1173, the tower of this Italian city began to lean mainly due to the fact that it sits on soft ground. The tower has continued to lean for centuries until thanks to the work of a team of engineers it has finally been stabilized (how was it achieved?). Well, this structure did not finally overturn because its center of gravity never fell outside of its base. Fortunately, the problem was fixed in time, but you can be sure that if no action had been taken the tower would have continued to lean, and eventually would have collapsed.

In the image on the right, the tower’s center of gravity (black point) has been approximately calculated. You can see how, despite the inclination, that point falls inside the base of the structure (blue line):

The **resistance **and **stiffness **of a structure depend on two factors:

- Of the
**materials used**in its construction: for example, a structure made of steel will be probably more resistant and stiff than one made of wood elements. In other words, to make a wooden structure rigid enough it will be necessary to use much more material than if it was metallic.

*(Metalic triangulated cover, original image)*

*(Wooden triangulated cover, original image)*

**How the elements of the structure have been joined**: it is useless for a structure to have pieces of a very resistant material if they are not assembled correctly. That is why it is so important to choose the most suitable way to join its parts. There are many joining techniques: adhesives (cement, glue …), screws, welding …

*(Bricks joined with cement, original image)*

*(Riveted joints in a bridge, original image)*

**Exercises 1 and 2.*