0:05

When we want to proceed with the dimensioning of steel beams,

we are going to proceed in a way which is similar to what we have seen with concrete before.

It is important - we are going to see why -

to use Newtons and millimeters as units,

that is a bit different from what we usually have

but that is not very serious,

and then we will look a bit at the dimensions of these steel shapes.

We are going to start with exactly the same condition,

we are going to predimension a steel beam with large flanges,

which has a span of 10 meters,

a depth of 1.32 meters,

we do not know the width of the flanges.

Here you go, we have our steel beam.

The first thing we are going to do is to put the screen to scale.

This time we do not have a distance of ten or or one hundred

but a distance of ten thousand between the supports.

1:05

You can see that the applet always automatically puts the forces to scale,

se we cannot see when we insert forces

if they are ten, one hundred, or one thousand times too large.

So, we have to be careful,

I insert here the left support

1:36

at first,

I activate the resolution pushing control

and we can see something very thin which appears

and if I make it go down into the cross-section,

here I can see that I would only need,

for the width of 300 millimeters which I have indicated,

a steel thickness of approximately 13.5 millimeters.

We are going to be able to do something a bit more efficient,

probably decreasing the width:

instead of a width of 300 millimeters,

I put 100 millimeters.

2:08

And then I restart the resolution,

we can indeed see a slightly larger thickness,

and I can move the supports

in such a way that the internal forces remain inside the cross-section.

Here you go, we can see that I only need now

an upper flange with a width of 100 millimeters

and a thickness of approximately 41.5 millimeters.

So I could order a steel beam

asking for a 41 or 42 millimeters thick upper flange

and probably approximately the same thing for the lower flange.

That would absolutely be possible.

However, for steel shapes,

cross-sections are standardized.

Here, I show you a part of the Swiss table

but that is available almost everywhere in the world

for the double T cross-sections.

There are many more,

in some countries, there are many more than in Switzerland,

so it depends on the countries

but what we can very clearly notice

is that there are nominal depths

which vary between one hundred and one thousand millimeters so up to one meter.

The profile I had before - 1.32 meters - that is not standard,

that is not going to be possible.

And then we have three range of weigths:

HEA, HEB and HEM,

if we take one of 320,

you can see that the HEA weighs 97.6 kilos per meter,

the HEB 127 kilos

and the HEM 245 kilos

so a very big difference of weight for these different shapes.

We will see that it also changes their efficiency.

3:42

So, for the pre-dimensioning, we are going to have

at once a variation of the depth and of the thickness

and then we are going to use a special grid

for the free dimensioning of beams.

If you start the i-Cremona applet,

in the folder containing the common pictures, you will find at the beginning,

this picture which is called "Abaque poutre".

I have activated it here,

I am now going to put the screen to scale,

I have a maximum distance of 15 000

between this point here, for example, and this point there,

so I put it to scale.

Then, I am going to insert my forces,

my forces have a value of 100 000 Newtons,

I stay here in Newtons and in millimeters,

which I always place in the middle of the interval,

that is why we have these intervals, here,

4:46

and of 10 000.

I place them a bit higher, as you can see,

to already take into account the position of the center of gravity of the lower flange

and afterwards, I define the properties of my material.

For example, here, a grade 355 steel

with a width of 300 millimeters,

which, you will see, is quite standard for what we want to do.

5:20

and the depth, well, I am going to see,

I could for example, take here a cross-section

which is, let's say, 700 millimeters deep,

so I am going to have here a depth of approximately 700

and here, it is said to me that with 700,

I need to have a width of the upper flange... of both flanges,

of about 17 millimeters.

5:45

We are at the level of 700 millimeters, here

and we want a thickness,

the thickness can be read on T and we get roughly 17.

So here, it would work with the HEA 700, but it has 27,

so the depth is probably too large.

I come back to my applet

and I am going to decrease this depth to, let's say, 600.

For 600 millimeters, I would need a width of 300

and a thickness of about 20 millimeters according to the applet.

I am now at 600 millimeters,

I need a width of 300,

we can see that the width 2c is 300,

that is constant over a large portion

so it is no coincidence that I have chosen this value

And then, we have a thickness of 25

and, what has been asked to me was a thickness of 20,

so that is still too large.

7:12

This is the HEB 550 and it weighs 187 kilos per meter,

compared to the HEA 600 which weighs 178 kilos per meter.

So, if we have a bit a space, we can easily use the HEA

which makes us save some material.

The question is, what happens -

could we only have, for example,

a beam depth of 400 millimeters?

I come back here, I activate the funicular polygon and I try to go to 400 millimeters,

that is here and we start looking at the thickness, which is significant,

I need a thickness of approximately 31 millimeters.

8:46

So, the process of dimensioning of a steel double T cross-section

consists in the choice of a cross-section according to its efficiency

and its weight.

Finally, we can also pre-dimension

a composite steel-concrete beam, like I showed you

in the lecture about the superimposed beams,

so we have a steel beam in the lower part,

a system of connecting dowels

and then a concrete slab in the upper part.

Look, this is schematically drawn here,

obviously, what we do not know

is the width of this concrete slab

and also its thickness.

9:23

Here we have the applet which has already been put to scale,

in meters by the way

since we are going to work with concrete

and in which I have already inserted the forces.

So, we are now going to define these dimensions,

I am going to consider a strength for the concrete

of 20 megaNewtons per square meter

and a width of 0.8 meters like before,

like for the T cross-section

and I am going to activate the resolution

with the funicular polygon

and here once again, like for the T cross-section,

what we can see is that we only need, for a width of 0.8 meters,

about 60 millimeters of compression

so actually this slab here could be thinner,

it corresponds well, by the way, to the principle of composite construction

in which we try to have relatively thin concrete slabs.

The part in tension, that is interesting,

the tension is not only supported

by the lower part in this case,

we can absolutely consider that

the center of gravity of the lower part of the cross-section

is where the internal forces are going to be supported

so the dimensioning is a bit more complicated in this case here,

we are not going to get into the details

but these 1.25 megaNewtons can be carried

by a considerable amount of steel

which is placed in the lower part of the cross-section.

In this video, we have seen how to proceed to the pre-dimensioning

of various types of beams

using the i-Cremona applet.

We have seen that it is very important to use

coherent working units,

good units being megaNewton and meter for the concrete structures,

Newton and millimeter for the steel structures.

we have applied this dimensioning method

to various types of cross-sections,

first to rectangular cross-sections for a concrete beam

and then to T-shaped cross-sections

then to double T shapes for the steel cross-sections

as well as for a composite steel-concrete beam.

We have seen that the predimensioning can be done quite quickly,

I draw your attention on the fact that the final dimensioning

will have to take into account other parameters

which are not dealt with within the framework of this introductory course.