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Studiot
Studiot is offline
#12
Mar1-10, 06:25 PM
P: 5,462
I'm glad page1 made some sense, we can move on to page2. Sorry I don't have time for pretty.

If you go on to study any subject involving mechanics of materials you will become very familiar with the type of analysis I have been showing.
I have done it in a simplified form to avoid discussing internal stresses, bending moments and other more advanced stuff.

If you can, get hold of a copy the small book
Introducing Structures by A J Francis is a wonderfully comprehensible introduction. He is one of the few Architects who really understand structures and can put it across in an easy way.

Anyway to continue. You haven't indicated what sort of cardboard is available - you will perhaps need to discuss with your teacher. I am assuming you are going with the cellular 'door' approach. (Corrugated will not do see Fig 8.)

Fig 6
Shows a section of the construction with laminated skins several sheets thick and cardboard tube cells, probably simlar to the centres of toilet rolls.

Fig 7
Shows a cutaway drawing of the arrangement. The stack of tubes is much stronger for this application than the typical corrugated cardboard construction which looks like Fig 8 (b)

Fig 8
Shows alternative spacing arrangements can you see why (a) representing the cells is stronger than (b) ? A good point to discuss with your teacher or in your report.

Fig 9
This answers your question about abutments / bearing areas. Since someone will walk across the walkway and could stand anywhere, the space he occupies has to be able to support him, on one foot as he walks. This space is just under 1ft of beam and is labelled A.
Since one end reaction is equal to the full 160 lbs when the man is standing at that end the reaction will need a similar area to bear upwards on. So the bearing length will be about 1 ft.

Fig 10
Here we go back to the analysis in Figs 3 nd 4 with some numbers.
The couple (clockwise this time) is formed by the 80 lb reaction and the (160 - 80) forces acting wherever the man is standing. The magnitude of this couple is therefore 80d where d is the distance from the support.
This reaches a maximum when the man is halfway.

This couple or moment is countered by the horizontal forces in the skins. Now this couple has a substantially shorter lever arm I have labelled e. Since the Tension = Compression the couple = Ce or Te.

Thus Ce = 80d.

C = 80d/e

Thus the magnification factor if d is 42 inches and e is 2 inches is 21 times or 1680 lbs.

Now you can see why engineers like beams to be as deep as practicable.

You can get an idea of the tensile strength of your cardboard laminations by making a strip and measuring its breaking strength.

The cellular construction should be enough to stabilise the compression skin against buckling which is the reason why thin cardboard has difficulty with compression.

You should discuss this with your teacher. Remember the 1680 lbs (or whatever) is the total force. The stress will depend upon the width of the walkway as stress = Force/area.
Attached Thumbnails
beams2.jpg