Gentleman,
I like to bring some practical strength calculations into this discussion about the necessity of reinforcement.
The concrete slabs i am talking about are made for the garden to make a nice straight end of a lawn or a pavement made of smaller square bricks. In that situation the slab is put into the soil with the long side vertical up, and often positioned completely below zero soil level.
This results in a pretty good lateral support, generated by the internal friction of the soil layers both sides next to the slab.
Any load vertical on the slab can be coped with very well, since the height of the bending profile now is 15 cm, which is 3 times larger than the slab thickness of 5 cm. We can explain this as follows:
The maximum tension stress S at the lowest point of a square beam is S=M/W.
M is the bending moment caused by the load on top of the beam and W is the resistance moment of the vertical cross section of the beam.
The resisting moment of a square beam can be calculated as W=1/6*B*H^2 with H=height of the beam and B=width of the beam.
So by putting the slab vertical the resistance moment W against a vertical load becomes a factor 3^2=9 times higher.
When such a slab is vertically loaded the result will most probably be rather a larger penetration into the ground instead of breaking the slab.
Now back to our train track bed: i use a flat position of the slab in a sand bed of course sand. This sand bed has a high angle of internal friction, so there will allways be a good spread of the load when the slab is loaded with a vertical load at one point, worst case the middle point of the length.
In my garden the max load on the slabs is most likely the load of my body 90 kg . that load can be easily taken by the slab in the sand.
Some extra remarks about steel reinforement:
The steel reinforcement bars/wires must be as far as possible down in the pulling stress zone of the slab since there are the highest pulling stresses. The pulling stress zone lies under the middle height of the beam. The compression zone is above this middle height. So this give us only 2,5 cm height with stress tensions to position the reinforcement. Moreover there must be at least a cover of lets say about 1 cm of concrete in order to prevent rusting of the bars. Since one slab can be used in two flat positions there must be steel bars at both sides of the slab. This makes a reinforced slab quite expensive !
Concrete slabs 100x15x5 cm without steel bars are very cheap, you can find them on internet for about €2,- each. So even if one breaks during rough transport its no problem.
Gerard
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