Re: Maximum height of a building

Anthony, good to hear from you. I graduated in Engineering from Reading 
myself in 1989. Hope all is well there. My regards to the department.

Your question:
A great question, the answer to which affects so much more than the 
scenario you use here. The limitations of building height are basically 
set by the limitations of material strength and practicality of land 
availability. I'll explain. Stress - the criteria used to determine unit 
loading by cross section of any element is dependant on dimension squared. 
Units: Force per square Length. Mass is length cubed multiplied by 
density. It is therefore easy to spot that doubling the size of an object 
will quadruple it's cross-section, but octuple its mass. Before long, the 
scaled up object will verge upon destroying itself under its own weight. 
For this reason, larger objects tend to be more "chunky". Let's veer away 
from construction for a moment and look at nature. Seek out the book "The 
New Science of Strong Materials" by Prof. JE Gordon (an ex lecturer of 
Reading University). Compare the skeletons of the light spider monkey to 
the hefty gorilla. Compare your common bath spider to his tarantula 
brother. Four times larger spider with about twenty five times the leg 
cross-sectional area.

Now let's return to the tall buildings. Unless we come up with super-steel 
to cope with the huge weight of the tall building, we will need to come up 
with some monster cross-section to withstand it. Compare the footprint of 
the Sear's tower, Chicago with that of the Empire State Building. 
Additionally, the Earth can only stand so much compression per sqaure 
millimetre - even with piled foundations. The Egyptians realised this and 
came up with the shape of the pyramids - a huge footprint to bear a 
monster mass that wasn't all that tall. Stone is great under compression 
but poor in tension. Bear in mind that high buildings don't just compress 
their structures but pull on them too, under windy conditions. Half a mile 
up it gets awfully windy. These are the basic physical problems of tall 
structures.

Now add the logistical problems of finding sufficient space, materials, 
transporting people around inside, evacuating them...... Big structures 
bring big problems.

I hope this answers your question but doesn't disuade you from designing 
something marvelous!

Best Regards,
Justin Roux