You are Jason Millions (yes that’s your real name), architect for the millionaires of the world. You fly around the world first class, visiting the most exclusive locations and designing fantastic once off buildings for your rich and famous client base.
Your latest project is an all glass building in upstate New York. You’ve been tasked to design a modern building with as much glass as possible. There are two challenges facing you:
- You need to make sure that glass makes up at least 70% of the walls in the entire building. There are 100 metres of walls in the building, with an average height of 3 metres.
- The building is on a shaky foundation, so the total glass added to the building can’t weigh more than 30 tonnes, otherwise the building may sink. If you can’t meet this requirement, you will have to suggest a new glass percentage to your client, or suggest a thinner thickness of glass, and let your client choose.
The glass you’re ordering is a special type that can be made opaque (the opposite of transparent) to keep pesky paparazzi away, 50 mm thick. As a consequence, it’s quite heavy, weighing in at 200 kg per square metre of glass.
The first thing you need to do is work out whether it’s even possible to make glass cover at least 70% of the wall area.
Minimum glass area required = percentage of glass required x wall height x wall length
Minimum glass area required = 0.7 x 3 x 100
Minimum glass area required = 210 m^2
210 square metres is a lot of glass. Let’s work out how much it weights:
Glass weight = glass area x glass weight / square metre
Glass weight = 210 x 200 kg
Glass weight = 42000 kg
Glass weight = 42 tonnes
42 tonnes is too heavy – we can only have 30 tonnes of glass. The client wants two alternative options – use a smaller percentage of glass, or make the glass thinner.
Use a smaller percentage of glass
If we have 30 tonnes of glass allowed, we can work out what percentage of the wall area can be made up of glass:
Allowable area of glass = weight allowed / glass weight per square metre
Allowable area of glass = 30 / 0.2
Allowable area of glass = 150 m^2
To work out the maximum glass percentage, we can divide this number by the total area of wall:
Allowable glass percentage = area of glass calculated / total wall area
Allowable glass percentage = 150 / 300
Allowable glass percentage = 0.5 or 50%
Use thinner glass
The second option for your client is to still have 70% of their walls as glass, but to use a thinner, lighter glass pane.
The current pane choice is 50 mm thick and would result in 42 tonnes of glass. But we’re only allowed 30 tonnes. We can calculate the factor by which the glass thickness must be reduced:
Glass thickness shrink factor = allowable weight of glass / current total weight of glass
Glass thickness shrink factor = 30 / 42
Glass thickness shrink factor = 0.714
We can work out the glass thickness allowed by multiplying the current thickness (50 mm) by this shrink factor:
Glass thickness allowed = glass thickness shrink factor x current glass thickness
Glass thickness allowed = 0.714 x 50
Glass thickness allowed = 35.7 mm
Real Life Example – The Burj Khalifa
The Burj Khalifa is the tallest building in the world as of 2016, located in Dubai in the United Arab Emirates. Standing over 800 metres tall, it has an incredible amount of glass included in its construction.
There are over 26,000 glass panels on the outside of the tower , with a total area of more than 100,000 m^2.
That’s equivalent to about 16 soccer fields:
It takes 360 workers three to four months to clean all of this glass, and they have to be very brave indeed .
 “Structural Elements – Elevator, Spire, and More”. BurjDubai.com. Archived from the original on 15 December 2009. Retrieved 31 December 2009.