To the World Trade Centre Truthers


The 'Truther' conspiracy theory claims that the World Trade Centre buildings collapsed as a result of a controlled demolition.  Truthers put forward as their evidence the speed and uniformity of the collapse.  They also claim that the steel did not get hot enough as a result of burning jet fuel to cause a collapse.

 My 2nd year civil engineering students know better than the truthers.

 Steel is an impressively strong material with excellent strength to weight ratio.  Steel also has a unique capability (compared to other metals) of being able to withstand unlimited stress cycles provided that the stresses are below a certain stress threshold.  For these reasons, steel is a great material to use in structural applications such as buildings and bridges.  But, there are three serious downsides to using steel.  Firstly, steel rusts.  Secondly, steel loses strength as it gets hotter.  Thirdly, steel expands due to heat.

 To ensure the structural integrity of a building, we have to protect the steel from rusting and from getting too hot.  Rust can be managed by galvanising the steel, if it is exposed to moisture, or making sure that it remains dry.  Steel can be protected from getting too hot by covering it with fire rated lagging or 'boxing' it in fire rated gyprock.

 In the case of the twin towers, unfortunately, the impact from the planes compromised the fire protection around at least some steel columns.  The fire protection around many other columns should have remained intact; however, even it would have degraded due to sustained fire and changes in deflections due to changes in the load distribution, which were caused by localised failures and the weight of the planes.  Regardless of the specific localised failures, there was a hot fire burning uncontrollably in the tower for quite a long time.  Even the best fire protection doesn't stop the steel from heating up eventually.

 So, let's take a simple example and find out what the effect of temperature on the steel would be.  Let's say that a steel column has a cross-sectional area of 10,000 mm^2 and a length of 3,000 mm.  The yield stress of structural steel is typically about 350 MPa, so let's make a conservative assumption that the load on this steel column is only 10% of its capacity = 35 MPa.  Multiply the stress by the cross-sectional area and you get the load in Newtons = 350 kN (below).


Now, let's suppose that a fire occurs and the steel begins to heat up.  This changes the material properties of the steel in a couple of ways.  Firstly, the steel begins to lose strength.  Its yield strength drops off from 350 MPa.  Secondly, it tries to expand.  But, the column cannot get any longer, because it is restrained by the surrounding structure and architectural claddings.  Instead, what happens is that the compressive stress in the steel increases.  These stresses are called thermal stresses (see image below).


Now for a little math based on the principle shown above.  The deflection caused by the change in temperature must be equal to the deflection caused by the thermal stresses.  This condition of compatibility gives us a formula for the additional force, P.


The changes to material properties are shown in the next image.  Here you can see that yield strength reduces a little, but drops off dramatically from 400 deg C onwards.  The elastic modulus (E) of steel drops off more rapidly as the temperature increases.

Another important property of steel is the coefficient of thermal expansion, which is a little over 0.00001 per degree C.

 Now we have all the data we need to work out the stresses in the steel at different temperatures.

 If we increase the temperature of the steel by 100 degrees, E is unchanged at 200 GPa, but the yield strength is reduced to about 96% of 350 MPa = 336 MPa.  Using the formula above and transforming the force, P, into a stress using the relationship stress = P/A, we get thermal stresses of 160 MPa.  So, after raising the temperature from 20 degrees, to 100 degrees, the steel has gone from a stress of 35 MPa to 195 MPa.  It hasn't reached its yield stress of 336 MPa though.

 Let's see what happens at a temperature of 200 degrees C.  Now, E is reduced to 90% of 200 GPa = 180 GPa.  The yield strength of steel is reduced to 92% of 350 MPa = 322 MPa.  At 200 degrees C, the thermal stresses are now 324 MPa.  So, after raising the temperature just 180 degrees C, the stress in the steel has gone from 35 MPa to 359 MPa.  This exceeds the yield strength of the steel, which is 322 MPa, so the steel column will fail before the temperature has risen 180 degrees.

 I know that this example is simplified, but it clearly demonstrates how steel can reach its failure point a long, long time before it ever reaches its melting point of 1200 deg C or its melt-like point of 727 deg C.  Failures occur while the steel is still solid at relatively low temperatures.

 I hope this illustrates how utterly ridiculous the conspiracy theories of the truthers are.

Comments

Post a Comment

Popular posts from this blog

The Flood

Image
Last year, my family and I went on a whale watching trip which was operated by the Quandamooka mob, who are the traditional owners of Moreton Island and the Stradbroke Islands in Moreton Bay.  Local lore man, Uncle Josh Walker, told stories of his country; the people, the wildlife, the land and the ocean.  I was fascinated to hear him tell of a story of the inundation of Moreton Bay and how the flooding of the bay was verified by scientists who indicated that it happened thousands of years ago as the sea level rose when the last ice age came to an end.   The idea that an oral tradition dating back thousands of years could have its roots in an actual event piqued my curiosity.  I never would have thought that an oral tradition could preserve a memory for so long.  But, there seems to be some evidence that this story really does capture an ancient memory of coastal inundation.  At least that's what Patrick Nunn and Nicholas Reid argue in a 2016 paper in Australian Geographer
Read more

How did the idea of Satan emerge in the Jewish tradition?

Image
  Growing up in the Seventh Day Adventist church, I was told of a celestial battle between good and evil for the souls of every person on earth.  The main characters in this spiritual war were the trinitarian God ( i.e. , God the Father, Jesus and the Holy Spirit) on the 'good' side and the Devil / Satan / Lucifer on the 'evil' side.  I understood that Satan was, at one time, an important angel in Heaven (leader of the Heavenly choir, no less) who rebelled against God and was then cast out of God's presence and bound to the earth.  I was taught that, ever since his fall from grace, Satan spends all his time tempting people to reject God.  Adventists don't believe in the eternal conscious torment of hell, but they do preach that God will cast those who reject Him into a lake of fire where they will die a painful death and cease to exist.  Those who are 'saved' will be rewarded with eternal life in Heaven.  On this view, Satan, the great deceiver, is respo
Read more

Because of Her We Can

Image
That's my great Nanna, Amy Ridgeway, holding onto me in the chair as I squint into the sun.  My Poppy, Les Ridgeway, is standing next to my mum, Cheryl, who is dressed in that lovely yellow 70's summer dress.  Everyone I've ever spoken to about Nanna Amy has said she was a beautiful person, loving, kind, and generous.  I remember Nanna Amy and the house she lived in.  Was it Newcastle?  I remember mum and Aunty Min caring for all us kids.  I remember having fun with Aunty Sandra's kids, mostly Brad and Michael because they were close to my age.  I remember eating ice blocks at Nanna Amy's house and watching TV. Nanna Amy was born 110 years ago at Salt Ash near Port Stephens to Laura Maher, who would have been 19 years old at the time.  Laura worked as a housekeeper for an Englishman named Henry Waddingham who owned a shipping company based at Windi Woppa.  He never officially recognised the children he fathered with Laura, although my grandfather, Les Ridgeway
Read more