# The Leaning Tower of…Parliament?

As an Englishman, there are certain things that one expects to remain constant:

1. There will always be a royal family;
2. The summer sun will shine as England plays cricket at Lords;
3. Big Ben will chime every hour, every day.

So it is somewhat disconcerting to hear that the Palace of Westminster’s (also known as the House of Parliament) bell tower, housing Big Ben (Big Ben is the bell, not the tower) is mimicking the Tower of Pisa and is slowly leaning over. How can this be? We all know new buildings "settle," but the Palace of Westminster was finished around 1870, so what is happening?

Simply put, time is happening. We all imagine that the materials we use every day will remain in the shape we make them into, unless they corrode or otherwise degrade due to an outside agent. But time will affect many materials under load through the phenomenon known as creep. Creep is the tendency of solid materials to deform (or flow) under load. Generally speaking, engineering materials creep very slowly, unless the material is operating above 30% of its melting temperature–but if the time period is very long, creep is noticeable even at ambient temperatures. Stained glass windows in medieval churches are a good example of low-temperature creep in a material we would otherwise consider stable and unchanging.

So is this happening to the Palace of Westminster? Yes, but not only to the Palace, but also to its foundations and the ground it sits upon. So we have the classic recipe for a creep problem: a long time and a large load. Using a "building block approach" we can study the effects of creep inside SolidWorks Simulation. Below is a simple representation of the Palace of Westminster with the bell tower on the right and the foundations hidden (I hope Charles Barry isn’t too offended).

To carry out a simulation of how the palace would creep over time, we need to define a nonlinear analysis. The only load is gravity, but the trick is in defining the creep material parameters which are used to calculate the creep strain (?C ) and hence the structures deformation over time.

C1>1 and 0 <C2 ? 1

Where                  T = temperature

CT = creep temperature dependency

C0, C1 and C2 are the three creep constants

Now for the Palace of Westminster the temperature dependency is not a big issue, but varying moisture around and in the foundation can have a big impact on the support strength, and hence the creep rate. But if we model the varying moisture as a pseudo temperature, this effect can also be modeled. Getting the creep data can be hard but I have estimated some figures, and the results look reasonable.

So if your product life is measured in decades, or it's operating at high temperatures, you might want to consider a creep analysis to make sure your design is fit for purpose over its complete life span.

Luckily the creep rate is very low, so we have plenty of time (pun intended) to save Big Ben.

#### Stephen Endersby

Product Manager at SolidWorks