What’s The Worst That Can Happen? Avoiding Simulation Disasters

For a brief period—about four months—the Tacoma Narrows Bridge in the waters off Washington state stood as the most elegant suspension bridge in the world. Stretching over the Tacoma Narrows strait of Puget Sound in 1940, it was also one of the longest suspension bridges. But when the bridge started swaying in the wind, it acquired the name “Galloping Gertie,” a condition that ceased to be amusing one particularly windy day. The bridge began to convulse as if possessed. An entire section of the bridge fell into the water. It became the most famous bridge collapse of all time.

The destruction was the result of resonance caused by harmonic excitation from the wind—a condition that somehow had never come up during the design of the bridge. As if by vengeance, invisible forces not given their proper respect felled the mighty steel and concrete structure.

The black and white video of Galloping Gertie has since been viewed by virtually every engineering student. It serves as a chilling reminder of what can go wrong. Here was an unforeseen worst-case scenario. After accounting for every known force of nature and physics, there was still one more lurking out there.

It was the devil you didn’t see that would ruin you. We have been looking around with a sense of unease ever since.

We might fool ourselves again, thinking that unforeseen dangers are shrinking as we advance our body of knowledge, but each new technology leads to new worst-case scenarios. Advances in energy sources, such as nuclear energy, or materials and nanotechnology—each will have scary stories still to be written.

How is an engineering analyst to proceed under these circumstances? Let's say with caution, armed with an expanding list of known worst-case scenarios in one hand and some common sense guidelines in the other.

Dynamic Loads

Looking at a static load can be woefully insufficient—closer to a best-case scenario rather than the worst. A load applied suddenly generates many times the force of a static load. Masses that have acceleration or angular velocity also generate forces.

Galloping Gertie was certainly anything but static. Wind loads were surely considered, but probably only as constant high speeds—in effect, a static load case. Harmonic excitation causing resonance… surely that wouldn’t apply to something as big as a suspension bridge.

Consider a smaller dynamics example: the rung of a step ladder. You could design the step ladder with steps so strong that they would support a 300–pound person standing on one foot in the middle of a step. Worst case? Job done. But what if that person slips from one rung and lands on the next? The force generated from the impact would be far greater than 300 pounds.

Vortex shedding is another example of unseen dynamic force. Super tall buildings, which are beautifully slender lack a large base and can reach heights where high wind speeds prevail. They will be affected by alternating lateral forces resulting from periodically shed vortices. This could also lead to harmonic oscillation.

Linear Statics May Not Apply

Could the worst case failure be ignored by you and software? The finite element model can be effective in finding one mode of failure but not another. Those most prone to ignoring modes of failures are beginning computer-aided engineering (CAE) users using linear static programs.

It is common to start down the path of simulation with a finite element analysis (FEA) program that can handle only linear statics. Linear static FEA programs are relatively cheap, easy to use and are often given away with CAD packages these days. The “linear” means that results, deflection and stresses, for example, will be linearly proportional to the forces applied. “Static” means that the analysis will not consider forces due to dynamics, such as forces due to acceleration. They also make another dangerous assumption: that deflections will be small. While linear statics can solve many problems, most things in real life (like bridges) can be unexpectedly nonlinear, nonstatic and end up moving – a lot!

Stress Concentrations

It is common for an FEA model to be taken from a CAD model that has a lot of details. Analysts will “simplify” the model, often “cleaning up” the model but removing small details like radii, holes, fillet and so on. This can have a positive effect in solution times because small details lead to small elements, and a lot of them. However, it is sometimes a small detail that can result in a big failure. A small hole can result in a stress concentration, with many times the stress that would exist in a simplified model without the small hole. When removing holes, take care to ensure that the holes are not in highly stressed areas or where repeated deflection occurs (more about fatigue later).

Be careful with long beams and sheet metal structures in any compressive loading because they can often fail by buckling—a mode of failure not included in a normal static analysis. Parts in compression and/or shear will buckle at a fraction of their safe static load, making buckling the primary failure mechanism. Buckling, like most instability problems, is extremely difficult to predict even when using an FEA product that claims to have this capability.

Local material failure can result from high contact stresses, which are often overlooked. For example, consider a knife edge on a flat source. Should the edge be modeled to come to a point, the resulting stresses would be infinite. In reality, every sharp edge is thick, round and/or rough. As forces overcome the ability of a material to preserve its original shape, it will take on a different shape. A steel train wheel flattens when it comes in contact with the train track. How can you model that occurrence? A simplified model with an approximation would be best, but some FEA codes also offer contact stress elements that can be brought into play.

Imagine trying to model screw threads or bolted joints. Even if you did manage to model to that extreme level of detail, the size of the element would require such a vast number of elements that it would choke almost any computer. It is easier to let the FEA program determine forces and use the forces in a quick manual analysis.

Fatigue

Anyone who has tortured a paper clip, bending it back and forth until it breaks, has experienced what engineers call work hardening that results in fatigue failure. Repeated flexing of the metal changes the material properties until it loses its elasticity and becomes so brittle that it snaps. While a paper clip can snap after fewer than a hundred bending cycles, other materials take longer, with thousands and millions of cycles. Sadly, these failures are often analyzed in retrospect, sometimes after a disaster. Think of parts that flutter in the wind, like aircraft wings.

Seeing What You Don't See

Materials and models can behave outside the realm of ordinary experience beyond the intuition of the initiated, making for unforeseen consequences. So, too, can venturing into uncharted waters, even when attempted by seasoned analysts. Civil engineering was struck a blow with Galloping Gertie, not because wind was an unknown quantity but because of what wind could do to a bridge design that had been pushed beyond previously established limits. Civil engineering has since adjusted to harmonic excitation and its effect on big structures such as bridges. We have not had a Galloping Gertie since that 1940 disaster. Knock on wood. While engineers are not expected to be clairvoyant, they are expected to be cautious. For designs that depart from the norm, CAE may be insufficient, and testing and physical model may have to do.

As more analysis is being done by non-analysts—often with simple software and little or no experience—it may be wise to run through a checklist, such as the one in this article to see if there is a worst-case scenario that might have missed.