Ethan Grossman: Now you see it, now you don't!
A series of stories that borrow from daily life experiences to illustrate engineering concepts.
For those of us who like a good mystery, engineering can be a fun and exciting field. It is not uncommon for existing conditions to come up that we didn’t plan for.
Sometimes our designs do not get constructed exactly as we planned. Other times, systems just age with time and we have to figure out why they fail. The fancy term for solving mysteries in system failure is “forensic engineering.” If any of you have this term in your job description, it probably means you get paid to figure out why systems fail and offer a professional assessment. For the rest of us, it’s part of our day-to-day grind and our marching orders are usually to “just fix it.”
System failures in plumbing engineering can happen under interesting circumstances since they often involve the unique properties of water, and the unpredictability of both human nature and weather conditions. Well-engineered plumbing systems keep water where it is needed at temperatures and pressures suitable for use. What happens when water freezes or gets too hot? Sometimes the damage has been done, and the circumstances that caused the failure have passed.
A few years back, I was called to evaluate a roofing system failure. We went to see the jobsite in the spring and observed that the roof was constructed of corrugated sheet metal and insulated paneling supported by structural beams. The metal paneling had moved so much that it was sheared by the structural steel inside the building. Someone had already determined that the damage was caused by “falling snow” from the roof above during the winter. As I thought about the forces required for metal to shear itself, I was fairly certain the damage must have been caused by “ice damming,” a condition that was prevalent that past winter in the Northeast. Quite simply, snow and ice on a roof melt and trickle to a spot where it can refreeze.
By spring, the ice culprit was long gone. The extensive network of heat tracing on the upper roof only solidified the theory in my mind, as it must have continuously melted snow only to refreeze on the northern-facing roof below.
Water is one of a handful of substances that is less dense as a solid than a liquid. This means that it expands as it freezes and is why it can cause havoc on plumbing systems. Water expands about 9% as it freezes. By most naturally occurring accounts, freezing water will just keep expanding and push aside anything in its way. The heat trace on the roof above our damaged roof must have just kept adding water to the roof below, creating an ice dam of glacial proportions. Frozen water can exert pressures up to and exceeding 100,000 psi!
We can see how frozen water can crack copper pipes (3,000 psi limit) and cast-iron pipes (1,870 psi limit) without even flinching. The analysis can be performed by using the Barlow formula. The Barlow formula takes into account the thickness of the pipe, the outside diameter of the pipe and the working stress of the metal itself, S. The formula is: , and we can rearrange the formula to solve for P, the internal pressure that will begin to exceed the working stress: .
For a 6” cast iron pipe, , which is about 1,870 psi.
Riding a bike
One of my first experiences with material science was with a new bicycle I got as a kid. I remember going to set the kickstand when it just snapped off. “Something isn’t right here,” I thought. Metals have qualitative properties that we should be familiar with. The amount of force a metal can take before breaking is shown on a stress-strain curve, specific for each metal. These minimum strengths of metals are defined in ASTM standards, the ones we reference in our specifications. That is what helps make sure that the systems we design are not constructed with materials that are not suited for their purpose.
Stress is the amount of force per unit area impeded on a material. There are five main types of stress that materials are subjected to: compression, tension, torsion, shear and bending. I would categorize my kickstand failure as a bending stress. A failure due to roof ponding could also be a bending stress. One of the most common stress failures I can think of is torsional. How many of us go to tighten a screw or bolt that just “breaks?” We can all probably think of examples of the five types of stress listed above. Many failures are a likely combination of stresses, and are not easy to analyze without computer software. The example of a burst pipe is defined by something called “hoop stress.”
Strain is a dimensionless unit, and also is important in defining the quality of materials we specify. When you look at a stress-strain curve, you will see an area to the left that shows the amount of force that a material can sustain and still “bounce back.” As stress increases, a typical stress-strain curve starts to show increased strain or deformation, to a point where the material does not go back to its original dimensions. This point on the curve is referred to as the Yield Strength. As the stress increases beyond the Yield Strength, it reaches a maximum stress the material can sustain before it starts to fracture. This is known as the maximum Tensile Strength or Ultimate Strength.
The Yield Strength of structural steel is around 36,000 psi, and the Ultimate Strength is around 58,000 psi. To put this into perspective, if you take a solid piece of steel bar about the length of a pencil and pull on both ends with a force of 36,000 pounds, it would stretch about the thickness of cardstock and then start to yield. When you compare these properties of metal to the amount of force that freezing water exerts, you can see the amazing power of water, able to change state with the seasons, it’s only trace the displacement of that which was in its way.
Sometimes, the damage has been done, and it’s up to us to perform a PSI (plumbing scene investigation).