The Law of Unintended Consequences: or, What is Thermal Output?

From earliest human contemplative thought sprang social concepts and ideals; a fact which may suggest the popularity of social media today. Robert K. Merton followed this tradition. In his 1936 article, The Unanticipated Consequences of Purposive Social Action, Merton examines the completely unexpected consequences caused by seemingly well-intentioned actions (not to be confused with collateral damage). Generally speaking, unintended consequences are associated with actions normally beginning as attempts to rectify or improve a situation (a goal which those actions may indeed achieve), but inadvertently cause other, often catastrophic consequences. From the way strain gage thermal output has been presented and discussed over the past seventy-plus years, one would assume that it, too, falls under the heading of unintended consequences. What is thermal output and how should it be viewed?

To aid our understanding of strain gage thermal output, it is helpful to first understand thermal expansion. Often called Temperature Coefficient of Expansion (TCE) or Coefficient of Thermal Expansion (CTE), all materials change dimensions when subjected to a temperature change; some (unfilled polypropylene) much more than others (titanium silicate). At temperatures close to room temperature (20°C), aluminum, for example, changes length by approximately 23 ppm/°C (the TCE for aluminum). Meaning that if you grab a piece of aluminum that is 150 mm long after sitting at 20°C for several hours and hold it wrapped in your hands for a few more hours, then that piece of aluminum will expand to a new length of approximately 150.05 mm.

This change in length is a free expansion of the aluminum bar caused by the warming action of your hands. No external force or load is involved. With regard to structural failures at common service temperatures, free expansion does not harm the bar and it is typically undesirable to include free expansion as part of a strain measurement. Converting this temperature-induced change in length to strain, the result is (150.05-150)/150 = 333 µm/m. On a scale of 1 to Failure this isn’t a significant strain, even if it were caused by external forces. But it is certainly noticeable and measureable and undesirable when included in a strain measurement meant for determining structural design criteria. Putting this into perspective, if our aluminum bar is 25 mm wide by 6 mm thick and suspended vertically from one end with a 400 kg weight hanging from the other end, then the bar experiences the same magnitude of strain (333 µm/m). This is true load-induced strain, caused by the weight hanging from the bar, and is what experimenters usually want to measure.

400 kg? That’s the weight of a good-sized horse! And, we haven’t yet hooked the horse to the bar, only changed the bar’s temperature. What if we wanted to weigh a good-sized dog instead? Say, a St. Bernard at 100 kg? Now the strain caused by the weight of our furry friend is a fraction of the strain caused by the change in temperature. How is one separated from the other? Is it possible to automatically remove the temperature effect from the strain measurement?

The most popular strain gages for precision weighing and for precision structural testing are made from rolled-metal foil. The electrical resistivity of the metal is a function of temperature. This temperature dependent material characteristic is called Temperature Coefficient of Resistance (TCR), and causes the sensor to change resistance when subjected to a change in temperature. But, strain gages are also material and, therefore, have a TCE. One further complication is that during application the strain gage is intimately bonded to a specimen, forcing the gage to follow the specimen deformation (induced by temperature, or otherwise). What is a strain gager to do?

The change in electrical resistance of a strain gage caused only by a temperature change in the specimen/bonded-gage is commonly labeled thermal output. More specifically, the thermal output of properly manufactured strain gages, which are bonded to the intended specimen material, is a residual of the attempt to completely eliminate the temperature-induced free expansion of the specimen from the strain measurement. Returning to the aluminum bar example, when using a gage meant for aluminum, then the output from the gage caused by the free thermal expansion will only be a few micro-strain (µm/m), not 333. Now if we want to weigh our spirited horse or friendly, slightly chubby St. Bernard, then the strain gage mainly shows the change in bar length caused by the weight, not by the change in temperature.

The temperature response of rolled-foil strain gages can be adjusted for a broad range of materials (TCE’s), minimizing the residual thermal output over an extended temperature range. Try doing that with a steel ruler! Well, actually, if you are taking measurements on steel with a TCE similar to the ruler, and the specimen and ruler are at the same temperature, then the residual thermal output is small (as will be the strain measurement resolution). But, for making precision strain measurements, a strain sensor must to be capable of ignoring the undesirable thermal expansion present in all materials when subjected to a temperature change. This requires that the sensor have the inherent ability to compensate for such expansion over a broad range of materials and temperatures. Rolled-foil strain gages are experts at this, because the TCR can be adjusted to effect proper compensation of material thermal expansion. These gages are called Self Temperature Compensated (STC) strain gages and while there is a small residual measurement error caused by temperature-induced free expansion, which can be corrected using data supplied by the manufacturer, the ultimate result is much better than with strain sensors which have no compensation capability and simply report all of the undesirable specimen thermal expansion. Additionally, for a specific material over a limited temperature range, a custom STC can be produced that reduces the residual thermal output to practically zero.

Rely on Micro-Measurements products and support to keep your strain measurement data from becoming an unintended consequence. Learn more about thermal output and STC strain gages by visiting the Knowledge Base section at or call 919.365.3800 to discuss your application with a Micro-Measurements applications engineer.

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Bob Watson

Director of Engineering