Strain gauges and load cells are essential sensors in engineering because they turn tiny mechanical deformation into measurable electrical signals. This cheat sheet helps students connect stress, strain, resistance change, bridge circuits, and force measurement in one clear reference. It is useful for labs, design projects, robotics, materials testing, and instrumentation work.
Key Facts
- Normal strain is strain = change in length / original length, or epsilon = delta L / L0.
- Microstrain converts small strain values using 1 microstrain = 1 x 10^-6 strain.
- Gauge factor is GF = (delta R / R) / strain, so delta R / R = GF x strain.
- For a quarter-bridge with one active gauge and small strain, Vout / Vin is approximately (GF x strain) / 4.
- For a half-bridge with two active gauges in opposite strain, Vout / Vin is approximately (GF x strain) / 2.
- For a full-bridge with four active gauges arranged for maximum output, Vout / Vin is approximately GF x strain.
- Load cell sensitivity is often written as mV/V, where output voltage = sensitivity x excitation voltage x fraction of rated load.
- Calibration factor can be found from calibration factor = known load / measured output, using consistent units.
Vocabulary
- Strain
- Strain is the fractional change in length of a material when it is stretched or compressed.
- Strain gauge
- A strain gauge is a thin resistive sensor that changes resistance when the surface it is bonded to deforms.
- Gauge factor
- Gauge factor is the ratio of fractional resistance change to mechanical strain for a strain gauge.
- Wheatstone bridge
- A Wheatstone bridge is a four-resistor circuit used to convert small resistance changes into a measurable voltage difference.
- Load cell
- A load cell is a transducer that uses strain gauges to convert force or weight into an electrical signal.
- Signal conditioning
- Signal conditioning is the process of amplifying, filtering, exciting, and converting a sensor signal so it can be accurately measured.
Common Mistakes to Avoid
- Using percent strain instead of decimal strain, which gives outputs that are 100 times too large. Convert 0.05 percent strain to 0.0005 before using gauge factor formulas.
- Forgetting that bridge output is a differential voltage, which means it is measured between the two bridge midpoints. Measuring one midpoint to ground can give the wrong value.
- Ignoring excitation voltage, which is wrong because load cell output in mV/V scales directly with the supply voltage. A 2 mV/V load cell excited at 5 V gives 10 mV at full scale.
- Assuming all bridge types have the same sensitivity, which is wrong because quarter, half, and full bridges produce different Vout / Vin relationships. Use the correct bridge approximation for the gauge arrangement.
- Skipping calibration after installation, which is wrong because mounting, temperature, adhesive, and wiring can change the real output. Use known loads to create or verify the calibration curve.
Practice Questions
- 1 A 120 ohm strain gauge has gauge factor 2.0 and strain 500 microstrain. What is delta R?
- 2 A quarter-bridge strain gauge has GF = 2.1, strain = 800 microstrain, and Vin = 5.0 V. Estimate Vout in millivolts.
- 3 A load cell has sensitivity 2.0 mV/V and is powered by 10 V. What output voltage is expected at 75 percent of rated load?
- 4 Why does a full Wheatstone bridge usually produce a stronger and more temperature-stable signal than a quarter-bridge?