// Instrumentation & Testing · Spring 2025
Beam Deflection Measurement Rig
Measures the stiffness of a brass beam by bending it with a servo and reading the force back through a load cell.
The Problem
Young's modulus falls out of a one-line beam equation, but every term in that equation is a measurement you have to make. On a 240 mm brass beam the deflections are 1.5 to 9.4 mm — small enough that reading them off a ruler by eye puts the measurement error on the same order as the quantity being measured.
The Approach
Automated the load side to take human variability out of at least half the experiment. An Arduino Uno drives a servo that steps the beam through five fixed positions, triggered from the serial monitor, with an HX711 load cell and amplifier reading applied force at each stop. The cell was calibrated against a known 199 g mass to a factor of 405.8, and the full sequence repeated across five runs. The deflection side stayed manual — a ruler — which is precisely where the error ended up.
The Outcome
144 GPa, against a published range of 102–125 GPa for brass. Force repeatability was good: within 3.9% at full load across five runs. The error turned out to be the more useful result. The modulus came out high at every load point rather than scattered around the true value, which is the signature of a systematic offset rather than noise — so ruler resolution and load cell drift, both random, don't explain it. Since E scales with L³, the effective cantilever length is the one term that shifts every point by a similar proportion, and between 11 and 26 mm of unaccounted clamped length spans the entire published range: a clamp jaw plus a servo horn bearing inboard of the free end is a plausible source of that. Not confirmed by re-measurement, so it stands as the leading explanation rather than a closed one.