20-Bio-B6 Analytical Biochemistry · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2015 — 04-Bio-B6 Bioinstrumentation. Three hours, open book, non-communicating calculator permitted. Six questions of equal value (25 marks each); four constitute a complete paper and only the first four appearing in the answer book are marked. All six are solved here as a complete study resource. Every question is a design/essay question (block-diagram instrumentation-system design, or descriptive explanation).
Reference texts (the books a candidate should have reviewed for this subject):
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
A resistive strain gauge exploits the piezoresistive/geometric effect: when a conductor is stretched or compressed along its length, its resistance $R=\rho L/A$ changes both because its length $L$ and cross-sectional area $A$ change (Poisson contraction/expansion) and because its resistivity $\rho$ itself changes slightly with strain in most metals. The fractional resistance change is linearly proportional to the applied strain over the gauge's working range, $\dfrac{\Delta R}{R}=GF\cdot\varepsilon$, where $\varepsilon=\Delta L/L$ is the mechanical strain and $GF$ (the gauge factor) is the constant of proportionality — typically $GF\approx2.0$-$2.1$ for a constantan (copper-nickel) foil gauge, versus $GF\approx2$ for the geometric effect alone in an ideal isotropic conductor, confirming the resistivity term contributes only a small additional sensitivity for this alloy.
A typical metal foil strain gauge consists of a thin (a few micrometres) constantan or similar alloy foil, photo-etched into a repeating grid pattern (long parallel conductive lines connected by short end-loops) that concentrates most of the foil's length in the direction of the strain to be measured while minimising sensitivity to transverse strain, bonded to a thin polyimide or epoxy-glass backing that in turn is cemented directly onto the surface whose strain is to be measured. Nominal unstrained resistance is standardised at 120 Ω or 350 Ω (a compromise between self-heating power dissipation and signal level); the constantan alloy is chosen specifically because its resistance-temperature coefficient is very low and can be further self-compensated by matching the gauge's thermal-expansion coefficient to that of the mounting material, so that a temperature change alone (with no applied strain) produces only a small, predictable apparent-strain error rather than a large false signal.
A rigid handle is fixed to the free end of a cantilever bar built into a fixed frame; the subject pulls or pushes on the handle, loading the bar in bending. Four metal foil gauges are bonded near the fixed (built-in) end — two on the top surface (which goes into tension under the load) and two on the bottom surface (which goes into compression) — and wired into a full Wheatstone bridge with adjacent arms alternating tension/compression. This arrangement gives the maximum available bridge sensitivity (four active arms instead of one) and, because all four gauges see the same temperature, cancels thermal drift to first order — the bridge output tracks bending strain only, not ambient temperature.
Sizing the bar for a 30 kg full-scale load: $F_{max}=30\,\text{kg}\times9.81\,\text{m/s}^2=294.3\,\text{N}$. With the gauges bonded a moment arm $a=0.10$ m from the point of load application, the bending moment there is $M_{max}=F_{max}a=294.3\times0.10=29.43\,\text{N}\cdot\text{m}$. Choosing an aluminium (6061-T6) bar of rectangular section, width $b=25$ mm, thickness $t=8$ mm, gives a section modulus $Z=\dfrac{bt^2}{6}=\dfrac{0.025\times0.008^2}{6}=2.667\times10^{-7}\,\text{m}^3$ and a peak surface bending stress $\sigma_{max}=\dfrac{M_{max}}{Z}=\dfrac{29.43}{2.667\times10^{-7}}\approx110.4\,\text{MPa}$. With $E_{al}=69$ GPa this corresponds to a peak strain $\varepsilon_{max}=\sigma_{max}/E_{al}\approx1600\,\mu\varepsilon$ — only 40 % of the alloy's own yield strain ($\varepsilon_{yield}=\sigma_{yield}/E_{al}\approx4000\,\mu\varepsilon$ for a 276 MPa yield strength), giving a safety factor of about 2.5 against permanent deformation of the bar at maximum test load.
For a full active bridge, all four arms contribute additively to the differential output, giving $V_{out}=V_{ex}\cdot GF\cdot\varepsilon$ (four times the sensitivity of a single active arm). With $V_{ex}=10$ V and $GF=2.1$: $V_{out,max}=10\times2.1\times1.6\times10^{-3}\approx33.6\,\text{mV}$ at the full 30 kg load. An instrumentation amplifier with gain $\approx100\times$ raises this to $\approx3.36$ V, comfortably inside a 0-5 V single-ended (or bipolar) ADC input range while still using most of the available span for good resolution; the output is linear in applied force over the whole 0-30 kg range, so the computer converts the digitised amplifier output to a displayed force via a single calibration constant (a one-point or two-point calibration against known dead-weights on the handle).
Environmental/noise compensation is built in at three levels: (1) the four-arm alternating-sign bridge cancels common-mode temperature drift by construction, as noted above; (2) a regulated, low-noise excitation supply avoids injecting supply-ripple noise that would otherwise appear directly at the bridge output; (3) the same shielded, differential, high-CMRR philosophy used throughout this paper (twisted-pair bridge leads, guard shielding, 60 Hz notch if needed on the amplified signal) rejects mains and RF pickup on the millivolt-level bridge signal before it reaches the amplifier.
