Traverse Closure and Baseline Measurement for a Rectangular Building
A surveyor is setting out a rectangular building measuring 24.000 m by 12.000 m. A six-station closed traverse around the site has a total length of 240.000 m. The closure components are +0.028 m East and -0.021 m North. The project specification requires primary control to achieve relative precision 1:5000 and angular misclosure no greater than 30″√n. The observed angular misclosure is 18″. A 24.000 m baseline is measured with a steel tape at 32°C. The tape was standardised at 20°C, with coefficient of thermal expansion 11.5 × 10^-6/°C. The measured length is 24.012 m, and tension and sag are within the calibration. The proposed building corner is 28 m from one control point. Column tolerance is ±5 mm.
1. Compute the linear misclosure and relative precision, and compare them with the specification. Also check the angular misclosure.
Read the worked answer
Linear misclosure = √(0.028² + 0.021²) = √(0.000784 + 0.000441) = √0.001225 = 0.035 m. Relative precision = 0.035/240.000 = 1/6857, which is better than the required 1:5000. For n = 6 stations, the angular limit is 30″√6 = 30 × 2.449 = 73.5″. The observed 18″ is well within that limit. The traverse therefore meets the stated primary-control criteria. It should still be adjusted before coordinates are used for setting out; passing the closure test does not mean the coordinates are error-free.
2. Apply the temperature correction to the measured baseline and decide whether it is acceptable for ±5 mm setting out.
Read the worked answer
Temperature correction = L α ΔT = 24.012 × 11.5 × 10^-6 × (32 - 20) = 24.012 × 11.5 × 10^-6 × 12 = 0.0033 m. The tape is longer when hot, so the measured value overreads; subtract the correction: corrected length = 24.012 - 0.0033 = 24.0087 m. This is 8.7 mm longer than the nominal 24.000 m, which exceeds the ±5 mm column tolerance. Do not simply set out 24.000 m from this measurement. Check the tape calibration, tension, alignment and the control coordinates, and re-measure. The error may be in the measurement or in the control, so investigate before use.
3. Describe the setting-out procedure and the independent checks you would use for the building corners.
Read the worked answer
Set the total station on one control point, backsight a second control point, and enter or compute the corner coordinates. Set out each corner, then check all four sides and both diagonals; for a 24.000 × 12.000 m rectangle the diagonal is √(24² + 12²) = 26.833 m. Check the corner angles, preferably with a second setup from an independent control point. Record the residuals against the design coordinates. Do not rely on a single tape measurement or a single instrument setup. If the diagonals differ by more than the tolerance, adjust the setting out before fixing reinforcement or formwork, and document the final check.