Setting Out a 24 m × 15 m Shed: Diagonals and a Closing Error
A single-storey workshop shed 24.000 m × 15.000 m is to be set out on a levelled plot, and the plinth level is to be fixed from a temporary bench mark chiselled on a culvert 180 m away, with a reduced level of 312.450 m. The site has a 20-second theodolite, a 30 m steel tape and a dumpy level. Four corner pegs A, B, C, D have been driven and checked by tape: AB = 24.004 m, BC = 15.008 m, CD = 24.006 m, DA = 14.997 m. The two diagonals measure 28.352 m and 28.298 m, against a computed diagonal of 28.302 m. A closed level run of eight setups from the bench mark back to it shows a closing error of +0.032 m over a total run of 240 m. The mason wants the plinth lines and level marked the same afternoon because the excavator is booked for the morning.
1. Assess the setting out as measured. Is the quadrilateral acceptable for a building of this size? Show the tolerance you apply and the correction you would make.
Read the worked answer
Sides: AB, CD differ by 6 mm, BC and DA by 11 mm from 24.000 m and 15.000 m. Over 24 m that is about 1 in 2,000–4,000; acceptable for a shed, within a normal ±10 mm structural setting-out tolerance. Record the values but do not re-drive pegs for this alone.
Diagonals - this is the real problem. A rectangle requires equal diagonals. Computed diagonal = √(24² + 15²) = √(576 + 225) = √801 = 28.302 m. Measured 28.352 and 28.298: difference 54 mm, and the mean (28.325) is 23 mm longer than required. Unequal diagonals mean the figure is a parallelogram, not a rectangle - the corners are not at 90°, so the building is skewed and the wall on one side runs out of square to the grid. A working tolerance for a 24 m building is about ±10 mm on the diagonals; 54 mm is more than five times that.
Correction: do not average. Hold A and the direction AB fixed, re-set B at exactly 24.000 m, then re-establish C as the intersection of 15.000 m from B and 28.302 m from A, and D as the intersection of 24.000 m from A and 15.000 m from C. Re-measure all four sides and both diagonals; accept only when both diagonals agree within 10 mm. Pegs should then be referenced to permanent offsets or stakes outside the excavation, and the peg positions recorded on a sketch so the excavator cannot disturb the only record.
2. Evaluate the level run: is the closing error acceptable, and what will you do before marking the plinth level?
Read the worked answer
Permissible closing error: for ordinary building levelling, ±12√K mm, where K is the run in kilometres. K = 240 m = 0.24 km, √0.24 = 0.49, so permissible ≈ 12 × 0.49 = 5.9 mm, say 6 mm. The observed error is 32 mm - about five times the limit. It is a blunder or a systematic error, not random misclosure, and it must not be distributed across the change points.
Likely causes, in order of probability:
- Arithmetic error in the reduction - check ΣBS − ΣFS = last RL − first RL before anything else.
- Staff not held vertical or held on soft ground, or the staff rested on the peg rather than the ground.
- Bubble not centred at each reading, parallax in the eyepiece, or clamp not tightened, so the instrument moved between backsight and foresight.
- Tripod legs settled on loose fill or in the sun; instrument out of adjustment (collimation error) - test by the two-peg method.
- Bench mark value itself misread.
Action: do not mark the plinth level from this run. Re-run the loop in the morning with short sights (keep backsight and foresight roughly equal to cancel collimation error), a properly footed tripod, the staff on a firm base and bubble checked before every reading. Confirm the bench mark. Accept the re-run only if within 6 mm, then transfer the plinth level to at least four permanent reference points around the building and mark them in the level book with sketches. Meanwhile the excavator can start on the centre lines, with depth controlled by a traveller rather than a cut level, and the error and re-run entered in the survey record - that is how you defend the decision if a level dispute arises later.
3. The mason argues that the level error is small and the plinth can be adjusted in the masonry course. How do you answer him, and what is the correct sequence for the afternoon?
Read the worked answer
A 32 mm error carried into the plinth is not absorbed by a mortar joint: the mortar bed is 10–12 mm, so 32 mm forces either a thick bed (which shrinks and crushes) or a brick course cut on site, and it propagates into door and window sill levels, floor finish thickness, drainage falls and the roof beam bearings. Each of those becomes a separate correction later. The level is also the datum every downstream trade uses, so an error introduced at plinth is multiplied, not contained.
Sequence for the afternoon:
- Report the misclosure, record it, and inform the mason in writing that the plinth level is not released.
- Mark the centre lines and grid from the corrected pegs only, with lime and offset stakes clearly visible.
- Re-run the level loop with a second person on the staff and a closed check, in the cooler part of the day.
- If within tolerance, transfer the plinth level to four permanent reference points, mark one on each face, and record the RLs.
- Release excavation for footing only after the centre lines and the cut level are both signed off, with the excavator operator shown the offset stakes and told the spoil location.
Tell the mason the truth plainly: the delay is one morning; the cost of a wrong plinth is a whole storey.