A 22 mm levelling misclosure and a 40 mm out-of-square room
Your team must fix the plinth level for a single-storey health sub-centre on a sloping plot, and the layout of the 9.0 m × 6.0 m main room has already been pegged out. The nearest GTS benchmark is 320 m away across a busy road and its RL is 26.415 m. You run a closed loop of four instrument setups with a dumpy level and a 4 m staff, starting and ending on that benchmark; the booked RL of the closing sight is 26.393 m. The foreman says '22 mm is nothing on a village site' and wants the mason to start the plinth brickwork tomorrow. The layout was set with a 30 m steel tape using the 3-4-5 rule at 3.0 m, 4.0 m and 5.0 m in one corner only. When the mason measures the two diagonals he gets 10.845 m and 10.885 m. The plinth beam shutter is fixed and concrete is booked for tomorrow morning.
1. Is the levelling acceptable? Decide whether the plinth brickwork may start.
Read the worked answer
Check the tolerance first. For ordinary building levelling the permissible misclosure is about 6√n mm, where n is the number of instrument setups. Here n = 4, so allowable = 6 × 2 = 12 mm. Observed misclosure = 26.415 − 26.393 = 22 mm. Since 22 mm > 12 mm, the loop fails and its levels cannot be used to set the plinth.
Why the foreman is wrong. A misclosure nearly twice the tolerance is unlikely to come from pure random reading error over four setups; it usually signals a systematic cause - staff not held vertical, parallax not eliminated, a disturbed benchmark, tripod legs sinking on soft ground, sights longer than 60–80 m, or a booking/arithmetic error.
Actions: re-observe the loop with balanced back and fore sights, sights kept under 60–80 m, the staff on a firm peg or a benchmark plate, and a two-person booking. Check the GTS benchmark against a second reference if one is reachable. If the loop then closes within 12 mm, adopt it and set out the plinth; if it still fails, re-survey from a different benchmark.
Decision: brickwork does not start tomorrow on these levels. A known error can be absorbed in the floor bed thickness, but an unverified one changes floor levels, door thresholds and the drain invert with no way of telling by how much.
2. Diagnose the diagonal result and state exactly how the setting out should be corrected.
Read the worked answer
Computed diagonal of a true 9.0 × 6.0 m rectangle = √(81 + 36) = √117 = 10.817 m.
Interpretation: both measured diagonals (10.845 m and 10.885 m) are longer than the true diagonal, and they do not agree with each other - a 40 mm difference. So the quadrilateral is not a rectangle, and not even a proper parallelogram: opposite sides are not matching in length, or the corners are not at 90°.
Why it happened: the 3-4-5 check was made with a 3.0-4.0-5.0 m triangle in one corner only. A small triangle magnifies angular error - roughly 10 mm of error on a 5 m hypotenuse becomes some 20–30 mm at 9 m. Also, a steel tape sags unless held at constant tension, must be corrected for slope, and a single corner check leaves the fourth corner unchecked.
Correct method: fix the long side from a baseline, then either build a large 9-12-15 m triangle at the corner or swing arcs from both ends of the diagonal using the tape. Check all four corners, then both diagonals; they must agree within about 5 mm. Correct by moving the pegs half the discrepancy on the longer diagonal.
Decision: do not pour the plinth beam. A 40 mm out-of-square will show up as tapered rooms, door frames that will not sit square, and a beam that is out of position - and once the concrete sets, the error is permanent.
3. The foreman suggests simply adding 22 mm to every reduced level. Assess this proposal.
Read the worked answer
It is tempting because the loop closed on a known benchmark, but it is not a valid correction here.
A constant shift would only be justified if you knew the entire discrepancy lay in one identified source - for example a benchmark known to be 22 mm in error, or a single setup whose height of instrument was mis-booked. In a closed loop the misclosure is the accumulated algebraic sum of all the errors at every change point, and those errors are not equal or all of the same sign.
So the shift would over-correct some points and under-correct others: the plinth would be right at some locations and wrong by up to 22 mm elsewhere, which for a floor slab and a drain invert means ponding or a fall the wrong way.
There is also a procedural problem. Applying the correction would hide a systematic error that will repeat on the next loop, and the measurement record would no longer be truthful.
Better course: re-observe the loop within the 12 mm tolerance. If a large but consistent error is found later, adjust by distributing the misclosure in proportion to the number of setups - never by a flat addition. As a temporary measure, a water level or a straight edge and spirit level can confirm the plinth height locally, but it does not replace the loop.