Out-of-Square Setting Out on a Sloping Plot
A rectangular classroom block 12.0 m by 8.0 m is being set out on a sloping plot in Windhoek. The calculated diagonal is 14.42 m. The builder measures the two diagonals and gets 14.46 m and 14.38 m. The corners are marked with steel pegs, and the 12 m line is checked with a 30 m steel tape that has a noticeable kink near the 5 m mark. The site slopes about 1.0 m across the 8 m width, and the front pegs are 0.4 m lower than the back pegs. A neighbour's boundary wall is 1.8 m from the proposed side wall, and the local authority requires a 1.5 m side setback. The excavator is due in two days, and the builder wants to start trenching immediately.
1. Calculate the correct diagonal and assess the accuracy of the two measured diagonals. Explain what the results show about the setting out.
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Correct diagonal = √(12.0² + 8.0²) = √(144 + 64) = √208 = 14.42 m. The measured diagonals are 14.46 m and 14.38 m: one is 38 mm too long and the other 42 mm too short, and they differ by 80 mm. In a true rectangle the diagonals must be equal, so the setting out is out of square even though the average is close to 14.42 m. The shape is probably a parallelogram or one corner has moved. A tape with a kink near 5 m can easily cause 30–40 mm errors, especially if the tape is not pulled straight. I would not accept the setting out. I would first repair or replace the tape, then re-measure both diagonals from the same peg centres, and check a 6-8-10 triangle at one corner. The pegs should be adjusted by half the error and rechecked until the diagonals match within about 10 mm.
2. Describe how you would re-check and correct the setting out before the excavator arrives, including the checks you would make on the tape and pegs.
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Before the excavator arrives, I would clear the area and replace the kinked tape with a certified steel tape. I would establish the longest straight line first, then use a 3-4-5 or 6-8-10 triangle to set a right angle, and only then measure the rectangle. The tape must be pulled with consistent tension, supported so it does not sag, and read at the same temperature; a kink must never be straightened by eye. Pegs should be offset with profiles and nails so they are not disturbed by the machine. I would check the diagonals, the side lengths, and the level of the corners with a dumpy level or laser. If the ground slopes 1.0 m across 8 m, the diagonal measured on the slope will differ from the plan distance, so I would either measure horizontally or correct for the slope. The corrected diagonals should agree within 10 mm. I would record the check and only then release the excavator.
3. The site slopes 1.0 m across the width and the side wall is only 1.8 m from the boundary. Discuss the implications for excavation, drainage and the 1.5 m setback.
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The 1.8 m distance is greater than the 1.5 m side setback, so the siting is legal, but it leaves only 0.3 m spare. A strip footing 600 mm wide plus working space would need about 1.0–1.2 m from the boundary, so excavation could undermine the neighbour's wall. The 1.0 m fall across the width means the building will need a stepped or cut-and-fill platform; the uphill side will be cut and the downhill side filled. Fill must be compacted in layers and not used to support the footing. Surface water must be diverted around the uphill side, and the finished floor level must be above the surrounding ground. I would set profiles, check the boundary, and ask the engineer for a stepped foundation detail. The excavator should work from the site side, not the boundary side, and the neighbour's wall should be photographed before work starts.