Room Setting-Out with Unequal Diagonals
Two trainees must set out a 3.6 m × 4.2 m rectangular room for a small store before excavation. They drive four pegs, tie string lines, and measure the two diagonals with a 30 m steel tape. One diagonal reads 5.65 m and the other 5.62 m. They decide the 30 mm difference is 'small' and proceed to mark the foundation trench. The ground slopes about 150 mm across the site, and one tape end is held at the top of a peg while the other is read at the side. Pegs are loose, and the diagonal check is made only once. The mason later finds that the front wall is not parallel to the site boundary, and the column starter bars are 40 mm outside the intended line.
1. What setting-out errors are evident? Explain how each produces the observed mismatch.
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The diagonal difference of 30 mm shows the four corners are not a rectangle; if it were, the diagonals would be equal. The theoretical diagonal of a 3.6 m × 4.2 m rectangle is √(3.6² + 4.2²) = 5.53 m, but both measured values are about 90–120 mm longer, so the tape or the corner positions are also suspect. Holding the tape at the top of one peg and reading at the side of another adds an offset and parallax. Loose pegs move when the string is tensioned. The front wall is not parallel to the boundary because no baseline was established from the boundary. The starter bars are outside the line because they were set from the same incorrect strings.
2. Describe the correct procedure to re-establish the rectangle, including the checks.
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Clear the area and fix a baseline parallel to the site boundary at a measured offset. Set the first corner on the baseline and drive a sturdy peg with a nail. From that corner measure 3.6 m along the baseline and 4.2 m at right angles; use a 3-4-5 triangle or a theodolite to set the right angle. Set the fourth corner by measuring 3.6 m and 4.2 m from the other corners. Measure both diagonals; adjust the corners until they agree within about 5–10 mm. Keep the tape horizontal, read at the same mark on each peg, and apply consistent tension. Transfer the lines to the ground with lime or nails, then check column starter positions from the established grid before excavation.
3. Why is the 150 mm ground slope important, and how should it be handled?
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On a 150 mm slope, a tape pulled along the ground measures slope distance, not plan distance, and the error grows with the slope. The trench would also be deeper at one end if levels are not transferred from a datum. Use a dumpy level or a water level to establish a horizontal datum, measure horizontal distances with the tape held level, and use plumb bobs to transfer corner points to the ground. Check that the finished floor level and the top of the foundation are consistent, and record the levels so the mason can set out depths correctly.