For setting out a rectangular platform ABCD, a rotating construction laser was used. It gave a reading of 0·878 m on a temporary B.M., having a level 45·110 m. The lowest corner A has a level 45·30 m. The platform has a cross fall of 1 in 1000 longitudinally and 1 in 250 transversely. If the platform is 8 m longitudinally, i.e., along AD or BC, and 40 m transversely, i.e., along AB or DC, what is the offset from the laser beam to the corner C of the platform ?
- A0·688 m
- B0·528 m
- C0·520 mCorrect
- D0·680 m
Solution
Concept
Height of the laser beam and formation levels
Formula
HI = BM level + staff reading; offset = HI − formation level
Step-by-step solution
1. Laser beam level = 45.110 + 0.878 = 45.988 m. 2. Corner A (lowest) = 45.300 m. The level rises from A by 8/1000 = 0.008 m along AD and by 40/250 = 0.160 m along AB. 3. Level at C = 45.300 + 0.008 + 0.160 = 45.468 m. 4. Offset from the beam to C = 45.988 − 45.468 = 0.520 m.
Explanation
The laser plane is at a fixed height. The offset below it at any corner is the beam level minus the formation level at that corner, and the formation level at C is found from the two cross-falls.
Why the other options are wrong
0.688 m is the offset to corner A (45.988 − 45.30). 0.528 m and 0.680 m correspond to using only one of the two falls or an incorrect sum.
Shortcut
Beam level − (A level + fall along AD + fall along AB).
Common mistake
Using only one of the two falls.
Correct answer: C) 0·520 m