Levelling MCQ with answer and solution

Concept

In levelling, an inverted staff reading is taken with the staff held upside down, usually on the underside of a ceiling, beam, or bridge deck. Since the staff is inverted, the reading is treated as a negative value in reduction calculations, or alternatively, Height of Instrument = RL of floor + floor staff reading, and Elevation of beam = HI - inverted staff reading.

Formula

HI = RL_floor + Staff_floor Elevation_beam = HI - Staff_inverted Height = Elevation_beam - RL_floor

Step-by-step solution

1. Find the Height of the Instrument (HI): HI = Reduced Level of floor + Staff reading on the floor = 30.00 m + 1.40 m = 31.40 m. 2. Find the Reduced Level (RL) of the Tee-beam using the inverted staff reading: RL of beam = HI - Inverted staff reading = 31.40 m - 3.67 m = 27.73 m (Wait, let's re-verify). 3. Height of Tee-beam above the floor = RL of beam - RL of floor? No, the inverted staff reading is directly measured downwards from the beam to the HI plane. Therefore, Height of Tee-beam above floor = Staff reading on floor + Inverted staff reading = 1.40 m + 3.67 m = 5.07 m.

Explanation

The height of the instrument (HI) is calculated by adding the staff reading on the floor to the reduced level of the floor. Then, the height of the Tee-beam above the floor is obtained by subtracting the inverted staff reading from the HI.

Why the other options are wrong

A: 3.67 m is just the inverted staff reading. C: 24.93 m results from incorrect arithmetic or subtraction. D: 26.33 m results from wrong combination of levels.

Shortcut

When a staff is held inverted on an overhead point, the height of that point above the base floor equals the sum of the normal staff reading on the floor and the inverted staff reading.