Basic Civil Engineering & Mechanics (BT-204) - Unit 2 Short Notes

How unit 2 is examined

Levels, theodolites, plane tables, GPS, distance, bearing and levelling; the marks sit in the instrument sketches, the level-book numericals (rise and fall), local attraction and reciprocal levelling.

Introduction to surveying Instruments – levels, theodolites, plane tables and related devices

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">High weight</span>

Definition. A level gives a horizontal line of sight to read staff heights; a theodolite measures horizontal and vertical angles; a plane table plots the map in the field while observing.

Key points.

1. The dumpy level has a telescope rigidly fixed to its vertical spindle, so once levelled with the foot screws it sweeps a horizontal plane.
2. The telescope of a level has an objective, an eyepiece, a focusing screw and a diaphragm carrying the cross-hairs; the bubble tube on it shows when the line of sight is horizontal.
3. The tribrach with three foot screws sits on the trivet of the tripod and is used to level the instrument.
4. An auto (automatic) level uses a circular bubble for rough levelling, and an internal compensator (a pendulum prism system) that keeps the line of sight horizontal automatically, so it is quick and needs no bubble tube.
5. A transit theodolite has a levelling head (tribrach, foot screws), a lower plate carrying the graduated horizontal circle, an upper plate carrying the verniers, and standards (A-frame) that hold the telescope.
6. The telescope of a transit theodolite can be rotated fully about its horizontal axis, and the vertical circle attached to it measures vertical angles with an altitude bubble.
7. Plate levels level the instrument, the clamps and tangent screws give fine setting, and the plumb bob centres the instrument over the station; a compass may be fitted on the standards.
8. A plane table is a drawing board on a tripod, with an alidade for sighting, a plumb fork, a spirit level and a compass; observing and plotting are done together at the station.

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the auto level replaces the bubble tube by a circular bubble and a compensator</figcaption></figure>

Answer frame. Open with the instrument's purpose; draw the labelled sketch; then describe the parts from the base upward (points 1-8); close with the use, for example "the theodolite measures horizontal and vertical angles". For the auto level, stress the compensator in the middle of the answer.

Asked: [7 marks] (Nov 2022, Dec 2024) Explain the individual components of the theodolite with a sketch. Asked: [7 marks] (Jun 2022) Explain the description of the dumpy level with a neat sketch. Asked: [7 marks] (Jun 2023) Explain the 'auto level' with a neat sketch.

Electronic surveying instruments

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Low weight</span>

Definition. A total station combines an electronic theodolite and an EDM in one instrument; GPS fixes a position from satellite signals.

Key points.

1. GPS works by trilateration: the receiver measures its distance to several satellites, and the position is where these distance spheres intersect.
2. The distance is $d = c\,\Delta t$, where $c$ is the speed of light and $\Delta t$ the signal travel time.
3. Three satellites give $x, y, z$, but the receiver clock is inaccurate, so a fourth satellite is needed to solve the clock bias: minimum 4 satellites for a 3D fix.
4. The sketch shows the satellites above the Earth, each sending a signal to one ground receiver.

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Asked: [7 marks] (Jun 2025) With neat sketch explain the principle of positioning with GPS.

Measurement of distances – conventional and EDM methods

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Not asked since 2022</span>

Definition. Distance is measured conventionally by chain or tape (20 m or 30 m) and electronically by EDM.

Key points.

1. A chain or tape gives the horizontal distance by direct measurement, and slope distances are reduced to horizontal.
2. EDM sends a modulated wave to a reflector and back, and the distance is $D = \tfrac{1}{2}\,c\,\Delta t$.
3. EDM is fast and accurate over long lines and is built into the total station.

Measurement of directions by different methods

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">High weight</span>

Definition. Direction of a line is its bearing: the horizontal angle from a reference meridian, measured clockwise. True bearing is from the geographic north; magnetic bearing is from the magnetic north.

Key points.

1. Magnetic declination is the horizontal angle between the true meridian and the magnetic meridian, east or west.
2. Local attraction is the disturbance of the magnetic needle from the magnetic meridian by iron ore, steel poles, pipes or electric cables near the station.
3. Detection: observe the fore bearing (FB) and back bearing (BB) of every line; if $|FB - BB| = 180^\circ$ both its stations are free from local attraction.
4. If $|FB - BB| \ne 180^\circ$, one or both stations are affected; start from a line whose difference is exactly $180^\circ$ and correct the other bearings from it, or use the included angles, which are not affected.
5. Traversing by included angles: at each station the angle between the back and forward stations is measured (clockwise); for a closed traverse the sum is $(2n \pm 4) \times 90^\circ$, plus for interior angles minus for exterior.
6. Traversing by direct angles: at each station the angle is measured clockwise from the back-sight line, extended, to the fore-sight line; it suits open traverses.
7. Fore sight (FS) is the last staff reading before the instrument is moved, and back sight (BS) is the first reading after setting up; chain survey errors are personal, instrumental and natural, and cumulative (one direction) or compensating (both directions).
8. Short notes: Bow's notation letters the spaces between forces, clockwise; D'Alembert's principle adds the inertia force $-ma$ so that $\sum F - ma = 0$; a plane table plots while observing; staircases are straight, dog-legged, open-well, spiral or geometrical.

Diagram. <figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u2-04" viewBox="0 0 510 295" width="510" height="295" role="img" aria-label="Included angle at B, measured clockwise from BA to BC"><style>#dsfig-u2-04 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u2-04 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u2-04 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u2-04 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u2-04 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u2-04 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u2-04 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u2-04 .t{fill:#16181D;font-weight:500}#dsfig-u2-04 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u2-04 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u2-04 .dot{fill:#16181D}#dsfig-u2-04 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u2-04 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u2-04 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u2-04 .ah{fill:#454C5A}#dsfig-u2-04 .ah.hi{fill:#2340B8}#dsfig-u2-04 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u2-04 .wl .t{font-size:12px;font-weight:700}#dsfig-u2-04 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u2-04 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u2-04 .e{stroke:#B1B7C3}html.dark #dsfig-u2-04 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u2-04 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u2-04 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u2-04 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u2-04 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u2-04 .t{fill:#E6E8ED}html.dark #dsfig-u2-04 .t.inv{fill:#0F1115}html.dark #dsfig-u2-04 .kd{stroke:#E6E8ED}html.dark #dsfig-u2-04 .dot{fill:#E6E8ED}html.dark #dsfig-u2-04 .ann{fill:#8FA3FF}html.dark #dsfig-u2-04 .lbl{fill:#858D9C}html.dark #dsfig-u2-04 .ptr{fill:#8FA3FF}html.dark #dsfig-u2-04 .ah{fill:#B1B7C3}html.dark #dsfig-u2-04 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u2-04 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u2-04 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u2-04 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah6" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh6" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><path class="e" d="M51.9,240.2 L198.9,56.4" marker-end="url(#ah6)"/><path class="e" d="M226.6,52.2 L453.9,241.6" marker-end="url(#ah6)"/><g class="wl"><rect x="112.8" y="138.5" width="26.4" height="18" rx="9"/><text class="t" x="126" y="147.5" dy=".35em" text-anchor="middle">BA</text></g><g class="wl"><rect x="327.8" y="138.5" width="26.4" height="18" rx="9"/><text class="t" x="341" y="147.5" dy=".35em" text-anchor="middle">BC</text></g><circle class="n" cx="40" cy="255" r="18"/><text class="t" x="40" y="255" dy=".35em" text-anchor="middle">A</text><circle class="n" cx="212" cy="40" r="18"/><text class="t" x="212" y="40" dy=".35em" text-anchor="middle">B</text><circle class="n" cx="470" cy="255" r="18"/><text class="t" x="470" y="255" dy=".35em" text-anchor="middle">C</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">Included angle at B, measured clockwise from BA to BC</figcaption></figure>

Answer frame. Open with the definition; draw the traverse sketch; develop points 5 and 6 with the check, and for local attraction points 2-4 in that order; close with "the included angles are free of local attraction".

Asked: [7 marks] (Dec 2023) What is the local attraction in surveying? How is it detected at any survey station? Asked: [7 marks] (Dec 2023) Write short notes on any four: magnetic declination, Bow's notation, plane tables, D'Alembert's principle, types of staircase. Asked: [7 marks] (Jun 2023) Define true bearing and magnetic bearing; fore sight and back sight; local attraction; errors in chain surveying. Asked: [7 marks] (Jun 2025) Explain with neat sketch traversing by the method of included angles and by direct angles. Pitfall: Do not add $180^\circ$ blindly to the back bearing when the difference is not $180^\circ$; that is the sign of local attraction.

Measurement of elevations by different methods

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">High weight</span>

Definition. <mark>Levelling is the art of determining the relative heights of points on the Earth's surface, and the level book gives the reduced level (RL) of each point.</mark>

Key points.

1. Height of collimation (HI) method: $HI = RL_{BS} + BS$, and $RL = HI - IS$ (or $FS$).
2. Rise and fall method: rise or fall = previous reading minus current reading; $RL = \text{previous } RL \pm \text{rise or fall}$.
3. The check is $\sum BS - \sum FS = \sum \text{Rise} - \sum \text{Fall} = \text{Last RL} - \text{First RL}$.

4. Profile (longitudinal) levelling gives elevations along a fixed central line of a road or railway; cross-sectional levelling gives the profile at right angles to it.
5. Differential levelling finds the difference in elevation between two far-apart points, using change points; fly levelling is a rough check run from a BM to another, without intermediate sights.

Example (Jun 2022). Reduced levels start from A = 380.500. Change points after the 5th and 10th readings.

Check: $\sum BS = 1.895$, $\sum FS = 11.125$, difference $-9.230$; $\sum \text{Fall} = 9.230$; $371.270 - 380.500 = -9.230$ (correct). Length $= 14 \times 30 = 420$ m. Gradient $= 9.230/420 =$ 1 in 45.5 falling from A to B.

Example (Nov 2022, Dec 2024). Reading data, 20 m interval, shifts after the 4th and 8th readings, last RL = 110.200 m. Rise (+) and fall (-) between readings: $+0.645, +1.115, -2.835$ | CP $| +0.765, +0.235, +0.850$ | CP $| -1.195, -0.625, -1.375$. Working backwards from the last RL, the RLs are 112.620, 113.265, 114.380, 111.545, 111.545, 112.310, 112.545, 113.395, 113.395, 112.200, 111.575, 110.200 m. Check: $\sum BS - \sum FS = 5.645 - 8.065 = -2.420$; $\sum \text{Rise} - \sum \text{Fall} = 3.610 - 6.030 = -2.420$; $110.200 - 112.620 = -2.420$ (correct). The second data set (last RL = 125.250) gives the first RL = 124.670, then 125.315, 126.430, 125.595, 125.595, 124.360, 124.595, 126.445, 126.445, 128.250, 126.625, 125.250 m; check $11.645 - 11.065 = 5.650 - 5.070 = +0.580$.

Answer frame. For the numerical: draw the level-book table, classify readings as BS, IS and FS, compute RLs, then write the arithmetic check and the answer line. For the comparison: open with a one-line definition of each method, give the 4-row table, and close with the check formula.

Asked: [8 marks] (Jun 2022) Consecutive readings at a 30 m interval, RL of A = 380.500, instrument shifted after the 5th and 10th readings; make level-book entries, apply the check and find the gradient of AB. Asked: [8 marks] (Nov 2022, Dec 2024) Find the RLs of all points by rise and fall, with the arithmetic check (12 readings at 20 m, shifts after 4th and 8th, last BM RL given). Asked: [7 marks] (Nov 2022) Illustrate the difference between the height of collimation and rise and fall methods. Asked: [6 marks] (Jun 2022) Explain briefly the types of levelling: profile, cross-sectional, differential and fly levelling. Pitfall: Change-point readings (FS then BS at the same point) carry no rise or fall; RL stays the same.

Reciprocal leveling

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Medium weight</span>

Definition. Reciprocal levelling finds the difference in level of two points A and B, across an obstruction such as a river, by taking readings from both banks.

Key points.

1. Levelling is the art of determining the relative heights of points on the Earth's surface.
2. The instrument is set up near A and readings $a_1$ on A and $b_1$ on B are taken; then it is set up near B and readings $a_2$ on A and $b_2$ on B are taken.
3. Errors in the line of sight (collimation) and the combined effect of Earth's curvature and refraction are equal in both sets, since the sight lengths are nearly equal.
4. The error $e$ acts in opposite senses, so the mean cancels it: $h = \dfrac{(a_1 - b_1) + (a_2 - b_2)}{2}$.
5. Curvature and refraction correction (if needed) is $0.0673\,D^2$ m, with $D$ in km.
6. The readings are taken quickly, on both banks, to keep atmosphere conditions unchanged.

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Answer frame. Open by defining levelling; draw the river with both setups; develop points 2-4 and write the formula; close with "the mean of the two differences is free of collimation, curvature and refraction errors".

Asked: [7 marks] (Jun 2023, Dec 2024) What do you understand by 'levelling'? Explain 'reciprocal levelling' in detail.

Last-minute revision

• Levelling: relative heights; HI $= RL + BS$, $RL = HI - IS$.
• Check: $\sum BS - \sum FS = \sum \text{Rise} - \sum \text{Fall} = \text{Last RL} - \text{First RL}$.
• Jun 2022 numerical: last RL 371.270, gradient 1 in 45.5 falling; Nov 2022: first RL 112.620.
• Theodolite: trivet, tribrach, lower plate, upper plate with verniers, standards, telescope, vertical circle, plumb bob.
• Auto level: compensator (pendulum prism) plus circular bubble.
• Local attraction: $|FB - BB| \ne 180^\circ$.
• Closed traverse angle sum: $(2n \pm 4) \times 90^\circ$.
• GPS: $d = c\,\Delta t$, minimum 4 satellites.
• Reciprocal levelling: $h = \tfrac{1}{2}[(a_1 - b_1) + (a_2 - b_2)]$.
• BS is first reading after setup; FS is last before shifting.

Memory hooks

• "HI then IS": height of instrument, RL = HI minus IS.
• Three satellites give position, the fourth fixes the clock.
• Included angles add up to $(2n-4) \times 90^\circ$; think "interior".
• Reciprocal = two banks, two sets, take the mean.
• 180 apart is clean; anything else is local attraction.

Coverage checklist

• Introduction to surveying Instruments – levels, thedolites, plane tables and related devices: theodolite parts (Nov 2022, Dec 2024), dumpy level (Jun 2022), auto level (Jun 2023).
• Electronic surveying instruments etc.: GPS principle (Jun 2025).
• Measurement of distances – conventional and EDM methods: no past questions.
• measurement of directions by different methods: local attraction (Dec 2023), short notes (Dec 2023), definitions (Jun 2023), traversing (Jun 2025).
• measurement of elevations by different methods: level books (Jun 2022, Nov 2022, Dec 2024), HI vs rise and fall (Nov 2022), types of levelling (Jun 2022).
• Reciprocal leveling: reciprocal levelling (Jun 2023, Dec 2024).