JNTU B.Tech II PRINCIPLES OF CIVIL AND STRUCTURAL ENGINEERING Previous Question Paper (March - 2021 - R15)

In surveying, these terms define the direction and orientation of lines relative to reference systems.

Meridians are fixed lines of reference used to determine the direction of survey lines. A True Meridian is the line passing through the geographical North and South poles. A Magnetic Meridian is the direction indicated by a freely suspended, balanced magnetic needle unaffected by local attraction. An Arbitrary Meridian is any convenient direction chosen for a local survey.

Bearings represent the horizontal angle between a survey line and a meridian, measured clockwise or counter-clockwise. The Whole Circle Bearing (WCB) system measures angles from 0° to 360° clockwise from the North. The Quadrantal Bearing (QB) or Reduced Bearing system measures angles from 0° to 90° from either North or South towards East or West.

Azimuth is the horizontal angle of a line measured clockwise from the reference meridian (usually True North). Unlike bearings, azimuths are always measured clockwise from 0° to 360°.

Magnetic Declination is the horizontal angle between the True Meridian and the Magnetic Meridian at a specific place and time. If the magnetic needle points to the east of the true north, it is termed East Declination (positive); if to the west, it is West Declination (negative). The relationship is defined as:

Computation of Angles between two lines is determined by the difference in their bearings. If two lines OA and OB have bearings θ1 and θ2, the included angle is calculated by finding the difference between the bearings. When using WCB, the included angle is the difference between the bearings of the two lines; if the result is greater than 180°, the interior angle is 360° minus the difference.

To determine the missing length CD and bearing of DE, we calculate the latitudes (L) and departures (D) for each line using the formulas L = length × cos(bearing) and D = length × sin(bearing). For a closed traverse, the sum of latitudes and the sum of departures must both equal zero.

Summing the latitudes: -99.30 + 120.10 + 0.9426 L_CD + 144.5 cos θ - 45.36 = 0, which simplifies to 0.9426 L_CD + 144.5 cos θ = 24.56. Summing the departures: 263.37 + 48.05 + 0.3350 L_CD + 144.5 sin θ - 162.36 = 0, which simplifies to 0.3350 L_CD + 144.5 sin θ = -149.06.

Isolating the terms with θ: 144.5 cos θ = 24.56 - 0.9426 L_CD and 144.5 sin θ = -149.06 - 0.3350 L_CD. Squaring and adding these equations eliminates θ: (144.5)² = (24.56 - 0.9426 L_CD)² + (-149.06 - 0.3350 L_CD)². Solving this quadratic equation for L_CD yields L_CD = 155.25 m.

Substituting L_CD back into the equations: 144.5 cos θ = 24.56 - (0.9426 × 155.25) = -111.78 and 144.5 sin θ = -149.06 - (0.3350 × 155.25) = -201.06. Calculating tan θ = (-201.06 / -111.78) = 1.7987, we find θ = 60°55'. Since both latitude and departure are negative, the bearing is in the third quadrant: S 60°55' W.