Test: Curves - Civil Engineering (CE) MCQ

Mostly used in construction and also for converging or diverging light since radiation often needs to be concentrated at one point (e.g. radio telescopes, pay TV dishes, solar radiation collectors) also to be transmitted from a single point into a wide parallel beam (e.g. headlight reflectors). Boring uses single point cutting tools which are straight vertical shaped.

For 20 m chain length,
Degree of curve (D) is given by
⇒ D = 1146/R
For 30 m chain length,
Degree of curve (D) is given by
⇒ D = 1719/R
Calculation
∴ For 20 m chain length,
D = 1146/380 = 3.0157º

Cycloid is a curve generated by a point on the circumference of a circle which rolls along a straight line. It can be described by an equation,
y = a(1 – cosα) or x = a(α – sin α).

Simple circular curve:

Explanation:
The length of the curve (l): 
the length of curve T₁ K T₂ is given by 
Given: l = 30 m, D = 3°

R = 572.957 m
Additional Information
The degree of curve is given as,

• For 20 m chain length, 
• For 30 m chain length, 

Where,
D_a = degree of curve and R = radius of the curve 
Different parameters of Simple circular curve:
Tangent Length (T) = R tan (D/2)
Length of long Chord (L) = 2R sin (D/2)
Mid-ordinate (M) = R {1 -  cos (D/2)}
External distance (E) = R {sec(D/2) - 1}

Trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. The curve generated below shows us the inferior trochoid.

For the given curve:


Calculation:
Given angle of intersection = 120 ° 
But we need to find deflection Angle Δ 
Angle of intersection + Deflection angle = 180°
∴ Deflection angle, Δ = 60° 
Length of long chord = 2 × 600 × sin (60°/2) = 600 m.
Length of the mid ordinate (m) = 600 (1 – cos(60°/2)) = 80.4 m

Hyperbola concept originated in Greek, can be defined as a set of points in a plane whose distances to two fixed points in the plane have a constant difference. It is formed by the intersection of a plane with a right circular cone. Equation of parabola: x²/a² – y²/b² = ±1.

(a) if the length of the chord is 20 m

Where R = Radius of the curve in m
Dº = Degree of curve
(b) If the chord length is 30 m

Calculation:
Given data:
Curve radius (R) = 688 m
Chord length (L) =?
Degree of the curve (Dº) =?
Let the length of the chord is 20

Degree of curve 1.665º not given an option
Let the length of the chord is 30

Eccentricity can be defined as a parameter associated with every conic section. It can be thought of a measure of how much the conic section deviates from being circular. When (e < 1 Ellipse), (e = 1 Parabola), (e > 1 Hyperbola), (e = ∞ straight line), (e = 0 Circle).

Plane surveying:
In this surveying, the mean surface of the earth is considered as a plane and spheroidal shape is neglected.
All triangles formed by survey lines are considered plane triangles and the level line is regarded as straight.
In everyday life, we are concerned with the small portions of the earth's surface and the above assumption seems reasonable
So, the length of an arc 12 km long lying on the earth's surface is only 1 cm greater than a subtended chord.
The difference in length between the arc and the subtended chord on the earth's surface is taken as 500mm(or 50 cm) is = (12 × 50) / 1 = 600 km