Curves MCQ Quiz in తెలుగు - Objective Question with Answer for Curves - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Explanation:

The starting point of the curve is called ‘point of curve’ or ‘point of commencement. Different points on simple curve are denoted in figure as shown.

T1 = point of curve (or) point of commencement (or) Tangent point

T2 = end of curve (or) point of tangency

B = Point of intersection

T1FT2 = Length of curve

OF = Radius of curve

T1T2 = Length of long chord

Concept:

Degree of curve is given by :

\(D = \frac{{1146}}{{R }}\) degree........For 20 m chain length

\({\rm{D}} = \frac{{1720}}{{\rm{R}}}{\rm{\;degree}}\),.........For 30 m chain length

Where,

D = Degree of the curve (degrees) and R = radius of the curve (m)

Calculation:

\(D = \frac{{1146}}{{R }}\)

∴\(R = \frac{{1146}}{{D^\circ }}\)

\(R = \frac{{1146}}{{15^\circ }} = 76.4\)  metres

The tangent length of a simple curve of radius R and deflection angle D is \(R \times \tan \left( {\frac{D}{2}} \right)\)

Tangent length VT = \(R \times \tan \left( {\frac{D}{2}} \right)\)

Radius of the curve \( = \frac{{1720}}{5} = 344\;m\)

Tangent length = \(344 \times \tan \left( {\frac{{60}}{2}} \right) = 198.6084\;m\)

Concept:

Versine of curve: The versine is the perpendicular distance of the midpoint of a chord from the arc of a circle.

where, M = Versine of curve, Δ  = Deflection angle and R = Radius of curve

\(M = R \times (1 - Cos{\Delta\over 2})\)

Calculation:

Given: R = 600 m,  Δ  = 120⁰

\(M = 600 \times (1 - cos{120\over 2})=300m\)

Concept:

For the given curve:

Tangent length \(\left( \text{T} \right)=\text{R}\tan \frac{\text{ }\!\!\Delta\!\!\text{ }}{2}\)

Length of curve \(\left( \text{l} \right)=\frac{\text{ }\!\!\pi\!\!\text{ R }\!\!\Delta\!\!\text{ }}{180}\)

Long chord \(\left( \text{L} \right)=2\text{R}\sin \frac{\text{ }\!\!\Delta\!\!\text{ }}{2}\)

External distance \(\left( \text{E} \right)=\text{R}\left( \sec \frac{\text{ }\!\!\Delta\!\!\text{ }}{2}\text{ }\!\!~\!\!\text{ }-1 \right)\)

Mid-ordinate \(\left( \text{M} \right)=\text{R}\left( 1-\cos \frac{\text{ }\!\!\Delta\!\!\text{ }}{2}\text{ }\!\!~\!\!\text{ } \right)\)

The ratio of long chord to tangent length of a simple circular curve:

= \({2\text{R}\sin \frac{\text{ }\!\!\Delta\!\!\text{ }}{2}}\over{\text{R}\tan \frac{\text{ }\!\!\Delta\!\!\text{ }}{2}}\)= 2cos(Δ°/2)

The ratio of long chord to the length of simple circular curve:

= \({2\text{R}\sin \frac{\text{ }\!\!\Delta\!\!\text{ }}{2}}\over {\frac{\text{ }\!\!\pi\!\!\text{ R }\!\!\Delta\!\!\text{ }}{180}}\) = 360° sin (Δ°/2)/Δπ 

Locating various points along the length of the curve at equal and convenient distances is known as “setting out a curve”.

Methods employed for setting out a circular curve are:

1. Rankine Method of tangential angles: Rankine method is based on the principle that the deflection angle to any point on a circular curve is measured by one half the angle subtended by the arc from Point of curve to that point.

2. Two theodolite method: This method is used when the ground is unsuitable for chaining and is based on the principle that the angle between the tangent and the chord is equal to the angle which that chord subtends in the opposite segment.

Explanation:

The various methods used for setting curves are as follows:

Explanation:

For the given curve:

The length of the long chord, T1CT2 = \(2R\sin \frac{{\rm{\Delta }}}{2}\)

Tangent length \(\left( \text{T} \right)=\text{R}\tan \frac{\text{ }\!\!Δ\!\!\text{ }}{2}\)

Long chord \(\left( \text{L} \right)=2\text{R}\sin \frac{\text{ }\!\!Δ\!\!\text{ }}{2}\)

Length of curve \(\left( \text{l} \right)=\frac{\text{ }\!\!\pi \;\!\!\text{ R }\;\!\!Δ\!\!\text{ }}{180}\)

Mid-ordinate \(\left( \text{M} \right)=\text{R}\left( 1-\cos \frac{\text{ }\!\!Δ\!\!\text{ }}{2}\text{ }\!\!~\!\!\text{ } \right)\)

External distance \(\left( \text{E} \right)=\text{R}\left( \sec \frac{\text{ }\!\!Δ\!\!\text{ }}{2}\text{ }\!\!~\!\!\text{ }-1 \right)\)

Concept:

Total Grade = Grade 1 – Grade 2

Length of curve = (Total grade/Rate of change of grade per chain length) × Length of chain

Calculation:

An upgrade of + 1.2% joins another upgrade of + 0.8%.

Grade = + 1.2 – (+ 0.8) = 0.4 % (Upward)

Change of grade is 0.1% per 20 m chain.

Concept

Tangent length(T) = Rtan(Δ/2)
Length of curve(L) = πRΔ/180
Long chord(l) = 2Rsin(Δ/2)
External distance(E) = R(sec(Δ/2)-1)
Mid-ordinate(m) = R(1 - cos(Δ/2))

Given:

Angle of intersection = 120 °
Calculation:

we need to find deflection Angle = Δ
Angle of intersection + Deflection angle = 180°
∴ Deflection angle, Δ = 60°
Length of long chord(l) = 2 × R × sin (60°/2) = 2 × R × 1/2 = R.
Tangent length(T) = Rtan(60/2) = \({R \over \sqrt 3}\)

\({l \over T} = {R \over R /\sqrt 3} = \sqrt 3\) (Ans)