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    Horizontal Curves

    Uploaded by

    NabeelSaleem
    The document discusses horizontal alignment in road design. It describes how horizontal curves are used to connect straight road sections and change the alignment direction. There are different types of horizontal curves including simple circular curves defined by their radius, compound curves with changing radii, and reverse curves with centers on opposite sides of the road. The document provides formulas to calculate curve lengths, tangent points, and stationing along curves. It also describes methods for setting out horizontal curves in the field using offsets, deflection angles, and chord lengths.

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    Horizontal Curves

    Uploaded by

    NabeelSaleem
    9 views6 pages
    The document discusses horizontal alignment in road design. It describes how horizontal curves are used to connect straight road sections and change the alignment direction. There are different types of horizontal curves including simple circular curves defined by their radius, compound curves with changing radii, and reverse curves with centers on opposite sides of the road. The document provides formulas to calculate curve lengths, tangent points, and stationing along curves. It also describes methods for setting out horizontal curves in the field using offsets, deflection angles, and chord lengths.

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    The document discusses horizontal alignment in road design. It describes how horizontal curves are used to connect straight road sections and change the alignment direction. There are different types of horizontal curves including simple circular curves defined by their radius, compound curves with changing radii, and reverse curves with centers on opposite sides of the road. The document provides formulas to calculate curve lengths, tangent points, and stationing along curves. It also describes methods for setting out horizontal curves in the field using offsets, deflection angles, and chord lengths.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    9 views6 pages

    Horizontal Curves

    Uploaded by

    NabeelSaleem
    The document discusses horizontal alignment in road design. It describes how horizontal curves are used to connect straight road sections and change the alignment direction. There are different types of horizontal curves including simple circular curves defined by their radius, compound curves with changing radii, and reverse curves with centers on opposite sides of the road. The document provides formulas to calculate curve lengths, tangent points, and stationing along curves. It also describes methods for setting out horizontal curves in the field using offsets, deflection angles, and chord lengths.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 6

    Horizontal alignment

    The horizontal alignment consists of straight sections of the roads, known as tangents,
    connected by horizontal curves. The curves usually segments of circles. Horizontal curves
    are usually used to change the alignment direction

    Horizontal curves
    Types of horizontal curves

    Simple circular, compound, reversed , and spiral


    Simple circular curves
    The simple circular curve is described by the radius of the curve R

    Length of the curve L

    ∆rad=

    ∆ is the deflection angle between the two tangents, R is the radius of the circular curve.

    Length of the horizontal curve L= R ∆rad

    T= length of the tangent

    ∆
    Length of the long chord C= 2R sin
    Example: station calculations
    „ Δ = 55

    „ R = 1000m station P.I (station of the point of intersection of the two tangents) =20+00

    „ find station P.C (first tangent point), P.T (last tangent point)

    „ T= R tan ∆/2= 1000x tan 25= 466.31m

    „ Station P.C = station P.I –T= 2000- 466.31= 15+33.69

    „ L = 1000x 55x = 959.93 m

    „ P.T= station P.C + L = 1533.69+ 959.93= 24+93.62

    Setting out horizontal curves using tape only

    a-offsets from the tangent

    (R-y)2 +X2=R2 R-y= √ x

    Offset Y=R-√

    example: R=100m, ∆=70° y

    R R-y

    X(m) 0 10 20 30 40 50 60 70.02
    Offset 0 0.50 2.02
    y(m)
    b-offset from the long chord a

    ab=y+k y

    y=ab-k c/2 x

    offset length y=√ -k R k R y+k

    k= (constant for the whole curve) x b x

    example :
    Find the length of offsets from the long chord at distances of 10m

    R=90m, ∆=50°

    Solution: C= 67.62m, K= 72.51m y=√ -k

    x 0 10 20 30 33.81
    Offset y 7.50 6.87 4.96 1.66 0.00

    Setting out of simple circular curve using theodolite and tape


    Measure the deflection angle from the tangent at point P.C and chord joining
    consecutive whole station
    Example: a horizontal curve having R= 500m, ∆=40°, station P.I= 12+00 ,prepare a setting
    out table to set out the curve using deflection angle from the tangent and chord length
    method, dividing the arc into 50m stations.

    L= R ∆rad = 349.07m T= R tan ∆/2= 171.99m

    Station P.C= 1200- T= 10+18.01

    Station P.T= Station P.C+L=13+67.08


    .
    δ= δ1= =3° 39´ 57˝ δ2, 3,4..= ° ´ ˝

    station arc deflection angle δ/2 tangential chord


    length δ angle length
    (m)
    10+18.01
    10+50 31.99 3° 39´ 57˝ 1° 49´ 59˝ 1° 49´ 59˝ 31.99
    11+00 50 5° 43´ 46˝ 2° 51´ 53˝ 4° 41´ 52˝ 49.97
    11+50 50 5° 43´ 46˝ 2° 51´ 53˝ 7° 33´ 45˝ 49.97
    12+00 50 5° 43´ 46˝ 2° 51´ 53˝ 10° 25´ 38˝ 49.97
    12+50 50 5° 43´ 46˝ 2° 51´ 53˝ 13° 17´ 31˝ 49.97
    13+00 50 5° 43´ 46˝ 2° 51´ 53˝ 16° 09´ 24˝ 49.97
    13+50 50 5° 43´ 46˝ 2° 51´ 53˝ 19° 01´ 17˝ 49.97
    13+67.08 17.08 1° 57´ 26˝ 0° 58´ 43˝ 20° 00´ 00˝ 17.08
    ∑=349.07 ∑=39° 59´ 59˝ ∑=20° 00´ 00˝
    Compound curves : consist of two or more curves joined directly. They are different in
    radius. Their centers lies on the same side of the curve. They have common tangent.
    Compound curves are used mainly in obtaining desirable shape of the horizontal
    alignment…e.g at intersections, ramps, difficult topographic conditions.

    R1

    R2

    Reverse curves
    Reverse curves usually consist of two simple curves ( with equal or unequal radii )turning
    in opposite direction with a common tangent. Their centers lie on opposite sides of the
    curve. They are generally used to change the alignment of the highway .

    I1
    50°

    I2 50°

    Equal radius reverse curve : Common tangent I1-I2 =700m find R

    Equal radius reverse curve , Common tangent I1-I2 =700m ,∆1=40° ∆2=40°

    Straight section on the tangents= 150m … find R


    I1

    150m

    I2

    curves or be radii.

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