Topic 4 Part D Superelevation

8/13/2019 Topic 4 Part D Superelevation

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4) Superelevation (e):

(1)

Where: Rmin: minimum radius of curvature

e: maximum rate of superelevation. eranges from 1.5% to 12%. A minimum

value of 1.5% to 2% is required for side drainage.

f: Design value of coefficient of side friction on wet pavement

g: gravitational acceleration (9.81 m/s2or 32.16 ft/s

2)

Vd: Design speed

Metric Units:

Rmin: m, Vd: m/s, then equation (1) can be written as follows:

If Vdis given in km/hr, then equation (1) can be written as follows:

Centrifugal Force

Superelevation Force

Transverse Force

Superelevation


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U.S Units:

Rmin: ft, Vd: ft/s, then equation (1) can be written as follows:

If Vdis given in mph, then equation (1) can be written as follows:

If the Vd,f, and eare set, thenRmincan be found from equation (1) above.

From equation (1), ifR>Rminthen the superelevation ecan be calculated as follows:

[( ) ]. (2)

Achieving Superelevation:

For undivided highways, rotation is around the centerline of the roadway. For divided highways, each direction is separately rotated, around the inside or outside

edge of the roadway.


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Rotation is accomplished in three steps:1. The outside lane(s) are rotated from their normal cross-slope to a flat condition2. The outside lane(s) are rotated from the flat position until they equal the normal

cross-slope of the inside lanes

3. All lanes are rotated from the condition of step 2 to the full superelevation of thehorizontal curve

Tangent runout: the length of roadway needed to accomplish a change on the outside-lane cross slope from normal (i.e., 2 percent) to zero, or vice versa.

It is the distance taken to accomplish step 1

Superelevation runoff: it is defined as the distance over which the pavement cross slopeon the outside lane changes from zero (flat) to full superelevation of the curve (e).It is the distance taken to accomplish steps 2 and 3

Tangent runout andsuperelevation runoffare implemented for1. the transition from tangent section to horizontal curve, and2. the reverse transition from horizontal curve to tangent section

The recommended minimum length of superelevation runoff is given as: . (3)

Where:

Lr: minimum length of superelevation runoff (ftor m)

w: lane width (ftor m)n: No. of lanes being rotated

ed: design superelevation rate, %

: maximum relative gradient, % (a function of the design speed)


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bw: adjustment factor for number of lanes rotated

No. of lanes rotated bw

1 1

2 0.75

3 0.67


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The length of the tangent runout is given by: . (4)

Then,Ltis related to the length of the superelevation runoff as follows:

. (5)Where:

Lt: length of tangent runout (ftor m)Lr: length of superelevation runoff (ftor m)

eNC: normal cross-slope, %ed: design superelevation rate, %

The total transition length (total runoff) between normal cross-section to the fullysuperelevated cross-section is the sum ofLrandLt.

. (6) Define the superelevation runoff rate (SRR) or transition rate as follows:

Then equations (3), (4), and (5) become as follow:

. (3a) . (4a) . (5a)


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http://techalive.mtu.edu/modules/module0003/Superelevation.htm

The (1/3) and (2/3) rule:a) For the transition from tangent section to horizontal curve:

(2/3) Lris on the tangent (before PC) and (1/3) Lris on the curve (after the PC)

b) For the reverse transition from horizontal curve to tangent section:(1/3) Lris on the curve (before PT) and (2/3) Lris on the tangent (after the PT)
http://techalive.mtu.edu/modules/module0003/Superelevation.htmhttp://techalive.mtu.edu/modules/module0003/Superelevation.htmhttp://techalive.mtu.edu/modules/module0003/Superelevation.htm


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Example:A 6-lane highway curves to the right. Lane width is 12 ft, the design speed on the

highway is 60 mph, the normal crown slope is 2% and the superelevation is 0.062 ft/ft.

The station of the PC is (463+53) and the station of the curve length is 1066 ft. The SSRis 1/160.

The superelevation is attained by rotating about the centerline and using the 1/3 & 2/3rule.Calculate the stations of the following different points where: normal crown ends

(approaching the curve), runoff starts (approaching the curve), full superelevation is

attained (after entering the curve), full superelevation ends (before leaving the curve),

runoff ends (leaving the curve), and normal crown starts again (leaving the curve)

Solution:

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Topic 4 Part D Superelevation