Highway Geometric Design MCQ Quiz - Objective Question with Answer for Highway Geometric Design - Download Free PDF

Explanation:

Concept:

While negotiating curve on road by vehicle, the required centripetal force is provided by the frictional force between the road and tyre.

Centripetal force = \(\frac{mv^2}{R}\) and $\mu mg$

 For avoiding car to skid the centripetal force must be equal to the frictional force ⇒ \(\frac{mv^2}{R} =\mu mg \)   

∴ Maximum speed with which the cyclist can travel without the fear of skidding  \(v=\, \sqrt{\mu Rg}\)

Solution:

Given, Radius of corner = 50 m,  

coefficient of friction between the tires and track =  0.2,

 acceleration due to gravity = 10 m/s2

∴ Maximum speed with which the cyclist can travel without the fear of skidding 

 \(v=\, \sqrt{\mu Rg} = \, \sqrt{0.2\times 50\times 9.81} =\, 9.9 \approx 10\) m/s

Explanation:

The extra width of a carriageway that is required on a curved section of a road over and above that is required on a straight alignment is known as Extra Widening.

Mechanical widening: The widening required to account for the off-tracking due to rigidity of wheelbase is known as Mechanical widening. It can be calculated as:

\({W_m} = \frac{{n{l^2}}}{{2R}}\)

n = Number of lanes

l = length of wheelbase = 6.1 m

R = Radius of circular curve

Psychological Widening: Extra width of pavement provided for psychological reasons such as overhangs of vehicles, greater clearance for crossing, etc is known as Psychological Widening.

\({W_{ps}} = \frac{V}{{9.5\sqrt R }}\)

Explanation:

Grade Compensation:

1. The main purpose of applying grade compensation on a horizontal curve is to counteract the effects of both the curve and the gradient.
2. This is done by adjusting the cross-slope (cant) of the road, ensuring that vehicles experience less resistance due to friction, especially when navigating through curves on sloped surfaces.
3. Grade compensation helps in maintaining better vehicle control and reducing the likelihood of skidding or slipping.

 Additional Information

Grade compensation is a critical design feature in road engineering, particularly when horizontal curves are combined with inclines (or gradients). Here's a more detailed explanation:

1. Purpose: When vehicles travel on a curve, they experience a centrifugal force that pushes them outward, away from the center of the curve. On sloped roads (gradients), this force is further complicated by gravity, which can either aid or hinder the vehicle's motion depending on whether the slope is ascending or descending. Grade compensation addresses these issues by modifying the cross-slope of the road to balance the forces at play, ensuring the vehicle remains stable while navigating the curve.

2. How It Works: In a typical curve, the outer edge of the road surface is raised to counteract the centrifugal force. This is known as the cant or superelevation. On a curve with a gradient, this cant may need to be adjusted to account for the additional gravitational pull, which would otherwise increase friction between the tires and the road surface, making the turn more difficult and less safe.

Explanation:

As per IRC 73-1980, the reaction time of the driver is assumed to be 2 seconds for the calculation of Overtaking Sight Distance (OSD).

• Reaction time refers to the time taken by the driver to perceive a need to overtake, decide to do so, and then begin the overtaking maneuver. In road design, a 2-second reaction time is typically considered sufficient for a driver to respond to a situation on the road, especially during overtaking.

 Additional Information

• Overtaking Sight Distance (OSD) is the minimum distance required for a driver to safely overtake a vehicle, taking into account the driver's reaction time, the time taken to accelerate, and the distance needed to pass the vehicle.

• It depends on various factors such as the speed of the vehicle, road geometry, and visibility.

• The reaction time of 2 seconds helps ensure that the road provides adequate visibility and time for drivers to safely perform overtaking maneuvers without risking collision with oncoming traffic.

Explanation:

Camber or Cross slope:

(i) Transverse slope provided to the road to drainoff rain water from road surface is known as camber.

Excessive camber is not provided on the roads because:

(i) It will erode the surface

(ii) Due to too steep slope, transverse tilt of vehicle causes uncomfortable side thrust and a drag on the steering of automobiles.

(iii) Discomfort causing throw of vehicle when crossing the crown during overtaking operations.

(iv) Problems of toppling over of a highly laden bullockcarts and trucks

(v) Tendency of most of the vehicles to travel along the centre line.

Additional Information

The design values of cambers mainly depend upon the type of the pavement and also on the average amount of the rainfall in the area.

Concept:

The centrifugal force exerted on the vehicles while traversing through the curves is counteracted by providing superelevation, which is given by:​​

\( \;e = \frac{{{V^2}}}{{127R}}\)

However, it is assumed that the centrifugal force is completely nullified if the vehicle is travelling at its 75% of the vehicle design speed.

∴ \( \;e = \frac{{{(0.75V)^2}}}{{127R}} = \frac{{{V^2}}}{{225R}}\)

According to IRC,

Concept:

Lag distance = 0.278 × V × t_R

Where,

V = Speed in Kmph

t_R = Reaction time in sec

Calculation:

Lag distance = 0.278 × 47 × 2.5 = 32.665

For two way traffic on a single lane lag distance = 2 × 32.665 = 65.33 m

Explanation:

Transitions curve:

(i) When a vehicle traveling on a straight road enters into a horizontal curve instantaneously, it will cause discomfort to the driver. To avoid this, it is required to provide a transition curve. This may be provided either between a tangent and a circular curve or between two branches of a compound or reverse curve.

Different types of transition curve:

The types of transition curves commonly adopted in horizontal alignment highway are

(i) Spiral or clothoid

(ii) Bernoulli’s Lemniscate

(iii) Cubic parabola

(a) All the three curves follow almost the same path up to deflection angle of 4°, and practically there is no significant difference between even up to 9°. In all these curves, the radius decreases as the length increases.

(b) According to IRC ideal shape for transition curve is spiral because rate of change of radial acceleration remains constant. Generally, spiral curve provided on hilly road.

(c) Cubic parabola is provided for the railway.

Given:

Ruling gradient of hilly road = 6%

Radius of curve (R) = 60 m

Calculation:

Grade compensation = \(\frac{{30\; + \;R}}{R}\% \)

= \(\frac{{30\; + \;60}}{{60}}\% \) = 1.5%

This should not be more than

= \(\frac{{75}}{R}\% \) = \(\frac{{75}}{{60}}\% \) = 1.25%

Compensated gradient = Ruling gradient – Grade compensation

= 6% – 1.25% = 4.75%

Concept:

Design Speed:

• It is defined as the maximum speed at which vehicles can continuously travel safely under favorable conditions is called design speed. 
• It may also be thought of as the maximum approximate speed that will be adopted by most drivers, Choice of design speed has to be made carefully, so as to match the terrain condition and also to be acceptable to most road users.
• It is the basic parameter that determines all other geometric design features.

Design speeds for various classes of Roads are given below in the table:

Hairpin bends:

• A hairpin bend is a sharp curve and it is located on a hillside having the minimum slope and maximum stability.
• It must also be safe from the viewpoint of landslides and groundwater.
• For reducing the construction problems and expensive protection works, the hairpin bends should be provided with long arms and farther spacing. 
• The minimum design speed adopted where hairpin bends are provided at hill roads is 20 Kmph.

Explanation

Given,

 Upgrade of 2.0 % followed by the downgrade of 2 % 

 N1 = 2 % , N2 = - 2%

  Rate of change of grade is 0.05 % per 20 m chain.

 Total change in grade (N) = N1 – N2

 N= 2 % - (- 2%) = 2% + 2%

 N = 4 %

\({\rm{Total\;Length}} = \frac{4}{{0.05}} \times 20 =1600\;m\)

Width of formation or roadway width:

It is the sum of the widths of pavements or carriageways including separators and shoulders. This does not include the extra land of formation/cutting.

These values suggested by IRC:

∴ The width of National & State Highways in plain and rolling terrain for the two-lane is 12 m.

Concept:

The height of the crown with respect to edges is given by

 \(\rm Height~ of ~crown=\rm \frac{Width ~of ~pavement}{{2}} \times Camber \)

Calculation:

Given: Width of road = 8 m, camber (or) cross fall = 1 in 50 = 1/50 = 0.02

 \(\rm Height~ of ~crown=\rm \frac{8}{{2}} \times 0.02\)

⇒ Height of crown = 0.08 m

Additional Information

Camber of pavement depends on

• Type of pavement
• Intensity of rainfall (Light/Heavy rain)

Explanation:

The extra width of carriageway that is required on a curved section of a road over and above that is required on a straight alignment is known as Extra Widening.

Mechanical widening: The widening required to account for the off-tracking due to rigidity of wheelbase is known as Mechanical widening. It can be calculated as:

\({W_m} = \frac{{n{l^2}}}{{2R}}\)

n = Number of lanes

l = length of wheelbase = 6.1 m

R = Radius of circular curve

Psychological Widening: Extra width of pavement provided for psychological reasons such as overhangs of vehicles, greater clearance for crossing, etc is known as Psychological Widening.

\({W_{ps}} = \frac{V}{{9.5\sqrt R }}\)

Concept:

• If the pavement is rotated about the inner side, Then rise of outer edge = e × W
• If the pavement is the rotated about center line, Then rise of the outer edge =  \( \frac{e\;×\; W}{{2}}\)

Where e = Super elevation and W = Width of pavement

Calculation:

Given: Rise of outer edge with respect to inner = 40 cm, W = 10 m = 1000 cm

It is given outer edge is 40 cm higher with respect to inner edge

40 = e × 1000

\(e= \frac{40}{{1000}} =\frac{1}{{25}}\)

The required superelevation is 1 in 25

Additional Information

Superelevation:

To counteract the effect of centrifugal force and to reduce the tendency of the vehicle to overturn or skid, the outer edge of the pavement is raised with respect to the inner edge, thus providing a transverse slope throughout the length of the horizontal curve. This transverse inclination to the pavement surface is known as superelevation or cant.