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Question 1
ప్రశ్న 1
For a vehicle following a circular horizontal curve at a constant radius and speed, which relationship represents the magnitude of its centrifugal-force expression in the road-fixed frame?
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Explanation:
The familiar centrifugal-force magnitude in the road-fixed description is mv squared divided by R. Here m is vehicle mass, v is speed in metres per second and R is the curve radius. At constant radius and mass, the magnitude varies with the square of speed. Doubling speed therefore increases it by a factor of four. The same dependence explains why a tighter curve requires more banking, lateral friction or a lower operating speed.
వివరణ:
Question 2
ప్రశ్న 2
Which equation correctly states the approximate lateral equilibrium of a vehicle on a superelevated highway curve when V is in km/h, R is in metres, e is the superelevation ratio and f is the side-friction factor?
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Explanation:
The centrifugal ratio for highway-curve calculations is V squared divided by 127R. Banking of the pavement and lateral tyre friction together provide the required lateral resistance. The standard approximate balance is therefore e plus f equals V squared divided by 127R. Superelevation and side-friction coefficients are dimensionless. The equation is used with the applicable IRC limitations and does not replace other curve-design checks.
వివరణ:
Question 3
ప్రశ్న 3
A non-urban highway curve has sufficient pavement banking but develops excessive lateral-friction demand at its intended speed. Which modification most directly reduces that demand without increasing the banking?
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Explanation:
Required lateral acceleration grows with the square of speed and falls as the curve radius increases. The available banking has already been fixed in the question. A larger radius decreases the lateral-resistance requirement at the same speed. A lower speed has a similar effect when other factors remain unchanged. Either modification should be examined with sight distance, terrain constraints and applicable IRC geometric criteria.
వివరణ:
Question 4
ప్రశ్న 4
Under IRC:73-2023, the practical design expression e = V^2/(225R) for non-urban horizontal curves is derived using which assumption?
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Explanation:
IRC:73-2023 uses a practical design basis that accounts for mixed traffic operating at different speeds. Superelevation is calculated to balance centrifugal force corresponding to three-fourths of the design speed without using side friction in that initial step. Expressing V in kilometres per hour and R in metres gives e equals V squared divided by 225R. The resulting value is then assessed against normal camber and the relevant maximum permitted banking. Side friction must be checked at full design speed where the design is constrained by the banking cap.
వివరణ:
Question 5
ప్రశ్న 5
For a non-urban horizontal curve with design speed 60 km/h and radius 400 m, what superelevation is obtained from the IRC practical formula e = V^2/(225R), before any limit is applied?
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Explanation:
The practical formula is e equals V squared divided by 225R. Squaring 60 gives 3,600. The denominator is 225 multiplied by 400, or 90,000. Their ratio is 0.04, equivalent to 4.0 percent. The required adoption of that value must still respect the applicable minimum camber and maximum superelevation for the road category.
వివరణ:
Question 6
ప్రశ్న 6
A two-lane non-urban State Highway in plain terrain has a design speed of 80 km/h and a curve radius of 300 m, below the desirable minimum radius for its category. Under the applicable IRC:73-2023 maximum superelevation of 7%, what superelevation should be adopted from e = V^2/(225R), and what approximate lateral friction is then required at the full design speed?
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Explanation:
The practical banking formula gives 80 squared divided by 225 times 300, or about 9.48 percent. This exceeds the specified 7 percent limit, so the banking is capped at 0.07. At the full speed, lateral equilibrium requires f equals 80 squared divided by 127 times 300, minus 0.07. This gives f approximately 0.098, below the design value of 0.15. Other geometric requirements still need to be met before approving the curve.
వివరణ:
Question 7
ప్రశ్న 7
A vehicle negotiates a horizontal curve at 90 km/h with radius 500 m and a superelevation ratio of 0.04. Using e + f = V^2/(127R), what side-friction factor is demanded?
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Explanation:
The equilibrium equation gives f equals V squared divided by 127R minus e. Substituting V equal to 90 km/h, R equal to 500 m and e equal to 0.04 gives 8,100 divided by 63,500 minus 0.04. The centrifugal ratio is approximately 0.12756. The required friction factor is therefore about 0.08756, or 0.088. It is less than the IRC lateral design value of 0.15 under the stated assumptions.
వివరణ:
Question 8
ప్రశ్న 8
For a preliminary lateral-equilibrium check at 80 km/h, assume the permitted banking is e = 0.07 and maximum design side friction is f = 0.15. What radius results from R = V^2/[127(e + f)]? This question asks only for the theoretical equilibrium radius, not the final IRC tabular minimum.
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Explanation:
The combined lateral resistance coefficient is 0.07 plus 0.15, or 0.22. The theoretical radius is 80 squared divided by 127 times 0.22. The denominator is 27.94 and the result is approximately 229.06 metres. This is a lateral-equilibrium calculation and not automatically an acceptable final geometric radius. IRC tabular minima, design-vehicle turning requirements and other controls must also be considered.
వివరణ:
Question 9
ప్రశ్న 9
A circular curve has R = 250 m, banking e = 0.06 and available design side-friction allowance f = 0.15. What maximum speed follows from V = sqrt[127R(e + f)], neglecting other geometric restrictions?
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Explanation:
The formula is obtained by rearranging e plus f equals V squared divided by 127R. Here the total lateral-resistance coefficient is 0.06 plus 0.15, or 0.21. The value under the square root is 127 multiplied by 250 multiplied by 0.21, or 6,667.5. Its square root is approximately 81.65 km/h. This calculated upper bound does not override an applicable IRC design-speed or radius restriction.
వివరణ:
Question 10
ప్రశ్న 10
A single-plane superelevated pavement is 7.5 m wide from inner edge to outer edge and has banking e = 6%. Neglecting any local shoulder changes, what is the vertical difference between its pavement edges?
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Explanation:
Superelevation is the transverse rise divided by horizontal width. A rate of 6 percent corresponds to a slope of 0.06. The pavement width across the fully banked surface is 7.5 metres. Multiplying 7.5 by 0.06 gives an edge-level difference of 0.45 metre. The result applies to the stated single-plane crossfall and should not be calculated using half the width of a crowned straight road.
వివరణ:
Question 11
ప్రశ్న 11
Under IRC:73-2023, which statement correctly differentiates the maximum superelevation for two-, four-, six- or eight-lane non-urban highways with radius below the desirable minimum from curves at or above that radius and specified urban or major-junction sections?
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Explanation:
IRC:73-2023 does not set one universal superelevation cap for every context. For the specified major highway categories, a maximum of 7 percent applies on curves below the desirable minimum radius. A 5 percent limit applies at or above that radius and in the specified urban or major-junction situations. These are upper limits, not mandatory banking values at every curve. Designers must also check the calculated need, road camber and the remaining lateral-friction demand.
వివరణ:
Question 12
ప్రశ్న 12
Which pair correctly states the IRC:73-2023 maximum allowable superelevation for MDR, ODR and Village Roads in plain/rolling terrain and in hilly areas not snowbound, respectively?
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Explanation:
IRC:73-2023 provides separate maximum-superelevation provisions for MDR, ODR and Village Roads. In plain and rolling terrain, the listed maximum is 7 percent. In hilly areas not affected by snow, the listed maximum is 10 percent. The less restrictive hilly value should not be transferred automatically to major highways or snowbound roads. The actual design value still follows the practical banking formula and applicable safety checks.
వివరణ:
Question 13
ప్రశ్న 13
For a non-urban bituminous road with normal straight-section camber 2.5%, design speed 60 km/h and circular radius 900 m, the practical banking calculation gives e = V^2/(225R). Which IRC:73-2023 treatment is appropriate when the calculation is lower than the normal camber?
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Explanation:
The practical banking ratio is 3,600 divided by 225 times 900, approximately 0.01778. This corresponds to about 1.78 percent. The calculated rate is less than the specified normal camber of 2.5 percent. IRC:73-2023 provides for retaining normal camber on sufficiently broad curves in this situation. Additional checks remain necessary for sight distance, drainage and the selected horizontal alignment.
వివరణ:
Question 14
ప్రశ్న 14
Which set of functions best describes a properly designed horizontal transition curve between a tangent and a circular highway curve?
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Explanation:
A transition curve connects zero curvature on a tangent to finite curvature on the circular portion. It progressively introduces lateral acceleration instead of imposing it abruptly. The geometry gives drivers a smoother steering path. The transition also provides space to develop superelevation and additional pavement width when required. These functions promote ride comfort, safety and a coherent visual alignment.
వివరణ:
Question 15
ప్రశ్న 15
For an ideal spiral or clothoid transition, which mathematical property explains why curvature develops progressively from the tangent toward the circular arc?
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Explanation:
In a clothoid, curvature increases linearly with distance measured along the spiral. Equivalently, the local radius of curvature is inversely proportional to that distance. The product of spiral length from its origin and the corresponding radius is therefore constant. This property permits a smooth progression from a straight tangent to the circular-arc radius. It is a principal reason why spiral transitions are favoured in highway horizontal design.
వివరణ:
Question 16
ప్రశ్న 16
IRC:73-2023 gives two criteria for the minimum length of a highway transition curve: passenger comfort from the rate of change of centrifugal acceleration and the permissible rate of introducing superelevation. How should the governing length be selected?
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Explanation:
The comfort criterion limits how quickly a vehicle experiences a change in centrifugal acceleration. The superelevation criterion limits the relative longitudinal slope produced while rotating the pavement. The transition needs to satisfy both independently. Adopting the larger of the calculated lengths accomplishes this under the stated design procedure. Additional geometric and field constraints must also be reviewed before fixing the final layout.
వివరణ:
Question 17
ప్రశ్న 17
Under IRC:73-2023, what maximum relative longitudinal grade for the development of superelevation is specified for the relevant non-urban highway sections in plain/rolling terrain and mountainous/steep terrain, respectively?
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Explanation:
Developing crossfall causes one pavement edge to rise or fall relative to the road centre line. IRC:73-2023 limits the resulting relative longitudinal grade. The specified limit is 1 in 150 in plain and rolling terrain. The corresponding value is 1 in 60 for mountainous and steep terrain. The limits help produce a smooth and visually acceptable change in pavement banking.
వివరణ:
Question 18
ప్రశ్న 18
For a highway pavement rotated about its inner edge, the required banking is e = 0.05 across a total width of 9.0 m, with no extra widening. If the allowable relative gradient is 1 in 150, what transition length is required from the superelevation-runoff criterion alone?
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Explanation:
Rotation about the inner edge raises the outer edge by e multiplied by pavement width. The height change is 0.05 times 9.0, or 0.45 metre. A relative gradient of 1 in 150 needs 150 metres of length for every metre of rise. Multiplying 0.45 by 150 gives a runoff length of 67.5 metres. The overall transition length must also be checked against the separate comfort criterion.
వివరణ:
Question 19
ప్రశ్న 19
For the centrifugal-acceleration comfort criterion, IRC:73-2023 uses Ls = 0.0215V^3/(CR), with C = 80/(75 + V) subject to the prescribed bounds. At V = 60 km/h and R = 300 m, what transition length is obtained from this criterion alone?
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Explanation:
At 60 km/h, the allowable change coefficient is 80 divided by 135, approximately 0.5926. This value is within the stated IRC bounds of 0.5 and 0.8. The numerator of the length formula is 0.0215 times 60 cubed, or 4,644. The denominator is approximately 0.5926 times 300, or 177.78. The resulting comfort-based length is approximately 26.12 metres, which must be compared with the banking-development criterion.
వివరణ:
Question 20
ప్రశ్న 20
For a proposed highway transition, the centrifugal-comfort criterion requires 62 m and the superelevation-runoff criterion requires 85 m. What is the minimum length based on these two constraints?
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Explanation:
A single transition must simultaneously satisfy the comfort and crossfall-development requirements. The comfort calculation gives a lower bound of 62 metres. The runoff calculation gives a larger lower bound of 85 metres. Selecting 85 metres satisfies both of the stated length criteria. Any additional applicable geometric or site constraint should still be examined before final adoption.
వివరణ:
Question 21
ప్రశ్న 21
In the sequence used to attain full superelevation, what do 'tangent runout' and 'superelevation runoff' describe?
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Explanation:
Normal tangent sections often have an outward drainage crossfall on each side. Tangent runout is the length over which the outside-lane normal cross slope changes to a flat condition. Superelevation runoff then develops the cross slope from flat to the full banking rate. The stages are reversed when leaving a horizontal curve. They should be coordinated with the transition geometry and drainage arrangement.
వివరణ:
Question 22
ప్రశ్న 22
Where an appropriate spiral transition is provided on a non-urban horizontal highway curve, when should the designed full superelevation ordinarily be attained under IRC:73-2023?
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Explanation:
The pavement must change gradually from the normal tangent cross-section to the fully banked curve section. IRC:73-2023 provides for this change over the transition curve. Full design superelevation should be present at the beginning of the circular portion. An abrupt crossfall change would impair ride quality and could introduce drainage difficulties. The associated runoff and tangent-runout lengths therefore need careful layout.
వివరణ:
Question 23
ప్రశ్న 23
A vehicle travels around a curve at 70 km/h with radius 400 m and actual banking e = 0.05. From the horizontal-equilibrium equation, what lateral-friction factor is required at that speed?
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Explanation:
The full-speed equilibrium equation gives f equals V squared divided by 127R minus e. For the stated curve, the centrifugal ratio is 4,900 divided by 50,800, about 0.09646. Subtracting the provided banking ratio of 0.05 gives 0.04646. Thus the friction factor required is approximately 0.046. This is below the IRC design value of 0.15, though a complete design must also check other requirements.
వివరణ:
Question 24
ప్రశ్న 24
At the same speed, two otherwise comparable circular curves have radii 200 m and 400 m. What is the ratio of lateral acceleration on the 200 m curve to that on the 400 m curve?
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Explanation:
The magnitude of lateral acceleration is v squared divided by curve radius. Speed is identical on the two curves, so its squared term cancels in the comparison. Acceleration is therefore inversely proportional to radius. The 200 metre curve has half the radius of the 400 metre curve. Its lateral acceleration is consequently twice that of the larger-radius curve.
వివరణ:
Question 25
ప్రశ్న 25
An IRC:73-2023 two-lane non-urban State Highway curve is in a context where the allowable banking limit is 7%. Its design speed is 90 km/h and circular radius is 350 m. Using e = V^2/(225R), followed by f = V^2/(127R) - e at full speed, which decision is correct?
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Explanation:
The practical formula gives 8,100 divided by 225 times 350, or approximately 0.10286. The corresponding 10.29 percent banking exceeds the specified allowable limit, so use 0.07 for the next check. At full speed, required friction equals 8,100 divided by 127 times 350 minus 0.07. This gives approximately 0.11223, which is lower than the IRC design value of 0.15. The curve still requires applicable radius, sight-distance, transition and cross-section checks before final acceptance.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: C. It equals mv^2/R and becomes four times as large if speed is doubled at the same radius. సమాధానం: C.
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Question 2 ప్రశ్న 2Answer: A. e + f = V^2/(127R). సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: D. Increase the curve radius or reduce the operating speed after checking the resulting horizontal alignment. సమాధానం: D.
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Question 4 ప్రశ్న 4Answer: B. Banking alone balances centrifugal force corresponding to approximately 75% of the design speed, before applying camber and maximum-superelevation limits. సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: A. 4.0%. సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: D. Adopt 7.0% and require f approximately 0.098, which is below the IRC design limit of 0.15. సమాధానం: D.
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Question 7 ప్రశ్న 7Answer: B. 0.088. సమాధానం: B.
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Question 8 ప్రశ్న 8Answer: C. Approximately 229 m. సమాధానం: C.
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Question 9 ప్రశ్న 9Answer: A. Approximately 81.7 km/h. సమాధానం: A.
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Question 10 ప్రశ్న 10Answer: D. 0.450 m. సమాధానం: D.
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Question 11 ప్రశ్న 11Answer: B. The usual maxima are 7% below the desirable minimum radius and 5% at or above that radius or in the specified urban/junction sections. సమాధానం: B.
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Question 12 ప్రశ్న 12Answer: C. 7% and 10%. సమాధానం: C.
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Question 13 ప్రశ్న 13Answer: A. Continue the normal cambered section rather than introduce a separately banked superelevation section solely for this broad curve. సమాధానం: A.
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Question 14 ప్రశ్న 14Answer: D. It allows gradual development of curvature, steering response, superelevation and any necessary extra widening. సమాధానం: D.
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Question 15 ప్రశ్న 15Answer: C. The product of distance measured along the spiral from its origin and local radius of curvature is constant for a given spiral. సమాధానం: C.
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Question 16 ప్రశ్న 16Answer: B. Adopt the greater length calculated from the two criteria, subject to applicable design provisions. సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: A. Not steeper than 1 in 150 and 1 in 60, respectively. సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: C. 67.5 m. సమాధానం: C.
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Question 19 ప్రశ్న 19Answer: D. Approximately 26.1 m. సమాధానం: D.
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Question 20 ప్రశ్న 20Answer: A. 85 m. సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: B. Tangent runout changes the outside-lane normal crossfall to zero, while runoff changes that crossfall from zero to full superelevation, or vice versa. సమాధానం: B.
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Question 22 ప్రశ్న 22Answer: C. At the beginning of the circular portion, by gradual development through the transition. సమాధానం: C.
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Question 23 ప్రశ్న 23Answer: D. 0.046. సమాధానం: D.
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Question 24 ప్రశ్న 24Answer: B. 2:1. సమాధానం: B.
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Question 25 ప్రశ్న 25Answer: A. Cap the calculated 10.29% banking at 7%, then check f approximately 0.112, which is below 0.15; separately verify other geometric conditions. సమాధానం: A.