Simple Curves
A simple curve is a horizontal curve formed by one continuous circle, used to change the direction of an alignment gradually instead of abruptly at an intersection of straight lines.
A simple curve is a horizontal curve formed by one continuous circle, used to change the direction of an alignment gradually instead of abruptly at an intersection of straight lines.
A simple curve connects two tangents, AB and BC, with bearings of N76ºE and S63ºE, respectively. If the stationing of the vertex is 3+988 and the stationing of PC is at 3+866, determine the stationing of a point on the curve which intersects with the line making a deflection angle of 6º with the tangent passing through the PC.
A simple curve connects two tangents, AB and BC, with bearings of N76ºE and S63ºE, respectively. If the stationing of the vertex is 3+988 and the stationing of PC is at 3+866, determine the offset distance of a point on the curve which intersects with the line making a deflection angle of 6º with the tangent passing through the PC.
If the degree of simple curve whose central angle is 26º is 6º, determine the area of the fillet of curve in m2. Use arc basis and S.I. units.
A simple curve has an angle of intersection of 30º. If the middle ordinate is 16m, determine the radius of the simple curve.
A simple curve has a degree of curve of 5º. If English Units are to be used, determine the length of chord (in ft) if I=36º. Use chord basis.
The offset distance of the simple curve from the PT to the tangent line passing through the PC is equal to 126.2m. The stationing of PC is at 2+978. The simple curve has an angle of intersection of 26º. Determine the stationing of PT.
Additional board-style practice items for this topic.
A simple curve connects two tangents, AB and BC, with bearings of N81ºE and S63ºE, respectively. If the stationing of the vertex is 4+358 and the stationing of PC is 4+301, determine the following:
Radius of the curve
External distance
Middle ordinate
Chord distance
Length of the curve
Stationing of PT
Stationing of a point on the curve which intersects with the line making a deflection angle of 7º with the tangent passing through the PC
The offset distance, x, of such a point along the curve
Part 1.
The intersection angle is the change in bearing from N81°E to S63°E. These azimuths are 81° and 117°, so:Part 2.
External distance for a simple curve:Part 3.
Middle ordinate:Part 4.
Long chord:Part 5.
Length of curve using arc length:Part 6.
Station of PT is station of PC plus curve length:Part 7.
For a point with tangential deflection $\delta=7^\circ$, the central angle from PC is $2\delta=14^\circ$. Arc length from PC:Part 8.
The offset from the tangent to the curve at central angle $14^\circ$ is:A 5º curve intersects a property line CD at point D. The back tangent intersects the propertly line at point C, which si 105.72m from the PC, which is at station 2+040. The angle that the property line CD makes with the back tangent is 110º50'. Assume that the vertex angle at D is obtuse. Compute the following:
The length of curve from the PC to point D.
The stationing of point D
The distance CD
Solution pending in psadquestions/q492.json.
The tangents of a simple curve intersect at an angle of 32º. It has a radius of 402.21m.
Compute the degree of the curve using arc basis.
Determine the area of the fillet of the curve in m2
Part 1.
Using arc basis with a 20 m arc, the degree of curve is:Part 2.
The fillet area is the tangent triangle minus the circular segment:Determine the degree of simple curve whose central angle is 26º if the shortest distance from the curve to the point of intersection is 7.54m. Use arc basis.
Answer:
The offset distance of the simple curve from the PT to the tangent line passing through the PC (OR from PC to PT) is equal to 120.2m. The simple curve has an angle of intersection of 50º.
Find the radius of the simple curve
If the stationing of PT is 45+158.32, what is the stationing of PI?
Part 1.
The offset from PT to the tangent through PC is:Part 2.
First compute tangent and curve length:A reverse curve connects two converging tangents with an angle of intersection of 32º. The distance from PI of the second curve to this point of intersection is 180m. The deflection angle of the common tangent from the back tangent is 22º and its degree of curve is 5º.
Determine the radius of the 2nd curve
Determine the tangent distance of the 2nd curve
Determine the degree of curve of the 1st curve by arc basis
If the stationing of PC is 3+600, determine the stationing of PT
Solution pending in psadquestions/q501.json.
A reverse curve connects two converging tangents intersecting at an angle of 30º. The distance of this intersection from the PI of the curve is 150m. The deflection angle of the common tangent from the back tangent is 20º, and the azimuth of the common tangent is 320º. The dgree of curve of the second simple curve is 6º, and the stationing of the point of intersection of the first curve is 4+450.
Determine the radius of the first curve.
Determine the stationing of PRC.
Determine the stationing of PT
Solution pending in psadquestions/q502.json.
If the degree of simple curve whose central angle is 26º is 6º, determine the area of the fillet of curve in m2. Use arc basis and S.I. units.
Solution pending in psadquestions/q581.json.
Two tangents AB and BC intersect at an angle of 24º. A point P situated along the curve is located 21.03m from point B and has a perpendicular distance of 2.79m from line AB. Calculate the radius of the simple curve, assuming that it is greater than 200m.
Solution pending in psadquestions/q582.json.
The radius of a simple circular curve is 400m. PC is at Sta. 4+456.21. Determine the deflection angle at Sta. 4+645.64.
Solution pending in psadquestions/q583.json.
A circular curve with a radius of 280 m, a central angle of 70°, and its PC at station 10 + 300 must be stalled by deflection angles and chords. What is the deflection angle to station 10 + 450?
Solution pending in psadquestions/t1188.json.
A 3-degree simple curve is used to connect two highways whose bearings are S 11° W and S 47° W. Use arc basis.
What is the length of the curve in meters?
What is the external distance in meters?
What is the tangent distance in meters?
What is the middle ordinate in meters?
Solution pending in psadquestions/t1190.json.
From point A on a simple curve, the perpendicular distance to the tangent, at point Q, is x m. The tangent passes through the PC. The distance from Q to PC is 450 m. Find x if the radius of the curve is 1600 m.
Solution pending in psadquestions/t1194.json.
The offset distance from PC to PT of a simple curve is 8 m. If the length of the curve is 60 m, what is the radius of the curve?
Solution pending in psadquestions/t1195.json.
The angle of intersection of a circular curve is 45° 30' and its radius is 198.17 m. PC is at Sta. 0 + 700. Compute the right angle offset from Sta. 0 + 736.58 on the curve to tangent through PC.
Solution pending in psadquestions/t1196.json.
A 4-degree simple curve have tangents with bearings of N 20° E and N 60° E, respectively. The stationing of PI is 3 + 980.
Determine the middle ordinate in meters.
Determine the stationing of PT.
Determine the stationing of a point Q on the curve whose deflection angle from PC is 12°.
Solution pending in psadquestions/t1198.json.
The offset distances of two points A and B of a simple curve are 2 m and 6 m, respectively. The chord length from PC to A is 30 m.
What is the radius of the curve?
What is the chord length from PC to B in meters?
What is the length of curve from PC to B in meters?
Solution pending in psadquestions/t1202.json.
A simple curve is to connect two tangents whose angle of intersection is 36°. The curve is to pass a point B whose perpendicular distance from the tangent through PC (at point C) is 12 m. Point C is 36 m from the point of intersection of the tangents.
What is the distance from PI to B in meters?
What is the radius of the curve in meters?
Find the length of the curve in meters.
Solution pending in psadquestions/t1205.json.
What is the superelevation of the outer rail above inner rail of a 3° railroad curve with 100 kph design speed if friction factor is neglected? Use chord basis.
Solution pending in psadquestions/t1208.json.
A 1800-kg truck travels at 85 kph around a banked curve with a radius of 250 m. What should the superelevation be so that the tire friction is not needed to prevent the car from sliding?
Solution pending in psadquestions/t1209.json.
Two tangents intersecting at V with bearings N 75° 12' E and S 78° 36' E are connected with a 4 degree simple curve. Without changing the direction of the two tangents and with the same angle of intersection, it is required to shorten the curve to 100 m starting from the PC.
By how much shall the point of intersection of the tangent be moved?
What is the distance between the two parallel tangents?
By how much shall the PT be moved and in what direction from the old tangent?
Solution pending in psadquestions/t1210.json.
A reversed curve of a railroad track has the following properties: D1 = 3°, D2 = 2°, Stationing of PT = 32 + 121. What is the stationing of PC? Use chord basis.
Solution pending in psadquestions/t1218.json.
A reversed curve with diverging tangent is to be designed to connect to three traversed lines for the portion of the proposed highway. The lines AB is 185 m, BC is 122.40 m, and CD is 285 m. The azimuth are Due East, 242°, and 302° respectively. The following are the cost index and specification: Type of Pavement = Item 311 (Portland Concrete), Number of Lanes = Two Lanes, Width of Pavement = 3.05 m per lane, Thickness of Pavement = 20 cm, Unit Cost = P780 per square meter. It is necessary that the PRC (Point of Reversed Curvature) must be one-fourth the distance BC from B.
Find the radius of the first curve.
Find the length of road from A to D. Use arc basis.
Find the cost of the concrete pavement from A to D.
Solution pending in psadquestions/t1229.json.
A spiral easement curve has a length of 100 m with a central curve having a radius of 300 m. Determine the offset distance from the tangent to the third-quarter point of the spiral.
Solution pending in psadquestions/t1239.json.
A car traveling at 105 kph applies a brake and stopped at a distance of 105 m. The coefficient of friction between the tires and the road is 0.5. If the perception-reaction time is 1.5 seconds, what is the grade of the road?
Solution pending in psadquestions/t1264.json.
The following data were taken on five cars traversing a 1.5-km highway. [Table omitted] Determine the space mean speed.
Solution pending in psadquestions/t1309.json.
A raised structure, including bridge and building supports and walkways, over water, typically supported by widely spread piles or pillars.
Solution pending in psadquestions/t1323.json.
Refers to number of vehicles on a given stretch of road.
Solution pending in psadquestions/t1324.json.
A method of locating the position of an object by observing the direction and/or distance to the object from two or more observation points.
Solution pending in psadquestions/t1325.json.
The uppermost layer of a sealed pavement. It provides the riding surface for the road users.
Solution pending in psadquestions/t1326.json.
A premixed asphalt surfacing is sometimes laid in two layers of different materials. The lower layer of such a construction is known as the:
Solution pending in psadquestions/t1327.json.
The main load-spreading layer of a pavement.
Solution pending in psadquestions/t1328.json.
The secondary load-spreading layer of a pavement.
Solution pending in psadquestions/t1329.json.
The soil acting as a foundation for the pavement.
Solution pending in psadquestions/t1330.json.
The process by which a soil is improved and made more stable.
Solution pending in psadquestions/t1331.json.
A black to dark brown sticky material, composed principally of high molecular-weight hydrocarbons.
Solution pending in psadquestions/t1332.json.
May consist of pedestrians, ridden or herded animals, vehicles, streetcars and other conveyances, either singly or together, while using the public way for purposes of travel.
Solution pending in psadquestions/t1337.json.
A bridge, road, railway or similar structure that crosses over another road or railway.
Solution pending in psadquestions/t1340.json.
A person traveling on foot, whether walking or running.
Solution pending in psadquestions/t1341.json.
The driver sees a control device, warning sign, or object on the road.
Solution pending in psadquestions/t1342.json.
The driver identifies the object or control device and thus understands the stimulus.
Solution pending in psadquestions/t1343.json.
The driver actually executes the action decided on during the emotion sub-process.
Solution pending in psadquestions/t1345.json.
Distance traveled by a vehicle from the point of application of force to the brake control to the point at which the vehicle reaches a full stop.
Solution pending in psadquestions/t1346.json.
Distance within which material is moved without extra compensation.
Solution pending in psadquestions/t1347.json.
Pavement structure that maintains intimate contact with, and distributes loads to the subgrade and depends on aggregate interlock, particle friction, and cohesion for stability.
Solution pending in psadquestions/t1350.json.
Transport of excavation beyond specified limits.
Solution pending in psadquestions/t1352.json.
The shortest distance from a circular curve to the point of intersection of the tangents.
Solution pending in psadquestions/t1355.json.
A curve of constantly changing radius.
Solution pending in psadquestions/t1356.json.
The perpendicular offset distance from point A on a simple curve to Q on the tangent line is 64 m. If the distance from the P.C. to Q on the tangent is 260 m. Compute the radius of the simple curve.
An engineer designs a simple curve at a certain point of a highway. The data are: $I = 44^\circ$, $R = 400$ feet, PC is at Station $11 + 10.57$, PI is at Station $12 + 72.18$, and PT is at Station $14 + 17.75$. What is the deflection angle of Station $13 + 00$?
An 80-m spiral connects a tangent with a 180-m radius circular curve. The maximum velocity in kph that a car could pass through the curve without skidding is nearest to:
The cross-sectional area of a road with a width of 10 m is 42.9 square meters. The cross-section (format = height/distance) is as follows:
$\dfrac{9.8}{2.4}\quad \dfrac{0}{x}\quad \dfrac{7.4}{1.2}$
Determine the value of $x$.
In the measures of congestion of highway capacity, what will happen as the density continues to increase?
The table below lists data for an asphalt paving mix design — Asphalt cement: specific gravity 1.03, 6.0% of weight; Mineral filler: 3.10, 8.0%; Fine aggregates: 30.0% (bulk sp. gr. 2.690); Coarse aggregates: 56.0% (bulk sp. gr. 2.611). If the maximum specific gravity of the mixture is 2.535, determine the effective specific gravity of the aggregates in the mix.
For an asphalt paving mixture, the maximum specific gravity of the paving mix is 2.535 and the bulk specific gravity of the compacted paving mix is 2.384. Determine the air voids in the compacted mix, in percent.
Ways of avoiding traffic conflicts:
Cracks approximately at right angles to the pavement centerline. These may be caused by shrinkage or differential thermal stress of the asphalt concrete, or may be reflective cracks.
The provision of safety sight distance depends on the characteristics of the road environment such as: I. Road geometry, II. Road surface, III. Road illumination at night, IV. Road topography.
One of the provisions of safety sight distance depends on the characteristics of the vehicle, which are as follows: I. Type of vehicle (car or truck), II. friction between the tire and the road, III. eye height of the driver, IV. speed of vehicle.
Wearing away of the pavement surface caused by dislodging of aggregate particles and binder. This is usually a result of insufficient asphalt binder in the mix or stripping of asphalt from particles of aggregate.