These are sample problems about simple curves. Elementary Surveying for Engineering Students
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Route Surveying
INTRODUCTION Engr. Voncy
Route Surveying
Introduction What is curve?
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Engr. Voncy
Chapter 11: Flow
bodies; lift and drag
Route Surveying
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Engr. Voncy
Chapter 11: Flow
bodies; lift and drag
Route Surveying
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Engr. Voncy
Chapter 11: Flow
bodies; lift and drag
Route Surveying
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Engr. Voncy
Chapter 11: Flow
bodies; lift and drag
Route Surveying
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Engr. Voncy
Chapter 11: Flow
bodies; lift and drag
Route Surveying
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Chapter 11: Flow
bodies; lift and drag
Route Surveying Introduction Curves are generally used on highways and railways where it is necessary to change the alignment. When two straights of a highway or railway are at same angle each other, a curve is introduced between them to avoid an abrupt chan change ge in dire direct ctio ion n and and to make make the the vehi vehicl cle e move move safe safely ly,, smoo smooth thly ly and and comfortably. A curve is provided at the intersection of the two straights to effe effect ct a gr grad adua uall chan change ge in the the direc directi tion on.. Th This is chan change ge in dire direct ctio ion n of the the straights may be in a horizontal or a vertical plane, resulting in the provision of a horizontal or a vertical curve, respectively.
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Chapter 11: Flow
bodies; lift and drag
Route Surveying Introduction A horizontal curve is provided at the point where the two straight lines intersect in the horizontal plane. When the curve is provided in the horizontal plane, it is known as a horiz horizon onta tall curv curve. e. Th The e horiz horizon onta tall curv curves es are are furt furthe herr clas classi sifi fied ed as simp simple le circ circul ular ar,, compound, reverse, transition and combined curves.
A verti vertica call curv curve e is provi provide ded d at the the poin pointt wh wher ere e the the two two strai straight ght line liness at diffe differe rent nt gradients intersect in the vertical plane. In such a case, a parabolic curved path is provided in the vertical plane in order to connect the gradients for easy movement of the vehicles. Vertical curves are usually parabolic and are classified as summit and sag vertical curve.
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Chapter 11: Flow
bodies; lift and drag
Route Surveying
Different Forms of Curves Curve
Horizontal Curve Compound Curve
Simple Curve
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Vertical Curve Reverse Curve
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Spiral Curve
Summit Curve
Sag Curve
Engr. Voncy
Chapter 11: Flow
bodies; lift and drag
SIMPLE CURVE A simple curve is a circular arc, extending from one tangent to the next.
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Chapter 11: Flow
bodies; lift and drag
SIMPLE CURVE
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SIMPLE CURVE Terminologies in Simple Curve PC = Point of curvature. It is the beginning of curve. PT = Point of tangency. It is the end of curve. PI = Point of intersection of the tangents. Also called vertex T = Length of tangent from PC to PI and from PI to PT . It is known as subtangent. R = Radius of simple curve, or simply radius. L = Length of chord from PC to PT . Point Q as shown below is the midpoint of L L. Lc = Length of curve from PC to PT . Point M in the the Lc. the figure is the midpoint midpoint of L E = External distance, the nearest distance from PI to the curve. m = Middle ordinate, the distance from midpoint of curve to midpoint of chord. I = Deflection angle (also called angle of intersection and central angle). It is the angle of intersection intersection of the tangents. The angle subtended by PC and PT at O is also equal to I, where O is the center of the circular curve from the above figure. x = offset distance from tangent to the curve. Note: x is perpendicular to T . θ = offset angle subtended at PC between PI and any point in the curve D = Degree of curve. It is the central angle subtended by a length of curve equal to one station. station. In English system, one station station is equal to 100 ft and in SI, one station is equal to 20 m. Sub chord = chord distance between two adjacent full stations. ME33
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Chapter 11: Flow
bodies; lift and drag
SIMPLE CURVE
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Chapter 11: Flow
bodies; lift and drag
SIMPLE CURVE
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Chapter 11: Flow
bodies; lift and drag
SIMPLE CURVE
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Chapter 11: Flow
bodies; lift and drag
SIMPLE CURVE
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Chapter 11: Flow
bodies; lift and drag
SIMPLE CURVE Problem 1 A simple curve has a central angle of 36 o and a degree of curve of 6 o. a. Find Find the neares nearestt dista distance nce from the midpoi midpoint nt of the the curve curve to the point of intersection of the tangents. b. Compute Compute the distance distance from the midpoint midpoint of the curve to the long chord joining the point of curvature and point po int of tangency. tangency. c. If the stationing stationing of the the point of curvature is at 10+020, compute the stationing of a point on the curve which intersects with the line making a deflecti d eflection on angle of 8 with wit h the tangent through throug h the P.C.
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SIMPLE CURVE Problem 2 The tangents of a simple curve have bearings of N 20 o E and N 80o E respectively. respectively. The radius of the curve is 200m. 200m . Compute for fo r the: a. External Distance of the the curve b. Middle Ordinate of the the curve c. Stationing Stationing of point A on the curve curve having a deflection deflection angle angle of 6o from PC which is at 1 + 200.
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bodies; lift and drag
SIMPLE CURVE Problem 3 A simple curve curve connects two tangents AB and BC with bearings N 85 o 30’ E and S 68o 30’ E respectively. If the stationing of the vertex is 4 + 360.2 and the stationing at PC is 4 + 288.4, determine the following: a. Radius of the curve b. External distance c. Middle ordinate d. Chord distance e. Length of curve ME33
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SIMPLE CURVE Problem 4 The tangent distance of a 3 o simple curve is only ½ of its radius. a. Compute the the angle of intersection intersection of the curve. b. Compute the length of curve curve c. Compute the area area of the fillet fillet of a curve.
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SIMPLE CURVE Three tangent lines AB, BC and CD of a traverse have azimuths of 228 o 15’, 253o 30’ and 315o 18’ respectively. respectively. The stationing of B I (10+585) and that of C is (10+885). A proposed highway curve is to connect these three tangents. a. Compute the radius radius of the simple curve that connects these tangents. b. Compute the stationing at PC. c. Compute Comput e the stationing at PT. d. Compute Comput e the length of curve from PC to PT. PT.
