Mapua Institut I nstitute e of Technology Intramuros, Manila
School of Civil, Environmental and Geological Engineering Surveying Department CE121!"2
IE#D$%&' ( #)*I+G #)*I+G % ) &EE&SE &EE&S E C-&E -SI+G T&)+SIT )+D T).E Su/mitted /y0 /y0 .ascual, Ma +adine Stephanie D G&%-. +% Dale
Chief of .arty0 .arty0 as3ue4, Cli5ord
Date of ield6or70 )ugust 28, 291: Date of Su/mission0 Septem/er 1(, 291: Su/mitted to0 Engr "ienvenido Cervantes Data0 ST)TI%+ %CC-.IED
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Discussion0 %ur professor, Engr "ienvenido Cervantes gathered us for the discussion of the things 6e 6ill do for the Beld6or7 ( )lso, he gave us the data 6e needed for the Beld6or7 ;e gave us an adviced to compute all the necessary data in /eforehand so it 6ouldn@t /e a pro/lem 6hen 6e start accomplishing the Beld6or7 )fter these, 6e 6ent to the Surveying Department to /orro6 the instruments 6e 6ill /e utili4ing for #aying of a &everse Curve using theodolite and tape These instruments 6ere range poles, >9 meter tape, and theodolite )fter that, 6e proceed to the South .ar7ing lot to start plotting the points and create the reverse curve The concept of the reverse curve 6as discussed /efore the Beld6or7 $e used a di5erent data for this Beld6or7 The Brst curve 6as ust easy to lay /ecause it is similar 6ith the previous Beld6or7 /ut the second 6as challenging /ecause 6e had to thin7 of a 6ay 6here 6e can lay the other curve /y using the .C $e sight for the .C and set the vernier to 4ero then rotate it until the angle reaches 189 < the second intersection angle divided /y t6o )fter that, 6e sight for the intermediate points until the second curve 6as completed +ecessary computations 6ere made after the Beld6or7
.hotos0
#aying out and plotting of the reverse curve
Setting up and sighting of the stations &esearch $or7s0 .&%.E&TIES % C-&ES
The center line of a road consists of series of straight lines interconnected /y curves that are used to change the alignment, direction, or slope of the road Those curves that change the alignment or direction are 7no6n as hori4ontal curves, and those that change the slope are vertical curves The initial design is usually /ased on a series of straight sections 6hose positions are deBned largely /y the topography of the area The intersections of pairs of straights are then connected /y hori4ontal curves Curves can /e listed under three main headings, as follo6s0 1F ;ori4ontal curve 2F ertical curves ;ori4ontal Curves $hen a high6ay changes hori4ontal direction, ma7ing the point 6here it changes direction a point of intersection /et6een t6o straight lines is not feasi/le The change in direction 6ould /e too a/rupt for the safety of modem, highspeed vehicles It is therefore necessary to interpose a curve /et6een the straight lines The straight lines of a road are called tangents /ecause the lines are tangent to the curves used to change direction The smaller the radius of a circular curve, the sharper the curve or modern, highspeed high6ays, the curves must /e Hat, rather than sharp The principal consideration in the design of a curve is the selection of the length of the radius or the degree of curvature This selection is /ased on such considerations as the
design speed of the high6ay and the sight distance as limited /y headlights or o/structions The hori4ontal curve may /e a simple circular curve or a compound curve or a smooth transition /et6een straight and a curve, a transition or easement curve is provided The vertical curves are used to provide a smooth change in direction ta7ing place in the vertical plane due to change of grade Types of ;ori4ontal Curves There are four types of hori4ontal curves They are descri/ed as follo6s0 ) Simple The simple curve is an arc of a circle The radius of the circle determines the sharpness or Hatness of the curve " Compound re3uently, the terrain 6ill re3uire the use of the compound curve This curve normally consists of t6o simple curves oined together and curving in the same direction C &everse ) reverse curve consists of t6o simple curves oined together, /ut curving in opposite direction or safety reasons, the use of this curve should /e avoided 6hen possi/le vie6 C, Bg 2F D Spiral The spiral is a curve that has a varying radius It is used on railroads and most modem high6ays Its purpose is to provide a transition from the tangent to a simple curve or /et6een simple curves in a compound curve vie6 D, Bg 2F ;ori4ontal curve or Circular curves of constant radius ) simple circular curve sho6n in ig, consists of simple arc of a circle of radius & connecting t6o straights lines, intersecting at .I,
called the point of intersection .IF, having a deHection angle The distance E of the midpoint of the curve from . I is called the eJternal distance The arc length from T1 to T2 is the length of curve, and the chord T1T2 is called the long chord The distance M /et6een the midpoints of the curve and the long chord, is called the midordinate The distance T1 .I 6hich is e3ual to the distance . IT2, is called the tangent length Elements of ;ori4ontal Curves The elements of a circular curve are sho6n in Bgure > Each element is designated and eJplained as follo6s0 K
.oint of Intersection .IF The point of intersection is the
point 6here the /ac7 and for6ard tangents intersect Sometimes, the point of intersection is designated as verteJF K DeHection )ngle F The central angle is the angle formed /y t6o radii dra6n from the center of the circle %F to the .C and .T The value of the central angle is e3ual to the I angle Some authorities call /oth the intersecting angle and central angle either I or ) K &adius &F The radius of the circle of 6hich the curve is an arc, or segment The radius is al6ays perpendicular to /ac7 and for6ard tangents K .oint of Curvature .CF The point of curvature is the point on the /ac7 tangent 6here the circular curve /egins It is sometimes designated as "C /eginning of curveF or TC tangent to curveF K .oint of Tangency .TF, The point of tangency is the point on the for6ard tangent 6here the curve ends It is sometimes designated as EC end of curveF or CT curve to tangentF
K
.oint of Curve The point of curve is any point along the
curve #ength of Curve #F The length of curve is the distance from the .C to the .T, measured along the curve K Tangent Distance TF The tangent distance is the distance along the tangents from the .I to the .C or the .T These distances are e3ual on a simple curve K #ong Cord CF The long chord is the straightline distance from the .C to the .T %ther types of chords are designated as follo6s0 C The fullchord distance /et6een adacent stations full, half, 3uarter, or one tenth stationsF along a curve K C1 The su/chord distance /et6een the .C and the Brst station on the curve K C2 The su/chord distance /et6een the last station on the curve and the .T K EJternal Distance EF The eJternal distance also called the eJternal secantF is the distance from the .I to the midpoint of the curve The eJternal distance /isects the interior angle at the .I K Middle %rdinate MF The middle ordinate is the distance from the midpoint of the curve to the midpoint of the long chord The eJtension of the middle ordinate /isects the central angle K Degree of Curve The degree of curve deBnes the sharpness or Hatness of the curve ;ori4ontal Curve #ayout )F &ectangular %5 sets rom the Tangent !Coordinate! Method This method is also suita/le for short curve and, as in the previous method, no attempt is made to 7eep the chord of e3ual lengths "F .olar Sta7ing ! DeHection Method! .olar sta7ing methods have /ecome increasingly popular, especially 6ith the availa/ility of electronic tachometers ) simple
method can /e derived using the starting point of the circle L is e3ual to the angle /et6een the tangents and chord or e3ual arc lengths the polar sta7ing elements are determined 6ith respect to the tangent ertical curves %nce the hori4ontal alignment has /een determined, the vertical alignment of the section of high6ay can /e addressed )gain, the vertical alignment is composed of a series of straight line gradients connected /y curves, normally para/olic in form These vertical para/olic curves must therefore /e provided at all changes in gradient The curvature 6ill /e determined /y the design speed /eing sucient to provide ade3uate driver comfort 6ith appropriate stopping sight distances provided ertical curves should /e simple in application and should result in a design that is safe and comforta/le in operation, pleasing in appearance, and ade3uate for drainage The maor control for safe operation on crest vertical curves is the provision of ample sight distance for the design speedN 6hile research has sho6n that vertical curves 6ith limited sight distance do not necessarily eJperience safety pro/lems, it is recommended that all vertical curves should /e designed to provide at least stopping sight distances $herever practical, more li/eral stopping sight distances should /e used urthermore, additional sight distance should /e provided at decision points or driver comfort, the rate of change of grade should /e 7ept 6ithin tolera/le limits This consideration is most important
in sag vertical curves 6here gravitational and vertical centripetal forces act in opposite directions )ppearance also should /e considered in designing vertical curves ) long curve has a more pleasing appearance than a short oneN short vertical curves may give the appearance of a sudden /rea7 in the proBle due to the e5ect of foreshortening The vertical o5set from the tangent grade at any point along the curve is proportional of the vertical o5set at the .I, 6hich is )#!899 The 3uantity #!), termed O'P, is useful in determining the hori4ontal distance from the ertical .oint of Curvature .CF to the high point of Type I curves or to the lo6 point of type III curves
If the a4imuth of the /ac76ard and the for6ard tangents are given, the intersection angle I can /e solved using0 I =azimuth of the forward tangent – azimuth of thebackward tangent
The tangent distance must /e solve using0 T = R ∙ta n
1 2
The middle ordinate distance MF can /e computed using0
M = R ∙
[
1−co s
1 2
]
The length of the curve #cF can /e computed using0 Lc =πRI / 180 ;whenI is∈ degreesLc = RI ; when I is ∈radians
The station of .C can /e computed using0 PC = PI −T
The station of .T can /e found /y0 PT = PI + Lc
The length of the Brst su/ chord from .C, if .C is not eJactly on a full station other6ise C1Q a full chord lengthF C 1= First fu stationon the cur!e− PC
The length of the last su/ chord from .T, if .T is not eJactly on a full station other6ise C2Q a full chord lengthF C 2= PT −ast fu station onthecur!e
The value of the Brst deHection angle d10 d 1=2 ∙ sin
−1
C 1 2 R
The value of the last deHection angle d20 d 2=2 ∙ sin
−1
C 2 2 R
Incremental Chord and Tangent %5set Method The tangent o5set distance J1 must /e solved using0 " 1= c 1∗cos
( ) d1 2
The tangent o5set distance y1 must /e solved using0 # 1 =c 1∗si n
( ) d 1 2
The tangent o5set distances J2 must /e solved using0 " 2 =c∗co s
[
]
d 1+ $ 2
The tangent o5set distance y2 must /e solved using0 # 2 =c∗ si n
[
d 1 + $ 2
]
The tangent o5set distance J>, must /e solved using0 " 3 =c∗co s
[ ] $ + $ 2
" 3= c∗co s $
∨
The tangent o5set distance y> must /e solved using0 # 3 =c ∗si n
[ ] $ + $ 2
# 3 =c ∗sin $
∨
The tangent o5set distance Jn, must /e solved using0
"n= c∗co s
[
d 2+ $ 2
]
The tangent o5set distance yn, must /e solved using0 #n= c∗ sin
[
d 2 + $ 2
]
Conclusion0 rom the Beld6or7 entitled #aying of a &everse Curve using Theodolite and Tape, the follo6ing o/ectives had /een achieved and accomplished rom laying of a simple and compound curve /y using the tape, 6e ac3uired the 7no6ledge in laying a reverse curve 6ith the use of the theodolite and tape The theodolite is
hard to setup /ecause 6e have to put all of the /u//les in the center for it to have a correct reading )side from the Brst o/ective mentioned, 6e 6ere a/le to master the s7ill in leveling, orienting and using the theodolite e5ectively In addition to revie6ing 6hat 6e learned from Elementary Surveying, our Solid Mensuration s7ills 6ere also improved as 6e analy4ed di5erent parts of the simple curve %n the other hand, 6e can say that the Beld6or7 is a matter of computations ;ence, the most important thing is the practical application 6hich in this case, the laying of the curve using the meter tape, t6o range poles, and the theodolite rom the data 6e have o/tained, 6e can conclude that 6e have conducted the Beld6or7 6ell This sho6s on the t6o near values of length of chord 6e have arrived from the actual and the computed Moreover, the climaJ of this Beld6or7 is ho6 6e esta/lished the art of leading and follo6ing the designated and desired tas7 on the group In addition, responsi/ility is a very critical part of the performance in each mem/er of the group $ith the things 6e learned, our minds 6or7ed harmoniously, thin7ing of the right 6ay 6e can get more accurate results These Beld 6or7s are designed for students to utili4e their minds and apply it in the simplest possi/le 6ay that they can %rgani4ation and proper 7no6ledge of the activity is really a 7ey to attaining precise outcomes
