Laying of Simple Curve By Transit and Ta PDF

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

-TA -TABL BL BLE E CO CONT NT NTEN EN ENTS TS TS--

Introduction-------------------------------------------------------2-3 Objectives & Instruments--------------------------------------4 Procedures & Computations----------------------------------5-6 Preliminary Data Sheet-----------------------------------------8-9 Final Data Sheet--------------------------------------------------10-13 Research & Discussion------------------------------------------14 Conclusion---------------------------------------------------------15 Field Work Peer Assessment----------------------------------16

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

INT INTROD ROD RODUC UC UCTIO TIO TION N Curves are provided whenever a road changes its direction from right to S (vice versa) or changes its alignment from up to down (vice versa). Curves are a critical element in the pavement design. They are provided with a maximum speed limit that should lie followed very strictly. Following the speed limit becomes essential as the exceed in speed may lead to the chances of the vehicle becoming out of control while negotiating a turn and thus increase the odds of fatal accidents. Also, it is very necessary that appropriate safety measures be adopted at all horizontal and vertical curves to make the infrastructure road user friendly and decrease the risks of hazardous circumstances. The center lines of highways and railroads consist of a series of straight lines connected by curves. The curves of fast traffic are normally circular, although spiral curves may be used to provide gradual transitions to or from the circular curves. There are different kinds of curves, the simple curve, compound curve, the reverse curve, and the spiral curve. The simple curve is consists of a single arc. The compound curve consists of two or more arcs with different radii. The reverse curve consists of two arcs that curve in different directions. And the spiral curve (or transition curve) has a varying radius, so that the curve starts out very flat and increases in sharpness as we move into the curve.

Simple

Compound

Reverse

In this field work, simple curve is the one that was focus. A curve is initially laid out with two straight lines or tangents. These lines are extended until they intersect and the point of intersection is called P.I. The first tangent encountered is called the back tangent and the second one is called the forward tangent.

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

The goal of this field work is to be able to lay a simple curve by deflection angle. In this method, curves are staked out by use of deflection angles turned at the point of curvature from the tangent to points along the curve. The curve is set out by driving pegs at regular interval equal to the length of the normal chord. Usually, the sub-chords are provided at the beginning and end of the curve to adjust the actual length of the curve. The method is based on the assumption that there is no difference between length of the arcs and their corresponding chords of normal length or less. The underlying principle of this method is that the deflection angle to any point on the circular curve is measured by the one-half the angle subtended at the center of the circle by the arc from the P.C. to that point.

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

OBJE OBJECTIVE CTIVE CTIVESS  To be able to lay a simple curve by deflection angle.  To master the skill in leveling, orienting and using the transit effectively.

INS INSTRU TRU TRUMENT MENT MENTSS 

2 Range Poles - is a surveying instrument used for marking the position of stations and for sightings of those stations as well as for ranging the straight lines.





Chalk – used to put marking on pavements

50 Meter Tape – These are designed for most conventional measurements in surveying and in engineering work.



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Theodolite - a surveying instrument with a rotating telescope for measuring horizontal and vertical angles.

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

PRO PROCE CE CEDU DU DURES RES AN AND DC COMP OMP OMPUTATI UTATI UTATION ON ONSS 1. The professor gives data: R = 80m Backward Tangent Direction: 48°13’ (azimuth or bearing) Forward Tangent Direction: 113°30’ (azimuth or bearing) Station of the Vertex: 30 + 001 Adopt Full Chord length of 20m 2. The student compute the elements of the simple curve using the following formulas:  

Intersection Angle I = azimuth of the forward tangent – azimuth of the backward tangent Tangent Distance 𝐼

T= R*tan( ) 2 

Middle Ordinate 𝐼

M = R*[1-cos( )] 2 

Length of Curve 𝐿𝐶 = 𝐼 ∗ 𝑅



Long Chord 1

𝐶 = 2 ∗ 𝑅 ∗ sin 2 

Station of PC 𝑆𝑡𝑎𝑡𝑖𝑜𝑛 ∙ 𝑜𝑓 ∙ 𝑃𝐶 = 𝑆𝑡𝑎 ∙ 𝑉 − 𝑇



Station of PT 𝑆𝑡𝑎𝑡𝑖𝑜𝑛 ∙ 𝑜𝑓 ∙ 𝑃𝑇 = 𝑆𝑡𝑎 ∙ 𝑃𝐶 + 𝐿𝐶



Length of first subchord from PC 𝐶1 = 𝑓𝑖𝑟𝑠𝑡 ∙ 𝑓𝑢𝑙𝑙 ∙ 𝑠𝑡𝑎𝑡𝑖𝑜𝑛 ∙ 𝑜𝑛 ∙ 𝑡ℎ𝑒 ∙ 𝑐𝑢𝑟𝑣𝑒 − 𝑆𝑡𝑎. 𝑃𝐶



Length of last subchord from PT 𝐶2 = 𝑆𝑡𝑎. 𝑃𝑇 − 𝑙𝑎𝑠𝑡 ∙ 𝑓𝑢𝑙𝑙 ∙ 𝑠𝑡𝑎𝑡𝑖𝑜𝑛 ∙ 𝑜𝑛 ∙ 𝑡ℎ𝑒 ∙ 𝑐𝑢𝑟𝑣𝑒



First Deflection Angle

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method 𝐶

1 ) 𝑑1 = 2 ∗ sin−1(2∗𝑅



Last Deflection Angle 𝐶

2 ) 𝑑2 = 2 ∗ sin−1(2∗𝑅

3. Set up the transit/theodolite over the vertex V, level the instrument and sight/locate PC and PT using the computed length of the tangent segments. Mark the position of PC and PT by marking pins if on soft ground or chalk if on pavement. 4. The instrument over PC, level and start locating points of the curve using the following procedures: a. Initialize the horizontal vernier by setting the zero reading. Tighten the upper clamp and adjust it with the upper tangent screw. b. Using the telescope, sight the vertex PI with the Vernier still at zero reading. c. Tighten the lower clamp and focus it using the lower tangent screw. d. With the lower tangent screw already tight, loosen the upper clamp and start to measure half the first deflection angle. Mark the direction with a range pole. Along this line, using marking pin/chalk, mark point A measured with a tape the length of the first subchord. e. Locate the next point B, a full chord length from point A but this time intersecting the line sighted at an angle of half the sum of d1 and the full D of the curve. Note that the transit/theodolite still positioned over station PC. f. Proceed in locating other points on the curve following step e until you cover all full chord stations on the entire length of the curve. g. Measure the distance 𝐶2 and from the last full station on the curve and intersecting the line of sight with a deflection angle equal to half the intersection angle, mark the last point as PT. 5. Check the position of PT by determining the length of PC from PT and compare it to the computed total length of the chord of simple curve

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

FIN FINAL AL D DATA ATA SH SHEE EE EETT FIELD WORK 1: LAYING OF A SIMPLE CURVE BY TRANSIT AND TAPE (THE INCREMENTAL CHORD AND DEFLECTION ANGLE METHOD) DATE: October 8, 2015

GROUP NO. 5

TIME: 12:00-4:30

LOCATION: Luneta Park

WEATHER: Sunny

PROFESSOR: Engr. Valerie Ira C. Balmoris

DATA SUPPLIED: R = 80m Backward Tangent Direction: 48°13’ (azimuth or bearing) Forward Tangent Direction: 113°30’ (azimuth or bearing) Station of the Vertex: 30 + 001 Adopt Full Chord length of 20m STAT STATIO IO ION N INC INCRE RE REMEN MEN MENTAL TAL ME METH TH THOD OD OCC OCCUPI UPI UPIED ED OBSE OBSERVED RVED PC A A B B C C D D E(PT) COMPUTED LENGTH OF CHORD: 85.97 m

9.9656 m 20 m 20 m 20 m 20 m

CEN CENTR TR TRAL AL INC INCRE RE REMEN MEN MENTAL TAL ME METH TH THOD OD 7°8’ 14°19’ 14°19’ 14°19’ 14°19’

DEFL DEFLEC EC ECTION TION A ANG NG NGLE LE FRO FROM M BACK TA TANGEN NGEN NGENTT 3°34’ 10°44’ 17°53’ 25°3’ 32°13’

ACTUAL LENGTH OF CHORD: 85.5m

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

COM COMPUTA PUTA PUTATION TION TIONSS  Tangent Distance

 First Deflection Angle

𝐼

𝐶1 𝑑1 = 2 ∗ sin−1 ( ) 2∗𝑅

T= R*tan(2) 65

= 80*tan( 2 )

𝑑1 = 𝟕°𝟖′  Last Deflection Angle

T=50. 50. 50.9656 9656 9656m m  Length of Curve

𝑑2 = 2 ∗ sin−1(

𝐿𝐶 = 𝐼 ∗ 𝑅 = 65(

𝜋 180

𝐶2

2∗𝑅

)

𝑑2 = 𝟕. 𝟎𝟐° ) ∗ (80)

 D

𝐿𝐶 = 90 90.757 .757 .7571m 1m

𝐷=

𝑆 𝑅

𝐷=

20 180 ( ) 80 𝜋

 Station of PC 𝑆𝑡𝑎 ∙ 𝑃𝐶 = 𝑆𝑡𝑎 ∙ 𝑉 − 𝑇 = 30 + 001 − 50.9656

𝐷 = 𝟏𝟒°𝟏𝟗′

𝑆𝑡𝑎 ∙ 𝑃𝐶 = 𝟐𝟗 + 𝟗𝟓𝟎. 𝟎𝟑

𝑑1 +𝐷

 Station of PT

 

𝑆𝑡𝑎. 𝑃𝑇 = 𝑆𝑡𝑎 ∙ 𝑃𝐶 + 𝐿𝐶



= 29 + 950.03 + 90.7571



𝑆𝑡𝑎. 𝑃𝑇 = 𝟑𝟎 + 𝟎𝟒𝟎. 𝟕𝟗



= 𝟏𝟎°𝟒𝟒′

𝟐 𝑑1 +2𝐷 𝟐 𝑑1 +3𝐷 𝟐 𝑑1 +4𝐷 𝑰 𝟐

𝟐

= 𝟏𝟕°𝟓𝟑′ = 𝟐𝟓°𝟑′ = 𝟑𝟐°𝟏𝟑′

= 𝟑𝟐°𝟑𝟎′

 Length of first subchord from PC 𝐶1 = 𝑓𝑖𝑟𝑠𝑡 ∙ 𝑠𝑡𝑎𝑡𝑖𝑜𝑛 − 𝑆𝑡𝑎. 𝑃𝐶 = 960 − 950.03 𝐶1 = 9. 9.97 97  Length of last subchord from PT 𝐶2 = 𝑆𝑡𝑎. 𝑃𝑇 − 𝑙𝑎𝑠𝑡𝑓𝑢𝑙𝑙 𝑠𝑡𝑎𝑡𝑖𝑜𝑛 = 30 + 040.79 − 1 + 060 𝐶2 = 𝟗. 𝟕𝟗𝒎

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

SKE SKETCH TCH

Pho Photo to 1: After we have set the vertex point, we’ve check where we will locate the station of PC and PT. After locating our PC we’ve started to compute for the deflection angles. In this photo, we illustrate how we locate each stations (A, B, C, D and PT)

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

Pho Photo to 22:: In this photo, we’ve showed how we move to the next point by Maintaining the straight line using the theodolite

Pho Photo to 33:: In the last part of the field work is getting the length of long chord using the tape measure. As a technique, we have decided to measure it partially by 20m. To check if it is going straight, we’ve used the theodolite.

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

RESE RESEARCH ARCH AN AND D DI DISCUSSI SCUSSI SCUSSIONS ONS The degree of curvature is defined as the central angle to the ends of an arc or chord of agreed length. Various lengths are commonly used in different areas of practice. This angle is also the change in forward direction as that portion of the curve is traveled. Curvature is usually measured in radius of curvature. A small circle can be easily laid out by just using radius of curvature, but if the radius is large as a km or a mile, degree of curvature is more convenient for calculating and laying out the curve of large scale works like roads and railroads. By this method curve setting can be easily done with the help of a transit or theodolite and a chain, tape or rope of a prescribed length. One of the methods in getting a simple curve is by incremental chords and deflection angle method. In this method, curves are staked out by use of deflection angles turned at the point of curvature from the tangent to points along the curve. The curve is set out by driving pegs at regular interval equal to the length of the normal chord. In the incremental method, the instrument is set up on the PC, deflection angles are measured from the back tangent, and chords are measured from the previous set station. Usually, the sub-chords are provided at the beginning and end of the curve to adjust the actual length of the curve. The method is based on the assumption that there is no difference between length of the arcs and their corresponding chords of normal length or less. The underlying principle of this method is that the deflection angle to any point on the circular curve is measured by the one-half the angle subtended at the center of the circle by the arc from the P.C. to that point. The deflection method is the premier curve location method for use when running grade lines. It allows you to check special situations, such as sharp, v-shaped draws to see if a particular curve will fit to the location without undue cuts or fills. It can also be used to check grade line (the variation or deflection from one tangent to the next, or from one ribbon location to the next) to see if the deflection-angle exceeds a critical value, meaning that the minimum radius rule (e.g. 60 ft) may not be met.

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

CON CONCL CL CLUSI USI USION ON There are too many process how surveyors does a curve on a railroad, highways, expressways, and etc. It is not easy for it to just set a curve without any aid of surveying. If we will notice some of the roads, some of it has its mistakes, which led to accidents, particularly in the sharp curves, it has the most critical part on the roads. In civil engineering, we do not only consider on the structure itself but also the safety of each individual who will benefit to it. In this field work, I’ve learn how to they make curves by using an incremental and deflection angle method. It’s true that it is not easy to make a curve. It takes analyzation and application of geometry to find out how it is done. What I’ve learn also in this field work is to find out techniques in measuring some distances, like in getting the chord, if you will get its measurement by using the full length of the tape, it would take you a large error because of the sag due to gravity and also the air resistance, that is why we make our techniques to lessen the error and get the true value precisely. This field work also lets me realize that the work of each surveyors is not that easy. Working on a sunny weather really drains your energy even though you are loving and enjoying the things that you do. Being surveyor is not a joke, a simple mistake makes a project a big problem, and that is why, working in this like of a job should be taken very seriously because, it is not only as simple as structure, but also it considers lives. In our field work, based on our data and results, we got very low percent error, this is because in what technique we did in using the tape measure. One thing I can see that makes an error is the sag on tape. Since the distances that was measure is too far, the instances is that, it can create sag due to gravity and also to the air resistance, and also, one thing that makes error on the field work is that, the alignment when moving to other station is not properly checked, which has a tendency to change its direction and will give farther than the precise value. As a recommendation to this field work, as what we did in field work 1, we’ve measured distances by 20m, in this length, it is fair enough to pull the tape measure and also has the fair sag on it, and also by using the theodolite, we checked if we are moving in an aligned position.

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method FIELD WORK PEER ASSESSMENT COURSE: CE121F

SECTION: B2

FIELD WORK Title:

DATE: 10/16/15

LAYING OF A SIMPLE CURVE BY TRANSIT AND TAPE

GROUP MEMBERS:

1. Calangian, Austin 2. Isorena, Matt 3. Landrito, Nylah 4. Petterson, Royell 5. Ramos, Ken 6. Santos, Renz Carlo N. 7. Santos, Reiner 8.

CRITERIA

EXCELLENT 4

TIME ELEMENT

Arrives on time

PREPAREDNESS COOPERATIVENESS

ACCURACY

OVERALL CONTRIBUTION ON THE GROUPWORK

Knows what exactly is to be done in the field Performs assigned task well and is willing to help groupmates Computes for the required value accurately and in such a short time Performs efficiently a very important task assigned

GROUP NO. 5

Score: 20 Score: 20 Score: 20 Score: 20 Score: 20 Score: 20 Score: 20 Score: 20

VERYGOOD 3

LIMITED 2

POOR 1

1

2

3

4

5

6

7

8

Arrives within the grace period of 15 minutes Familiar with the procedure Performs only assigned task

Late for at most 30 minutes

Late for more than 30 minutes

4

4

4

4

4

4

4

4

Needs further explanation Limited in performing assigned task Computes the required value with some assistance Performs the secondary load assigned

Does not know what is to be done Does not want to help at all

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

Computes for the required value with little assistance Performs the important task assigned

Fails to compute the required value

MEMBERS

Does nothing

EVALUATOR’S NAME/SIGNATURE: Serrano, Jodel Christian R. /

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Laying of Simple Curve By Transit and Tape: The Incremental Chords and Deflection Angle Method

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