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N1/2

N1/2

L

Bc D

t

t

R

L2

Pull

ACPA 2007

21M

DD 21 October 2007

Changes in direction of sewer lines are usuallyaccomplished at manhole structures. Grade and align-ment changes in concrete pipe sewers, however, can beincorporated into the line through the use of deectedstraight pipe, radius pipe or specials.

DEFLECTED STRAIGHT PIPE

With concrete pipe installed in straight alignmentand the joints in a home (or normal) position, the jointspace, or distance between the ends of adjacent pipesections, is essentially uniform around the periphery ofthe pipe. Starting from this home position any joint maybe opened up to the maximum permissible on one side

while the other side remains in the home position. Thedifference between the home and opened joint spaceis generally designated as the pull. The maximum per-missible pull must be limited to that opening which willprovide satisfactory joint performance. This varies fordifferent joint congurations and is best obtained fromthe pipe manufacturer.

The radius of curvature which may be obtained bythis method is a function of the deection angle per joint(joint opening), diameter of the pipe and the length ofthe pipe sections.

The radius of curvature is computed by the equa-tion:

R =

L

2 TAN( )1 2 N(1)

where:

R = radius of curvature, meters

L = length of pipe sections measured along

the centerline, meters

= total deflection angle of curve, degrees

N = number of pipe with pulled joints

= total deflection of each pipe, degrees

= SIN-1 or SIN-11

2 N

1 D

2 N

PULL

2 D + 2t

PULL

2Bc

(2)

N

From Figure 1, the deflection angle is further

defined as:

where:PULL = joint opening, millimeters

D = inside pipe diameter, millimeterst = wall thickness, millimeters

Figure 1 Defected Straight Pipe

Curved Alignment

Figure 2 Curved Alignment Using DefectedStraight Pipe

RAD

IUSN

ormal

Directio

nof

Laying

P.C. P.T.

L

L

2

P.I.

/N

/N

/N

/N

/N

/N/N

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DD 21 October 2007

Bc = outside pipe diameter, millimetersThe joint opening and pipe length required to provide

a curved pipeline alignment may be calculated usingthe unit values found in Table 1 on page 3. The tabletabulates the radius of a pipeline constructed of stan-dard 2.44 meter laying length pipe with a 13 mm jointopening (PULL). Other pipeline radii may be calculatedby changing, rst, the joint opening, and if necessary,the pipe laying length. An 2.44 meter laying length isstandard for most concrete pipe manufacturers. Otherlengths may require special manufacturing procedures.Changes in the design radius are directly proportional tothe pipe laying length and inversely proportional to the

joint opening. The specic pull per pipe joint is found bythe equation:

PULLx =

Rx = (Lx/L8)(PULL8/PULLx) Ru

(3)

(4)

PULL8( )L8Lx ( )( )Rx

Ru

where:

PULL = the joint openingRu = the Unit Radius (Taken from Table 1)Lx = Length of deected pipe

Specic radii may be calculated by the following pro-cedure:

Select the unit radius of curvature for the speci-ed diameter pipe from the chart.

Increase or decrease the joint opening (PULL)in Equation 1 to obtain the design radius. If therequired joint opening exceeds the pipe manu-facturers recommendations, select a pipe witha shorter laying length. 1.22 and 1.83 meter arecommon non-standard pipe lengths. Check withthe pipe manufacturer for availability of non-

standard lengths. Recalculate the pull for the shorter pipe.As illustrated in Figure 2, when concrete pipe is installedon curved alignment using deected straight pipe, thepoint of curve (P.C.) is at the midpoint of the last unde-ected pipe section and the point of tangent (P.T.) is atthe midpoint of the last pulled pipe.

RADIUS PIPERadius pipe, also referred to as bevelled or mitered pipe,incorporates the deection angle into the pipe joint. Thepipe is manufactured by shortening one side of the pipe.The amount of shortening or drop for any given pipe isdependent on manufacturing feasibility. Because of thepossibility of greater deection angles per joint, sharper

curvature with correspondingly shorter radii can be ob-tained with radius pipe than with deected straight pipe.As in the case of deected straight pipe, the radius ofcurvature which may be obtained by radius pipe is afunction of the deection angle per joint, diameter of thepipe, length of pipe sections and wall thickness.The radius of curvature is computed by the equation:

R = + tL

TAN( )

N

D

2- (5)

where:

= total deflection angle of curve, degrees

N = number of radius pipe

L = standard pipe length being used, mete

N= total deflection angle of each pipe

From Figure 3, the radius of curvature can be expressedin terms of the drop and is given by the equation:

= total deflection angle of curve, degre

N = number of radius pipe

L = standard pipe length being used, me

N= total deflection angle of each pipe

From Figure 3, the radius of curvature can be expressedin terms of the drop and is given by the equation:

R =

R = Bc

L(D + 2t)t

DROP

((

)

)--

+

L

DROP

1

2

DROP =LBc

Bc/2R+

D

2

(7)

(8)

(6)

where:Bc = outside diameter of the pipe, meters

Figure 5 presents R/Bc ratios for drops from 25mm through 375 mm and commonly manufacturedpipe lengths. Since the maximum permissible dropor any given pipe is dependent on manuacturingeasibility, it is essential to coordinate the design oradius pipe with the pipe manuacturer. Many manu-acturers have standardized joint congurations anddefections or specic radii and economics may berealized by utilizing standard radius pipe.

As illustrated in Figure 4, when concrete pipe is

installed on curved alignment using radius pipe, thepipe sections are oriented such that the plane of thedropped joint is tangent to the theoretical circular curve.Projection of the joints do not converge at a commonpoint, but are tangents to a common circle of diameterequal to the length of pipe sections. The point of curve(P.C.) is at the midpoint of the last straight pipe and thepoint of tangent (P.T.) is one half of the standard pipelength back from the straight end of the last radius pipe.The required number of pieces of radius pipe is equalto the length of the circular curve in feet divided by thecenterline length of the radius pipe (L-1/2 DROP). Wherepossible, minor modications in the radius are normallymade so this quotient will be a whole number.

Minimum radius of curvature obtained from equa-tions (1) and (5) are approximate, but are within a rangeof accuracy that will enable the pipe to be readily installedto t the required alignment. A reasonable amount of eldadjustment is possible for radius pipe by pulling the jointsin the same manner as with deected straight pipe.

BENDS AND SPECIAL SECTIONSSpecial precast sections can be used for extremely

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DD 21 October 2007

short radius curves which cannot be negotiated witheither deected straight pipe or with conventional radiuspipe. Sharper curves can be handled by using specialshort lengths of radius pipe rather than standard lengths.These may be computed in accordance with the methodsdiscussed for radius pipe. Certain types of manufactur-ing processes permit the use of a dropped joint on bothends of the pipe, which effectively doubles the deection.Special bends, or elbows can be manufactured to meetany required deection angle and some manufacturersproduce standard bends which provide given angulardeection per section.

One or more of these methods may be employed tomeet the most severe alignment requirements. Sincemanuacturing processes and local standards vary,local concrete pipe manuacturers should be con-sulted to determine the availability and geometricconguration o special sections.

The following example illustrates proper use of theTables and Figures.

Given: A 1,050 mm diameter concrete pipe stormsewer is to be installed on curved alignment

corresponding to the roadway curvature.The pipe will be manufactured in 2.44 meterlengths with a 113 mm wall thickness. Thecurve data for the roadway curb is:point of intersection station P.I. = 50+00point of curve station P.C. = 49+29.6point of tangent station P.T. = 50+63.1total deection angle = 45radius of curvature R = 170 meters

Find: The required pull per joint for deected straightpipe or the required drop for radius pipe.

Solution:From Table 1, for a 1,050 mm diameter pipe,the radius of curvature for a 25 mm pull is 124.4meters. The required pull for 51.8 meters is:

( )PULLX = = 31.22 mm2.442.44 ( )

124.4

51.8 ( )25To evaluate the required drop for radius pipeto negotiate the roadway curvature, it is rstnecessary to calculate the R/Bc ratio:

R= =

51.8

Bc 1.27640.8

Enter Figure 5 on the vertical scale at R/Bc 40.Proceed horizontally until the line representingL = 2.44 meters is intersected. At this point thehorizontal scale shows the required drop to be59 mm. Or

Drop = = 0.059 m = 59 m

(2.44) (1.27)

51.8 + 1.27/2

Answer: Radius pipe with a 60 mm drop would berequired. It is important to consult localconcrete pipe manuacturers to determinethe easibility o manuacturing a 1,050 mmdiameter pipe with the required drop.

Figure 3 Radius Pipe Figure 4 Curved Alignment Using Radius Pipe

Table 1 Unit Radius o Curature For 2.44 Meter Straight Defected Pipe With 25 mm Pull

N

L

R

DROP

D

t

t

L

N

D

Dir

ectio

n

ofL

ayin

g

Drop

90

90 +

t

N

L2

P.T.

LL2

P.C.

Radius

TrueRadiusPoint

Projection of joints

do not converge atcommon point, butare tangents to acommon circlewhose diameteris equal to pipe length.

Common method ofmanufacturing radius pipe.

L2

Size 12 15 18 20 24 27 30 33 36 42 48 54 60 66 72 78 84 90 96

Radius 128 156 184 212 240 268 286 364 352 408 464 520 576 632 688 744 780 856 912

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DD 21 October 2007

100

90

80

70

60

50

40

30

20

10

9

8

7

6

5

4

325 50 75 100 125 150 175 200 225 250 300 325 350 37

R/Bc

Ratio

Drop in Millimeters

3.66m

LengthL=4.88m

3.05m2.44m

1.22m

1.83m

2.28m

Inside

Diameter

D, mm

600

675

750

825

900

1050

1200

1350

1500

1650

1800

1950

2100

2250

2400

2550

2700

2850

30003300

3600

0.750

0.840

0.930

1.010

1.100

1.276

1.450

1.626

1.800

1.976

2.150

2.326

2.500

2.675

2.850

3.026

3.200

3.380

3.5563.912

4.268

Outside

Diameter

Bc, Meters

B wall

Technical data herein is considered reliable, but no guarantee is made or liability assumed.

Figure 5 Radius o Curature For Radius Pipe