1 INTRODUCTION

In the design calculation, the effective prestress forces per strand must be estimated in order to select the adequate number of strands required. If the ef-fective forces per strand are overestimated, the ten-sile stresses may exceed the deisgn allowable stress-es. If the effective forces per strand are underestimated, the excessive prestress may cause over-shorten or over camber of the members.

In order to calculate the effective prestress forces, the prestress losses must be correctly estimated. The prestress losses can be divided in to two types: (1) immediate losses and (2) long-term losses. The im-mediate losses occur immediately during the jacking including friction, concrete shortening and anchor-age slip losses. The Long-term losses occur after the jacking process including strand relaxation, concrete creep and shrinkage. The friction loss occurs along the entire length of the strand during the jacking process therefore the effective force in the strand varies along the length. In the popular design codes such as ACI318-11 and BS8110-1997, the friction loss is separated into two parts: the friction by wob-ble and the friction by curvature. The wobble fric-tion caused by the out of straightness of the strand from the layout in horizontal direction and by sag-ging of the strand between supports in vertical direc-

tion (see Figure 1) The curvature friction caused by the action of tensile force in the strand forcing the strand to push against the inner side wall of the curvy conduit. This type of friction depends on the amount of angle bends of the conduit. The friction loss can be estimated from equation (1) below.

Figure 1. Vertical wobble due to sagging.

( )Kx x

x jP P e µα− += (1) where

xP is the prestress force at distance x from the jack-

ing end. Pi is the prestress force at the jacking end.

K is the wobble friction coefficient per unit length.

A New Simple Method for Post-tension Strands Friction Coefficient Measurement

C. Suchinda Sripatum University, Bangkok, Thailand

ABSTRACT: This article describes a new simple method of measuring the friction coefficients and their val-ues from construction sites in Thailand. The friction coefficients between prestressing strands and their con-duits are related to both wobble and curvature. The method requires both measured jacking force and elonga-tion of each strand so the average tensile force along the entire length can be determined from non-linear stress-strain relationship. Then, the total length and total curvature of each strand were calculated from shop drawing to simulate the friction calculation in the design process. The determined friction coefficients will include the effect due to misplace of the conduit layouts from shop drawings. From the experimental meas-urement of 624 bonded system strands with spiral galvanized metal sheet conduits in post-tensioned slabs structures from two construction sites with two different post-tensioned sub-contractors, the wobble coeffi-cient is 0.0035 per foot and the curvature coefficient is 0.536 per radian for sub-contractor 1 and the wobble coefficient is 0.0040 per foot and the curvature coefficient is 0.578 per radian for sub-contractor 2. The fric-tion coefficients significantly differ than those recommended by ACI318-11 and BS8110-1997 standards.

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Fdead

end

Fjacking

Load

Cell

µ is the curvature friction coefficient per unit angle in radian.

x is the distance from the jacking end α� is the accumulated angle changes in radian at x

distance from the jacking end For any parabola profile as shown in Figure 2, the

angle change � in radian can be calculated as follow

2

my ≅

When α is a very small angle change for a parabola

profile,

2

2 2 / 2 / 2

m ytan

L L

α α≈ = = , therefore

8y

Lα =

or 4

2

y

L

α=

Figure 2. Angle change in parabolic profile. For the strand profile composed of several parab-

olas the total angle shall be the sum of α�′s. The values of the wobble friction coefficient K

and curvature friction coefficient μ depend on the material of strands, conduit and the work quality of laying the conduit. ACI318-11 gives the values of both friction coefficients in Table 1 below.

Table 1. Friction coefficient given by ACI318-11.

Wobble coef-ficient K, per

foot

Curvature co-efficient μ, per radian

Gro

ute

d te

ndo

ns

in

met

al s

hea

thin

g Wire tendons 0.0010-0.0015 0.15-0.25

High-strength bars

0.0001-0.0006 0.08-0.30

7-wire strands 0.0005-0.0020 0.15-0.25

Un

bo

und

ed T

end

on

Mas

tic c

oat

ed

Wire tendons 0.0010-0.0020 0.05-0.15

7-wire strands 0.0010-0.0020 0.05-0.15

Pre

-gre

ased

Wire tendons 0.0003-0.0020 0.05-0.15

7-wire strands 0.0003-0.0020 0.05-0.15

BS8110-1997 also recommended the values for friction coefficients are described in Table 2.

Table 2. Friction coefficient given by BS8110-1997

Strong rigid sheaths or duct formers K=0.00033

closely supported so that they are not dis-placed during the concreting operation

K=0.00017

Greased strands running in plastic sleeves K=0.00025

Lightly-rusted strand running on unlined concrete duct

μ=0.55

Lightly-rusted strand running on lightly-rusted steel duct

μ=0.30

Lightly-rusted strand running on galvanized duct

μ=0.25

Bright strand running on galvanized duct μ=0.20

Greased strand running on plastic sleeve μ=0.12

Both ACI318-11 and BS8110-1997 clearly stated

that the values of friction coefficients are given as a guideline for better estimation of the friction in the strands, a method of determining these friction coef-ficients must be conducted by suitable tests.

Because of the material, workmanship and way of practice in Thailand may or may not different from USA and British, using the friction coefficients rec-ommended by these or the other standards may not correctly estimate the effective prestress forces. However, the determination of these friction coeffi-cients does not come easily for post-tensioning sys-tems. First, two sets on prestressing strands must be pre-embeded in the concrete. Set 1 need to have no profile therefore there is no intended curvature in the conduits as shown in Figure 3(a).

(a)

(b)

Figure 3. Pre-embedded strands for friction coefficient meas-urements.

(a) Strands without profiles (b) Strands with profiles

Fjacking

Load

Cell

Fdead

end

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From straight profile strands, the wobble friction

coefficient K can be solved from the data collected from no profile strands in equation (2)

( )Klpdead end

jacking no profile

Pe

P

− =

(2)

where

dead endP is the prestress force of the no profile.

strand measured from the load cell at the dead end.

jackingP is the prestress force of the no profile

strand measured from the load cell at the jacking end.

pl is the length in horizontal direction of the no

profile strand. After the wobble friction coefficient K is known,

finally the curvature friction coefficient μ can be solved from the data collected from set 2 profile strands as shown in Figure 2(b) by substitute the K value from equation (2) into equation (3).

( )Kl µαpdead end

jacking profile

Pe

P

− + =

(3)

where

pdP is the prestress force of the profile strand meas-

ured from the load cell at the dead end,

pjP is the prestress force of the profile strand meas-

ured from the load cell at the jacking end, � is the total angle changes in vertical direction of the profile strand.

The method described above has limitations. First, a group of no profile and profile strands must be pre-embedded in the structure before the meas-urements. Second, during the jacking process, the load cell must be attached to the dead end of the strand. The new simple method presented in this paper requires no pre-embedded strands in the struc-ture, no force measurement at the strand dead end. This method only requires the data regularly collect during the jacking process. Therefore, there are plenty existing of data available for analyses.

2 RESEARCH METHOLOGY

This new simple method mainly depends on the elongation measured during the jacking process. Using stress-strain relationship of the prestressing strands as shown in Figure 4,

Figure 4. Stress-strain relationship used for calculating prstressing force from elongation.

record the jacking force jackingP and elongation ps∆

for each strand. The post tensioning subcontractor typically attempts to jack the strands at 75.8, 77.5 and 80% so that the measured elongations are within ±5% of the calculated elongation.

1. For each strand, calculate total horizontal length

pl and total angle changes �� from shop drawing.

2. For each strand, calculate strain psp

plε =

∆

3. For each strand, using stress-strain relation ship given by equation (4), calculate the average stress for the entire length psf

( ){ }1

1ps ps pu

D D

ps

Bf A f

C

ε

ε

= + ≤

+

(4)

For 270 ksi strands / 0.9py puf f = , A = 887, B =

27,613, C = 112.4 and D = 7,360. 4. For each strand, calculate average force avgP for

the entire length. 5. For each strand, back calculate dead endP from

2jacking dead end

avg

P PP

+= or

2dead end avg dead endP P P= −

6. Convert equation (3) from the non-linear rela-tionship to linear relationship as equation (5)

( )dead endp

jacking

Pln Kl µα

P

= − +

(5)

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7. Using multiple linear regressions forcing the in-

terception to be zero, treat dead end

jacking

Pln

P

as a depend-

ent variable, pl and pα as independent variables,

finding constants wobble friction coefficients =� and curvature friction coefficients = .

3 RESULTS

From the multiple regression analysis of the data corrected from two project: (1) 4 story hotel building at Hua Hin (sub-contractor 1) and (2) 4 story factory employee residence building at Bangna Trat km. 25 (sub-contractor 2), yields the wobble and curvature friction coefficients shown in Table 3 below. Table 3. Friction coefficients recommended by ACI318-11.

Buildings Friction Coefficients

R2 Wobble (ft-1)

Curvature (rad-1)

Four story ho-tel building at Hua Hin (sub-contractor 1)

0.0034 0.536 0.829

Four story fac-tory employee

residence building at

Bangna Trat km. 25 (sub-contractor 2)

0.0040 0.578 0.975

ACI318-11 0.0005 -0.0020 0.15 -0.25 BS8110-1997 0.00010 0.25

4 DUSCUSSIONS, CONCLUSION, SUGGESTIONS

1. Based on the analysis, the coefficients from the construction sites. (1) Four story hotel building on Hua Hin Soi 10 has the wobble friction coeffi-

cient 0.0035 per feet and the curvature friction 0.536 per rad (2) Four story factory housing for workers at Bangna-Trad km. 25 has wobble friction coefficient 0.0040 per foot and curvature friction coefficient 0.518 per radian.

2. Comparing the friction coefficients between these construction sites, they have similar values. The wobble friction coefficients differ by 16.2 % and The curvature friction coefficients differ by 7.5%.

3. Comparing the friction coefficients of with the values suggested in standard ACI318-11 ( grouted tendons in metal sheathing: 7-wire strands) The wobble friction coefficient is ranged from 0.0005 to 0.0020 per foot and the curvature friction coefficient is ranged from 0.15 to 0.25 per radian. BS8100-1997 recommended wobble friction coefficient is 0.00010 and curvature friction coefficient is 0.25. The measured friction coefficients from theses pro-jects are higher than both the maximum recom-mended by ACI318-11 and BS8110-1997.

REFERENCES

ACI Committee 318. 2011. Building Code Requirements for Structural Concrete (ACI318-11). Farmington Hill, MI: American Concrete Institute.

Devalapura, R.K. and Tadros, M.K. 1992. Stress-strain model-ing of 270 ksi low-relaxation prestressing strands. PCI Journal. Mar-Apr. Portland Cement Association:100-106.

Ning Ming-zhe and Li De-jian. 2011. A new measuring meth-od of friction losses of prestressed tendon in post-tensioning. Mechanic Automation and Control Engineering (MACE) Second International Conference on Digital Ob-ject Identifier: 6300–6303.

Thai Industrial Standards Institute. 2540. Standard for Steel wire for Prestressed Concrete (TIS 95-2540). Bangkok.

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