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PRESTRESS PRESTR ESS LOSSES IN POST P OST--TENSIONING TENSIO NING TENDON Ultimate strength of strand
f p&
dulus of elasticity of strand ross-sectional ross-sectional area of strand umber of strands in tendon oss-sectional area of tendon Tendon Tendon length urvature riction Coe!cient "obble riction Coe!cient Anchor set
"s
270 )si 29000 0.27 2 2.%0 2.%04 4 220 0.25 0.0002 0.375
m - DS Df L
Additional #restress losses
+nits:
+S
)si in, in, in, ft /ft in
20 )si
longterm an1 elastic shortening
$eft $eft Pul Pulll %ight %ight Pul Pulll &tressing ratio &tressing order
8ac)/f p&
0.
0. 2
Summary of Results Average stress after seating inal average stress inal average force in tendon 'ac(ing stress stress 'ac(ing force force Anchor set in*uence +one Prestress losses at anchor &tress at anchor ress at end of inluence +one longation before anchor set Elongation after anchor set
7. 7.4 4 )si )si %7. %7.4 4 )si )si 435. 435.23 23 -ip -ip %ight $eft Pull Pull 8ac) 2% 2% (si Pac) 5%2.4%4 5%2.4%4 )i# Lc
42.70 34.5
D8 f anchor
.42 #L+"6 %.%0 %.22
&tress ratio at anchorage , stress ratio along tendon
42.70 ft 34.5 34.5 )si )si .42 9.7 .9 0.
) si ) si in in in in
0.%72 0.73%
i s k , s s e 30 r t s e 290 r P 270 250 230 20 90 70 50 0 2 'ac(ing from left end
i na l label #oints
4
% 'ac(ing from righ t end
Afte r se a tin g o n le ft
0 After After sea ting
After s ea tin g o n r ig ht
2
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PRESTRESS LOSSES IN POST-TENSIONING TENDON
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PRESTRESS LOSSES IN POST-TENSIONING TENDON Angular Change #er &egment .istance &egmen /ertical from left t $ength Pro0le end ft
ft 0 22 40 50 %0 0 %0 70 0 9 220
rad 0 22 0 0 50 50 0 0 22
0.037 0.709% 0.709% 0.094 0.094 0.094 0.094 0.709% 0.709% 0.037
1ori+ont Total al accumul Pro0le ative rad 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
rad 0.032 0.254 0.425 0.5%5 0.%079 0.%993 0.7907 0.9%7 .32% .25
.istance from left end ft 0.00 22.00 40.00 42.70 50.00 %0.00 0.00 0.00 %0.00 70.00 77.30 0.00 9.00 220.00
&tress &tress after after anchor addition set al losses (si .4 %. 9%.3 9.7 92.3 7.% .5 .5 7.% 92.3 9.7 9%.3 %. .4
(si %.4 %%. 7%.3 7.7 72.3 %7.% %.5 %.5 %7.% 72.3 7.7 7%.3 %%. %.4
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TENDON PROFILE 2.500 2.000 1 8 n o i t a v e l E
.500 .000 0.500 0.000 0
50
ll 1imensions are
ft
00
50
eb slo#e 12/ 3
0
Vertical Prole &egment ty#e &ag falling &ag rising Cro7n rising Cro7n falling &ag falling &ag rising Cro7n rising Cro7n falling &ag falling &ag rising
45
D4
22 0 0 50 50 0 0 22
0 22 40 50 %0 0 %0 70 0 9
200
.istance from left end8 4
46 22 40 50 %0 0 %0 70 0 9 220
Angle correction factor 3
ori!o"tal Prole 15
16
2 .03
.03 3.5
3.5 0.75 0.75 3.5 3.5 .03
.03 2
4
&egme %adius nt ty#e
0 220 Tangent
250
.000
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TENDON VERTI#$L PROFILE "eb slo#e 12/ 3 Angle correction factor 3
YP %/2/7
ORI%ONT$L PROFILE Units: ft
0 .000
Parabola coe!cients
A;
2 ### ### ### ### ### ### ### ### 75.3%
Angle Change 0.032 ### ### ### ### ### ### ### ### 0.032
&tation
&egme nt ty#e
0 220 Tangent
%adius
Angle Change 0.0000
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E&'IV$LENT POST-TENSIONING LO$DS Steel rea of ten1ons; ps 2.%04 in= (onstr&ction stage: After anchor set %ight $eft end End Elevation of section C> : 2.25 2.25 ft
E"( forces at a"c)ora*es P4 - hori+ontal force ?#ositive left to right@ PY - vertical force ?#ositive is u#@ M - moment ?negative 7hen cloc(7ise@
Left en1 *ight en1
P4 )i# 470. 470.
PY )i# 39.2 39.2
M )i# ft 7.7 7.7
$A ft 0 220
E+ui,ale"t PS loa(s 5 9F 9 9D 96 9 9
9
599
59
E+ui,ale"t Prestress Loa( ertical Linear Loa1 positive +p
"A )i#2ft .790 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 .43
"B )i#2ft .43 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 .790
$ist. from left en1
$A ft 0.00 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 9.00
$B ft 22.00 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 220.00
"4 )i#2ft 0.%3% #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 #L+"6 0.%3%
699
69
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TEOR PRESTRESSING LOSSES D'E TO FRI#TION $ND $N#OR SET Stress before anchor set f , 3 'ac(e-?maG),@
'ac(
DA
b b
D
d n e g n i s s e r t S
A
Note: stress after anchor set is symmerical to stress before anchor set within L c.
Stress after anchor set
d n e d a e D
$c $tendon
Fig. 1 Stressing from one end Stressing from one end Stress before anchor 2 set
Stress before anchor 1 set
'ac(6
Stress after anchor 2 set D6
D5
1 d n e g n i s s e r t S
Stress after anchor 1 set
A6
A5 $tendon
Fig. 2 Stressing from two ends
2 d n e g n i s s e r t S
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Stressing from one end (refer to Fig. 1 above) f , 8 'ac(e-?maG),@ 8 'ac( a m
DL /" s "s DS D /"s D
Lc D8
Stress along the tendon at distance 'x' from the stressing end. Jacing stress at anchor !cc"m"lati#e angle change from stressing end to 'x' $"r#at"re Friction $oefficient %obble Friction $oefficient Strand elongation d"ring stressing o&erations. Strand mod"l"s of elasticity !rea below the gra&h of 'stress before anchor set' and abo#e the line of ero stress -yellow colored area on Fig. 1 !nchor set !rea below gra&h 'stress before anchor set' and abo#e gra&h 'stress after anchor set' -shaded area on Fig. 1 Length of stress con#ersion one. (restress losses at anchor Stressing from two ends (refer to Fig. 2 above)
$om&"te stresses at second &"ll before and after anchor set inde&endently from first &"ll. ,he res"lting stress is the maxim"m of stresses d"e to first and second &"lls -red line on Fig. 2 DL6 6/"s
6
)longations d"ring second &"ll !rea below gra&h 'stress before anchor 2 set' and abo#e gra&h 'stress after anchor 1 set' -orange shaded area on Fig. 2.
Angle change within a parabolic segment of tendon (arabolic e*"ation of tendon > a?=@'?@c a atanA2a?@'/sinbB Start angle ad+"sted for web slo&e v/sinb a2 atanA2a?2@'/sinbB )nd angle ad+"sted for web slo&e Da a'sa2a !ngle change within a &arabolic segment (arabolic coefficients a; '; c ?; ?2 Start and )nd stations of &arabolic segment %eb slo&e angle to horion b atanv/h
b
v
h
Combining tendon angular changes in vertical and horizontal planes
,otal ang"lar change within a segment Dav; Dah !ng"lar change in ortogonal &lanes cosDacosDavCcosDah Da
!uivalent beam loads due to post"tensioning
,he ex&lanatory &a&er on this s"b+ect was &resented at 2//2 0, S,DL "ser gro"& conference. 3t's a#ailable on 0!,)$4 website at http://DDD.gtstr&1l.gatech.e1&/
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Follow ',echnical (a&ers' then scroll down to 2//2 5!nalysis of (ost6 ,ensioned $ontin"o"s S&an 7ridges5 by !bhi+it Nai 8 Jay !. 9"io*"e $alifornia De&artment of ,rans&ortation. Download ;<7 &ower&oint &resentation.
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INSTR'#TIONS FOR 'SING PSLoss SPRE$DSEET Spreadsheet functionalit#$
$om&"tes friction and anchor set losses in &restressing tendon · $om&"tes tendon elongations · De#elo&es tendon #ertical and horiontal &rofiles · $alc"lates e*"i#alent beam loads d"e to &ost6tensioning ·
Capabilities$ · ("lling from one or both ends · <"lti&le angle changes in three6dimensional tendon &rofile · S3 and S meas"rement systems · S and international codes %nstruction for data input
!ll in&"t cells in the s&readsheet are formatted as a bl"e text on yellow bacgro"nd
4.35
&he custom toolbar menu provides the following functions$
(erforms iterati#e calc"lations necessary to com&"te &restress losses !cti#ates ',endon (rofile' worsheet !cti#ates 'Losses' worsheet !cti#ates ')*"i#alent (ost6,ensioning Loads' worsheet !cti#ates c"rrent worsheet ,oggles S and S3 "nits Dis&lays (SLoss disclaimer 'Soss Step b# Step
1. =&en ',endon (rofile' worsheet -"se men" ,endon (rofile 6 )dit or clic on '(rofile' tab below. 2. )stablish tendon #ertical &rofile b"ilt o"t of &arabolic or tangent segments. (ro#ides location of tangent and radial segments of horiontal &rofile. >. =n the worsheet 'Losses' enter re*"ired stressing data and clic command '$alc"late ?' @. (rint file.
