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This sample problem (courtesy of International Bridge Technologies, San Diego) is for time-dependent construction analysis for a transit crossing which has post-tension concrete deck supported by two concrete piers. The structure has 3 spans and 2 concrete piers. Each span has 3 bottom tendons. There are also 2 top slab continuity tendons.


The deck concrete properties are:


f'c = 6500 psi
Poisson ratio = 0.2
Mean T = 64 Farhenheit
Density = 0.155 kip/ft3
s = 0.25 ( see CEB FIP 2.1.6.1)
RH = 70% (relative humidity)
h = 0.762 ft (notional thickness)
bsc = 5 (shrinkage coeff, see ceb fip 90)


The pier concrete properties are:


f'c = 5000 psi
Poisson ratio = 0.2
Mean T = 64 Farhenheit
Density = 0.155 kip/ft3
s = 0.25 ( see CEB FIP 2.1.6.1)
RH = 70% (relative humidity)
h = 2.545 ft (notional thickness)
bsc = 5 (shrinkage coeff, see ceb fip 90)


The tendon properties are:


STRAND AREA = 0.00151
ANCHOR-SET = 0.03125
FRICTION = 0.25
WOBBLE = 0.0002


Tendon Layouts

Tendon layouts are defined using the bottom of segments as reference. In this example, we will be using several reference points defined from the bottom of the reference segment : at 5.330 feet (1), at 0.500 ft (2), at 5.833 ft (3), at 3.833 ft (4), at 4.330 (5), at 1.670 (6), at 3.000 ft (7), at 6.500 ft (8).

Span 1 Bottom Tendon Layouts (PI is for POINT OF INTERSECTION)

TENDON ID 11
38 STRANDS
LEFT ANCHOR AT 1.208 FT FROM START OF SEGMENT 100 AND 5.330 FT OFFSET FROM BOTTOM
RIGHT ANCHOR AT 1.46 FT FROM END OF SEGMENT 114 and 5.833 FT OFFSET FROM BOTTOM
(PI) AT 7.25 FROM START OF SEGM 104 AND 5.833 FT OFFSET FROM BOTTOM WITH RADIUS 20 FT
(PI) AT 3.25 FROM START OF SEGM 109 AND 0.500 FT OFFSET FROM BOTTOM WITH RADIUS 20 FT
(PI) AT 3.50 FROM START OF SEGM 113 AND 5.833 FT OFFSET FROM BOTTOM WITH RADIUS 20 FT


TENDON ID 12
38 STRANDS
LEFT ANCHOR AT 1.208 FT FROM START OF SEGMENT 100 AND 3.833 FT FROM BOTTOM
RIGHT ANCHOR AT 1.46 FT FROM END OF SEGMENT 114 and 3.000 FT FROM BOTTOM
(PI) AT 7.25 FROM START OF SEGM 103 AND 0.500 FT FROM BOTTOM WITH RADIUS 20 FT
(PI) AT 3.25 FROM START OF SEGM 110 AND 0.500 FT FROM BOTTOM WITH RADIUS 20 FT
(PI) AT 3.50 FROM START OF SEGM 113 AND 4.330FT FROM BOTTOM WITH RADIUS 20 FT



TENDON ID 13
38 STRANDS
LEFT ANCHOR AT 1.208 FT FROM START OF SEGMENT 100 AND 1.670 FT OFFSET FROM BOTTOM
RIGHT ANCHOR IS AT 1.46 FT FROM END OF SEGMENT 114 AND 1.670 FT OFFSET FROM BOTTOM
(PI) AT 3.625 FT FROM START OF SEGMENT 101 AND 0.500 FT OFFSET FROM BOTTOM WITH RADIUS 20 FT
(PI) AT 3.500 FT FROM START OF SEGMENT 113 AND 0.500 FT OFFSET FROM BOTTOM WITH RADIUS 20 FT


(SPAN 2 BOTTOM TENDONS)


TENDON ID 21
30 STRANDS
LEFT ANCHOR AT 1.46 FT FROM START OF SEGMENT 113 WITH OFFSET 5.833 FT
RIGHT ANCHOR AT 1.46 FT FROM END OF SEGMENT 211 WITH OFFSET 5.833 FT
(PI) AT 3.625 FT FROM START OF SEGMENT 114 AND 5.833 FT FT OFFSET FROM BOTTOM WITH RADIUS 20 FT
(PI) AT 7.250 FT FROM START OF SEGMENT 203 LEVEL 0.500 FT RADIUS 20 FT
(PI) AT 3.250 FT FROM START OF SEGMENT 206 LEVEL 0.500 FT RADIUS 20 FT
(PI) AT 3.500 FT FROM START OF SEGMENT 210 LEVEL 5.833 FT RADIUS 20 FT


at 5.330 feet (1), at 0.500 ft (2), at 5.833 ft (3), at 3.833 ft (4), at 4.330 (5), at 1.670 (6), at 3.000 ft (7), at 6.500 ft (8).


TENDON ID 22
30 STRANDS
LEFT ANCHOR SEGM 113 RECESS 1.46 OFFSET ELEV 3.000 FT
RIGHT ANCHORSEGMENT 211 RECESS 1.46 OFFSET ELEV 3.000 FT
(PI) AT 3.625 FT FROM START OF SEGMENT 114 LEVEL 4.330 RADIUS 20 FT
(PI) AT 7.250 FT FROM START OF SEGMENT 202 LEVEL 0.500 FT RADIUS 20 FT
(PI) AT 3.250 FT FROM START OF SEGMENT 207 LEVEL 0.500 FT RADIUS 20 FT
(PI) AT 3.500 FT FROM START OF SEGMENT 210 LEVEL 4.330 RADIUS 20 FT
TENDON ID 23
30 STRANDS
ANCHOR LEFT SEGM 113 RECESS 1.46 OFFSET ELEV 1.670
RIGHT SEGM 211 RECESS 1.46 OFFSET ELEV 1.670
(PI) AT 3.625 SEGM 114 LEVEL 0.500 RADIUS 20
(PI) AT 3.5 SEGM 210 LEVEL 0.500 RADIUS 20


(SPAN 3 BOTTOM TENDONS) (LEVEL ELEV BOTTOM 5.33 0.5 5.833 3.833 4.33 1.67 3.0 )


TENDON ID 31
18 STRANDS
ANCHOR LEFT SEGM 210 RECESS 1.46 OFFSET ELEV 3
RIGHT SEGM 309 RECESS 1.208 OFFSET ELEV 1
(PI) AT 3.625 SEGM 211 LEVEL 3 RADIUS 20
(PI) AT 7.25 SEGM 303 LEVEL 2 RADIUS 20
(PI) AT 3.25 SEGM 305 LEVEL 2 RADIUS 20



DEFINE 32
AREA 0.0453 STRAND 30 JACK 1 DUCT 1 TYPE 1
ANCHOR LEFT SEGM 210 RECESS 1.46 OFFSET ELEV 7
RIGHT SEGM 309 RECESS 1.208 OFFSET ELEV 4
(PI) AT 3.625 SEGM 211 LEVEL 5 RADIUS 20
(PI) AT 7.250 SEGM 302 LEVEL 2 RADIUS 20
(PI) AT 3.250 SEGM 306 LEVEL 2 RADIUS 20



DEFINE 33
AREA 0.0453 STRAND 30 JACK 1 DUCT 1 TYPE 1
ANCHOR LEFT SEGM 210 RECESS 1.46 OFFSET ELEV 6
RIGHT SEGM 309 RECESS 1.208 OFFSET ELEV 6
(PI) AT 3.625 FT FROM START OF SEGMENT 211 LEVEL 2 RADIUS 20
(PI) AT 1.500 FT FROM START OF SEGMENT 308 LEVEL 2 RADIUS 20


(TOP SLAB CONTINUITY TENDONS)


DEFINE 40
24 STRANDS
ANCHOR LEFT SEGM 103 RECESS 2 OFFSET ELEV 1
RIGHT SEGM 205 RECESS 2 OFFSET ELEV 1
(PI) AT 7.500 FT FROM START OF SEGMENT 103 LEVEL 6.5 FT OFFSET FROM BOTTOM WITH RADIUS 20
(PI) AT 2.500 FT FROM START OF SEGMENT 205 LEVEL 6.5 FT OFFSET FROM BOTTOM WITH RADIUS 20



DEFINE 41
24 STRANDS
ANCHOR LEFT SEGM 204 RECESS 2 OFFSET ELEV 1
ANCHOR RIGHT SEGM 306 RECESS 2 OFFSET ELEV 1
(PI) AT 7.500 FT FROM START OF SEGMENT 204 LEVEL 6.5 FT OFFSET FROM BOTTOM WITH RADIUS 20
(PI) AT 2.500 FT FROM START OF SEGMENT 306 LEVEL 6.5 FT OFFSET FROM BOTTOM WITH RADIUS 20


The model has 53 joints and 50 beam elements. Five (5) structure groups and seven (7) load cases are used. Time dependent stage analysis is performed starting from Stage 1 (day 30) to Stage 24 (day 6000).

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