ST110 Schokker Scanlon

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ANALYTICAL STUDY OF THE EFFECTS OF TENDON LAYOUT ON THE

PERFORMANCE OF POST-TENSIONED TWO-WAY SLAB SYSTEMSA.J. Schokker, S.C. Lee, and A. ScanlonDepartment of Civil and Environmental Engineering, The Pennsylvania State University, United States

ABSTRACT:

This paper presents the results of an analytical study based on finite element analysis to evaluate theeffects of different arrangements of tendons on the performance of post-tensioned cast-in-place concretetwo-way slab systems. Various arrangements from uniform cable layouts to closely banded arrangementsadjacent to column centerlines are considered. The slab is modeled using plate-bending elements in thesoftware package SAP 2000.

Equivalent loads based on cable profiles are applied to the slab according to the tendon layout. Moment

fields and deflected shapes are compared for the various tendon patterns. Gravity loads are applied in theusual way and superimposed on the results from the equivalent tendon loads to determine net momentsand deflections at service load levels. In addition to a study of tendon layouts, the finite-element model iscompared with experimental results.

1. INTRODUCTION

Post-tensioned flat plate slabs provide an economical alternative to traditional reinforced concrete slabsdue to their relatively reduced thickness. The load-balancing technique is typically used in the design ofthese sections. A portion of the service load is balanced by the prestressing; typically all of the dead loadand sometimes a portion of the live load will be balanced. Various tendon arrangements may be utilizedto provide this balancing. The two extremes of tendon spacing vary from uniformly spaced to a fullybanded arrangement where tendons are concentrated along column lines. A slab containing uniformtendons in one direction and banded tendons in the perpendicular direction would behave similarly to a

one-way slab system supported on beams. A pattern between the two extremes is often used, providingtendons across the entire slab with a concentration of tendons nearer to the column lines. There does notappear to have been a systematic analytical study of the effects of various tendon arrangements on thedistribution of moments and deflections in two-way post-tensioned slabs. This paper presents ananalytical study of the effects of tendon layouts including comparisons with experimental results.

4e

Confrence spcialise en gnie des structures

de la Socit canadienne de gnie civil

4th

Structural Specialty Conferenceof the Canadian Society for Civil Engineering

Montral, Qubec, Canada5-8 juin 2002 / June 5-8, 2002


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2. TEST PROGRAM FOR TENDON LAYOUT STUDY

1.1. Analysis

The structural analysis software, SAP 2000, was used for finite element analysis of the slabs. Theprestressing force in the slabs was modeled using the load-balancing concept as described in the Post-Tensioning Manual published by the Post-Tensioning Institute (2001). For the tendon layout study, atypical interior panel of a two-way flat plate system with a thickness of 165 mm is modeled. Dimensionsand boundary conditions of the panel are shown in Figure 1.

6.1 m

7.6 m

Figure 1. Slab panel dimensions and boundary conditions.

The slab panels were analyzed with their self-weight and equivalent prestressing load from the load-balancing method. The two load cases were run separately and then superimposed to obtain net momentand deflection values. The tendon force for each direction is kept at a consistent value to produce auniform compression in the slab of approximately 175 psi. The average equivalent load is approximately1.25 times the self-weight in the long direction and approximately 0.86 times the self-weight in the shortdirection. The average equivalent load is 1.06 times the self-weight.

1.2. Tendon Layouts

Four tendon layouts were considered in the study. Layouts fully uniform in both directions and fullybanded in both directions were considered as extremes. A panel with one direction banded and onedirection uniform was considered as a case approaching one-way system behavior. A layout of 75%tendons within the column strip in both directions with the remaining 25% in the middle sections was alsoincluded in the study. The four tendon layouts are summarized in Table 1 and illustrated in Figure 2.

Case 100C-100C is essentially unreinforced over most of the slab and is included to demonstrate theeffect of the extreme case producing line loads in each direction. Case Uni-Uni provides the oppositeextreme. Case 100C-Uni and 75C-75C are more traditional layouts.

Y

X

Columns 360mm x 510mm

Thickness = 165mm

0

0

=

=

=

yx

0=

y

0=

x


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Table 1. Tendon Layouts Considered.

Case Tendon Layout

100C-100C 100% of tendons banded along the column line in each direction

75C-75C 75% of tendons within the column strip and 25% within the middle strip ineach direction

100C-Uni 100% of tendons banded along the column line in one direction anduniformly distributed across panel in perpendicular direction

Uni-Uni Uniform distribution of tendons in each direction

Figure 2. Tendon layouts.

1.3. Results

Deflection results for each case are summarized in Figure 3. Results from prestress forces alone, self-weight alone, and the combined effect are shown. As shown in the figure legend, Point A represents the

deflection at mid-span along the column line in the long direction, point B represents the deflection at mid-span along the column line in the short direction, and point C is the mid-panel deflection.

The most effect layout for producing upward camber is the 100C-100C case, while the least effective isthe Uni-Uni case. The least variation in the deflection values is seen in the mid panel values with amaximum difference of only 0.7 mm. Larger variations are seen in the deflections at the mid-span alongthe column lines. A slight upward camber is produced at each of the three points in the 100C-100C caseand a slight downward deflection is produced in the Uni-Uni case.

100%C-100%C 75%C-75%C

Uni-100%C Uni-Uni

tendons


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Figure 3. Deflection comparison for different tendon layouts.

Figures 4 and 5 show the effect of tendon layout on bending moment distribution. Bending moments areplotted for each case along the column face line in the long direction. The largest moment intensities dueto prestressing are seen in the 100C-100C case near the columns. When these positive prestressmoments are combined with the negative self-weight moments, a positive moment results at the column.In all other cases, the combined effect produces a negative moment near the columns. Overall, the leasteffective layout for balancing the self-weight with the prestress is the Uni-Uni case. Moments in the shortdirection are similar to those shown for the long direction, except in the 100C-Uni case which shows

behavior similar to the 100C-100C case in the short direction.

Figure 4. Bending moment distribution long direction, 100C-100C layout

-5

-3

-1

1

3

5

7

Deflection(mm

)

100C-100C 75C-75C

100C-Uni Uni-Uni

Self-weight

Combination

Pt.A

Pt. B

Pt. C

Pt. A

Pt. B

Pt. C

Pt. A

Pt. B

Pt. C

Pt. B

Pt. A

Pt.C

Prestress

100C-100C

-25

-20

-15

-10

-5

0

5

10

15

20

25

-4 -3 -2 -1 0 1 2 3 4

Global X-Direction (m)

Mo

ment(kN-m)

Prestress Self-Weight Combined


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Figure 5. Bending moment distribution long direction, 75C-75C layout

Figure 6. Bending moment distribution long direction, 100C-Uni layout

75C-75C

-25

-20

-15

-10

-5

0

5

10

15

20

25

-4 -3 -2 -1 0 1 2 3 4


Moment(kN-m

)


100C-Uni

-25

-20

-15

-10

-5

0

5

10

15

20

25

-4 -3 -2 -1 0 1 2 3 4


Mom

ent(kN-m)



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Figure 7. Bending moment distribution long direction, Uni-Uni layout

3. COMPARISON WITH EXPERIMENTAL RESULTS

The analysis procedure used in the tendon layout study was also compared to experimental test results byBurns and Hemakom at the University of Texas (Hemakom, 1975; Burns and Hemakom, 1985). Figure12 the tendon layout and points where deflections were monitored during testing. Figure 13 shows theexperimental test slab dimensions and layout. The finite element model included the slab stubs and rollersupports at the base of the columns that was used in the experimental test. A comparison of thedeflections between the test slab and the modeled slab is shown in Figure 14. Deflection measurementswere not reported for Panels A and B. Results show good agreement for most of the slab points assummarized in Table 2. The maximum difference of less than 0.6 mm is seen at point 7 located in themiddle of the center panel.

Figure 12. Deflection monitoring locations

Uni-Uni

-25

-20

-15

-10

-5

05

10

15

20

25

-4 -3 -2 -1 0 1 2 3 4


Moment(kN

-m)


1 32

4 9 10865 7

11 16 1715141312


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Figure 13. Experimental test slab dimensions

Table 2. Summary of experimental and analytical results

PointMeasured

(mm)SAP2000

(mm) SAP2000/Measured

1 -1.68 -1.40 1.202 -2.01 -2.06 0.98Panel C

3 -1.02 -1.02 1.00

4 -1.17 -1.07 1.105 -1.52 -1.83 0.836 -0.94 -1.17 0.807 -1.09 -1.68 0.658 -1.12 -1.22 0.929 -1.78 -2.03 0.88

Panels D, E, F

10 -0.81 -0.76 1.07

11 -1.35 -1.25 1.0812 -1.60 -1.70 0.9413 -1.32 -1.37 0.9614 -1.55 -1.68 0.9215 -1.63 -1.42 1.1416 -2.31 -1.91 1.21

Panels G, H, I

17 -1.30 -1.09 1.19

Average 1.02

3

m

100mm

3m

3m

0.8

m

0.8 m 3 m 3 m 3 m

100 mm

A B C

D F

G

E

H I

536 mm

70 mm

25 mm ball

bearing


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Figure 14. Experimental versus analytical deflection comparison

Panel C Deflection

-2.5

-2

-1.5

-1

-0.5

0

1 2 3

Deflection

(mm)

Test 203 (Measured) SAP2000

Column ColumnMidspan

Panel DEF Deflection

-2.5

-2

-1.5

-1

-0.5

0

4 5 6 7 8 9 10

Deflection(mm)


Column Column Column Column

Panel D Panel E Panel F

Panel GHI Deflection

-2.5

-2

-1.5

-1

-0.5

0

11 12 13 14 15 16 17

Deflection(mm)


Column Column Column Column

Panel G Panel H Panel I


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4. CONCLUSIONS

This analytical study of tendon layouts demonstrated the following in uncracked slabs:! A finite element model with prestressing forces applied as loads using the load-balancing

technique can accurately predict deflection behavior.! Mid panel deflection values are relatively insensitive to tendon layout for the cases considered.! Moment distributions across the slab panels may vary significantly between different tendon

layouts, sometimes resulting in different signs at critical sections.! Both of the banded tendon arrangements, 100C-100C and 100C-Uni, produced a prestress

moment at mid panel with the same sign as the self-weight moment resulting in a larger combinedmoment at mid panel.

Further studies will be performed to investigate behavior at ultimate.

5. REFERENCES

Post-Tensioning Institute (2001)Guide Specification for Grouting of Post-Tensioned Structures, FirstEdition, PTI Committee on Grouting Specifications, Post-Tensioning Institute, Phoenix, Arizona, USA.

Hemakon, R. (1975) Strength and Behavior of Post-Tensioned Flat Plates with Unbonded Tendons, Ph.D.Dissertation, the University of Texas, Austin, Texas, USA.

Burns, N.H. and Hemakom, R. (1985) Tests of Post-Tensioned Flat Plate with Banded Tendon, ASCE

Structural Journal, 3:1899-1915.

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ST110 Schokker Scanlon