Field Measured Two Way Slab Deflections

Field measured two-way slab deflections1

ERIC P. JOKINEN Eric P . Jokirlen Associates Ltd., Edtnonton, Alta., Cattadn

A N D

ANDREW SCANLON Department of Civil Engineering, University of Alberta, Edmonton, Alta., Canada T6G 2E1

Received December 4, 1986

Revised manuscript accepted July 2 , 1987

Results of a survey of two-way slab deflections both during and after construction of a 28-storey office tower are presented. A comparison is made between measured deflections and deflections computed using a finite element program that includes the effects of cracking. Effects of construction loading and time-dependent deformations are included in the calculations. The measured and calculated deflections illustrate the high variability that can be expected in two-way slab deflections.

Key words: concrete construction, deflection, finite elements, loads, multistorey construction, two-way slabs, variability.

Les risultats d'une Ctude des fleches de dalles armies dans les deux sens durant et apres la construction d'une tour de bureaux de 28 Ctages sont prCsentCs. Une comparaison est effectuCe entre les flkches mesurCes et celles calculCes a l'aide de la methodedes C lhen t s finis qui inclut les effets de la fissuration. Les effets de la rnise en charge de la construction et des deformations en fonction du temps sont inclus dans les calculs. Les fleches calculCes et mesurCes illustrent la tres grande variabilitt des fleches de dalles armCes dans les deux sens.

Motsclks: construction en bCton, flkche, ClCments finis, charges, construction a Ctages multiples, dalles armCes dans les deux sens, variabilitt. [Traduit par la revue] Can. 1. Civ. Eng. 14,807-819(1987)

Introduction Contract documents for construction of the twin office towers

of Scotia Place located in downtown Edmonton, Alberta, in- cluded a requirement to monitor deflections of the concrete two-way slab floor system both during and after construction. As a result, a valuable data base was established to provide needed information on the response of floor systems to construc- tion loads and long-time sustained loads.

The data obtained from the deflection surveys of the south tower are presented. In addition, results of a finite element analysis of the slab system are presented and compared with the measured data.

Building description The complex consists of two towers, one 28 storeys and one

20 storeys in height. Each tower has an identical L-shaped floor plan for all floors above the 8th as shown in Fig. 1. The floor system consists of a 200 mm thick two-way flat slab with 3000 X 3000 x 150 mm drop panels and 1520 X 1520 mm column capitals. Columns are spaced at 9000 mm on center. Floor slabs were cambered 15 mm at bay centers and 10 mm on grid lines.

For purposes of this study the slab panels are categorized according to the boundary conditions along each side of the panel and the panel reinforcement details. Panel types desig- nated A, B, C, D, and E are identified in Fig. 1. Types D and E differed only in minor reinforcing details and could for all practical purposes be taken as the same type. The triangular- shaped panels were not included in the study. Typical reinforce- ment arrangements for column and middle strips are shown in Fig. 2.

NOTE: Written discussion of this paper is welcomed and will be received by the Editor until March 31, 1988 (address inside front cover).

'This paper was presented at the 1985 Canadian Society for Civil Engineering Conference, Saskatoon, Saskatchewan.

FIG. 1. Floor plan (levels 8 through 28).

Construction schedule Construction of floors 8 through 28 of the south tower took

place between May, 198 1 and October, 198 1. The construction schedule is outlined in Appendix A.

The floors were constructed using a system of flying form- work with each table being approximately the size of one (1) full bay. Three levels of heavy timber reshoring were provided below the level on which the formwork rested. The upper two floors of reshoring were to 100% of the capacity of the form- work. The lowest floor of reshoring was provided at 50% of the

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808 CAN. 1. CIV. ENG. VOL. 14. 1987

Edge of Exterior Span a Interior Span 4 Slab deflection measurements

Slab Column Column I Slab deflections were measured both during construction and 1 ,/,4-20T 13-20T 12- 20 T at approximately 1 year after completion- of construction.

Measurements were made on each slab during the period in which it was subjected to loads from slabs above through the

15-20 B 12-20 B shores and reshores. Deflection measurements for floors 8 through 20 were made

COLUMN S T R I P during the construction phase using standard level surveying techniques. A bench mark was established on each floor in the

M I D D L E STRIP stripped from the top slab. Measurements adjacent to columns

FIG. 2. Typical slab reinforcement arrangement (f, = 400 MPa). were taken at a distance of approximately 300 mm from the face of the column in order to eliminate errors caused bv increased

core area adjacent to a structural wall. Level readings were taken

/ 1 7 - I O T ! at mid-panel, at mid-span between columns, and adjacent to columns. Mid-panel and mid-column strip deflections were then r I I established relative to the datum established by the first reading

capacity of the formwork. One set of formwork was provided thickness of concrete in these areas resulting from trowelling for the entire project. This necessitated stripping and reshoring machines pushing the concrete toward the column. of each level at an age of approximately 3 days. A view of the Deflection measurements were made at approximately I year shoring and reshoring arrangement is shown in Fig. 3. after construction for floors 8 through 28. These measurements

Owing to the large size of the formwork panels an entire bay were made by stretching a string line along the diagonal between had to be stripped at one time. In many cases, reshoring was not columns and measuring the deflection of the slab relative to the

14-15 B1

done immediately and thus the 3-day-old slab was left Gnshored string line at mid-panel. The 1-year measurements therefore are for up to 5 or 6 h in some cases. not true deflections since any camber provided should be added

to the measured values. Unfortunately camber measurements Cylinder compressive strength tests are not available for all slabs. Based on the limited data available

Specified 28-day cylinder compressive strength was 30 MPa in the job records it appears that the camber provided was for the floor slabs. For each floor a series of standard 100 x 300 generally somewhat less than the specified value, although in

1 1 -15 B y

mm cylinder compressive strength tests was made at (a) 2-5 some cases larger than specified camber was provided. days, (b) 7 days, and (c) 28 days. Mid-panel slab deflections were obtained from the job re-

The results for 7 and 28 days are listed in Appendix A and cords and are tabulated in Appendix B. Figures 3 and 4 show the summarized in Fig. 2 in the form of histograms. The mean deflection vs. time plots for panel types A and B respectively. strength at 28 days was 34.93 MPa with a coefficient of varia- Also included in the plot are the average measured deflections at tion of 12.6% and range of 26.0-45.4 MPa. each stage of construction and at 1 year after construction.

! prior to stripping of formwork. Measurements were taken at I I each shored and reshored level immediately after forms were

FIG. 3 . Floor slabs under construction.

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JOKINEN AND SCANLON 809

(a) Strength at 7 days

n = 72 R = 25.61 MPa s = 2.91 MPa V = 11.4%

5 10 15 2 0 25 30 35 4 0 45 5 0 55 COMPRESSIVE STRENGTH ( MPa)

n (b) Strength at 28 days

t rl : ::.93 MPa

5 10 15 2 0 25 3 0 35 4 0 45 5 0 55 COMPRESSIVE STRENGTH (M Pa)

Fig. 4. Histograms of cylinder compressive strengths at 7 and 28 days.

Deflection statistics Slab deflection statistics developed from the tabulated

measurements for the slabs of the south tower are given in Appendix B . The " 1 -year deflections" actually represent measurements taken within the range of 278-417 days. The plot shown in Fig. 5 for type-A slabs illustrates that although there appears to be a slight tendency towards increase of deflection with time during the measurement period, there is much more variation between individual slabs within the time period con- sidered. Similar plots were obtained for the other slabs in the survey (Scanlon and Ho 1984). It is therefore considered to be reasonable to lump all measurements together as 1 -year deflec- tions. Histograms of measured 1-year deflections are plotted in Figs. 6-8 for slabs A-E of the south tower. The statistics for these slabs are summarized in Table 1. It will be noted in Table 1 that for type-A slabs there is only 112 the number of data points available as one type-A slab contained the crane opening and thus survey shots were not available at this location.

The mean 1-year deflection ranges from 32.53 to 39.05 mm while the coefficient of variation ranges from 24.8 to 31%.

It is interesting to note that there is not a large difference in mean deflection among the various slab types. In fact the deflec- tion for type C with three continuous edges is slightly greater than for type B with two continuous edges. Other finite element studies (Scanlon and Thompson 1987) indicate that, if signifi- cant cracking occurs, deflections of corner and interior panels tend to be of similar magnitude. This is thought to be related to the redistribution of moments that occurs after cracking.

Field measured deflections of the order of 35 mm would seem to suggest that a specified camber greater than 15 mm would in this case be appropriate. However, it should be noted that it is easier to correct large deflections by applying a self-levelling grout than to correct excessive camber. Given the large variabil- ity in the measured deflections and the difficulties associated

0 2 3 4 5 6 7 8 9 1 0 30 50 100 200300 1000

TIME (days)

FIG. 5. Deflection vs. time for type-A slabs.

f LEGEND

Meosured Volue @< fr =0.16& M P a 5 Mean M w w r d Volue

@ Colculoted Volue . . 0-

d3 oo ' @< i r =O.Q&MPO .. - .

0 0

.* .bO . . C 3t0 " @< t=0.6&MPo . a .

: / /

d o * * . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I I 1 1 1 1 1

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CAN. J. CIV. ENG. VOL. 14. 1987

Meosured Volue

Meon Measured Volue

TlME (days)

FIG. 6. Deflection vs. time for type-B slabs.

7 0

sustained load with providing camber in two directions, it is probably prefer- ASL = Amax maximum load during construction able to err on the side of too little rather than too much camber.

60-

50 +. E - z 40- - + W

2 3 0 - o

20

10

Finite element analysis Deflections were computed for a typical comer panel using a

version of the general purpose computer program SAPIV (Bathe et al. 1974), modified to incorporate effects of cracking (Gra- ham and Scanlon 1984). Effects of construction loading and time-dependent effects were included using the following proc- edure suggested by Graham and Scanlon (1984).

(1) Calculate the maximum deflection, A,,,, due to construc- tion load. The applied load is calculated from

LEGEND 0 Grid FF78

'250 3 0 0 3 M 4 0 0 450 (2) The maximum deflection, A,,,, is scaled to the sustained TIME I d o y 4 load level, assumed in this study to be (dead load + 20% live

FIG. 7. Measured deflections at approximately I year(type-A slabs). load), to obtain the immediate deflection due to sustained load,

- 0 0 0

0

0 @ @ 0

0 0 0 0

0 @ 00 0

- 0 0 0

-

w = (2)(wD)(l. 1) + construction live load = 2(4.709)(1.1) + 2.414 = 10.97 kPa

Cracking is accounted for in the analysis using Branson's effective moment of inertia. The modulus of rupture must be specified. In this study, three values were considered.

(a) f, = 7.5@ psi (0.6- MPa)

(b) f, = 4 e c psi ( 0 . 3 2 e C MPa)

(c) f, = 2 e c psi (0.16-, MPa)

Case (a) represents the value specified in the ACI code (ACI Committee 3 18 1983) and CSA A23.30M (Canadian Standards Association 1984). Cases (b) and (c) are reduced effective values to account for additional cracking due to restraint of shrinkage (Tam and Scanlon 1984). The calculations were made using the specified compressive strength of 30 MPa.

(3) Deflection at 1-year is multiplied by a long-time multi- plier, as recommended by Graham and Scanlon (1986). The long-time multiplier depends on the value assumed for modulus of rupture. Graham and Scanlon recommended a multiplier of 4.25 forf, = 7.5- psi ( 0 . 6 a MPa), and a multiplier of 3.00 forf, = 4 e psi (0.32- MPa). No value was suggested forf, = 2% psi ( 0 . 1 6 a MPa). For this last case a multiplier of 2.75 was selected. The variation in value of multiplier occurs because both creep and shrinkage warping effects are lumped together. While the total shrinkage warping deflection is assumed to be independent of the degree of cracking, (immedi- ate + creep) deflection is significantly affected by the degree of cracking.

Calculated deflections are summarized in Table 2 and the

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JOKINEN AND SCANLON

10 - -- TlPE A SLABS

> U Z 8 - n = 2 0 W

1 = 9.50mm V = 27.6 %

5 15 2 5 35 45 55 6 5 DEFLECTION lmml

I / / I TYPE B SLABS

TYPE C SLABS

n = 41 P = 35.24 mm r = 8.76mm

l2 1 TYPE D SLABS

-

TYPE E SLABS > 10

n = M P = 39.05(mml r = 10.34(mml V = 26.5 %

4

0 10 2 0 3 0 4 0 M 6 0 70 8 0

DEFLECTION (mml

V = 24.8%

-

FIG. 8. Histograms of measured I-year deflections (not including camber).

15 25 35 45 55 65 DEFLECTION I mml

TABLE 1. Summary of statistics of slab deflections for the south tower

Time of Slab type deflection measurements Parameters A B C D E

1 week No. of data points Mean deflection (mm) Standard deviation (mm) Coefficient of variation (%) Range (mm)

4 weeks No. of data points Mean deflection (mm) Standard deviation (mm) Coefficient of variation (%) Range (rnrn)

l year No. of data points Mean deflection (mm) Standard deviation (mm) Coefficient of variation (%) Range (mm)

TABLE 2. Calculated deflections 1-year calculated deflection is shown superimposed on the de- flection-time plots for panel types A and B shown in Figs. 3 and (MPa) A m a x (mm) As, (mm) A ( 1 year) (mm) 4. It can be seen that the calculated deflections corresponding to 4 G psi ( 0 . 3 2 G MPa) modulus of rupture are close to the 0.60- 10.2 5 .0 21.1 mean values, while the calculated values for 7.5@ ( 0 . 6 G ) 0 . 3 2 G 21.9 10.7 32.0 and 2@ (0.16@) psi (MPa) are closely related to the lower

0 . 3 2 ~ 36.2 17.5 48.4 and upper ranges of measured deflection respectively.

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812 CAN. 1. CIV. ENG. VOL. 14, 1987

Summary and conclusions Grant A5 153. Assistance provided by E . Ho and C. J . Graham

~~~~l~~ of a survey of field measured deflections for a 28- in data reduction and structural calculations is gratefully ack-

storev office tower have been ~ re sen t ed . Mean deflections (not nowledged.

incluhing camber) at approxihately 1 year after construction ACI COMMITTEE 3 18. 1983. Building code requirements for reinforced

ranged from 32'5 to 39' with coefficients of variation concrete (ACI 3 18-83), American Concrete Institute, Detroit, MI. ranging from 24.8 to 3 1.5%. BATHE, K. J., WILSON, E. L., and PETERSON, F. E. 1974. SAPIV-a

based On a finite structural analysis program for static and dynamic response of linear provided good estimates of the range of deflections for a typical systems, University of~a l i forn ia , Berkeley, CA. slab panel, depending on the modulus of rupture assumed in the CANADIAN STANDARDS ASSOCIATION. 1984. Code for the design of analysis. The wide variation in measured deflections for nomi- concrete structures for buildings. CAN3-A23.3-M84, Canadian nall; identical panels and the sensitivity of calculated deflec- tions to the effective tensile strength of the concrete emphasize the need for care in interpreting results of deflection calcula- tions.

Acknowledgements Data on field measured deflections as well as access to

structural design drawings and specifications were provided by Quinn, Dressel, Jokinen Associates, consulting structural en- gineers for the project. Funding for the analysis of the survey data was provided by the Province of Alberta Summer Tempo- rary Employment Program (STEP) and by the Natural Sciences and Engineering Research Council (NSERC) through Operating

Standards Association, exd dale,-0nt. GRAHAM, C. J., and SCANLON, A. 1984. Deflection of reinforced

concrete slabs under construction loading. Structural Engineering Report No. 1 17, University of Alberta, Edmonton, Alta.

1986. Long-time multipliers for estimating two-way slab de- flections. ACI Journal, Proceedings, 83(6): 899-908.

SCANLON, A,, and Ho, E. 1984. Analysis of field measured deflec- tions, Scotia Place Office Complex, South Tower. Structural En- gineering Report No. 125, University of Alberta, Edmonton, Alta.

SCANLON, A,, and THOMPSON, D. P. 1987. Evolution of minimum thickness requirements for two-way slab systems. Proceedings Vol. I, CSCE Centennial Conference, Montreal, Que., pp. 573-584.

TAM, K. S. S., and SCANLON, A. 1984. The effects of restrained shrinkage on concrete slabs. Structural Engineering Report No. 122, University of Alberta, Edmonton, Alta.

Appendix A

TABLE Al . Construction schedule and compressive strength test results

Mean compressive strength results

Date concrete Floor number placed 7days 28 days

Main 2 3 4 S 6 7 8 9

10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

March 21, 1981 March 31, 1981 April 15, 1981 May 1, 1981 May 9 , 1981 May 15, 1981 May 22, 1981 May 30, 1981 June 5, 1981 June 12, 1981 June 19, 1981 June 25, 1981 July 2, 1981 July 9, 1981 July 17,1981 July 27, 1981 August 4, 198 I August 1 1, 198 1 August 15, 198 1 August 21, 1981 August 28, 1981 September 4, 198 1 September 12, 198 1 September 19, 198 1 September 25, 198 1 October 1, 1981 October 9, 1981 October 16, 1981

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Appendix B

TABLE B1. Mid-panel deflections-slab type A

Time since form removal and corresponding measured deflection

Forms Load from Load from Load from Load from Shores removed 1 floor 2 floors 3 floors 4 floors removed April182 July182

-

I1 a, I2 a? I3 A3 I4 A 4 I5 a, 16 17 A7 18 A 8 Floor Grid (days) (mm) (days) (mm) (days) (mm) (days) (mm) ( d a y s ) ( m m ) (days) (mm) (days) (mrn) (days) (mm)

No. of data points Mean Standard deviation Range: From

To Coefficient of

variation (%)

NOTE: Deflections at In do not include camber Can

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TABLE B2. Mid-panel deflections-slab type B

Time since form removal and corresponding measured deflection

Forms Load from Load from Load from Load from Shores removed l floor 2 floors 3 floors 4 floors removed April182 July182

tl A I t 2 A 2 [ D A 3 [4 A4 15 A 5 f6 A 6 t7 A 7 t~ A 8

Floor Grid (days) (mm) (days) (mm) (days) (mm) (days) (mm) (days ) (mm) (days) (mm) (days) (mm) (days) (mm)

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Time since form removal and corresponding measured deflection

Forms Load from Load from Load from Load from Shores removed l floor 2 floors 3 floors 4 floors removed April182 July182

1 I A I 12 Az 13 A 3 14 A 4 1s As 16 17 A 7 I8 AH Floor Grid (days) (mm) (days) (mm) (days) (mm) (days) (mm) (days ) (mm) (days) (mm) (days) (mm) (days) (mm)

No. of data points Mean Standard deviation Range: From

To Coefficient of

variation (%)

NOTE: Deflections at t8 do not include camber

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TABLE B3. Mid-panel deflections-slab type C - - --

Time since form removal and corresponding mcasurcd deflection

Forms Load from Load from Load from Load from Shores removed 1 floor 2 floors 3 floors 4 floors removed Apr11182 July182

1 l A 1 12 A2 I3 A3 13 A4 ( 5 AS 16 A6 17 A7 18 A 8

Floor Grid (days) (mm) (days) (mm) (days) (mm) (days) (mm) (days)(mm) (days) (mm) (days) (mm) (days) (mm)

8 FG89 8 6 17 13 19 20 24 26 28 24 41 7 34 9 FG89 -6 7 - 2 14 5 20 10 27 14 20 41 1 3 1

10 FG89 4 7 10 13 13 20 12 27 14 17 306 33 404 43 11 FG89 10 6 11 13 19 20 24 28 28 26 397 42 12 FG89 7 2 14 8 22 13 32 17 11 39 1 38 13 FG89 4 7 14 15 21 25 23 33 24 25 384 3 1 14 FG89 5 8 16 18 25 26 28 33 33 27 279 47 377 24 15 FG89 13 9 18 18 22 25 3 1 29 33 26 369 46

0 > 16 FG89 13 8 13 15 20 19 22 25 28 24 359 35 Z

c-

17 FG89 7 19 11 23 17 26 26 35 1 32 CI 18 FG89 4 15 10 19 3 1 246 64 344 33 < 19 FG89 6 16 22 340 32 rn

Z 20 FG89 7 12 24 334 36 0

21 FG89 327 37 <

22 FG89 320 23 9 - 23 FG89 214 32 312 23 e

24 FG89 305 22 a m -

25 FG89 19 4

299 26 FG89 27 FG89 285 32 28 FG89 278 22 8 HJ67 18 417 33 9 HJ67 35 41 1 25

10 HJ67 10 306 24 404 45 1 I HJ67 14 397 42 12 HJ67 23 391 4 1 13 HJ67 27 384 38 14 HJ67 23 179 45 377 35

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TABLE B3. (concluded)

Time since form removal and corresponding measured deflection

Forms Load from Load from Load from Load from Shores removed 1 floor 2 floors 3 floors 4 floors removed April182 July182

f l A 1 f2 A2 b A3 f4 A4 [s A5 [6 A6 f7 A7 f8 A8

Floor Grid (days) (mm) (days) (mm) (days) (mm) (days) (mm) (days)(mm) (days) (mm) (days) (rnm) (days) (mm)

15 HJ67 30 9 2 1 18 23 25 9 29 30 24 369 59 16 HJ67 8 9 15 16 19 18 20 359 44 25 20 17 HJ67 11 7 14 11 17 17 27 29 35 1 47 18 HJ67 344 41 19 HJ67 6 13 20 340 45 20 HJ67 7 12 22 334 48 21 HJ67 327 45 22 HJ67 320 25 23 HJ67 21 214 24 3 12 25 24 HJ67 20 305 39 25 HJ67 299 30 26 HJ67 34 29 3 35 27 HJ67 285 32 28 HJ67 278 36

No. of data points Mean Standard deviation Range: From

To Coefficient of

variation (%)

NOTE: Deflections at r8 do not include camber.

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TABLE B4. Mid-panel deflections-slab type D

Time since form removal and corresponding measured deflection

Forms Load from Load from Load from Load from Shores removed 1 floor 2 floors 3 floors 4 floors removed April182 July182

t I A1 b Az t3 A3 t4 A4 ts As t6 A6 t7 A7 t n Ax Floor Grid (days) (mm) (days) (mm) (days) (mm) (days) (mm) (days ) (mm) (days) (mnl) (days) (mm) (days) (nlnl)

No. of data points Mean Standard deviation Range: From

To Coefficient of

variation (%)

NOTE: Deflections at r8 do not include camber.

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TABLE B5. Mid-panel deflections-slab type E

Time since form removal and corresponding measured deflection

Forms Load from Load from Load from Load from Shores removed l floor 2 floors 3 floors 4 floors April182 July182 removed

I! A , 12 A 2 (3 A 3 14 A 3 15 AS I6 A 6 17 A 7 18 A 8 Floor Grid (days) (mm) (days) (mm) (days) (mm) (days) (mm) (days ) (mm) (days) (mm) (days) (mm) (days) (rnm)

No. of data points Mean Standard deviation Range: From

To Coefficient of

variation (%)

NOTE: Deflections at t8 do not includc camber. Can

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