Experimental prediction of joint movements in buildings

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Materials Research and Standards, 10, 4, pp. 16-21, 1970-04

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Experimental prediction of joint movements in buildings

Karpati, K. K.; Gibbons, E. V.

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test

methods

nrum

Experiments

Prediction of

Joint Movements in Bui dings

K. K. Karpati/E. V. Gibbons

R E F E R E N C E : 6 . E . Eiu-pati i~ncl E. V. (;il)l~ons, "Espcri~ncntnl Prccliction of Joint Xlovcmcnts in Buildings" .\foterirrlr Hcserrrcl~ rfrlrl Slnr~rlnrrls, blTRS:\, \'ill. 10, so, 3 , 1). 16.

ABSTRACT: T h c ~novellrcnt of L\vo expansion joints is follo\\,ecl esperimc~lt:~lly, ancl the possibility of cor- relating rllovelncnl with ternper;lturc cxplorccl 1)s st. t ' . t ' . 1 .

. ,I IS 1c.1 ,unalysis. T h e tcmpelxture of the air end :~f

the wall at different depths a t the joint gave good corrclatioll with the movcmclll. T h e highest dcgrcc of corl.clatiol~ was forlnd in winter, the lo\vcst in sulnlncr; I I I O V C I I I C I ~ ~ per dcgrcc Fahrcnhcit (i.c., the slopc of the regression line) \\.as twice as ~ n u c h in w i ~ ~ t c r as in sullllner. Corrclalion wilh ~nctcorological tc~nllwaltlrc records for thc region \\us only fair. KEY WOIIDS: Joint ~novernenl. Building joint movc- rllcnt. ISrpn~~sioll joint movements. I \ l o \ ' c ~ ~ ~ c n l s of I ~ ~ ~ i l c l i ~ ~ g joil~ts

I n the construction of buildings expansion

joints must be provided to take up movements resulting from changing weather conditions. Thc joints require sealing with materials called sealants that are capable of moving with the joint without clevelop- ing cracks where rain ancl wind can pene- trate. Sealants can perform successfully only if their working capabilities are not exceeded by the movelnents of the joints. 130th the move~nent of the joint and the properties of the sealant, therefore, must be known to ensure a failure-free opem- tion. The study involvi~lg the properties of sealants will be reported separately.

Expansion joints move when tlle interaction of weather factors such as air temperature, radiation, wind speed, humidity, ancl rainfall causes a temperature or moisture content change in the building ele-

}This paper i s a contribution from the Division of Building Research. National Research Council of Canada, and is published with the approval of the Director of the Division.

E. V. Gibbons, rosu;~~.cl~ olliccr Clru~nical cogi~rccr, Div. of Ilrtildiog Resenrcl~, National Roscarcl~ Council of C;u~ad;t.

nlents. Because of the complex interaction of the multi-component system, accurate prediction of such ~novements is not possible and n~easurements must be made on actual structures to estal~lish guide lines for building practice.

This paper reports the measur.:d movement of expansion joints on actual strut..

tures. The main purpose in taking these me:1cnrements was to evaluate by statistical methods the correlation between daily joint movement and temperature change and to use the correlation for predicting

inovement. Tenll~erature is not considered to be the sole cause of movement but only as one of the factors that can be used as a guide for prediction purposes. .4 low correlation coefficient \iroulcl indicate that temperature cannot serve this purpose.

Experimental

The instrument llsecl for obtaining simul- taneous records of joint movement and ambient air temperature has been de-

Fig. 1 -Typical curves obtained with joint movement recorder, solid line-joint movement, dotted line-temperature

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Jan Feb M a r A p r May J u n e J u l y A u g Sept O c t N o v Dec 1 9 6 7

Fig. 2-Superpositions of daily temperature fluctuations over the yearly cycle

scribed in a separate publication A

typical record obtained for a one-week period is illustrated in Fig. 1. The solicl line represents joint movement, and the dotted line the temperature variations. One circular division of the chart is equal

to 0.010 in. of ~novenle~lt or 4.02 F. Sup-

plenlentary temperature measurements were taken with ther~nocouples installed within the case of the instru~nent, at an exposecl surface of wall near the instru-

ment, and

1/,

in. and 1 in. below the surface

of the exposed area.

The ill-strument was mounted at mid- height on a south-facing joint of the two- story Building Research Center at Ottawa.

The expansion joint creates a separation

between an 81-ft long wing and the 201-ft long main building. The wall section con- sists of a structural steel frame and 12-in. hollow clay tiles, with white-painted stucco on the outside and gypsum plaster on the inside.

Measurements were also taken on a high-rise apartment block where access was given to a four-level basement. The two top levels are exposed on the south- west and it is near this side, on the top level, that an instrument was mounted for a short period on an inside column (split by the joint) which passed through the entire width of the building. In-sit11 cast concrete construction extended 140 ft on one side of the joint and 160 ft on the other. In addition, a metal plug was placed on each side of the joint with the center- line perpendicular to the length of the joint. Readings were taken monthly with calipers acrois these plugs in order to re-

'The italic numbers in brackets refer to the list of ref. appended to this paper.

cord yearly movement. The instllument was

mounted at the same place for a non nth

to measure daily changes.

Daily ~ n a x i ~ n u n l and minimum temper-

ature measurenlents were obtained fro111 the Meteorological Station of the National Research Council (NRC), Ottawa, and used in the evaluation of the data collected. :I desk-top con~puter was programmed to carry out necessary calculations.

Discussion

Examination of the instrument readings showed that joint rnove~llent as well as temperature goes through a cycle almost everyday. When the temperature in- creases, the joint narrows and vice versa.

These daily cycles are superimposed on a

yearly cycle, which is illustrated for temperature by Fig. 2. The daily cycles are drawn for representative periods of the

year. Joint inove~nent for a full year woulcl

show a sinlilar super-position of daily cycles over the yearly cycle. However, such a chart would offer little accuracy and make little provision for preclicting joint nlovements for several years, since it woulcl give only one cycle per year. Therefore, daily temperature changes and joint movements were exanlined to discover whether they could serve as a basis for predicting yearly movements. Daily tem-

perature and joint nlove~nent changes were

read from the circular charts a ~ l d analysecl

by statistical methods for the degree of correlation existing between them.

Figure 3 illustrates the chart-reading method on a linear scale. The continuous line indicates joint movement; the dotted line indicates temperature fluctuations.

The distances between minimum and maximum points were read for each varia- ble for the same period of time and plotted against each other, as illustrated in Fig. 4. Srllall time lags of a few hours were disregarded because the time lag was only

a fraction of the half cycle. Change of

direction of the temperature curve either preceded that of the nlovenlent curve or coincided with it. Increasing values of changes were given positive signs, and decreasing changes 11egative ones. Reversal of direction usually occurred about 7:00 a.m. and 4:00 p.m. giving a separate set of clata for clay a::d uight. The usefulness of this separation wil! be discussed.

Because none of the factors could be

experimentally controllecl, statistical

treatment of the collected data seemed

appropriate [2]. The statistical evaluation

consisted of the following steps: (1) ana- lysing the degree of correlation and giving limits for the correlation coefficient at a chosen confidence level; (2) establishing the straight regression line represented by the data; and (3) predicting the yearly movement, within pre-assigned confidence

limits, by sul~stituting the measured yearly

temperature difference in the equation that clescribes the line.

Comparisoll of Temperature Measure- ments a t the Joint/ Temperature measurements taken by the bimetallic element in the instrument and by the thermo- couples previously described showed very high correlation coefficients with joint ~llovenlent with a narrow band of confidence linlits at the 95 percent level. It was

c o n c l ~ ~ d e d that further calculations would

be based on data obtained with the bimetallic elenlent of the instrument alone; the

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to 20 ilpril, 1967 are plotted in Fig. 4 and the regression line provided I)y them is

0 1

T i m e , D a y s

Fig. 3-Method of reading daily joint width and temperature changes

Table 1-Correlation of Joint Movement with Temperature Changes. DBR/NRC, Ottawa

A. Temperature measured by bimetal - A L V S + l t O 01 +ALvs - AtD ot

(day-time) (night-time) / ? A l l Confidence limits ol 1) Confidence limits ol Confidence limits of Date r at the 95% level r at the 95% level r at the 95% level

B. Temperature measured by Meteorological Station, NRC. Ottawa

-11: decreasing jo~nt width change in lo-:' in + 1 l : increasing join1 width change in 1 0 , ' i n . -Ato: decreasing temperature in O F +Ato: increasing temperature in 'F

r: correlation coefficient

0 : correiation coefficient of the population

latter showed correlation coefficients as good as any other ten~perature ineasurements and this was true for various periods of the year.

Correlation of Joint Moveme~it with Temperature challges/ Continuous nleas- urements made with the instrument were available for the first half of 1967. They were cliviclecl into shorter ueriocls accord- ing to turning points observed in the trend of daily teinperature cycles; a further clivi- sion was ~nacle for clay ant1 night timc. All pcl.ioc1s were analysecl separately as were the combined data.

The Ilirrh correlation coefficients. with _" their narrow bancl of confidence liinits (Table l), present proof that there is a

linear correlation between joint movement and teinperature change. One can, therefore, proceed to a regression analysis with-

out plotting all the data. There are only two exceptions to the generally high cor- relations: two winter clay time periods for joint movement versus ineteorological teinperature readings. They will be discussed latcr.

Regression Analysis of Joirit Movement versus Temperature Change/ The regression line around which the data are scat- tered can be described as:

where x is temperature change ancl y is joint width change. The constant, a,, and slope, b,, of the equation are given for the various periods in Table 2. The scatter around the line is measured by the standard error of estiinate, s,. As an illustration of the type of plotting obtainable, the readings for the period of 21 Xlarch, 1967

drawn in.

It is reasonal)le to suppose that when there is no temperature change, i.e. when

x = 0, the movement is not significantly

different from zero. This call I)e proved by

using a formula that gives the prediction interval for an individual value of joint width change, y:

where t is the t-value at 95 percent confidence level and n-2 degree of freedom (see other symbols in Table 2). One assumes that y = 0 at x = 0 , \vithin errors set 1)y

the data. At the 95 percent confidence

level the confidence interval is given in column 4 of Table 2. A comparison of columns :3 and 4 shows that the calculated intercepts, a,, stay within these limits, i.e. that the joint movements of various periods are not significantly different from zero when there is no temperature change.

The slopes, which are movement in inches per deg. obtainecl by the instru- nlent for various periods, show a continuous decrease from winter to summer, as illustrated in Fig. 5. There is more movement per cleg. cl~ange in winter than in summer. For ineasurements made with the bimetal, the slope change is a genuine difference since the 95 percent confidence li~ilits of the winter slope do not overlap those of the summer slope (Table 211, columns 5 and 6).

The difference between day ant1 night time slopes in winter could be attributed to the fact that the joint is partially shaded by deciduous trees in summer but fully exposed in winter. As the orientation is south, the radiation received during the clay can be quite considerable.

This idea is further supported by the low correlation coefficient for day time in winter I~etween joint movement and meteorological data (Table 2B), the latter being a ~neasurement of air temperatiire, excluding radiation. In this case the correlation is good for night time, but the 95 percent confidence limits of the slope show overlapping, i.e. the slope change is \vithin errors. Except for clay time periods in \vinter, Table 2 R confirms the findings of Table 2 h in genewl.

Prediction of Yearly illovement from Daily A,lovement/ I3y comparing the measured ancl calculated valucs of yearly movement it is possil~le to (letermine \\~llether the regression line continues straight into the high movement region that col.responds to yearly movement. The regression equation of daily cycles 01)- MATERIALS RESEARCH AND STANDARDS

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A t Temperature Change i n Degree F a h r e n h e i t

tainecl with the instrument for the half- yearly accumulated clata is (see last row in Table 2A):

The temperature difl'erence recorded by

the instr;ment during the entire perioh

ol)servecl was x = 109.4 F deg. S u l x t i t u t i ~ ~ g

this in Eq (2) one obtains 0.171 in. for the total yearly width change. A comparison of the last two columns of Table 2A shows

that the value actually ~ u e a s ~ u e d 11y the

instrument is 0.177 in. for the correspond- ing period. Therefore, prediction of yearly joint movement is possil~le froin daily movement records and is accurate if reacl- ings are available for half a year.

Similarly, one can give the regression equation of claily cycles for the half-yearly accumulated data obtained horn meteorological temperature readings (see Tal~le

2R) :

Here, the temperature difference for the

half year was x = 115 I: _{cleg. which prc-}

dicts a yearly movement of 0.154 in. When this is compared with the measured cliffer- ence (last two columns, last row of Table 2R) and with the prediction of equation (3), 0.171 in., one can see that prediction is less accurate when nleteorological clata are used.

A prediction interval can be given at the 95 'percent confidence level for both pre- dicted figures, using E q (2).

Upper limit Lower limit (in.) (in.)

Records of the

instn~ment 0.190 0.151 Meteorological data 0.183 0.125

Although ~neteorological data provide less

accurate prediction, the measured value of 0.177 in. still falls within the 95 percent

I

_\

D a y - l o r A f N i g h t -..,or A e ) B i r ~ ' e l a l l ~ t S t r i p 0 . 2 - o

6

30 60 90 120 150 180 210 240 D a y s F e b M a r A p r h l a y J u n e J u l y A u g 1967

Fig. 4-Daily joint width change vs temperature change lor the

period 21 March 1967 to 20 April 1967 (left)

Fig. 5-Joint movement regression line slopes vs time (above)

I 1 1 I 1 I I I I I

Feb M a r A p r M a y J u n e J u l y A u g S e p t O c t N o v Dec J a n

1 9 6 7 1 9 6 8

Fig. 6-Joint movement of high rise apartment building, Ottawa

confidence li~nits of the predicted yearly

movement.

Application of Proposed Prediction Method/ The applicability of the method of prediction using average temperature periods of the year has been verified on

a high-rise apartment building without air

conditioning (see Experimental). Results of

~nonthly readings over a pair of wall plugs

are illustrated for a complete year in Fig. 6. Data were collected at the same location by the instrument from 20 March to 3 May 1968, except for temperature measure- ~ n e n t s which were omitted because this part of the building was heated. Joint nlovement was correlated with meteorological temperature measurements. The regression line (see Table 3) for clay and night periods combined was:

y

+

13.17

+

2 . 8 4 ~ . . . . . . (5)

The maximum temperature difference was 113 F cleg, nieasul.cd cluring the l~criocl from summer 1967 to winter 1967,438,

When this is substituted in Eq (5), the total

~novement is 0.334-in., with confidence

limits of 0.380-in. and 0.288-in. 011 the 95

percent level. The value actually ~neasured was 0.344-in., which falls well within these

limits. It is therefore considered that the

proposed metl~ocl of predicting yearly movement was app1ical)le to this building.

Calculation of &laximum Possible

Movement of DBR Joint under Given

Climatic Conditions/ It is possil~le to es-

timate the maximum possil~le movement for the Division of Ruilcling Research, National Research Council of Canada IIRRJNRC joint from the maximum temperature difl'erence recorded for the region by the Meteorological Station. For APRIL 1970

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Table 2-Statistics of the Joint Movement vs. Temperature Measured on the Building of DBR/NRC, Ottawa A. Temperature measured by bimetal

Calculated Measured Interval Movement Yearly

ol y at ts - in. Movement Date n" a, x

-

0" bx bx S,. X sx x = 109.4" F ~ n . $)."?j.2-67 '"."-"].3.67 + I [ vs. - I t " 21.:3-20-4-67 (night-time) 2l.-1-31-5-67 1 .(i-31 -7-(i7 9.2-:31-7-Ci7 / * I t /

for llalf a veal. !).2-01-7-67

- -

B. Temperature measured by Meteorological Station, NRC, Ottawa

/ * I ( /

:3.2-31-7-67 319 7.60 2 2 7 1.27 t 0 . 2 0 1-1.10 for half a y u ; ~ ~ .

"n: number of pairs of readlngs

a,. constant of regression line in 1 0 ' in. b,: slope of regression line in 1 0 : in./"F. s,: standard error of estimate in 1 0 ' in.

X: average of temperature changes in "F. s,: standard deviation of the sample in "F.

" a t the 95% confidence level; In 1 0 : ' in. '.at the 9556 confidence level; In lo--:' i n . I e F .

the Ottav;; r c ~ i o n _" the maximum difference

m e a s ~ ~ r e d during the past several decades

is 1.38 I: deg. \vl~icl~, sul)stit~~ted in ccluation

(3), gives 0.216-in. maximum change per year wit11 0.233-in. ant1 0.196-in. limits at the 95 percent confidence level. Therefore, this joint is not expected to nlove more than 0.235-in., i.e., about 25 percent in 95 cases out of 100, being designed to 1-in. width.

Limitations of Prediction Method/ In view of the fact that the present analysis of joint movement is based on only two cases, it is not possible to state that the method can be applied in all cases. It is expected, ho\vever, that it will be applica- ble Inore generally ancl that tlie proof will be a high correlation coefficient between daily joint movement and tenlperature changes.

The prediction of maximum movement

in a given geographical region can be

accurate if measurements are available for

a six months' period that includes tlie

hottest and the coldest temperatures. If data are available for only a few weeks,

then the choice of a winter periotl would

have an added safety factor because it

woulcl slightly overestinlate yearly niove-

nlent (see Table 2, Colunln 10). Alterna-

tively, an average tenlperature period for the year could be chosen. Summer, however, sllould be avoitled because it can dangerously underestimate yearly move- 11ien t.

I-Iumiclity may be a co~nplicating factor.

Records of average humidity for several decades slio\v that tlie outside humitlity in

Ottawa, measul.ed four times a day, is

higher in winter than in summer, but that

its fiuctuation is greater in summer [.3].

Feb., Jan. June, July percent percent

Ilcan llelative Ilr~midity 77.5 69 .8

Standard deviation 4 .8 I1 .li

In addition, insicle relative h~unidity and

temperature are practically constant during the winter, whereas buildings without air conditioning are affected in sunlmer inside and outside. More short-term movement can therefore, be expected from hu- 111iclitv in sunimer.

1-111 opportunity arose to investigate the

effect of humidity fluctuatio~i dl~ring tlie

summer of 1968. In this period tlie correlation coefficient was low (-0.3 as opposed

to Inore than -0.9 for 1967), indicati~lg

that the two-month period in question was not suital~le for prediction purposes. Changes in daily temperature, joint widtli, and relative humidity have been plotted

side-by-side in the search for a correlation

with hnmiclity. Although a definite nrl-

mel.ica1 correlation has not yet been con- firmed concerning the effect of li~m~idity, there are indications of its influence. It has been observetl that shorter periods, within

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the two months, had relatively higher correlation coefficients (-0.8) but smaller slope than that obtained during the pre- vious summer when the correlation coefficient was high. Examination showed that there was an extensive and regular

relative humidity change indicating a de- -

crease of humidity with increasing temperature and vice versa. Because under these circumstances movement caused by changes in humidity would counteract changes resulting from temperature, it is possible that the decrease in slope was caused by fluctuations in relative humidity. The water content of the porous wall, however, depends on many factors other than relative humidity and cannot be

Table 3-High-Rise Apartment Building

Limits of p at the L)5'!i,

confidence level 0.60

<

p

<

0.83 n 8 2 :I.. 13.17 in 10-" in. Sc. 19.48 in 1 ( r " in. S

a

in 'F sx 7.63 in "F Calculated vcarlv movement 0 034 , .

95% confidence linlits of the

calulllatetl _. , I l , o v e m e n t ~ 0.380 in. and 0.288 in.

kleasured yearly ~novetncnt

'

0.34'4 in. "For meanlng of slgns see Tables I and I I

"Joint movemenl versus meteorological temperature measurements. Ottawa. 20 March 1968 to 3 May 1968.

Combined results of day- and night-time differences

evaluated at present. These unknown moisture content changes, probably having longer and more irregular cycles, diminish the degree of correlation between joint movement and temperature change. An attempt has been made to find a numerical correlation between relative humidity changes and joint movement in a short period where the correlation with temperature was zero. For clay time a relatively high correlation coefficient (0.87) has been found, but for night there has been practically no correlation (0.4). Investigations

are continuing in an attempt to obtain a better understanding of the reasons for low correlation between joint movement and temperature changes for some periods. The degree of correlation between temperature and joint width changes was equally good for the winters of 1967 and 1968, another reason for preferring prediction based on winter data as opposed to summer readings when a half year's records are not available.

Conclusion

High correlation has been established between daily temperature and joint width changes for expansion joints in two types of non-air-conditioned buildings. Statistical analysis gave a regression line between the above mentioned variables that could be extrapolated into the region of large yearly movements because extrapolated and measured values were in good agreement. The correlation of joint movement was equally good with ambient temperature measured by the instrument and temperatures measured at various points in the wall (up to a 1-in. depth).

It is expected that accurate prediction of the possible maximum movement of any joint in similar construction may be possible from linear correlation with temperature if half a year's daily fluctnations are available, including the coldest and hottest periods of the year and using meteorological tables for the maximum temperature differences in a given geographical region. If records of only shorter periods of time are available, an average annual temperature period or a winter period should be chosen. The latter would slightly overesti- mate movement in the cases observed but would increase the safety factor. During the summer period the correlation coefI- cient between movement and temperature and the width change per deg. (i.e., the slope of the regression line) was found to diminish, probably owing to the influence of hunlidity. An extrapolatio~l from this period would, therefore, underestimate the yearly movement and be less accurate.

If temperature recordings by the instru-

ment are not available because the joint is accessible only from the inside of the building, then the maximum-nlinirnu~n temperature records of the local meteorological station could be used with fair accuracy. Attention must be drawn to the fact that the buildings examined had sur- faces relatively inlpervious to moistnre pick-up. Where unpainted, highly-porous materials such as brick are used, moisture may play a bigger role and the nature of the correlation with temperature alone may be different.

Acknowledgement

The authors are grateful to Mr. N. T.

Gridgeman for reading the manuscript and for giving invaluable assistance in the application of statistics to this problem. The authors also wish to express their apprecia-

tion to S. W. Raymond and C. C. Barrett

for their assistance.

REFERENCES

[ I ] Gibbon,, E. V. and Karpati, K. K. "A Recorder to Measure the Joint Movenlent in a Building." ASTM, Materials Research and Standards, :\pril 1069. 11. 16.

[2] Mode, E. R. Elerr~er~ts of Stotisticv, l'rcntice-Hall, 3rd Ed. 1961 p. 143.

Cuming, 11. C.. and Anson, C. J. .\lotlicrr~ntic.~ o n d Statistics for Tecl~nologists. Ileywood Hooks, Lon- don, England, 1966.

Snedecor, G. W. "Statistic;tl Llethods," Iowa State College l'ress, 5th Ed., 1956.

Crow, E. L. Statistics ~Wanfrnl, Dovcr Pub., 1960. Fisher, R. :\. Stotisticol dlctlto(1s fol. lieve~~rclr Workers, Oliver and Boyd, 13th Ed. 1958. Natrella, M. G. Er/~crin~entnl Stntistics, U.S. Dept. of Conrmerce Ilnndbook 01, 1960.

1.31 Canada, Department of Tr;~nsport, "hlontllly hteteorolngical Srlmmary," nornral relative Ilumid- ities based on the period 1021-50. Records of observations take11 at Ottawa International Airport 1966.

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