volume change response of precast concrete buildings

Fal l 2009 | PCI Journal112

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Editor’s quick points

n Precast concrete buildings usually perform satisfactorily if PCI Design Handbook: Precast and Prestressed Concrete methods are used to design for volume-change effects, but misconcep-tions still exist about their performance.

n This research was funded by PCI and Wiss, Janney, Elstner Associates Inc. to gain a better understanding of the volume-change response of actual precast concrete buildings and to compare measured performance with analytical models—and provide calibration if needed. The full research report is avail-able from PCI.

n Another objective of this research is to recommend revised design procedures that account for flexible connections.

Volume-change response of precast concrete buildingsGary J. Klein and Richard E. Lindenberg

Volume-change effects are the combined result of creep, shrinkage, and temperature strains. In standard load com-binations, elastic shortening and differential settlement are included with volume-change effects. Because elastic shortening occurs before the members are connected, it does not affect precast concrete structures. Differential settlement is not addressed in this paper.

Volume-change damage is second only to chloride-induced deterioration as a leading cause of problems and failures in parking structures.1 Figures 1 and 2 show examples of volume-change distress. The expansion joints used to alleviate volume-change restraint are frequently the weak point of exposed structures, especially parking structures. They add significantly to construction costs and frequently fail, resulting in unintended moisture entry and related deterioration.

Volume changes are different from other load effects. Unlike forces from gravity and wind, volume-change forces are self-straining forces. That is, they are created as members deform. The fundamental demand resulting from volume change is a movement, not a force, but substan-tial forces can develop where volume-change movement is restrained. The American Concrete Institute’s (ACI’s) Building Code Requirements for Reinforced Concrete (ACI 318-08) and Commentary (ACI 318R-08)2 requires that volume-change forces be based on “realistic assessment of such effects occurring in service.” However, ACI 318 does not otherwise differentiate volume-change-force effects from gravity loads.

Procedures for determining volume-change movement and forces in precast concrete buildings have been available in the PCI Design Handbook: Precast and Prestressed Con-

113PCI Journal | Fal l 2009

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Evaluate the need for and location of expansion joints.5.

Determine the expansion-joint width and movement.6.

Estimate equivalent volume-change strains (reduced 7. by K factors that account for creep and microcracking of precast concrete members) for analyzing volume-change forces.

Estimate fixity of column bases.8.

Calculate volume-change-restraint forces based on 9. frame analysis or approximate methods.

Proportion members based on calculated forces.10.

Also, section 3.4 of the PCI Design Handbook provides helpful advice regarding connection design for volume-change effects. “Properly detailed connections can minimize the effects of volume change strains. Connections should be detailed so that ductile deformation of one of the elements such as the connecting plate or connection bolt assembly can take place. Neglecting the effect of this connection deformation will produce unrealistically high computed restraint forces and can actually have a negative effect if connections are too strong, and inhibit necessary ductility.”

crete3 for 30 years. When developed by the PCI Committee on Design Handbook in 1977,4 the methods were believed to provide realistic estimates of volume-change forces. The PCI Design Handbook provides a procedure for evaluating volume-change movements and forces:

Determine the maximum seasonal temperature change.1.

Determine the annual average ambient relative humidity.2.

Determine the volume-change strains caused by creep 3. and shrinkage as influenced by the following:

concrete type (normalweight or lightweight)•

curing conditions•

age at erection•

volume-to-surface ratio•

relative humidity•

concrete strength and level of prestress•

Determine the design temperature strain.4.

Figure 1. Volume-change distress is evident at this rigid spandrel-beam connection.


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When the PCI Design Handbook methods are used, precast concrete buildings usually perform satisfactorily. In his paper summarizing a 1971 symposium on design for ef-fects of creep, shrinkage, and temperature, Robert Philleo5

supports the notion that “it makes no difference what you do as long as you do something.” In that sense, the PCI Design Handbook procedures have been successful.

Nonetheless, questions and concerns regarding volume-change response of precast concrete buildings remain, as described in the following paragraphs.

Design for volume-change forces

Treating volume change as an external force can lead to irrational decisions, as described in the following scenario. Based on PCI Design Handbook procedures, a designer calculates the volume-change forces using educated assump-tions about the material properties, volume-change strain, force-reduction coefficients, member sizes, and reinforce-ment ratios. According to the ACI 318 requirements, the volume-change forces are then factored and combined with gravity loads to determine the needed reinforcement.

If, for example, the bending forces in corner columns due to volume-change effects are greater than expected, the design-er then adds longitudinal column reinforcement, or worse, increases the column size. Performance is not enhanced by this increase in strength. In fact, volume-change forces will only increase, escalating the likelihood of wide cracks, column shear failures, connection failures, and the like.

However, in practice, designers generally do not calculate volume-change forces, even though they are included in the basic load combinations of ACI 318 and the Struc-tural Engineering Institute (SEI) of the American Society of Civil Engineers (ASCE)’s Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-05).6 Rather, designers rely on rules of thumb and successful past practices. When volume-change forces are calculated, hand calculations and two-dimensional frame analyses are generally used.

Accuracy of volume-change strains and forces

Design for volume-change effects is complicated by the ex-treme variability of concrete strain and the resulting forces. Furthermore, there are few actual data on volume-change effects in precast concrete buildings. Due to the wide scat-ter in material properties, thermal exposure, and structural response, it is not possible to predict volume-change forces with accuracy comparable with the prediction of gravity-load forces. At the same time, using conservative assump-tions leading to upper-bound estimates of volume-change force leads to highly impractical and costly designs.

Iqbal7 measured thermal movements in several precast concrete parking structures. Figure 3, developed from this study, is a plot of the ratio of actual to predicted joint movement. Although actual movements are generally less than predicted, the data are widely scattered. These data confirm the unpredictability of volume-change response.

Volume-change response of precast concrete buildings

Developments in connection details have changed the volume-change response of precast concrete buildings. In particular, pretopped double-tees (or wall panels) with semiflexible flange-to-flange connections respond dif-ferently from a monolithic structure. Semiflexible flange connections permit small volume-change movements that reduce both volume-change forces and movement at expansion joints. None of the available procedures for estimating volume-change effects account for the behavior of precast concrete structures with flexible connections.

This paper summarizes the findings of the authors’ recent study conducted for PCI on the volume-change response of precast concrete buildings.8 This research was designed

Figure 2. Spandrel connection distress shown by the arrow is caused by unin-tended volume-change restraint from a grade-level barrier.


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Field instrumentation program

Selection and description of buildings

More than any other precast concrete building type, park-ing structures present the greatest challenge with respect to volume-change movement and forces. Parking struc-tures are frequently large in plan and unheated, resulting in significant thermal movements. Furthermore, parking structures are an important building type in the precast concrete industry. For these reasons, the field instrumenta-

to gain a better understanding of volume-change response starting with the observed behavior of actual precast concrete structures. Accordingly, the objective of this research was twofold: develop a better understanding of volume-change movement and forces based on the measured performance of precast concrete structures and calibration to analytical model, and recommend revised design procedures that reflect this understanding and account for the influence of flexible connections. The primary research tasks included field moni-toring and finite-element analyses of actual structures, as well as evaluating the predictability of volume-change forces.

Figure 3. This plot of the ratio of actual to predicted joint movements in precast concrete parking structures illustrates the extreme variability of volume-change movement.

0.6181630

0.308587

200 40 60 80

Government center

Judicial center

Ameritech

O’Hare

Riverway l

Sears east

100 120 140 160 180

Mov

emen

t rat

io, a

ctua

l/pre

dict

ed

1.500

1.000

0.500

0.000

-0.500

-1.000

-1.500

Table 1. Instrumented structures

Metropolitan area (climate)

Double-tee spans

Dimensions, ftSupported levels

Longitudinal expansion joint

Field toppingLongitudinal Transverse

Chicago, Ill. (northern) 2 120 364 1 Yes No

Denver, Colo. (desert/mountain)

5 293 399 2 Yes No

Washington, D.C. (mid-Atlantic)

3 186 384 4 Yes No

Atlanta, Ga. (southern) 3 183 342 5 No Yes

Note: 1 ft = 0.3048 m.


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is perpendicular to the floor members. Three of the four structures include a longitudinal expansion joint.

The Atlanta, Ga., structure is field topped; that is, a cast-in-place concrete wearing surface is placed in the field on the double-tees. The other three structures use pretopped double-tees. The flanges of pretopped double-tees are thickened to withstand traffic loading without a cast-in-place concrete topping.

Table 2 summarizes the column and connection data for the instrumented portions of the structures. The Washing-ton, D.C., structure employs intermittent shear walls at the structure perimeter where measurements were made. Else-where, conventional square columns are used along the frames that were monitored for volume-change movement.

Monitoring program

Continuous monitoring A battery-powered data-acquisition system was used to continuously collect hourly temperature and movement data over a two- to three-year period. Figure 4 shows a typical continuous monitoring system. The following measurements were made at the lowest supported level and at the upper level:

tion program focused on parking structures. New parking structures were selected in order to obtain early-age data on creep and shrinkage strain.

Four structures were selected in locations representing a wide range of structural and climatic conditions. Table 1 summarizes basic data on each of the parking structures. All parking structures employ precast, prestressed concrete double-tee floor members supported by precast concrete spandrel beams and columns. The dimensions of the structures and numbers of supported levels are provided in Table 1. The longitudinal dimension is parallel to the span of the double-tee floor members. The transverse dimension

Table 2. Support type and connection data

Structure Support typeDouble-tee connections Beam connections

Flange-to-flange Flange-to-beam/column Bearing Torsion

Chicago, Ill. 24-in.-square columns on continuous footing

F: JVI Vector connectors F: Bolt in slotted insert F: 1/2 in. ROF pad F: Threaded rod in open hole

Denver, Colo. 20-in.-square columns on iso-lated footings with central shear wall

R: Typically, embedded plates welded to reinforcing-bar and chord-steel connector with welded cover plates at perimeter

R: Welded angles at columns and inverted-tee beams

F: 1/2 in. Masticord ROF pad

R: Steel plate aligned parallel to beam line and welded to embedments

Washington, D.C. 12 in. × 128 in. shear walls on isolated footings

R: JVI Vector connec-tors and chord steel connector with welded cover plates at perimeter

R: Embedment with welded cover plate

F: 1 in. Masticord ROF pad

F: Inclined plate welded at opposite ends

Atlanta, Ga. 28-in.-square columns on pile supported footings

F: Hairpin reinforcing-bar connector

F: Plate welded to reinforc-ing-bar hairpin

F: 1/2 in. Masticord ROF pad

F: Threaded rod in open hole

Note: F = flexible connection; R = rigid connection; ROF = random-oriented fiber. 1 in. = 25.4 mm.

Figure 4. This photograph shows a typical installation of the continuous monitor-ing system. The red arrow indicates the data-acquisition system, and the blue arrows indicate potentiometers for monitoring joint movement.


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5 illustrates typical measurement locations. Periodic mea-surements included the following:

Movement at spandrel-beam joints and double-tee •joints. Movement data were collected using a digital caliper that measured the distance between machined measurement points affixed to the structure (see Fig. 6).

Column-tilt measurements.• A uniaxial tiltmeter mounted on a custom-designed bracket was used for column-tilt measurements.

Strain measurements of spandrel beams and •double-tees. Strain measurements were made using a 10 in. (250 mm) Whittemore strain gauge.

The measurements of movement at spandrel-beam and double-tee joints were especially useful. However, the re-peatability of tiltmeter measurements was suspect, so those results were less useful.

Field instrumentation findings

Temperature range Thermal-contraction strains dur-ing cold weather are of primary interest because they add to creep and shrinkage strain. Winter temperature measure-ments indicated significant differences between the struc-

Expansion-joint/structure movement.• Typically, a potentiometer was used to measure expansion-joint movements. Because the Atlanta structure did not have an expansion joint, a laser measurement system was employed to measure changes in out-to-out width.

Air temperature at structure.• Thermocouples were typically located below the deck at the lowest sup-ported level and upper level.

Temperature of structural elements.• Thermocouples were inserted into drilled holes (drilled to half the member depth) in the spandrel beams and double-tee flanges at the lowest supported level and upper level.

Local weather data.• Local weather data were down-loaded from the National Oceanic and Atmospheric Administration in electronic form and were integrated with continuous monitoring data.

Measurements were generally successful, though there were several gaps in the data due to power outages and vandalism.

Periodic monitoring At about six-month intervals (summer and winter), volume-change data were collected in study areas at the top and first supported levels. Figure

Figure 5. Typical periodic measurement locations are illustrated in this plot.

Joint gap

Column tilt

Data acquisition computer

Temperature

Joint movement potentiometer

Periodic monitoring

Legend

Expansion jointContinuous


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ture temperature, ambient parking-structure temperature, and local weather-station temperature. Figure 7 is a plot of January 2004 temperatures at the Chicago, Ill., parking structure, which is typical of cold-weather temperatures in the instrumented parking structures.

As can be seen, the ambient temperature in the one-level structure lags the extreme cold temperatures measured by the National Weather Service near the site. This difference was observed in the lower level of all structures. Appar-ently the structure warms the air, probably because of heat from the ground. There is not much difference between the temperature of the concrete deck and the ambient parking structure temperature, indicating that the relatively thin ele-ments have little thermal inertia.

In U.S. practice, thermal-contraction strains are calculated based on the difference between the mean temperature during the construction season and the temperature that is exceeded 99% of the time during winter months, as shown in PCI Design Handbook Figure 3.10.11. For unheated structures, the PCI Design Handbook recommends a 25% reduction in thermal strains computed on this basis. The recommended reduction for heated structures is 50%.

These reductions are incorporated into the design temper-ature-strain values given in PCI Design Handbook Figures 3.10.17, 3.10.18, and 3.10.19. As previously described, the temperature difference is primarily due to the less extreme microclimate inside the structure.

To evaluate the apparent temperature lag, low-temperature events at each structure were analyzed for the differ-ence between deck temperature and local weather-station temperature, both relative to the mean temperature during the construction season. Specifically, the coefficient to ac-count for the lag between weather-station temperature and structure temperature Ks is given by

Ks =

Ts−T

m

Tws

− Tm

where

Ts = structure temperature

Tws = weather-station temperature

Tm = mean temperature during the construction season

The 25% reduction in design temperature strains incorpo-rated into the PCI Design Handbook corresponds to a Ks of 0.75. Likewise, the 50% reduction in design temperature strains for heated structures corresponds to a Ks of 0.50. The 10 coldest events in the winter season were evaluated. Table 3 shows the summarized results.

These results indicate that PCI Design Handbook recom-mendations reasonably approximate the thermal-lag effect at the lower level but overestimate the lag at the upper level. However, as noted, the design low temperature is the temperature exceeded 99% of the time during winter months. As such, the design low temperature is warmer than the expected low temperature in any given year, and much warmer than the expected 50-year low. For example, the 50-year low temperature for Chicago is -27 °F (-32.8 °C), 24 °F (13.3 °C) colder than the design temperature of -3 °F (-19.4 °C), which is the temperature exceeded 99% of the time during winter months and the basis of U.S. de-sign practice. To be consistent with other load effects, the design low temperature should be the 50-year low.

In developing design recommendations for thermal-bridge movements, Roeder9 studied weather data in several U.S. cities over a 60- to 70-year period. Roeder recommends design for a temperature fall taken as the difference be-tween the probable low temperature of the structure and the installation temperature. The low structure temperature depends on the structure type but correlates with average of the low temperatures over four consecutive days. The installation temperature is assumed to be 20 °F (11.1 °C)

Figure 6. Movements at flange joints were determined by periodic measurements using a digital caliper.


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warmer than the average of the probable high and low temperatures.

Table 4 summarizes the temperature statistics for the study locations. The temperature fall for the design of bridge bearings and expansion joints as recommended by Roeder is provided for comparison.

Review of Table 4 indicates that the seasonal temperature fall is comparable with the adjusted 50-year temperature

fall. The difference is only a few degrees Fahrenheit, except in Atlanta, where the adjusted 50-year temperature fall is 9 °F (5 °C) lower than the seasonal temperature fall. Apparently, the temperature-lag effect makes up for the difference between the 50-year low and seasonal low, assuming a temperature-lag coefficient Ks of 0.75, as observed at the lower level of the monitored structures. Accordingly, it is reasonable to design both the structural frame and expansion joints for the same temperature fall in any given climate. The lower level of the structural frame

Figure 7. Air and deck temperatures in parking structures lag National Weather Service temperatures during cold weather, as can be seen in this plot of January 2004 temperature data from a Chicago, Ill., parking structure. Note: °C = (°F - 32)0.56.

Garage air

National Weather Service

Deck

70

50

30

10

-10

0

Tem

pera

ture

, °F

Time

January 1, 2004 January 11, 2004 January 21, 2004 January 31, 2004

Table 3. Temperature coefficients

Structure

Structure temperature coefficient Ks

Lower level Upper level

Mean Standard deviation Mean Standard deviation

Chicago, Ill. 0.78 0.10 n.a. n.a.

Washington, D.C. 0.73 0.07 0.88 0.07

Denver, Colo. 0.71 0.08 0.87 0.10

Average 0.74 0.08 0.87 0.09

Note: n.a. = not applicable.


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Temperature strain As described previously, strain measurements at double-tees and spandrel beams were taken at two structures during each periodic visit. The mea-sured strains were adjusted for expected creep and shrink-age strain between monitoring periods. Using the adjusted strain and values and the measured deck and spandrel-beam temperatures, the coefficient of thermal expansion was cal-culated. Table 5 summarizes the results.

The thermal expansion coefficient varies significantly with aggregate type,10,11 and there is a wide range of values for most aggregate types. The Chicago values are typical of precast concrete with limestone aggregate (which was used) but lower than the thermal expansion coefficient of 6 microstrains/°F (10.8 microstrains/°C) recommended by the PCI Design Handbook for precast concrete. The precast concrete in the Washington parking structure used granite aggregate, so the observed values are lower than the published ACI 209 values of 4.5 microstrains/ºF to 5.7 microstrains/ºF (8.1 microstrains/°C to 10.3 microstrains/°C).

Creep and shrinkage strain Measurement of creep and shrinkage strain in an exposed structure is especially difficult. Strain due to temperature changes obscures the more subtle changes in strain due to creep and shrinkage. To partially overcome this problem, the structure move-ment data were analyzed within narrow temperature bands. An example of this analysis can be seen in Fig. 8, which is a plot of expansion-joint movement at the upper level of the

does not experience the 50-year low temperature due to the temperature-lag effect, and expansion joints can be designed based on seasonal temperature range.

The seasonal temperature range values given in PCI Design Handbook Figure 3.10.11 are reasonable for these purposes, though they may be somewhat unconservative in Southern states. Furthermore, as can be seen by com-paring columns C and H of Table 4, the proposed design temperature range for exposed precast concrete buildings is somewhat lower than the range recommended for design of concrete bridges.

Table 4. Summary of temperature statistics for study locations, °F

A B C D E F G H

Mean construc-

tion season temperature

Annual low temperature*

Seasonal temperature

fall, A - B†

Adjusted seasonal

temperature fall 0.75,*

A - B‡

50-year low temperature**

50-year temperature

fall, A - E

Adjusted 50-year

temperature fall,†† 0.75 ×

(A - E)

Concrete bridge design temperature

fall

Structure

Chicago, Ill. 60 -3 63 47 -27 87 65 77

Denver, Colo. 62 -2 64 48 -25 87 65 77

Washington, D.C.

63 16 47 35 -5 8 51 66

Atlanta, Ga. 62 18 44 33 -8 70 53 64

Sources: Data in column A from Standing Committee on Structural Engineering of the Federal Construction Council, Building Research Advisory Board, Division of Engineering, and National Research Council, Expansion Joints in Buildings: Technical Report No. 65 (1974). Data in column H from Roeder 2003. * The temperature was exceeded 99% of the time during winter months. † Basis for PCI Design Handbook: Precast and Prestressed Concrete Figure 3.10.11. ‡ Basis of temperature strain indicated in PCI Design Handbook Figure 3.10.17. ** Based on annual low temperatures according to National Weather Service data. †† Adjusted for temperature-lag effect (Ks = 0.75). Note: Ks = coefficient that accounts for the lag between weather-station temperature and structure temperature. °C = (°F - 32)0.56.

Table 5. Observed coefficient of thermal expansion

Structure

Thermal expansion coefficient, microstrain/ºF

AverageStandard deviation

Chicago, Ill., double-tees

4.4 0.72

Chicago, Ill., spandrel beams

3.2 0.95

Washington, D.C., double-tees

3.8 1.40

Note: 1 microstrain/°F = 1.8 microstrains/°C.


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Joint movements It is useful to compare the observed movements at double-tee joints and the expansion joint. Figure 9 plots the movement at the double-tee joints and the expansion joint in the lower level of the Washington structure during a cooling cycle. As can be seen, the expan-sion joint moves much more than any individual double-tee joint. However, the total of the individual movements at the double-tee joints is nearly the same as was observed at the expansion joint. This movement pattern was observed at the lower levels of both of the Washington and Chicago structures, where flexible beam connections were used. Little movement at intermediate joints was observed at the upper levels, apparently due to the relative flexibility of the columns.

Refer to the idealized one-story structure shown in Fig. 10. If the expansion joint shown is at the middle of a sym-metrical structure and each half is also symmetrical, the movement at the end of the structure will equal one half of the movement at the expansion joint ∆EJ. Note that ∆EJ is also equal to the total shortening of each half of the structure ∆TS. In this idealized structure, movement at each intermediate joint ∆IJ reduces the demand for movement at expansion joints and forces in the structure due to volume-change shortening. The joint flexibility factor KJ is an

Washington structure over the two-year monitoring period. Data taken when the temperature was between 50 °F and 54 °F (10 °C and 12 °C) are highlighted. The resulting upward slope of the movement-versus-time plot is consistent with creep and shrinkage.

The PCI Design Handbook provides procedures for deter-mining creep and shrinkage strain as a function of age at erection, relative humidity, concrete strength, volume-to-surface ratio, and level of prestress. Table 6 compares the observed creep and shrinkage strain with those determined using PCI procedures.

As can be seen in Table 6, the strains predicted using PCI Design Handbook procedures are both significantly greater and smaller compared with those observed. The differ-ences are partly attributable to movement at intermediate joints. As explained in the following section, movement at intermediate joints reduces movement at expansion joints, which reduces the apparent creep and shrinkage strain. Furthermore, field measurement of creep and shrinkage strain of an exposed structure is inherently inaccurate. Nonetheless, these observations indicate that the creep- and shrinkage-strain values in the PCI Design Handbook are reasonable.

Figure 8. This plot of upper-level expansion-joint movement versus time at the Washington, D.C., structure illustrates the long-term opening of the joint due to creep and shrinkage. Note: 1 in. = 25.4 mm

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1

Mov

emen

t, in

.

January 2005June 2004 January 2006 January 2007 July 2007

Total movementMovement from 50 ºF to 54 ºFCurve fit


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ture with rigid joints, the expected global volume-change movement of a symmetrical structure with flexible joints is reduced by a factor of (KJ + 1).

Table 7 summarizes the joint flexibility factor KJ based on measurements at the double-tee deck joints and spandrel-beam joints. KJ predicted by finite-element models of the instrumented frames is provided for comparison purposes.

Finite-element-model analysis

Description of models

Two-dimensional models of the instrumented frames were developed and analyzed using SAP2000. Volume

indicator of the relative flexibility of the intermediate joints and is given by the following expression:

KJ =

∑ΔIJ

ΔEJ

=∑Δ

IJ

ΔTS

where

Σ∆IJ = the sum of the movements at the intermediate joints

Thus, KJ is an indicator of the relative flexibility of inter-mediate joints. Current PCI Design Handbook procedures treat precast concrete structures as monolithic in that intermediate joint movement is not considered, which is equivalent to assuming a KJ of zero. Relative to a struc-

Table 6. Creep and shrinkage strain

Structure upper levelCreep and shrinkage strain, microstrain

PCI/observedPCI procedure Observed

Chicago, Ill. 132 83 1.59

Washington, D.C. 182 120 1.52

Denver, Colo. 239 223 1.07

Atlanta, Ga. 50 78 0.64

Figure 9. This plot illustrates the relative magnitude of movement at intermediate and expansion joints. The data are from the lower level of Washington, D.C., structure after a cooling cycle. Note: 1 in. = 25.4 mm

2 2.3 2.6 3 3.3 3.6 4 4.3 4.6 5.3 5.6 6 6.3 6.6 7 7.3 7.6 8 8.3 8.6 95

Tot

al m

ovem

ent,

in.

0.5

0.4

0.3

0.2

0.1

0

Expansion joint


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when calculating a volume-change movement.) For design purposes, the recommended range of Kl is 4 to 6. Likewise, the PCI Design Handbook recommends that the design temperature strain be divided by a Kt value of 1.5, where Kt is the softening factor for temperature effects.

The selection of the Kl values is explained in a 1977 paper4 by the PCI Committee on Design Handbook. Creep studies by Mattock12 indicated that the effect of creep reduces the volume-change force by a factor of 2 to 3 relative to the force computed using gross member stiffness. The PCI Committee on Design Handbook reasoned that, because this force reduction applies to both axial and rotational restraint, it would apply to both the beam and the column, and the total reduction would be equal to the square of the reductions in the beam and column; that is, the correspond-ing Kl value ranges from 4 to 9. As noted previously, the sixth edition of the PCI Design Handbook recommends a Kl of 4 to 6. The basis for selecting a value of 1.5 Kt is not dis-cussed; however, the smaller value of 1.5 is consistent with the shorter time frame for changes in temperature strain.

The previous development of Kl was reevaluated as part of the PCI research project. The authors concluded that the

change due to creep, shrinkage, and temperature change was simulated as an equivalent-strain load on the beams. These models were analyzed two ways: assuming that all intermediate mechanical connections (not including expan-sion joints) were rigid and assuming flexible connections. For the latter case, nonlinear link elements were required because the resistance of deck joints to closing is much greater than the resistance to opening.

Member stiffness

The PCI Design Handbook recommends calculating equivalent volume-change strains that are reduced to account for creep and microcracking of precast concrete members. Section 3.4.3.1 of the PCI Design Handbook gives the rationale for this reduction: “Since the shorten-ing takes place gradually over a period of time, the effect of the shortening on the shears and moment of the sup-port is lessened because of creep and microcracking of the member and its support.” Specifically, the PCI Design Handbook recommends dividing the calculated strains due to creep and shrinkage by the coefficient Kl when calcu-lating volume-change forces, where Kl is the softening factor for creep and shrinkage effects. (Kl is not to be used

Table 7. Reduction coefficient for movement at deck and spandrel joints

Structure

Average flexibility factor KJ*

Lower level Upper level

Deck joints Spandrel joints Model† Deck joints Spandrel joints Model†

Chicago, Ill. 2.19 1.57 2.06 n.a. n.a. n.a.

Washington, D.C. 1.13 2.78 2.22 -0.10 0.09 0.0

Denver, Colo. 0.22 n.a. 0.25 0.32 n.a. 0.0

Atlanta, Ga. 1.65 0.62 0.48 0.51 -0.08 -0.042

* A negative number indicates that the intermediate joints were closing during cooling cycles.

† See “Finite-Element-Model Analysis.”

Note: n.a. = not applicable.

Figure 10. This graphic of a symmetrical one-story structure illustrates idealized volume-change response, including movement at the intermediate and expansion joints. Note: ∆EJ = expansion-joint movement; ∆IJ = movement at each intermediate joint.

∆EJ ∆IJ /2∆EJ


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this table, most connection types exhibited ductile behav-ior. The displacement at ultimate load generally exceeded 0.1 in. (2.5 mm). Displacements greater than this amount were usually associated with the onset of cracking in the connection region.

For the models, the opening stiffness of the deck connec-tions was taken as the secant stiffness at 0.1 in. (2.5 mm) deformation; that is, the tensile force at an opening of 0.1 in. divided by 0.1 in.. Although the closing stiffness of the deck connections was not tested, it is obvious that these would behave much more rigidly in compression. Ac-cordingly, the closing stiffness was taken as 100 times the opening stiffness.

In a Winter 2009 PCI Journal paper, Naito et al.14 recom-mend a more complex nonlinear stiffness response for seismic analyses—a response model that captures the high initial stiffness and the decline in stiffness after peak load-ing. The bilinear stiffness response described previously was chosen for volume-change analyses because it simpli-fies combining the deck-joint stiffness with the stiffness of the bearings in the simplified two-dimensional models. Of course, the more complex response models can be used for more accurate results, but the response beyond 0.1 in. (2.5 mm) at deck joints is irrelevant for volume-change analyses.

Bearing pads The stiffness of the elastomeric bearings was estimated based on the pad size, thickness, and type. PCI Design Handbook Figure 6.11.1.2 plots resistance to

softening in both the beam and column are not synergistic; that is, the total reduction is not proportional to the square of the fundamental reduction due to creep-related soften-ing. On the contrary, the beam and column behave like springs in a series. If the effective stiffness of both beams and columns is reduced by a factor of 3, the resulting force is reduced by exactly a factor of 3. Accordingly, based on the creep studies by Mattock, Kl should vary between 2 and 3, not 4 and 6 as currently recommended. A Kl value of 2.5 is recommended by the authors and was used for the finite-element models.

For temperature strain, it may be assumed that roughly one-half of the temperature difference used to calculate tem-perature strain occurs seasonally, over a period of approxi-mately three months, while the other half can occur in less than a day. The ACI 318 provides guidelines for estimating long-term creep behavior. Section 9.5.2.5 gives an equation for estimating the additional long-term deflection result-ing from creep and shrinkage of flexural members, which depends on the duration of load and compression reinforce-ment ratio. Using the ACI 318 equation, the corresponding Kt is about 1.5, as currently recommended by PCI.

Connection stiffness

Deck connections Estimates of deck-connection stiffness were taken from research conducted at Lehigh University on development of a seismic design methodol-ogy for precast concrete diaphragms.13 Table 8 shows a summary of capacity and stiffness properties. As shown in

Table 8. Tensile capacity and stiffness of diaphragm connections

Connection type Topped

Yield, ~75% of ultimate Ultimate Stiffness, kip/in.

Capacity, kip ∆, in. Capacity, kip ∆, in. InitialSecant stiff-ness at 0.1

in. ∆*

A: JVI Vector connector No 5.7 0.065 9.7 1.26 88 58

B: Chord connector No 28.0 0.042 36.4 0.32 667 297

C: Hairpin connector No 2.6 0.092 3.8 0.26 245 27

D: Hairpin connector Yes 15.8 0.014 25.0 0.05 1129 †

E: Cover-plate connector Yes 36.6 0.020 43.4 0.15 1828 408

F: Pour-strip connector Yes 46.7 0.031 62.3 0.14 1507 569

G: WWR topping Yes 19.4 0.035 24.86 0.08 555 †

Source: Data from Naito, Peter, and Cao 2006.

* Connections with a secant stiffness of less than 150 kip/in. are classified as flexible; rigid connections are those with a secant stiffness exceeding 150 kip/in.

† Peak load reached before 0.1 in. displacement.

Note: WWR = welded-wire reinforcement; ∆ = displacement. 1 in. = 25.4 mm; 1 kip = 4.448 kN; 1 kip/in. = 0.175 kN/mm.


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ing of the baseplate. Similar to the deck connections, a deformation (liftoff of the baseplate) of 0.1 in. (2.5 mm) was assumed in calculating the secant stiffness. According to LaFraugh during a conversation in October 2008, there was no unusual distress at rotations of this magnitude. Note that this procedure gives a lower stiffness than the initial stiffness predicted by the PCI Design Handbook method, but the lower stiffness is appropriate for calculat-ing the volume-change forces.

The procedure explained in PCI Design Handbook section 3.6.1 was used to estimate the stiffness of the footing on the soil. This combined flexural stiffness of the base-plate connection and footing/soil interface was calculated as the inverse of the combined flexibility of each element.

Analysis results

Table 9 compares the results of the rigid models with those employing flexible connections. Note that small move-ments at flexible connections substantially reduce volume-change forces. For the models with flexible connections, the shear force at the exterior columns is reduced 74% to 99% compared with the models with rigid connections.

Figure 11 compares the deformation of the Washington structure with completely rigid (top model) and flexible connections (lower model). Even though some of the con-nections in the Washington structure are relatively stiff, movement at intermediate joints drastically changes the deformation pattern, as well as the volume-change forces. The rigid joints in the top model impose equal overall shortening of both levels and relatively sharp column curvature. In the lower model, the column is more gently curved because the overall shortening in the lower level is less than that at the upper level.

horizontal movement versus compressive stress for vari-ous pad materials (on concrete or steel bearing surfaces), assuming 70% shear and slippage strain. For example, the PCI figure indicates a shear resistance of about 220 psi (1500 kPa) of contact surface for a cotton duck pad bear-ing on concrete under a dead-load stress of 1000 psi (7000 kPa). The pad stiffness (pounds per inch of lateral move-ment) was calculated as the shear resistance (according to PCI Design Handbook Figure 6.11.1.2) times the pad area divided by 70% of the pad thickness.

Combined stiffness of the deck connectors and bearing pads As noted previously, a single non-linear link element was employed at each spandrel-beam-to-column connection to simulate the performance of double-tee and spandrel-beam connections. To do so, the opening stiffnesses of individual connections were com-bined according to the behavior of springs in parallel and in series. That is, the stiffness of the combined spring was taken as the stiffness of individual springs multiplied by the number of springs in parallel and divided by the number of springs in a series.

Flexural stiffness at column base The current PCI Design Handbook procedures for estimating the stiff-ness of column baseplate connections is based on work by LaFraugh and Magura.15 LaFraugh and Magura found that the initial stiffness of the baseplate connection depends on the stiffness of the anchor bolts and the baseplate itself. They tested a variety of column base details under increas-ing load at constant eccentricity. The current PCI Design Handbook procedure is based on LaFraugh and Magura’s test results and recommendations.

The flexural stiffness of the column baseplate connections was calculated as the secant stiffness after flexural yield-

Table 9. Volume-change-analysis summary

StructureStiffness of spandrel/

column connection

Movement at exterior column, in.

Average movement at spandrel joints, in. Maximum

column base rotation, %

Forces in exterior column

Lower level Upper level Lower levelUpper level

Shear, kipBending,

ft-kip

Chicago, Ill.Case 1: rigid 0.55 n.a. 0 n.a. 0.0 577 1612

Case 2: 133 kip/in. 0.16 n.a. 0.06 n.a. 0.06 6 17

Washington, D.C.

Case 1: rigid 0.34 0.53 0 n.a. 0.16 505 2949

Case 2: 830 kip/in. 0.15 0.51 0.10 -0.0003 0.09 52 517

Denver, Colo.Case 1: rigid 0.64 0.67 0 0 0.0 60 391

Case 2: 1520 kip/in. 0.50 0.64 0.02 -0.0001 0.36 16 92

Atlanta, Ga.Case 1: rigid 0.62 0.72 0 0 0.13 105 766

Case 2: 3070 kip/in. 0.53 0.74 0.04 -0.0036 0.36 27 212

Note: n.a. = not applicable. 1 in. = 25.4 mm; 1 kip = 4.448 kN; 1 ft-kip = 1.356 kN-m.


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the authors estimated the COV based on engineering ex-perience. As recommended in the following example, the specified mean and the values in the PCI Design Hand-book should be adjusted for these factors. The flexibility factor KJ is not considered in this example.

The bias and variation of the volume-change force were calculated using Monte Carlo simulations and using the statistical parameters shown in Table 10. The resulting bias and COV are also shown in the table. The bias of 0.68 indicates that PCI Design Handbook procedures underes-timate the potential volume-change force by 32% without considering flexible connections.

This difference is primarily attributable to the bias in two variables: the softening factor for creep loading Kl and a temperature change that is less than would be expected for the life of the structure. The overall bias would be even worse except that the assumed coefficient of thermal ex-pansion was chosen closer to an average value rather than the PCI Design Handbook’s recommended value. Figure 13 shows the probability distribution of the calculated force due to volume change using PCI Design Handbook procedures for this example.

For this example, if rigid connections were employed and current practices were followed (including a load factor of 1.2 on volume-change effects), the probability that the volume-change force will exceed the factored design load is roughly 50%. In well-designed precast concrete build-ings, the connections between precast concrete elements yield before the volume-change movement can cause seri-ous damage. Even where rigid connections are used, past experience indicates that cracking generally alleviates the volume-change force before global safety of the structure is threatened.

The flexible-connection model indicates that the intermedi-ate joints at the upper level actually close slightly during cooling cycles. The difference in column shear and bend-ing forces is dramatic. In Table 9, note the substantial de-crease in volume-change forces due to small movements at intermediate joints. Rotations at column base connections also help to reduce forces in the flexible models, especially for the one-story Chicago structure.

As can be seen in Fig. 11, small movements at intermediate connections allow for a gentle transition of volume-change response from the ground to the upper level, whereas rigid connections impose equal shortening at all levels.

Predictability of volume-change forces

Consider the simple structure shown in Fig. 12. Creep, shrinkage, and thermal shortening induce footing rotation, shear, and bending forces in the supporting columns as well as a horizontal force at the column-to-beam connec-tion.

In U.S. practice, the volume-change and gravity-load effects are added together as forces in a factored load combination. According to ASCE/SEI 7, the load fac-tor on volume-change effects is 1.2. However, even for the simplest structures, such as the frame shown in Fig. 12, the magnitude of the volume-change forces depends on numerous factors. All of these factors can vary, some significantly.

Table 10 lists the primary factors influencing volume-change forces and provides an estimate of their bias (the specified mean divided by the true mean) and coefficient of variation (COV). Where COV data were not available,

Figure 11. These two-dimensional models of the Washington, D.C., structure illustrate the influence on flexible connections on the deformation pattern. The intermediate joints in the top model have no flexibility, whereas the bottom model has flexible intermediate joints, which dramatically reduce curvature of the exterior columns.


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Summary of findings and recommendations

The following findings and recommendations are based on the research work described in this paper.

Findings

Thermal expansion coefficient.• The coefficient of thermal expansion varies significantly with aggregate type. For some concrete, especially that produced with limestone aggregate, a thermal expansion coefficient significantly less than the commonly accepted value of 6 microstrains/°F (10.8 microstrains/°C) can be re-liably used, provided that the coefficient is determined

In U.S. practice, the load factors for dead, live, and wind loads are based on the bias and COV. Assuming that the variability from this single example is typical, a much higher load factor on volume-change forces is warranted. Considering the bias in current PCI Design Handbook procedures, a load factor of 2.0 on volume-change effects would result in a probability of exceeding the factored load comparable with that for other loads. If the current proce-dures are adjusted to remove the bias, the comparable load factor could be reduced to 1.6.

In the ASCE/SEI 7 load combinations, volume-change effects are included with dead load as part of the basic dead-plus-live-load combination. The inclusion of volume-change effects in this basic load combination technically requires that temperature- and shrinkage-induced forces be included for the design of every concrete building frame. However, like wind load, maximum volume-change effects occur during an extreme weather event.

In ASCE/SEI 7, extreme wind load is considered in com-bination with a point-in-time live load. A similar approach for volume-change effects would be appropriate. At the time of writing, the ASCE/SEI committee on design loads is reconsidering load combinations that include volume-change effects.

It should be reemphasized that the limited study described previously was undertaken to get a general sense of the inherent variability of volume-change force. It was not the purpose of this study to make broad recommendations on volume-change load factors. In any case, the factored volume-change force should only be used for determining the required strength of nonductile elements in the volume-change load path—strengthening ductile elements for volume-change movement is unnecessary and counterpro-ductive, though serviceability should be evaluated.

Figure 12. This figure illustrates the response of a simple single-span structure to volume-change shortening.

Table 10. Key variables influencing volume-change force

Variables Bias COV

Dimensions 1.00 0.07

Temperature difference* 0.72 0.15

Ks 0.99 0.11

Coefficient of thermal expansion* 1.22 0.27

Creep and shrinkage strains/age at erection 1.00 0.25

Column fixity 1.00 0.13

Concrete MOE 1.10 0.14

Kl* 1.92 0.20

Kt 1.00 0.20

Volume-change force from Monte Carlo simulation 0.68 0.31

* A substantial difference exists between the specified mean according to the current PCI Design Handbook and the true mean.

Note: COV = coefficient of variation; Kl = softening factor for creep and shrinkage effects; Ks = coefficient that accounts for the lag between weather-station temperature and structure temperature; Kt = softening factor for temperature effects; MOE = modulus of elasticity.


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volume-change movement and force at the lowest supported level, where volume-change forces are most significant. Rotation at flexible column-base con-nections also helps reduce volume-change force. For the structures analyzed in this study, the reduction in shear force at exterior columns due to movement at flexible connections ranged from 74% to 99%.

Load factor for volume-change effects• . Prediction of volume-change force is inherently inaccurate due to the underlying variability in volume-change strain and structure response. Monte Carlo simulation of the possible range of the volume-change force in a sample structure suggests that the current ASCE/SEI 7 load factor of 1.2 is much too low to account for this inherent variability. However, the factored load should only be used for determining the required strength of nonductile elements in the volume-change load path. Strengthening ductile elements for volume-change movement is unnecessary and counterproductive, though serviceability should be evaluated. Furthermore, building codes should evaluate inclusion of volume-change effects in the dead-plus-live-load combination.

Design recommendations

For typical structures, a qualitative approach to vol-•ume-change design is recommended in lieu of explicit calculation of volume-change forces. Designers may rely on successful past practices, employing compliant members and flexible connections that accommodate volume-change movement while providing the needed resistance to gravity and lateral loads.

by laboratory testing of specimens produced using the project mixture proportions.

Design temperature range• . The temperature-range values provided in the PCI Design Handbook are based on outdoor temperatures that are much warmer than the expected 50-year low. However, the ambient temperatures in the lower levels of parking structures lag the extreme cold temperatures measured by the National Weather Service. Design temperature ranges that account for these offsetting effects are recom-mended.

Creep and shrinkage effects• . Measurable creep and shrinkage strains were observed during the course of the two- to three-year monitoring period. Although the variability of the limited measurements precludes quantitative evaluation, the observed long-term move-ments were reasonably consistent with creep and shrinkage predictions of the PCI Design Handbook. Regardless, temperature change dominates volume-change behavior of exposed precast concrete build-ings. By comparison, creep and shrinkage effects are much less significant.

Member softening due to creep and• microcracking. The PCI Design Handbook recommends dividing the calculated strains due to creep and shrinkage by a Kl value from 4 to 6. A more realistic value for Kl is 2.5.

Flexible connections• . Deformations of flexible double-tee and spandrel connections substantially change the deformation pattern and thereby reduce

Figure 13. This figure illustrates the wide probability distribution of volume-change force based on the Monte Carlo simulation of the controlling parameters. The mean force value is 13.4 kip. Note: 1 kip = 4.448 kN.

12,000

9000

6000

3000

00 10

Force, kip

20 30 40 50


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References

American Concrete Institute (ACI) Committee 362. 1. 2002. Guide for the Design of Durable Parking Struc-tures (ACI 362-97). Farmington Hills, MI: ACI.

ACI Committee 318. 2008. 2. Building Code Require-ments for Reinforced Concrete (ACI 318-08) and Commentary (ACI 318R-08). Farmington Hills, MI: ACI.

PCI Industry Handbook Committee. 2004. 3. PCI Design Handbook: Precast and Prestressed Concrete. MNL-120. 6th ed. Chicago, IL: PCI.

PCI Committee on Design Handbook. 1977. Volume 4. Changes in Precast Prestressed Concrete Structures. PCI Journal, V. 22, No. 5 (September–October): pp. 38–53.

Philleo, R. E. 1971. Designing for Effects of Creep 5. and Shrinkage Temperature in Concrete Structures. In Summary of Symposium on Designing for Effects of Creep, Shrinkage, and Temperature. SP-27, V. 27, pp. 247–256. Detroit, MI: ACI

Structural Engineering Institute (SEI) of the American 6. Society of Civil Engineers (ASCE). 2006. Minimum Design Loads for Buildings and Other Structures. ASCE/SEI 7-05. Reston, VA: ASCE.

Iqbal, M. 2007. Thermal Movements in Parking Struc-7. tures. ACI Structural Journal, V. 104, No. 5 (Septem-ber): pp. 542–548.

Klein, G. J., and R. E. Lindenberg. 2009. Volume 8. Change Movement and Forces in Precast Concrete Buildings. Research report, PCI, Chicago, IL.

Roeder, Charles W. 2003. Proposed Design Method 9. for Thermal Bridge Movements. Journal of Bridge Engineering, V. 8, No. 1 (January–February): pp. 12–19.

Brown, R. D. 1972. Thermal Movement of Concrete. 10. Journal of the Concrete Society, V. 6, No. 11 (November): pp. 51–53.

ACI Committee 209. 2008. 11. Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures. ACI 209R-92. Farmington Hills, MI: ACI.

Mattock, A. H. 1961. Precast-Prestressed Concrete 12. Bridges 5. Creep and Shrinkage Studies. Journal of the PCA Research and Development Laboratories, V. 3, No. 2 (May): pp. 32–66.

Quantitative assessment of the volume-change force •is appropriate only in special cases, such as structures that have dimensions or details beyond the limits of successful past practices. PCI Design Handbook pro-cedures may be used to estimate volume-change forces with modifications to account for the findings as described previously. However, the quantitative results should be viewed with a high degree of circumspec-tion, given the uncertainty and variability inherent in prediction of a volume-change response.

PCI Design Handbook• procedures may also be used to estimate volume-change movement for expansion-joint design, with applicable modifications to account for the listed findings. The expected movement at intermediate joints should also be considered in their design.

Acknowledgments

Funding for the research project was provided by the PCI Research and Development Committee, with additional contribution by Wiss, Janney, Elstner Associates Inc. The research effort was guided by an advisory committee com-prising precast concrete experts Helm Wilden of Wilden Enterprises Inc., Tom D’Arcy of The Consulting Engineers Group; Anant Dabholkar of Neilsoft Inc., Harry Gleich of Metromont Corp., Jim Sirko of Sirko Associates Inc., Doug Sutton of Purdue University, and A. Fattah Shaikh of the University of Wisconsin–Milwaukee. The support of PCI and Wiss, Janney, Elstner Associates Inc. is gratefully acknowledged. Likewise, the guidance provided by the advisory committee was instrumental to the success and relevance of this research.

Access to the structures was arranged through the follow-ing contractors and precast concrete producers, respec-tively:

Chicago: Castle Construction Corp. and Dukane •Precast

Denver: Saunders Construction Inc. and Stresscon •Corp.

Washington: Donley’s Inc. and Tindall Corp.•

Atlanta: Holden Construction Co. and Metromont •Corp.

This research would not have been possible without their cooperation.


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Naito, Clay, Wesley Peter, and Liling Cao. 2006. De-13. velopment of a Seismic Design Methodology for Pre-cast Diaphragms–Phase 1 Summary Report. Research report, PCI and National Science Foundation.

Naito, C., L. Cao, and W. Peter. 2009. Precast Con-14. crete Double-Tee Connections, Part 1: Tension Behav-ior. PCI Journal, V. 54, No. 1 (January–February): pp. 49–66.

LaFraugh, R. W., and D. D. Magura. 1966. Connec-15. tions in Pre-Cast Concrete Structures - Column Base Plates. PCI Journal, V. 11, No. 6 (November–Decem-ber): pp. 18–39.

Notation

COV = coefficient of variation

K = factors that account for creep and microcracking of precast concrete members when estimating equiva-lent volume-change strains

KJ = joint flexibility factor, which indicates the relative flexibility of the intermediate joints

Kl = softening factor for creep and shrinkage effects

Ks = coefficient that accounts for the lag between weather-station temperature and structure tempera-ture

Kt = softening factor for temperature effects

Tm = mean temperature during construction season

Ts = structure temperature

Tws = weather-station temperature

∆ = displacement

∆EJ = expansion-joint movement

∆IJ = movement at each intermediate joint

∆TS = total shortening of the structure


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About the authors

Gary Klein, S.E., is a senior principal with Wiss, Janney, Elstner Associates Inc. in Northbrook, Ill. He is a member of American Concrete Institute building code committee (ACI 318) and specializes in structural investigations and research.

Richard Lindenberg, S.E., is a senior associate with Wiss, Janney, Elstner Associates Inc. He specializes in structural monitoring and the correlation to analytical models.

Synopsis

This paper summarizes the findings of the authors’ recent study on the volume-change response of precast concrete buildings. The objective of this research was twofold: to develop a better understanding of volume-change movement and forces based on measured performance of precast concrete parking structures and calibration to analytical models and to recommend re-vised design procedures that reflect this understanding and account for the influence of flexible connections. The primary research tasks included field monitoring and finite-element analyses of actual structures as well as evaluation of the predictability of volume-change forces.

The research revealed that deformations of flexible deck and spandrel connections change the deforma-tion pattern and thereby substantially reduce volume-change movement and force at the lowest supported

level, where volume-change forces are most signifi-cant. The study also developed new findings with respect to other volume-change parameters, including the thermal-expansion coefficient, the design tem-perature range, the degree of member softening due to creep and microcracking, and the load factor for volume-change effects.

Design recommendations are provided for qualita-tive consideration of volume-change effects as well as quantitative analysis. Although the new research indicates that the procedures recommended in the PCI Design Handbook: Precast and Prestressed Concrete result in a conservative estimate of volume-change force, certain aspects of the PCI Design Handbook procedures were found to be unconservative. There-fore, the research findings should be considered in their entirety. The full research report is available from PCI.

Keywords

Coefficient of thermal expansion, connector, creep, double-tee, field testing, flange connector, load fac-tor, parking structure, shrinkage-flexible connection, temperature, volume change.

Review policy

This paper was reviewed in accordance with the Precast/Prestressed Concrete Institute’s peer-review process.

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