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Diaphragm Behavior of Floor Systems and hs Effect.

on Seismic Building Respons

AN EXPERIMENTAL STUDY OF THE IN-PLANE CHARARCTERISTICS

OF WAFFLE SLAB PANELS

"~~rrz ENGINEERING JWUl0RATORY LIBRARY

Sponsored by National Science Foundation CEE-8120589

by Xuerun Ji Ti Huang Le-Wu Lu

Sheng-Jin Chen

August 1985

Fritz Engineering Laboratory Report. 481.3

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Table of Contents

1. Introduction

2. Design and Fabrication of the Specimens

3. Mechancial Properties of Materials

3.1. Reinforcing Bars 3.2. Concrete

4. Testing Facilities

4.1. Loading systems 4.2. Instrumentation and recording of data

5. Testing of Specimens

5.1. Testing sequence 5.2. Stiffness test 5.3. Strength test 5.4. In-Plane Vibration Tests

6. Test Results

6.1. Stiffness Tests 6.2. Behavior Under Gravity Load 6.3. Results of Strength Tests--- General Description 6.4. Results of Individual Strength Tests.

6.4.1. WH1MN (Figs. 6.8, 6.17, 6.18) 6.4.2. WH2CY (Figs. 6.9, 6.10, 6.19, 6.20) 6.4.3. WH5MN (Figs. 6.11, 6.21, 6.22) 6.4.4. WV2MN (Figs. 6.12, 6.23, 6.24) 6.4.5. WV1CY (Figs. 6.13, 6.14, 6.25, 6.26) 6.4.6. FH5MN (Figs. 6.1.5, 6.27, 6.28)

7. Comparison and Discussion

7.1. Stiffness and Flexibility 7 .2. Behavior Under Service Vertical Load 7.3. Behavior Under In-Plane Load

7.3.1. General Description 7.3.2. Effect of Nature of In-plane Loading 7.3.3. Effect of Vertical Load 7.3.4. Effect of Shear Span 7.3.5. Effect of Reinforcement

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6 7

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8 9

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11 12 12 15

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17 18 19 20 20 22 23 24 26 27

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29 30 31 31 33 34 35 37

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7.4. Frequencies of In-plane Free Vibration

8. Conclusion and Recommendations

9. Reference

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Chapter 1

Introduction

The pnmary function of floor systems in a building structure IS to carry vertical

loads by their out-of-plane bending action and to transmit these loads to the supporting

members such as walls or columns. They also combine with these supporting members

to forrn vertical frames which resist. the lateral load, again ultilizing the out-of-plane

bending action of the floor systems. Both of these actions are taken into consideration in

the traditional design of the building structures. Recently, structural engmeers have

recognized another important function of the floor system. Under lateral loads, the floor

systems must act as diaphragms between parallel vertical systems, transmitting and

distributing these horizontal loads. Here the performance of the floor system is controlled

by its in-plane stiffness and strength. Furthermore as the lateral loads on building

structures are usually dynamic in nature (wind or seismic), the dynamic properties of the

slab systems also exert very significant influence.

The in-plane characteristics of two common reinforced concrete floor systems had

been studied in detail at. the Fritz Engineering Laboratory of Lehigh University from

1977 to 1981. The systems studied were the flat plate and the slab-on-edge-beams .

Results of these studies have been presented in several reports.(5,6,7,8,9,10)

In this report is described the experimental investigation of waffle slab floor

system, and additional studies on the flat plate system. The work was carried out

under a NSF grant entitled "Disphragm Behavior of Floor Systems and Its Effect on

Seismic Building Response." {Grant no. CEE-8120589) The experimental work was

conducted at Lehigh University from .luly, 1982 t,o February, 1983.

The waffle slab floor system has important economical advantage over the flat

plate, flat slab, or slab-on-edge-beam systems. The standardized dome forming and the

reduced weight make this system particularly suitable for structures intended for

moderate floor load. In addition, the waffle slab system also represents an extreme

condition with regard to the presence of intermediate beams. Therefore, combined with

the flate plate and the slab-on-edge-beam floor systems, the three systems studied

covered the entire range of rib-stiffening of slabs.

The basic test specimen chosen for the experimental study represented an interior

panel of a prototype building. Two spec1mens, each containing three consecutive slab

panels, were fabricated. Testing was done on each slab panel separately. Fig. 1.1 shows

the dimensions and supproting condition of specimens as well as the testing setup. All of

these characteristics were common to the tests of the three systems.

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Chapter 2

Design and Fabrication of the Specimens

The prototype floor slab for this study was taken to be a part of a rectangular

multi-story, multi-bay reinforced concrete building structure of medium- to high-rise.

Resistance to lateral loading was taken to be provided primarily by shear walls. General

dimensions of t.he structure were identical to those used previously in the study of other

concrete floor systems. The columns were 24 in. (610 mm) square, and spaced 24ft

(7.32m) center to center in both directions. The floor height was 12 ft (3.66m) center to

center of slabs. The service live gravity load was 80 psf (3.83 kPa). Following the

previous study, a scale ratio of 4.5 to 1 was used for the specimens, resulting in a panel

size of 64 in. (1.63m), and a column size of 5.33in. (135mm)

In order to be compatible with the gravity load distribution system developed

previously, the dome module for the waffle speCimen was chosen to be one-sixth of the

panel dimension, or 10.67in. (27lmm). This corresponded to a prototype dome module of

48 in. (1.22m), which was larger than the most common commercial sizes of 24 or 36

inches (0.61 or 0.91 m) .

Design of the test specimens were made by the direct design method of the ACI

Building Code, 1977 ( 1 ). The design was based on gravity load consideration using a

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concrete strength of 4,000 psi(27.6MPa), and a steel yield strength of 60,000 ps1

( 41 4MPa). Dimensions were in tially determined for the prototype structure, then reduced

to the specimen by applying the 4.5 to 1 scale factor. This procedure resulted m a 2 2

spec1men top plate thickness of 2/3 in .. (17mm), and rib stem size of 13in. x 23in.

(42mm x 68mm). These dimensions correspond to prototype values of 3in., 7.5in., and

12in. (76mrn, 191mm, and 305 mm), respectively. Figures 2.1 and 2.2 shows the detailed

dimensions of the waffle slab specimen.

The reinforcement arrangements were determined for the speCimens directly, with

no attempt to model the prototype structure reinforcing bars. This was necessary on

account of the very limited choice of available small-sized reinforcing elements.

Reinforcement in the specimen was chosen to satisfy the required tensile force at the

various critical sections. Table 2.1 a lists the critical design moments, the required

amounts of reinforcement, and the provided reinforcements.

As stat.ed earlier, two spec1mens were fabricated and tested. Each contained three

consecutive square panels. They were supported on two interior shear walls and four

columns. Quarter-panel extensions were provided all around beyond the column lines, m

order to provide continuity and anchorage for reinforcing bars.

The middle panel of one spec1men (designated as WS-2) was a flat plate panel

similar to the spec1men tested previously. Its thickness was 2.22 in. (56mm), same as the ..

prevwus specimen. However, the reinforcement arrangement was changed. Cutoff points

for negative reinforcement were extended from 1/4 panel to 1/3 panel distance. This was

done to examine the effect of reinforcing bar details on the behavior of the flat plat

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panel. Table 2.1 b lists t,he reinforcement. used in this panel, as well as a comparison

with the previous design. Figure 2.3 shows the arrangement of reinforcement for the

waffle slab as well as t,he flat plat,e panels.

The two spec1mens were fabricated simultaneously in the Fritz Engineering

Laboratory of Lehigh University. To form the waffle domes in the specimens, special

plastic molds were used. These box forms were made of 0.1 inch (2.5mm) thick material,

heat-formed to the desired shape with the ribs having tapered sides at a gradient of 1:8

(same as the commercial dome molds). These molds provided to be very successful in

forming the waffle panels, as can be seen from several photographs (Figs. 4.2, 4.4).

Fig.2.4 shows the details of the formwork .

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Chapter 3

Mechancial Properties of Materials

3 .1. Reinforcing Bars

Special small-sized deformed w1res (Dl, D2, D2.5) and standard No. 3 deformed

bars were used for reinforcement. in the specimens. The D2.5 wires and one lot of D2

Wires showed no clearcut. yield plateau when initially received. These were annealed in

order to achieve a clearcut yield point. The Dl wires and an older suply of D2 wires

(designated D02) behaved satisfactorily in a typical elastic-yield fashion, and were used

without. further treatment. The No. 3 deformed bars were used only in shear walls and

columns.

The mechanical properties of these w1res and bars were determined by standard

tension tests. Table 3.1 lists the average results from three tests. Fig. 3.1 shows the

typical stress-strain curves of the annealed deformed w1res, D2 and D2.5, used in the

waffle slab specimens.

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3.2. Concrete

The concrete m1x was designed for a 28 days compressive strength of 4,000 ps1

(27.6 MPa). The maximum size of aggregate was limited t.o 1/4 111. (6.4mm) in order to

maintain t.he approximately 3:1 ratio of slab thickness to s1ze of aggregate. Table 3.2

lists the detail of concrete m1x and table 3.3 lists the gradation of the coarse aggregate.

Plasticizer was used to facilitate the concrete placement m the narrow ribs.

Two batches of concrete were used in each floor slab speCimen. Eighteen 6in. x

12in. ( 1 52mm x 305mm) standard cylinders and twenty 3in. x 6in. (76mm x 152mm)

smaller cylinders were made from each batch. These were cured together with the

respective specimens under moist burlap at room temperature for 28 days. Nine of the

smaller cylinders for each batch were tested for compressive strength at the age of seven

days. Nine more small cylinders and twelve larger ones were tested at 28 days for

modulus of elasticity, Poisson's ratio, compressive strength and split tensile strength. The

remaining cylinders were tested for compressive strength, modulus of elasticity and the

Poisson ~s ratio after the completion of the correspondi.ng specimen test. Tabel 3.4 lists

the mechanical properties of concrete. Fig.3.2 shows a typical stress-strain curve of the

concrete cylinder. Fig.3.3 shows the typical stress-Poisson's ratio relationship.

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4.1. Loading systems

Chapter 4

Testing Facilities

The same test setup used in the previous study was used for this research. The

floor system specimen was supported on four reinforced concrete pedestals which were

tightly anchored to the laboratory test floor (Figs.l.l and 4.1). During the test, the

columns were supported against vertical movement only, and were allowed to rotate and

slide freely. The shear wall was either fixed to the pedestal, or allowed to slide freely,

according to the desired boundary conditions. Details of the flexibility of the supporting

conditions were given in several previous reports. (5,8,9,10) (Figs.4.2 to 4.4)

The in-plane load was applied by a double-acting mechanical jack. To simulate the

desired uniformly distributed shear force, two horizontal steel frames and five embedded

studs were used. The frames and studs were carefully designed so that each stud would

transmit approximately one-fifth of the total horizontal load to the center plane of slab.

The total applied horizontal load was measured by a loadcell located between the jack

and the frames ( Fig.4.5) .

During the stiffness tests, in-plane loads were applied at two points simultaneously.

As only one mechanical jack was available, the second load was provided with a

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turnbuckle, which was capable of delivering only a tensile force. In these stiffness tests,

loads were applied to the middle studs only, not distributed as in the strength tests.

(Fig. 5.1)

The uniform out-of-plane (vert,ical) loading was simulated by a senes of

concentrated loads acting at the centers of each ninth portion of the slab panel. As

pointed out earlier, the s1ze of the specimen waffle dome was seleted so that these point

loads would occur at the intersections of ribs. This was necessary to assure firm

anchorage of the metal insert loading devices. All loads within one panel width,

including those in the quarter panel extensions, were controlled by a single hydraulic

jack. A senes of statically determinate levers was used to distribute the jack load

equally among the fifteen load points. The other end of the hydraulic jack was

connected to a gravity load simulator which permitted substantial horizontal

displacement of' the specimen without affecting either the direction or the magnitude of

the applied vertical load (Figs.4.6 and 4.7).

For the quarter panels at the extreme ends of the three-panel spec1men, the out-of­

plane loading was supplied by heavy metal cylinders. Again, a series of levers was used

to deliver equal loads to the five load points in this strip (Figs.4.6 and 4.8).

4.2. lnstrun1entation and recording of data

Loads, displacements and strains were measured and recorded throughout the tests.

All loads (in-plane load and vertical load) applied to the specimens were monitored

by calibrated loadcells mounted at (or near) the source of loading (Figs. 4.5a, 4.7 and

4.8).

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In-plane displacements of the slab panel under test. were measured by Linear

Variable Differential Transformers (LVDT's), with m1mmum reading of 0.0001

in.(0.0025mm). The vertical deflection at vanous locations were measured by dial gages

having mm!Tnum graduations of 0.0001 in.(0.0025mm). All dial gages were attached to

a triangular frame, with three legs resting on the top of two columns and the middle

point of the shear wall. Thus the dial gage readings were not affected by any movement

of the column and wall supports (Fig. 4.9).

Strains m concrete and reinforcing bars were measured by electrical strain gages

and rosettes. The deformed w1res were filed to a smooth surface for the attachment of

the strain gages during fabrication.

Fig.4.1 0 shows the typical arrangement of strain gages, rosette gages, L VDT's and

dial gages for the strength test of an end panel. The instrumentation plans for specific

panels are given in the Appendix.

All L VDT's and strain gages were connected to a B&F data-aquisition unit, which

produced a print.ed record as well as a punched paper tape for each load step. The

LVDT 13 (Fig. 4.10) measuring the main displacement at the "free" edge of the test.

panel, was also connected to an X- Y plotter, as was the loadcell measuring the in-plane

load. A continuous and complete record was thus obtained for the load-displacement

relationship. Such a continuous record was very useful during the cyclic load tests.

A uniform s1gn convention for all loads and displacements was adopted. The

positive transverse (X) and longitudinal (Y) directions are indicated Ill Fig. 2.1.

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Chapter 5

Testing of Specimens

5.1. Testing sequence

A number of tests were carried out on each of the two floor slab speomens. The

sequence of the tests in each case was carefully designed to maxmize information that

could be obtained, and minimize the time and effort required to rearrange the supporting

and loading devices. Figs.5.1 and 5.2 show schematically the tests in each series and the

sequence of testing. Each test was identified by a five character alphanumerical

designation. Table 5.1 g1ves a complete description of these designations.

Before each test, the speomen was preloaded to about 10 percent of the estimated

ultimate load, and then unloaded. The purpose for this operation was to ensure that all

instruments worked properly and to stabilize the loading systems.

Application of loading was carried out, in multiple steps. Before the cracking of

concrete, the specimen showed essentially linear behavior, and the loading steps were

controlled by preselected loading increments. After cracking, and particularly after the

first. yielding of reinforcing bars, the specimen deformed much more rapidly, and the

loading was controlled by specified increments of the main displacement (LVDT 3). A

limit. of 0.1 in. (2.5mm) main displacement per loading step was imposed in all tests.

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Such a loading scheme permitted accurat.(> determination of both the ultimate resistance

and the maximum deflection of the test panel. These information are very important for

the evaluation of ductility.

5. 2. Stiffness test

Specimen WS-1 containing three waffle slab panels was initially tested for its

overall stiffness under symmetrical and anti-symmetrical in-plane loads (Fig.5.1). For

thesf' tests, only four of the 24 anchor bolts for each shear wall were tightened on the

pedestal (Fig.5.3). Under this condition, each shear wall was essentially free to rotate

about its central vertical ax1s. All columns were supported in the free-to-slide condition.

Each of the applied in-plane loads was limited to 2.5 kips (11.1 kN), corresponding to

approximately one eighth of the estimated ultimate strength of the structure. This low

load limit was chosen to maintain linear elastic structural response. The in-plane stiffness

characteristics of the slab system were determined from displacements and rotations

measured by L VDT's arranged as shown in Fig~ 5.3.

5.3. Strength test

In the strength tests, one of the shear walls was firmly attached to the pedestal

with 24 anchor bolts (Fig. 4.2) and two pairs of strong braces, while the other shear

wall and all columns were supported in the free-to-slide condition. In this manner, the

speCimen was structurally separated at the fixed shear wall, and each panel was tested

separately.

The in-plane load was applied along the column line parallel to the shear wall and

through the horizontal load distribution frame. In monotonic loading tests, the in-plane

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load was increased continuously until the ultimate resistance of the test panel was

reached. At the begining of each test, loading was increased in 2-kip (8.9kN) steps. This

was continued until the increment in ma.m displacement (L VDT 3) during one loading

step reached 0.1 in. (2.5 mrn). Afterwards loading was controlled by main displacement

increments of 0.1 in. (2.5rnm) for each step. After reaching the ultimate resistance, the

spec1men was unloaded and then reloaded in the opposite direction until the ultimate

resistance was again reached. The load was released again, and the test was completed.

In cyclic loading tests, the in-plane load was varied according to a. predetermined

loading spectrum. The load was applied in complete cycles with gradually increasing

load or displacement amplitudes. Three complete loading cycles were applied at each

amplitude. Initially, the loading cycles were controlled by load, with amplitude

increments of 4 kips (17.8kN). At later stages, loading was controlled by displacement a.t

the column line (LVDT 3) (Fig. 4.10). Figs. 5.4a and 5.4b show the loading spectrum

applied to the test WH2CY and WV 1 CY respectively.

For the tests including out-of-plane loading, the speCimen was first loaded vertically

to simulate full service dead and live loading condition, before the application of the in­

plane load. It was noted that the weight of the spec1men and the vertical loading

system was 26.7 psf (1.28kPa) which was far less than the weight of the prototype

structure. Therefore, the applied vertical loading included a compensatory dead load of

57.7 psf (2.76 kPa) in addition to the service live load of 80 psf (3.83 kPa). The load

required at each insert point was 435 lbs (1.94 kN). The required total load for a.n

interior panel (15 loading points) was 6530 lbs. (29.0 kN) and that for the end extension

(5 loading points) was 2180 lbs (9.7 kN). The load actually achieved were slightly

higher, being 6550 lbs (29.1kN) and 2200 lbs (9.8kN), respectively.

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For both specimens, the middle panels (panel 3) were tested under in-plane

monotonical load with a moment-shear ratio (M/Q) of 128 in. (3.25m). This was

accomplished by fixing the shear wall between panels 3 and 1, and loading along the

column line in panel 2, as shown in Fig. 5.1.5 and 5.2. 7. The role of panel 2 here was

merely to transmit the shear and moment to the middle panel. The characteristics of

panel 3, which were the goals of this test, would not be affected by the behavior of

panel 2. It was therefore immaterial that a severely damaged panel 2, having been tested

to failure previously, was being used. 1t. was only necessary to ensure that the strength

of panel 3 could be reached. Four steel plates were glued on the top surface of the

damaged panel 2 across the major cracked regiOn. (Fig.5.5) Such a crude repair

obviously did not restore the strength, nor the stiffness, of panel 2. However, as long as

a failure of panel 3 was achieved, there was no distoration on the response of panel 3 to

the applied in-plane load.

Each of the strength tests was conducted according to the following procedure:

1. The boundary conditions and instrumentation were checked. All channels m the B&F data-acquisition unit were balanced. The L VDT's were checked to ensure their proper orientation and positive directions.

2. Zero readings were taken from all measuring devices. These included all load cells, strain gages, L VDTs, and for the tests with vertical loading, the dial gages.

3. The test panel was preloaded by a 2-kip (8.9 kN) in-plane load and, where needed, a 35 psf (1.68 kPa) vertical load. All instrumentation were checked during the preloading to ensure their proper working conditions. The specimen was then returned to the unloaded condition.

4. Initial zero readings were again taken from all instruments.

5. When needed, the vertical load was applied gradually in eight equal increments. Details of the vertical loading sequence are shown in Table 5.3.

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After fully applied to represent the service live and dead load, the vertical load was maintained constant throughout. the remaining steps of the strength test.

6. The in-plane monotonically at frequent. measurements.

load was applied according to the preselected pattern, either or cyclically. The load was increased quasi-statically and held load or displacement, steps for strain and displacement

7. At each loading step, the specimen was visually examined for the formation and extension of cracks.

8. The loading was terminated when the resistance dropped significantly below the ultimated strength with increased displacement, when it became impossible to maintain the required vertical load, or when concrete crushed 111

compression, which was usually accompanied by a sudden loss of resistance.

9. ln monotonic load tests, the in-plane load was then removed and applied 111

the negative direction. Test continued as in steps 6, 7, and 8 until the ultimate strength was again reached. The specimen was then unloaded.

10. At the end of each strength test, after complete unloading, a set of final zero loadings was taken from all measuring devices.

11. Condition of the failed speCimen was recorded by photographs as well as manual sketching of the crack patterns.

12. The thickness of slab panel at the major crack was precisely determined by a micrometer.

5.4. In-Plane Vibration Tests

The in-plane vibration tests were done before and after the strength test for each

side panel. The panel was supported as in the strength test. A vibration sensor, a

frequency filter and an oscilloscope were used to measure and record the vibration of the

panel caused by a hammer impact. As shown in Fig. 5.6, vibration in the X- and Y-

directions were studied separately by changing the direction of the hammer impact and

the sensor. Each impact incited vibrations of many modes, in different directions and at

different frequencies. Tests were repeated several times with the frequency filter set at

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different ranges, until the dominant fundamental free vibration frequency was established.

Each frequency was measured at least three times.

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6.1. Stiffness Tests

Chapter 6

Test Results

The stiffness tests were made on the spenmen WS-1 only. The displacements at

the load points and the rotation of shear walls were determined from readings of nine

1VDT's, arranged as shown m Fig.5.3. Figs. 6.1 and 6.2 show the measured

displacements under 2-kip symmetrical and anti-symmetrical loading, respectively. The

movements at the supports (12 and 14), were more than originally expected, reflecting

some motion of the supporting pedestals themselves. The average displacement of the

loaded points (11 and 15), relative to the displaced location of the support line (12 and

14) was calculated to reflect the structural response of the specimen, as demonstrated in

Figs. 6.1 and 6.2. Nevertheless, the rather large support movements reduced the accuracy

of the calculated results, particularly for the anti-symmetrical case. Table 6.1 shows the

calculated initial flexibility, as the deflection under unit load.

During the strength tests, the initial flexibility of each panel was also monitored,

results are also listed in Table 6.1. It should be pointed out that because of the

different support conditions, the flexibilities from the three-panel stiffness tests and the

single panel strength tests were different structural quantities and should not be

compared directly. Under full service vertical load, there were several cracks in panels

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WV1 CY and WV2MN before the application of in-plane loading. As a consequence, the

initial flexibilities of these panels were higher than the coresponding panels without

gravity load.

6.2. Behavior Under Gravity Load

Panels 1 and 2 of specimen WS-2 were tested for their behavior under gravity load

up to the service load level prior to in-plane strength testing. As pointed out in Section

5.3, gravity load was applied m eight increments, eventually reaching the level

representing the full service live and dead loads. The first crack due to vertical load was

observed at approximate 60% full service load. Under full vertical load, a long line of

crack due to negative bending was observed along the slab-shear wall junction on the

top surface while several small cracks were found at the bottom near the middle of

span. Figs. 6.3 to 6.5 show the measured vertical deflections, residual deflections and

calculated results due to vertical loading for panel 1. Behavior of panel 2 was similar.

Under full service vertical load, the maximum vertical deflection at the center of the

panel (D 3) was 0.14 in.(3.55mm), which was 1/450 of the span length.

Figs. 6.6 to 6.7 show the typical relationship between vertical load and measured

strain (stress) m rib reinforcement at mid-span. The relationship were nearly linear.

Under full service vertical load, the largest measured steel stress was 22,550 psi

(155.4MPa) in the middle strip and 21,260 psi (146.5 MPa) in the column strip. It

should be pointed out that these stress values have been adjusted for the effect of the

specimen self-weight as indicated in Figs.6.6 and 6.7. These stress values were 50 to

60% of the yield strength of steel wire, very reasonable for service loading condition.

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6.3. Results of Strength Tests--- General Description

Primary interest in the strength tests was g1ven to the displacement at the

unsupported edge of the panel under test (1VDT 13 in Fig. 4.10). This 1VDT was

continuously monitored during the test: and plotted against the applied in-plane load by

an X Y -plotter. Figs.6.8 to 6.15 show these plots for the six strength tests. These plots

show clearly the general in-plane behavior of each test panel, including the minor

decreases in loads caused by intermittent support movements, cracking of concrete and

fracturing of reinforcing bars.

The displacements recorded by L VDT 3 included the effect of movements of the

"fixed" edge of the test panel. ln order to study the actual structural behavior of the

panel: the readings from several other 1 VDT's were used to eliminate the effects of any

rigid body motion associated with support movements. The results of these calculations

were also plotted in these figures, in dashed lines. For the sake of distinction, the

measurements of 1VDT 13 are refered to as the principal "displacements", while the

calculated values are designated principal "deflections". Calculation of principal

deflections could not be performed continuously during test, but only at pre-selected load

levels. Consequently, the dashed lines in these figures consisted of short straight line

segments.

Several fine cracks were obsered at the slab-shear wall junction at very early stages

of the tests. (In several cases, these were observed even before testing.) Shrinkage and

abrupt change of stiffness were believed to be responsible for these cracks. It was felt

that these cracks would have a relatively significant effect on the principal displacements

under low in-plane loads, but negligible effect under high loads. Accordingly, two values

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were calculated for the principal deflections, usmg the center line of shear wall and the

edge of the test. panel, respectively, as the reference line (Fig. 6.16).

designated t:.1

and t:.2

, respectively.

These are

Estimation of the initial stiffness (and flexibility) of the panel was based on t:. 2, in

order to remove the effect of the opening of the minute cracks at the face of shear wall.

The results are assembled in Table 6.1, m comparision with corresponding values

obtained from analytical methods.

The overall behavior of the test panels, shown in Figs. 6.8 to 6.15, are based on

t:.1

• It was reasoned that under high in-plane load, the relative movement. between the

edge of slab and the shear wall should be more appropritely considered as a part of the

structural response. Table 6.2 summarizes the various critical test results from the

strength test. Figs. 6.17 to 6.28 show the crack patterns of the panels at the end of the

strength tests. Numerals near the cracks represent the load values for test WH1MN

(Figs.6.17 and 6.18), and the load step numbers for other tests, when the crack was first

obsered.

6.4. Results of Individual Strength Tests.

6.4.1. WH1MN (Figs. 6.8, 6.17, 6.18)

The load-deflection relationship was essentially linear up to a load of 10 kips

( 44.5kN). The first flexural crack was observed about 15 in. (380mm) from the shear

wall at a load of 13.77 kips (61.2kN). The first shear crack was found in the middle

part of the panel near shear wall at a load of 15 kips (66.7kN). Although the flexural

crack was obsered first, the shear cracks developed faster once started. Most of shear

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cracks started in the middle part of the panel, and extended from both ends at an angle

of about 45 degree with the in-plane load. The widest openings of the shear cracks were

mostly located in the middle part of the panel. At a load of 15.96 kips (71.0kN), a.

strain gage reading indicated that yield strain had been reached in a rib reinforcing bar.

This load was designated as the first yield load. At a load of 20.5 kips (91 .2kN), many

new shear cracks were observed, while the cracks started earlier were seen to enlarge.

The stiffness of the panel had decreased significantly. At 21 kips (93.4 kN), several

cracks developed rapidly and merged into one major transverse crack extending from the

tensile edge to the compressional region. The maximum load reached was 22.12 kips

(98.4 kN). At this load, several reinforcing bars broke, and both stiffness and resistance

droped significantly. The largest principal displacement, as measured by L VDT L3, was

0.73 in (18.6mm), which occured when resistance had dropped down to 21.17 kips (94.2

kN). After unloading, the residual displacement was 0.563 in (14.3 mm). Examination

of the readings from the other L VDT's revealed that significant support movement was

included in these displacements. The corresponding deflection value, ( .6.1), were 0.31 7in.

(8.1mm) and 0.218in. (5.53 mm), respectively. These principal deflection values are

shown in Fig. 6.8.

During negative (push) loading, the ultimate load attained was 22.04 kips (98.0

kN). At this point several reinforcing bars broke and several pieces of concrete fell olf.

At the same time, the resistance was reduced greatly and the major cracks from

opposite edges became connected. This final major crack was located at 21 inches

( 533mm) from the shear wall. This location coincided with the cut-off point of the short

top reinforcing bars in the column strips (Fig. 2.3). The largest deflection .6.1

reached

under negative loading was 0.497 in. (12.6mm). The residual deflection upon unloading

was approximately 0.35 in. (8.9mm). 21

6.4.2. WH2CY (Figs. 6.9, 6.10, 6.19, 6.20)

For the three lowest amplitudes, with peak loads of 4. 8 and 12 kips {17.8, 35.6

and 5.4 kN), the behavior of the panel was essentially elastic. There was no change in

the principal displacement in successive cycles under the same load, no noticeable

residual deformation. Starting from the loading cycles at. 16 kips {71.2 kN) load, (cycles

no. 10, 11 and 1 2) the residual displacement became significant, and progressive

deterioration was evident from the three hysteretic loops m each group. Peak

displacement increased in each successive cycle to the same load, and in the later stages

when loading was controlled by displacement, the resistance of the panel decreased in

successi~e cycles. ln general, there was less difference between the last two cycles than

between the first. two cycles of each group. The opening and development of most cracks

were first observed during the initial cycle of a group, with few additional cracks

starting during the second and third cycles. Such a cracking behavior is compatible

with the observation of relatively little deterioration between the second and third cycles.

It was reasonable to expect only mmor change in the hysteretic loops under additional

cycles of loading. The maxmium load, for both positive and negative directions, was

reached during the first cycles at the seventh amplitude (cycle no. 19), with a peak

displacement of 0.4 inch (10.2 mm). The load values were 21.05 kips {93.6 kN) and

19.76 kips (87.9 kN), respectively. The more stable third-cycle loads were highest at

19.36 kips (86.1 kN) in the sixth amplitude (cycle no. 18, 0.3 inch or 7.6 mm) and

-18.0 kips (80.1kN) in the seventh amplitude (cycle no 21, 0.4 inch or 10.2 mm). After

reaching the maximum resistance, the peak load decreased appreciably in successive

cycles of the same amplitude.

22

At the end of the cycle load test, after three cycles at the ninth amplitude (0.6

inch or 15.2 mm), several reinforcing bars had broken, the major crack had extended

nearly the full width of the test panel and the resistance had dropped to approximately

65% of the maximum value observed earlier. The largest structural deflections (1:.1

)

attained during the last cycle of loading were 0.716 in. (18.2 mm) and -0.664 in.

(16.9mm), respectively.

Between the east and west column center line, (i.e. the panel proper), most cracks

were directed at an angle of 45 (or 135) degrees with the direction of the in-plane load,

signifying their being diagonal tension cracks. Outside of thesse column center lines,

cracks were basically parallel to the in-plane load, being flexural in nature.

6.4.3. WH5MN (Figs. 6.11, 6.21, 6.22)

The middle panel of the first specimen (WS-1) was tested with in-plane loading

applied at the outer edge of panel 2 (Fig.5.1). However, attention was. completely

focussed on the middle panel. Panel 2 was used only t.o achieve the desired large

moment-shear ratio. The placement of the measuring devices was similar to Fig. 4.10.

The principal displacement and principal deflection were determined at the center line of

the shear wall between panels 2 and 3, and reflected the behavior of panel 3 alone.

The first crack was observed near the fixed shear wall at an in-plane load of 6

kips (26.7kN). First yielding of reinforcing steel was observed at 8 kips (35.6 kN). This

was followed by yielding of several more steel bars, and the opening of diagonal tension

cracks in the middle of the panel. A major crack was then formed between the second

and third ribs from the fixed shear wall. The panel eventually failed at a load of 12.47

23

kips (55.5 kN) by crushing of concrete at. the north-east corner, near the fixed shear

wall and beyond the first longitudinal rib, where the compressive stress was high, the

thickness of slab was only 2/3 in. (16.7 mm), and many of the cracks converged

(Fig.6.21 ). The resistance of the panel decreased by 3 kips (13.3 kN) following the

crushing of concrete (Fig.6.29).

As shown by Fig. 6.1 1, this panel acted like a flexural member, and demonstrated

considerable ductility (significant mcrease of displacement with little change m

resistance).

Under negative loading, the load gradually increased to 10.22 kips (45.5 kN),

followed by a sudden slab concrete crushing at the maJor crack developed previously

under positive loading. Apparently, the closing of this crack was not complete, resulting

m very high local concrete compressive stresses. The largest deflection ~ 1 in both

positive and negative directions was over 1 inch (25 mm).

6.4.4. WV2MN (Figs. 6.12, 6.23, 6.24)

As pointed out in section 5.3, out-of-plane loading simulating the full serv1ce

gravity load was applied to panel 2 of specimen WS-2 before the application of in-plane

loading, and maintained throughout the test. Thus, this panel was subjected to the

combined action of full service gravity load and a varying in-plane shear load.

Under full serv1ce gravity load but no in-plane loading, there existed a long

negative bending cracking along the slab-shear wall interface as wei as a number of

positive bending cracks in the center region of the panel. On account of the preeminence

of the top plate of the waffle slab system in initial resistance to in-plane shear loading,

24

the positive bending cracks had very little influence on the initial in-plane stiffness of

the panel. On the other hand, to calculate the measured initial stiffness, principal

deflection ~ 2 was used instead of ~ 1 (Fig. 6.16), so that the effect of the negative

bending crack was removed. The first. yield of reinforcing bar was detected at a negative

load of lO.Ol kips (44.5 kN), which was significantly lower than the case without gravity

load (test WHlMN).

The ultimate load was reached at 21.36 kips (95.0kN) when the slab concrete at

the compression edge crushed (Fig.6.30). As soon as the concrete crushed, the resistance

of the panel decreased by 0.51 kips (2.3kN), and the principal deflection ~ 1 increased by

more than 0.1 inch (2.5mm). The ultimate deflection ~lu attained was 0.566 inch

(14.4mm).

During unloading, the rebar's stresses at, opened cracks were decreased and the

cracks were closed. However, the out-of-plane loading caused vertical displacements of the

opposite side of the cracks, particularly near a vertical load point. This resulted in a

vertical offset of the crack after closing, leading to highly concentrated local compresswn

stresses. The negative ultimate load was reached at. 19.02 kips (84.6 kN), nearly 10%

lower than the positive ultimate load. The mode of failure was again concrete crushing,

but at a closed crack about 25 in. (635mm) away from the compression edge (Fig.6.31).

The negative ultimate deflection was 0.576 inch (14.6mm), a little more than the

corresponding positive value.

25

6.4.5. WV1CY {Figs. 6.13, 6.14, 6.25, 6.26)

Similar to test WV2MN, the compensatory dead and live load was applied to panel

1 of specimen WS-2 before in-plane loading, and maintained throughout the test. A few

shrinkage cracks were found on top of the slab parallel to the shearwall before loading.

The cracks due to vertical load were similar to those in the test WV2MN.

The loading program for WV1 CY is shown in Fig. 5.4b. For the three lowest

amplitudes at peak loads of 4, 8, 12 kips (17.8, 35.6, 53.4 kN), the hysteresis loops for

the three cycles at each amplitude nearly conincided with each other. Deterioration was

first observed during the third cycle at 12 kips (53.4kN) load (cycle no. 9), when the

principal displacement increased slightly (Fig.6.13). Starting from the fourth amplitude,

peak load 16 kips (71.2 kN), the three hysteresis loops of consecutive cycles ran

differently. Weakening of the panel was clearly indicated by increased displacement under

the same load, or in later cycles, by decreased resistance at the same displacement.

The first yield of reinforcing steel was detected at a very low load of 7.92 kips

(35.2 kN). The ultimate load was 21.21 kips (94.3 kN) during the first cycle of the sixth

amplitude (cycle no.l6) when several rebars broke. Afterwards, the resistance of the

panel decreased cycle by cycle. The maximum deflection .6.1

obtained was 0.557 inch

(14.2 mm) under a load of 8.55 kips (38.0 kN). At the ultimat,e stage, the major cracks

from both side had merged together into one crack extending through the entire width

of the panel. Considerable damage could be attributed to the action of the out-of-plane

loading. The test was terminated after one and one half cycles at the eighth amplitude

when the slab concrete in compressive region was crushed.

26

6.4.6. FH5MN (Figs. 6.15, 6.27, 6.28)

The strength of the flat plate middle panel of speCimen WS-2 was tested usmg a

setup similar to that of test WH5MN, with the in-plane loading transmitted through the

reparied panel 2 (Fig.5.5).

The first crack was observed near the fixed shear wall at a load of 7.41 kips

(33.0kN). Under additional loads, several more flexural cracks deve)opd. The first yield of

a reinforcing bar was observed at a load of 10.8 kips ( 48.0 kN). At a load of 12.24

kips (54.4 kN), several cracks were seen to turn into a diagonal direction. One of these

eventually became the major crack causing failure.

The ultimate load was reached at 17.18 kips (76.4 kN) followed by the breaking of

several reinforcing bars and a decrease in resistance by 1.18 kips (5.25 kN). The

ultimate deflection reached was 0.606 in. (15.4 mm).

Under negative loading , the ultimate load was only 12.28 kips (54.6 kN), nearly

25% lower than the positive value. Failure was due to crushing of concrete at the

previous major crack, which was located about 19 in. (480mm) away from the center

line of the fixed shear wall.

It should be noted that the flat plate pannel was reinforced with bent-up (trussed)

bars, and the major crack developed very close to the bent-up location. The

straightening of the bent bars at the crack could have contributed to the increased

flexibility of the panel (Fig. 6.32).

The maximum negative load of 12.28 kips (54.6 kN) was reached with a deflection

27

.6. 1 of 0.203 inch (5.2mm), after which thP resistance gradually decreased with increased

deflection. Testing was terminated at a max1mum deflection of 0.44 inch (11.2 mm),

when the resistance had decreased to 7.91 kips (35.2 kN).

28

Chapter 7

Comparison and Discussion

7 .1. Stiffness and Flexibility

Elastic in-plane stiffness (load per unit t.2

) of each slab panel and its reciprocal,

the flexibility, were calculated by finite element analysis using the standard SAP IV

program. The following assumptions and idealizations were made regarding the geometry

and material properties:

1. Only linear elastic deformations were considered.

2. The concrete material was taken to be isotropic and homogeneous. The effect of reinforcement· was ignored.

3. The modulus of elasticity and Poisson's ratio for concrete were assigned values as obtained from standard cylinders tested after the strength test of each specimen.

4. The average slab thickness, from measurements of each specimen, was used m calculation.

5. The waffle slab was treated as a three dimensional system. The top slab of each waffle dome was represented by a plate element and the ribs were represented by beam elements. Rigid link were used to connect the rib segments to the top plate at its corners. The length of the rigid links was equal to the distance from center of top slab to the center of rib.

The method of equivalent thickness (12) was also used to calculate the elastic

flexibility of single slab panels.

29

Table 6.1 lists the calculated flexibility, together with the initial flexibility obtained

experimentally. For WH lMN and WH2CY, the FEM calculated flexibility was about 80

percent of the experimental values. The difference appears reasonalbe in view of the

unavoidable microcracks In the specimen, and the ]ower-bound nature (for flexibilities) of

the finite element analysis.

Comparing the experimental flexibility of WH1MN with that of WH2CY, it IS seen

that the cyclic loading has no effect on the initial flexibility.

For the symmetrical stiffness test. WH6SS, the flexibility calculated by finite

element analysis was very nearly the same as experimental result. ln contrast, the

companson was not. as good for the anti-symmetrical test WH6SA .. From Fig. 6.2,

considerable support movements are seen to have taken place during this test. The

experimental results were therefore subjected to larger inaccuracies.

Table 6.1 also lists the results calculated by equivalent thickness method (12). The

results are between experimental values and the values calculated by SAP IV.

7.2. Behavior Under Service Vertical Load

Figures 6.3, 6.4 and 6.5 show the vertical deflection of panel 1 of WS-2 under

various stages of vertical loading, as well as the residual vertical deflection after removal

of all supplemental loading (only specimen self-weight remaining). Also shown in these

figures are the deflection under service load calculated by a SAP IV elastic analysis. The

experimental deflections are seen to be nearly double the corresponding calculated values.

This difference is attributed to the flexural cracking of concrete and the resulting non-

30

linear behavior of the speCimen. From Fig. 6.5, it is seen that the SAP IV analysis

yielded reasonalbe estimates of the initial stiffness regarding 03

and 06

. The largest

measured deflection 03

, under full service gravity load, was 0.13 in. (3.3 mm), or

approximately 1/500 of the panel length, which was 64 in. (1630 mm). About half of

this deflection was non-elastic in natural, and not, recovered upon unloading.

The largest measured steel stress under full service gravit_Y load was about 22,550

psi (155.4 MPa), or 60% of the yield stress. The largest crack width under full service

gravity load was about 0.005 inch (0.13 mm). These deflection, stress and crack width

values all indicate an acceptable performance under service loading.

7 .3. Behavior Under In-Plane Load

7 .3.1. General Description

Under in-plane load the waffle slab panel behaved like a cantilever deep beam.

The ultimate strength was influenced by the nature of loading (monotonic or cyclic), the

moment-to-shear (span-to-depth) ratio, and the intensity of vertical load. In all cases the

ultimate strength was reached immediately before the development of a major crack

which extended parallel to the shear wall at a distance of 20 in. (510 mm), about 1/3

panel length, where a number of negative reinforcing bars were terminated. After the

formation of this major crack, the resistance of the panel gradually decreased with

additional displacement. During this phase of testing, the overall deformation of the

panel was controlled primarily by the opening and closing of the major crack, with few

new crack developed. The section at the major crack acted like a plastic hinge. The

opening of the major crack also caused a decrease of the compression region. In several

31

cases, the depth of the compressive regwn was as low as 7 in. ( 178mm), barely

including the first rib. Several of the panels finally failed by crushing of concrete in the

compression region.

The openmg of the maJOr crack enabled the slab panel to deflect greatly without

significant change of resistance. In comparision with other floor slab systems, waffle slab

is superior in ductility. Table 7.1 shows the ultimate deflection values of the waffle slab

panels, as well as those of flat and beam-supported slabs. It is clear that waffle slab

panels sustained much more ultimate deflection although all slab panels had the same

span length and were subjected to the same service gravity load. Table 7.2 lists the

comparison of the test results.

The capacity of a structure to sustain inelastic deformation without significantly

losing resistance is frequently represented by the ductility ratio of the largest attainable

deformation to the elastic (or yield) deformation. In Table 7.3 are listed the ductility

values of the various test specimens. As depicted in the sketch accompanying Table 7.3,

these values were determined at the level of the calculated ultimate strength of the

specimen panel, and the base deformation at yield, 6.Y, is obtained by extending the

linear portion of the load-deflection curve to the selected load level. Two ductility

values were show for each specimen, one based on the largest deflection measured

( 6. 1 ,maz), and the other based on the deflection at the maximum resistance ( 6. 1,J. It is

seen that in almost all cases, the 6.1

I 6. ratio exceeds 5.0 and 6. 1 I 6. execeeds 3.0. ,maz. y ,u y

Ductilities represented by these values appered to be quite adequate.

Figs. 7.1 and 7.2 show the growth of ductility for cyclic loading tests WH2CY and

32

WVlCY, respectively. For each half cycle of loading, the ductility was calculated as

!J.) !J.Y, where 11; was the total deflection during the current half cycle, starting from the

zero load position, and /::;. was the deflection determined from linear extrapolation, as y

before. These definitions are show in the figures.

In all strength tests, the ultimate resistance under negative loading was lower than

that under positive loading. This strength reduction was attributed to damages during

the last stages of positive loading. At the end of the positive loading phase, many cracks

had developed, and the major crack had extended almost. through the entire width of

the test panel. Most of reinforcing bars crossing the major crack had yielded, a few even

fractured. These damages would obviously weaken the panel when loaded in the opposite

direction.

Despite the anchoring of the floor system speCimen to the strong pedestals,

significant support movements were measured during the stiffness tests. These relatively

larger support movements reduced the precision of the test results.

7.3.2. Effect of Nature of In-plane Loading

The two pairs of test panels: WHlMN vs. WH2CY, and WV2MN vs. WV1CY,

were compared to determine the effect of the nature of loading (monotonic vs. cyclic).

Under cyclic loading, initial yield of steel occurred at a lower load than under

monotonic loading. The ratio of the first yield loads was 0.93 (without gravity load) and

0. 79 (with gravity load), respectively. In contrast, the ultimate resistance was not

significantly affected by the nature of loading. As shown in Table 7.2, the ratios of

corresponding maximum loads in positive and negative directions were 0.95 and 0.90 for

panels without gravity load and 0.99 and 0.96 for panels with gravity load. 33

The deterioration of the test panels under cyclic loading was more distributed than

the monotonically tested panels. There were more plastic deformation and more visible

cracks in the panel, but the cracks were better distrbuted over the entire panel, and

their widths were smaller. The ultimate deflections of panel WH2CY, +0.716 in. (+18

mm) and -0.665 in. (-17 mm), were much larger than those of panel WHlMN, +0.316

in. (8 mm) and -0.497 111. (12.6 mm). An approximately 70% increase in total

deflection was observed. On the other hand, the pair of specimen subjected to gravity

loads, WVJCY and WV2MN, developed approximately the same total ultimate

deflections, 1.11 in. vs. 1.14 in. (28.2 mm vs. 29.0mm). Apparently, the effect of nature

of in-plane loading in this case was overshadowed by that of the presence of out-of-plane

loading.

7 .3.3. Effect of Vertical Load

The effect of vertical (out-of-plane) loading was examined by comparmg the results

of test panels WH1MN with WV2MN, and WH2CY with WV1CY. As both the out-of­

plane and in-plane loads produce tensile stress in certain reinforcing bars, the initial

yield occurs at a much lower in-plane load level for panels subjected to vertical load.

The ratio of initial yield loads for WV2MN and WH1MN was 0.627 (Tables 6.2 and

7.2). For panels WV1CY and WH2CY, the corresponding ratio was an even lower 0.532.

Thus the presence of full service vertical load caused a 40 to 50% decrease of the first

yield load.

The vertical load had almost no effect on the positive ultimate in-plane resistance.

Apparently, the slab panel was sufficiently ductile that at the relative low level of out­

of-plane load (about 50% of ultimate), the in-plane strength was not severely impaired.

34

However, the same condition was not observed for the negative loading. Some material

failure (yielding and fracturing of reinforcing bars and crushing of concrete) has taken

place during the positive loading test. ln addition, the out-of-plane loading had caused

vertical offsets o( parts of the panel. As a result, the observed negative ultimate m­

plane strength was lower. The ratio of negative ultimate load for WV2MN to that for

WH1MN was 0.86. For the pair of panels WV1CY and WH2CY, this ratio was 0.92.

Thus, the service gravity load caused the in-plane strength to decrease by approximately

10 to 15 percent. Fig.7 .3 shows the resistance interrelationship of waffle slab panel under

combined out-of-plane (vertical) and in-plane loading. According to the ACI strength and

serviceability design concept, the full service load represents only about 50 to 60% of the

required structural capacity. The circular interaction relationship shown in the figure

indicated that this would only have a small effect on the in-plane resistance.

7 .3.4. Effect of Shear Span

While most waffle slab panels were tested with a shear span of 64 in. (1.63 m),

the middle panel test (WH5MN) used a shear span of 128 in. (3.25 m). Comparision of

test results from WH5MN and WH1MN provides an indication of the effect of the shear

span, or the moment-to-shear ratio.

The first yield load for WH5MN was 8 kips (35.6 kN) while that of WH1MN was

15.96 kips (71.0 kN). These loads are almost precisely in inverse proportion to the shear

spans, hence reflect almost identical in-plane bending moment at the fixed edges. 1t may

be concluded that the steel stress was primarily controlled by the bending action of the

slab at this stage.

35

The companson of ultimate in-plane resistance revealed a ratio of 0.56 for positive

loading and 0.46 for negative loading. Both ratio are somewhat different from that of

the moment arms. It is felt that the location of the major crack have an important

influence on the ultimate behavior under negative loading. For both WHlMN and

WH5MN, the major crack was located about 21 in. (533 mm) away from the fixed shear

wall. Therefore, the moment-to-shear ratio at the major crack (or the distance to applied

load) was lOi m. (2.i2m) for WH5MN, and 43 in. (1.09 m) for WHlMN. These

distance were approximately m mverse proportion to the negative ultimate loads. These

observation on the ultimate resistance in both directions indicate that the in-plane

strength of waffle slab pannels is controlled primarily by the flexural capacity at the

major crack section. The effect of the in-plane shear is small indeed. Panel WH5MN

with the larger moment-to-shear ratio, exhibitted considerably larger ductility than panel

WHIMN (Table i.3). This difference in ductility may be viewed as a consequence of the

different crack patterns in these specimens. A comparison between Fig. 6.li and Fig.

6.21 shows that the specimen tested under the large moment-to-shear ratio (FH5MN)

developed more flexural cracks, but fewer shear cracks. As the opening of the flexural

cracks and the yielding of reinforcing bars at these cracks contribute significantly to the

plastic deformation of the slab panel, the observed increase of ductility with the

moment-to-shear ratio is understandable.

36

7 .3.5. Effect of Reinforcement

For every one of the strength tested panels: the maJOr crack ran parallel to the

fixed shear wall and was located about 21 in. (533 mm) from the wall (Fig. 2.3). This

location nearly coincided with the third span point where many of the negative moment

reinforcing bars in the column strip were terminated.

The panel FH5MN: which contained bent (or trussed) bar reinforcements, behaved

less satisfactoriy under in-plane loading than the other panels, which used separate

straight top ane bottom bars. As described in section 6.4.6, the bent bars tended to

straighten out after cracking developed at the bent position, and accelerated the

widening of the crack. h is therefore recommended that bent bars not be used in floor

slabs subjected to large in-plane loading.

7 .4. Frequencies of In-plane Free Vibration

The results of free vibration tests are listed in Table 7 .4. It is clear that cracking

of concrete due to strength testing greatly reduced the stiffness, hence the freguency of

free vibration. The last column of Table 7.4 shows the natural frequencies calculated by

the finite element analysis (SAP IV). The generally lower frequencies predicated by the

finite element analysis are attributed to the neglect of friction resistance at the column.

General conclusions could not be drawn from the "after strength test" frequency

value. It was noted that after strength test, the panels were damaged to different degree

of severity, some almost becoming two separate parts. The frequency measured was more

closely related to the behavior of the part being impacted, than that of the entire panel.

Furthermore, the two sepaate parts were connected by reinforcing bars, the boundary

37

condition was completely changed. So the measured frequency would not be the real

frequency of the panel.

38

Chapter 8

Conclusion and Recommendations

The experimental research reported herein has provided information about the in-

plane behavior of waffle slab panels under various supporting and loading conditions.

From these experimental information, and from comparison with results generated by

various analytical methods, the following observations and conclusions are obtained:

1. Both the elastic finite element analysis and the equivalent thickness method resulted in flexibility values of the waffle slab panel approximately 15% lower than the experimental value. Microcracks and residual stress caused by shrinkage and accidental loading before testing are belived to be responsible for these discrepances.

2. Under vertical (out-of-plane) loading, the first crack was observed at about. two-thirds of the service dead load and live load. Under full service load, a long negative moment crack was located along the slab-shear wall junction, and several small cracks developed on the bottom of ribs in the middle of span.

3. The waffle slab panels designed in accordence with ACI Building Code performed satisfactorily under full service (out-of-plane) loading. The largest measured steel stress was about 60% of the yield strength. The maximum deflection was about. 0.2% of the panel span. And, the maximum crack width was about 0.005in. (0.13 mm).

4. The presence of service vertical load lowered the in-plane load of first yield by 40 to 50%, but had almost no effect on the ultimate in-plane resistance.

5. The lack of a rib along the extreme edges of the test panels appered to be a source of weakness.

6. Shrinkage cracks developed at the slab-shear wall connection caused a

39

significant decrease in initial stiffness against in-plane loading. However, the effect on ultimate load and ultimate deflection was negligible.

7. Cyclic loading led to more distributed cracking and plastic deformation. Cyclic loading did not significantly reduce the ultimate resistance of test panel and did not change the development of the major crack.

8. Except for very small loading or displacement amplitudes, the stiffness of the waffle slab panel decreased for each of the three successive cycles of the same amplitude.

9. In-plane strength of the slab panels was basically controlled by the flexural strength at the major crack. In all cases, the major crack was parallel to the fixed edge, and was located near where many of the negative reinforcing bars in the column strips were terminated. A modified reinforcement arrangement could improve the strength behavior of the slab panels.

10. The bent up (or trussed) bars in a slab panel tended to straighten after the opening of the major crack, and to accelerate the growth of the cracks.

11. The ultimate in-plane loading varies approximately inversly with the moment­to-shear ratio at the location of major crack.

12. In comparison with other floor systems, waffle slab exhibits larger ductility capacity.

Based on the above observations and conclusions, the following recommendation are

proposed:

1. The initial stiffness of waffle slab for in-plane loading may be estimated by a finite element analysis or the method of equivalent thickness considering both shear and bending deformation. To consider the effect of micro-cracks due to shrinkage, the calculated results may be reduced by 10 to 20 percent.

2. The arrangement and amount of reinforcement affect significantly the strength and crack pattern of the slab panel. Reinforcement with separate straight top and bottom bars is preferred to that with bent-up continuous bars. Extending negative reinforcement into the positive bending regions and placing additional bars near the edge of slab would improve the in-plane behavior of floor slab.

3. The use of an edge beam (rib) around the external edges of waffle slab IS

strongly recommended.

40

Chapter 9

Reference

1. American Concrete Institute BUILDING CODE REQUIREMENTS FOR REINFORCED CONCRETE AND COMMENTARY. ACI Standard 318-71, 318-77, 318-83, Detroit.

2. American Concrete Institute MANUAL OF STANDARD PRACTICE FOR DETAILING REINFORCED CONCRETE STRUCTURES, ACI Standard 315-65, Detroit.

3. American Society for Testing and Materials ASTM STANDARDS.

4. Concrete Reinforcing Steel Institute CRSJ HANDBOOK, CRSI, Chicago, 1972.

5. Nakashima, M., SEISMIC RESISTANCE CHARACTERISTICS OF REINFORCED CONCRETE BEAM-SUPPORTED FLOOR SLABS IN BUILDING STRUCTURES, PHD DISSERTATION, Department of Civil Engineering, Lehigh university, Bethlehem, Pa., March, 1981.

6. Nakashima, M., Huang, T., and Lu, L. W ., EXPERIMENTAL STUDY OF BEAM SUPPORTED SLABS UNDER IN­PLANE LOADING, ACI Journal, January-February, 1982

7. Karadogan, H. F., Huang, T., Lu, L. W., and Nakashima, M., BEHAVIOR OF FLAT PLAT FLOOR SYSTEMS UNDER IN-PLANE SEISMIC LOADING, Proceedings of the seventh World Conference on Earthquake Engineering, Istanbul, Turkey, September, 1980.

8. Nakashima, M., Lu, L. W., Huang, T., and Karadogan, H. F., CURRENT RESEARCH AT LEHIGH UNIVERSITY ON CONCRETE FLOOR SYSTEMS UNDER IN-PLANE SEISMIC LOADING, Proceedings of the seventh World Conference on Earthquake Engineering, Istanbul, Turkey, September, 1980.

41

9. Karadogan, H. F., Lu, L. W., and Huang, T., TECHNIQUES FOR IN-PLANE VIBRATION AND SHEAR TESTING OF MODEL FLOOR SLABS, Symposium on Dynamic Modeling of Concrete Structures, ACI Publication SP-73, Detroit, Michigan, 1982.

10. Nakashima, M., Huang, T., and Lu, L. W., EFFECT OF DIAPHRAGM FLEXIBILITY ON SEISMIC RESPONSE OF BUILDING STRUCTURES, Proceedings of the eigth World Conference on Earthquake Engineering, Sanfrancisco, California, 1984.

11. Wu, Z., and Huang, T., AN ELASTIC ANALYSIS OF A CANTILEVER SLAB PANEL SUBJECTED TO AN IN-PLANE END SHEAR, Fritz Laboratory Report No. 481.1, Lehigh University, May, 1983.

12. Wu, Z., and Huang, T., AN EQUJV ALENT THICKNESS ANALYSIS OF WAFFLE SLAB PANELS UNDER IN-PLANE SHEAR LOADING, Fritz Laboratory Report NO. 481.2, Lehigh University, May, 1983.

42

Idle 2 1 Ct REINFORCEMENT OF THE WAFFLE 5LAB PANELs;

POSITIVE STEEL * NEGATIVE STEEL

COLUtvlN 5TR IP M/PJ)LE STRIP COLUMN -STRIP 1'11PVLE STRIP

])ESitiN BENYIN6 f\JOMENT (ft-lb) &43 562 !95& 652 ------------~--------------- ------ ---·--· -- -

])ESIGN STEEL TEN~ILE FO!\CE lib) 3g34 25.2 0 1.2tf!J(J 3oo (J

--

1t k . 3 _]) J.S 13 ]).2. 0 .STEEL PJZDV /])ED 3.JJ .2. 0 2JJ/.O

3 ]) /, 0 4 j) ;, 0

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t POSITIVE STEEL BARS ARE EQUALLY PLACED IN 3 RIBS IN EACH 32" -STRIP _

;t * ~EE Fl~_ 23 , REINFORCEMENT OF SPECIMEMS

** i SEE TABLE 3./ , FOR AREA-S AN·:o YIELD STRENGTH OF THt VARIOU~ REINF{)RCING WIRES I /h = 4.J;-!( ; I {t-It= /.37 2 N-JVI

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POSITIVE STEEL NEGATIVE ~TEEL

COLUMN STRIP MJ])PLE STRIP COLUfv1N STRIP fv1/])j)LE STRIP . ··----------·- -· i------ ·--------

PREVIOUS SPEOFIEN:

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Table I. 2. SUMMARY OF THE TEST RESULTS

TEST J------1---------------------·

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Table. 7.1 COMeARISON OF ULTIMATE DEFLECTIONS

ULTIMATE PEFLEC I l ON ( INCH) TEST

POSITIVE NEGATIVE TOTAL PEFLE CT/ON ---------.'

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Tahle 12 COMPAP I SON OF THE TEST RESULTS -· --

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DELTA 1 OF WV1CY

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