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TECHNICAL REPORT SL-85-4
EFFECTS OF SHEAR STIRRUP DETAILS ON0 ULTIMATE CAPACITY AND TENSILE MEMBRANE
BEHAVIOR OF REINFORCED CONCRETE SLABSby
Stanley C. Woodson
NStructures Laboratory
__DEPARTMENT OF THE ARMYWaterwvays Experiment Station, Corps of Engineers
(0 P0 Box 631. Vicksburg, Mississippi 39180-0631__
AuguJst 1985Final Report
1965..........................
QTI0 A T0 Pdf~l ic M na(mtti A ec
Wv,,hmqtoriB DC Y04
Destroy this report when no longer needed. Do not return
it to the orignato!.
The findings in this report are not to be conmtiued as an official- Department of the Army position Unless so designated
by other authorized documents.
C:iation of trad' nfl.-. T~ Cit , LO'2 f XI
ef 'o s''n~rrf ~ t .
TECHNICAL REPORT SL-85-4
EFFECTS OF SHEAR STIRRUP DETAILS ONULTIMATE CAPACITY AND TENSILE MEMBRANE
BEHAVIOR OF REINFORCED CONCRETE SLABSby
Stanley C. Woodson
Structures Laboratory
DEPARTMENT OF THE ARMYWaterways Experiment Station, Corps of EngineersPO Box 631, Vicksburg, Mississippi 39180-0631
August 1985Final Report
Approved For Public Release; Distribution Unlimited
This report has been reviewed in the Federal EmergencyManagement Agency and approved for publication. Approvaldoes not signify that the contents necessarily reflect theviews and policies of the Federal Emergency ManagementAgency.
Prepared for
Federal Emergency Management AgencyWashington, DC 20472
i~~. . .-...... -. °* ..................... ,......
UnclassifiedSECURITY CLASSIFICATION OF THIS PAGE When Dte Entered)"
PAGE READ INSTRUCTIONSREPORT DOCUMENTATION PBEFORE COMPLETING FORM
I REPORT NUMBER ;zOVT .CEINj . ECIPIENT'S CATALOG NUMBERTechnical Report SL-85-4
4. TITLE (ad S.bgiti.) TYPE OF REPORT & PERIOD COVERED
EFFECTS OF SHEAR STIRRUP DETAILS ON ULTIMATE I Final reportCAPACITY AND TENSILE MEMBRANE BEHAVIOR OF .
REINFORCED CONCRETE SLABS 6. PERFORMING ORG. REPORT NUMBER
7. AUTHOR(a) S. CONTRACT OR GRANT NUMBER(.)
Stanley C. Woodson
9. PERFORMING ORGANIZATION NAME AND ADDRESS iGm PROGRAM ELEMENT. PROJECT. TASK
US Army Engineer Waterways Experiment Station AREA & WORK UNIT NUMBERSStructures LaboratoryP0 Box 631, Vicksburg, Mississippi 39180-06311 1. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
Federal Emergency Management Agency August 1985Washington, DC 20472 13. NUMBER OF PAGES
17714. MONITORING AGENCY NAME & ADDRESS(If different ftom Controlling Office) IS. SECURITY CLASS. (of this report)
Unclassified
Is. DECL ASSI FIC ATION/ DOWNGRADINGSCHEDULE
. 16. DISTRIBUTION STATEMENT (of this Report)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, If different from Report)
,. SUPPLEMENTARY NOTES.Available from National Technical Information Service, 5285
Port Royal Road, Springfield, Va. 22161. This report is essentially the sameas a thesis which was submitted by the author to Mississippi State Universityin 1984 in partial fulfillment of the requirements for the Master of Sciencedegree.19. KEY WORDS (Continue on rovere eide If necessary and Identify by block number)
Blast shelter Reinforced concrete Ultimate capacityKey worker StirrupsOne-way slab Tensile membrane
20. ABTRACT (Cwlue a reverem elsi If noceeary sd Identlfy by block number)
, At the time this study was initiated, civil defense planning in the
United States called for the evacuation of nonessential personnel to safe hostareas when a nuclear attack is probable, requiring the construction of blastshelters to protect the keyworkers remaining in the risk areas. The place-ment of shear stirrups in the one-way reinforced concrete roof slabs of theshelters will contribute significantly to project costs. Ten one-way
(Continued)
DI .r',°'7 1473 o1 Or I NOV 6s Is OOSOLETE UnclassifiedSECURITY CLASSIFICATION OF THIS PA-.E (Whan Date Entered)
. . . "
UnclassifiedSECURITY CLASSIFICATION OF THIS PAGEC(hu Dot Entermd)
20. ABSTRACT (Continued).
""reinforced concrete slabs were statically and uniformly loaded with waterpressure, primarily to investigate the effect of stirrups and stirrup detailson the load-response behavior of the slabs. The slabs had clear spans of24.0 inches, span to effective depth ratios of 12.4, tensile reinforcement of0.75 percent, and concrete strengths of approximately 5,000 psi.
The test series significantly increased the data base for uniformlyloaded one-way slabs. Support rotations between 13.1 and 20.6 degrees wereobserved. A more ductile behavior was observed in slabs with construction de-tails, implying better concrete confinement due to more confining steel (i.e.,closely spaced stirrups, double-leg stirrups, and closely spaced principal re-inforcing bars). The parameters investigated did not appear to have asignificant effect on ultimate load capacity.
In the case of the Keyworker Shelter, the test series resulted in therecommendation of constructior details which reduce construction costs to alevel less than the preliminary shelter design.
Unclassified
SECURITY CLASSIFICATION OF THIS PAGEI(flon Dot* Entered)
- -
EFFECTS OF SHEAR STIRRUP DETAILS ON ULTIMATE CAPACITYAND TENSILE MEMBRANE BEHAVIOR OF REINFORCED CONCRETE SLABS
At the time this study was initiated, civil defense planning in the
United States called for the evacuation of nonessential personnel to safe host
areas when a nuclear attack is probable, requiring the construction of blast
shelters to protect the keyworkers remaining in the risk areas. The placement
of shear stirrups in the one-way reinforced concrete roof slabs of the
shelters will contribute significantly to project costs. Ten one-way rein-
forced concrete slabs were statically and uniformly loaded with water pres-
sure, primarily to investigate the effect of stirrups and stirrup details on
the load-response behavior of the slabs. The slabs had clear spans of
i 24.0 inches, span to effectiye depth ratios of 12.4, tensile reinforcement of
* 0.75 percent, and concrete strengths of approximately 5,000 psi
The test series significantly increased the data base for uniformly
loaded one-way slabs. Support rotations between 13.1 and 20.6 degrees were
* observed. A more ductile behavior was observed in slabs with construction
details, implying better concrete confinement due to more confining steel
(i.e., closely spaced stirrups, double-leg stirrups, and closely spaced
principal reinforcing bars). The parameters investigated did not appear to
have a significant.effect on ultimate load capacity.
In the case of the Keyworker Shelter, the test series resulted in the
recommendation of construction details which reduce construction costs to a
level less than the preliminary shelter design.
Accession For
ANTIs rt21&1DTIC TA-
Jujtif c:.t i
r..,By~ . ..]"} ~Di st rib,,'!.
i~A;"." ~Avail oi ' ,e
Dist j . ,
I (QUJALITY
33%* . _ _
PREFACE
The research reported herein was sponsored by the Federal Emergency Man-
agement Agency (FEMA) through the US Army Engineer Huntsville Division (HND)
in support of the Keyworker Blast Shelter Test Program.
Construction and testing were conducted by personnel of the Structures
Laboratory (SL), US Army Engineer Waterways Experiment Station (WES), under
the general supervision of Mr. Bryant Mather, Chief, SL; Mr. J. T. Ballard,
Assistant Chief, SL; Dr.. J. P. Balsara, Chief, Structural Mechanics Division
(SMD), SL; and under the direct supervision of of Dr. S. A. Kiger of the Re-
search Group, SMD. This report was prepared by Mr. S. C. Woodson of the Re-
search Group, SMD, and is essentially the same as his thesis which was sub-
mitted to Mississippi State University in 1984 in partial fulfillment of the
requirements for the Masters of Science Degree.
Commanders and Directors of WES during the investigation and the prepa-
ration of this report were COL Tilford C. Creel, CE, and COL Robert C. Lee,
CE; Technical Director was Mr. F. R. Brown. Director at the time of publi-
cation was COL Allen F. Grum, USA; Technical Director was Dr. Robert W.
Whalin.
0
.
CONTENTS
Page
PREFACE .. ....... ............... .......... 1
CHAPTER 1 INTRODUCTION. .. ............. ........... 6
1.1 BACKGROUND. .. .............. ............. 6*1.2 OBJECTIVES .. ....... ............... ..... 16
1.3 SCOPE. ....... ............... ........ 17
CHAPTER 2 TEST DESCRIPTION. .. ............. ........ 22
2.1 TEST TIME PERIOD, LOCATION, ANDGENERAL DESCRIPTION. ....... ................ 22
2.2 CONSTRUCTION DETAILS. .. ............. ........ 222.3 REACTION STRUCTURE DETAILS. .. ............. ..... 232.4 INSTRUMENTATION. ....... ................... 232.5 PHOTOGRAPHY. ....... ................ .... 242.6 TEST PROCEDURE .. ....... ................... 242.7 MATERIAL PROPERTIES. ....... ................ 25
CHAPTER 3 TEST RESULTS .. ...... ................... 35
3.1 STRUCTURAL DAMAGE. ....... ................. 353.2 PHOTOGRAPHIC DATA. ....... ................. 35
*3.3 INSTRUMENTATION DATA. .. ............. ........ 36
CHAPTER 4 ANALYSIS. .. ............. .............46
4.1 COMPARISON OF STRUCTURAL DAMAGEAND RESPONSE .. ....... ............... .... 46
4.2 YIELD-LINE THEORY........................474.3 COMPRESSIVE MEMBRANE EFFECT .. ............. ..... 484.4 ROTATION CAPACITY. ....... ................. 50
*4.5 TENSILE MEMBRANE EFFECT .. ............. ....... 54
CHAPTER 5 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS. ...... .... 69
5.1 SUMMARY. ....... ............... ....... 695.2 CONCLUSIONS. ....... ............... ..... 705.3 RECOMMENDATIONS. ....... ................... 70
REFERENCES. ....... ................ ........ 72
APPENDIX A: POSTTEST PHOTOGRAPHS AND DATA. ....... ........ 77
APPENDIX B: STIRRUP SLAB TEST DATA. .. ............. .... 83
APPENDIX C: NOTATION .. ....... ................... 177
2I
LIST OF ILLUSTRATIONS
Figure Page
1.1 Stirrup details ....... ...................... ... 201.2 Temperature steel placement .... ................ ... 211.3 Principal steel spacing ..... .................. ... 21
2.1 Principal and transverse reinforcement layout (Slabs 1-8). 292.2 Principal and transverse reinforcement layout (Slabs 9
and 10) ....... .......................... .... 292.3 Stirrup placement, single-leg stirrups ............. .... 302.4 Stirrup placement, double-leg stirrups ............. .... 302.5 Slab 2 construction ...... .................... ... 312.6 Cross section of reaction structure .. ............ ... 312.7 Reaction structure ...... ..................... .... 322.8 Instrumentation gage location ..... ........ .. 322.9 Instrumentation gage location, Slab 4 .. ........... ... 332.10 Four-foot-diameter blast load generator . .......... ... 332.11 Membrane in place. ...... .... ...................... 342.12 Strain gage data. ....... ..................... .... 343.1 Posttest view of Slab 4 ..... .................. ... 403.2 Posttest view of Slab 2 ..... .................. ... 403.3 General deformation ...... .................... ... 413.4 Posttest view of undersurface of slabs ............. .... 413.5 Sequence of crack formation, Slab 8 .. ............ ... 423.6 Slab 8 photographic sequence .... ................ .... 453.7 General load deflection ..... .................. ... 454.1 Formation of three-hinged mechanism .. ............ ... 624.2 Rotation capacity vs. stirrup spacing .. ........... ... 634.3 Slab 1 tensile membrane prediction ............... .... 644.4 Slab 2 tensile membrane prediction .. ............. .... 644.5 Slab 3 tensile membrane prediction .. ............. .... 654.6 Slab 4 tensile membrane prediction ...... ............. 654.7 Slab 5 tensile membrane prediction ...... ............. 664.8 Slab 6 tensile membrane prediction .. ............. .... 664.9 Slab 7 tensile membrane prediction .. ............. .... 674.10 Slab 8 tensile membrane prediction .. ............. .... 674.11 Slab 9 tensile membrane prediction .. ............. .... 684.12 Slab 10 tensile membrane prediction .. ............ ... 68
LIST OF TABLES
Table Page
1.1 Test matrix ........................ 191.2 Slab characteristics ...... ........ ...... 192.1 Results of concrete cylinder tests .. ............. .... 272.2 Tensile test for.steel reinforcement .............. ... 283.1 Structural damage at midspan ....... ................ 33.2 Structural damage at supports. . .............. 373.3 Photographic data summary for Slab 8 .............. ... 383.4 Load-deflection summary ..... .................. ... 383.5 Residual midspan deflection .... ................ .. 394.1 Stirrup configuration ..... ................... .... 584.2 Temperature steel placement .... ................ ... 58
3
0
CONVERSION FACTORS, NON-SI TO SI (METRIC)UNITS OF MEASUREMENT
- Non-SI units of measurement used in this report can be converted to SI
-. (metric) units as follows:
Multiply ByTo Obtain
degrees (angle) 0.01745 radians
*feet 0.30148 metres
*foot-pounds 1.355818 Joules
-gallons (US liquid) 3.785412 litres per minuteper minute
inches 25.4 millimetres
inch-kips 0.113 kilojoules
*kips per 6.894757 megapascalssquare inch
megatons (nuclear 4.184 gigajoules
equivalent of TNT)
*microinches 1.0 millionthsper inch
pounds (force) per 0.006891475 megapascals
square inch
EFFECTS OF SHEAH STIRRUP DETAILS ON ULTIMATE
CAPACITY AND TENSILE MEMBRANE BEHAVIOR
OF REINFORCED CONCRETE SLABS
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND
The Federal Emergency Management Agency (FEMA) has the responsibility of
planning an appropriate civil defense program for the United States. At the
time this study was initiated, civil defense planning called for the evacua-
tion of nonessential personnel to safe (lower risk) host areas when a nuclear
attack is probable. The construction of blast shelters will be required to
protect the keyworkers remaining in the risk areas. Both expedient and delib-
erate types of shelters are planned. The shelters will be designed to resist
blast, radiation, and associated effects at the 50-psi peak overpressure
level for a 1-MT nuclear weapon. FEMA has tasked the US Army Engineer Hunts-
ville Division (HND) to develop keyworker shelter designs. The US Army Engi-
neec Waterways Experiment Station (WES) is supporting HND with design calcula-
tions and structural experiments to verify design calculations.
With the anticipation of the construction of 20,000 to 40,000 of the
shelters, economical design requirements are very important. Because of high
labor intensity, it is expected that the placement of shear stirrups in the
roof slabs of the shelters will contribute significantly to project costs.
The primary purpose of the research reported herein is to investigate the ef-
fects of stirrups and stirrup details on the moment capacity and ductility of
a one-way reinforced concrete slab. This research is a part of the support
provided to HND by WES.
In the past, concrete was considered to be a very brittle material. Re-
search by Lee (Reference 1) and Shah (Reference 2) indicates that concrete is
not as brittle as once considered. It is relatively more ductile than its
constituents, hardened paste or stone. This results from the composite action
ig A table of factors for converting non-SI to SI (metric) units of measurementis presented on page 5.
I-[.6
|S
.:
and slower growth of stable microcracks initiated at the interface between
hardened paste and stone. Barnard (Reference 3) concluded that while the in-4i ternal failure mechanism of concrete may be brittle on the microscopic scale,_
it is not brittle on the macroscopic or structural scale.
Park and Paulay (Reference 4) state that brittle failure of reinforced
concrete members should not occur. In the event of a structure being loaded
to failure, it should be capable of undergoing large deflections at near-
maximum load-carrying capacity to help prevent total collapse. Depending on
. the ductility of the members at the critical sections, a moment redistribution
- can take place. As ultimate load is approached, some sections may reach the
ultimate moment capacity before other sections. However, if plastic rotation
can occur at these sections, additional load can be carried as the moments
elsewhere increase to their ultimate value.
Cohn (Reference 5) and Cohn and Petcu (Reference 6) explain that the
rotation capacity of a plastic hinge may be expressed as the total rotation
accumulated along a short zone ko , plastic hinge length, where yield has
spread near the support under consideration. The rotation capacity of plastic
hinges depends essentially on the inelastic properties of the reinforced con-
crete sections.
Park and Paulay (Reference 4) also state that if the compression zone of
* a member is confined by closely spaced transverse reinforcement in the form of
closed stirrups. ties, hoops, or spirals, the ductility of the concrete may be
gretly improved. At low levels of stress in the concrete, the transverse re-
* inforcement is hardly stressed and the concrete is unconfined. The concrete
* becimes confined when the transverse strains become very high because of pro-
gressive internal cracking and the concrete bears out against the transverse
reinforcement which provides passive confinement.
Roy and Sozen (Reference 7) axially loaded 60 prisms with varying tie
spacing and amounts of longitudinal reinforcement. It seemed that the square
ties did not enhance the load-carrying capacity of the concrete, but did in-
crease the ductility of the concrete in the specimens. In contrast, Chan
(Reference 8), Soliman and Yu (Reference 9), Stockl (Reference 10), and
Bertero and Felippa (Reference 11) have observed an increase in strcn,<t due
to closely spaced rectangular hoops.
McDonald (Reference 12) experimentally investigated the effect of con-
fining reinforcement (plane meshes, helices, and closed stirrups) in
7
112 concrete prisms and 24 simply supported reinforced concrete beams. The
beams were tested to failure under two symmetrical line loads applied 6 inches
from the beam centerline. Results of the tests clearly demonstrated the abil-
ity of confining compressive reinforcement to significantly increase the duc-
tility of reinforced concrete beams using high-strength steel. Uniaxial tests
on the prisms demonstrated that concrete properly confined by lateral rein-
forcement had a considerable load-carrying capacity up to strains in excess of
* 2 percent, or more than six times the amount of strain usually considered as
ultimate for concrete.
- Sargin, Ghosh, and Handa (Reference 13) discuss confinement of concrete
by rectilinear lateral reinforcement. An experimental investigation was per-
*formed in which 63 prisms were tested, with the main variables being:
(1) concrete strength, (2) size, spacing, and grade of lateral reinforcement,
(3) strain gradient, and, (4) thickness of cover. Conclusions included:
(1) a laterally reinforced concrete member should be treated as a composite
member consisting of a confined core and an unconfined cover, (2) the amount
of confinement provided by lateral reinforcement is dependent not only upon
the volumetric ratio of lateral reinforcement but also upon the type of lat-
eral reinforcement (discrete square or rectangular ties, spirals, envelopes,
etc.); the spacing and grade of reinforcement; and the quality of confinedconcrete, (3) spacing is the most important parameter because the choices of
". 'bar size and qualities of concrete and steel are rather limited in practice.
The effect of transverse reinforcement decreases drastically with increasing
spacing and becomes negligible for spacings larger than the thickness of the
core, and (4) the ductility and hence the rotation capacity of the so-called
hinging regions in reinforced concrete members can be improved to a large ex-
tent through the use of lateral reinforcement.
Tests indicate that spiral reinforcement is more effective than rectangu-
lar hoops in confining concrete. Richart, Brandtzaeg, and Brown (Refer-
ence 14) showed that the strength of concrete confined by circular spirals is
similar to that confined by fluid pressure. Bertero and Felippa (Refer-
ence 11) loaded concrete prisms containing square ties. The effect of ties on
the ductility was not as great as in the case of spiral-reinforced cylinders
• 'tested by Iyengar, Desayi, and Reddy (Reference 15). Sheikh and Uzumeri (Ref-
erence 16) found that for columns with rectilinear reinforcement, the confin-
ing pressure is not uniformly applied throughout the volume of the concrete
83"
. * * * *. * .. . ..~.- *- . . * * . - .
, .: . . .. .. . .. .. . ... . . .-. -. . .. . . . . C...t -I.--. . .. . .. . .. _. ... , . , . ,
core, unlike the concrete specimen confined by hydraulic pressure or spiral
reinforcement.
Kent and Park (Reference 17) explain that rectangular or square hoops do
not confine the concrete as effectively as circular spirals. This is because
the confining reaction can only be applied in the corner regions of the hoops,
* since the bending resistance of the transverse steel between the corners is
insufficient to restrain the expansion of the concrete along the whole length
of the bar. Since the concrete is only effectively confined in the corner and
,. central regions of the cross section, a disruption of a considerable portion
* of the core area occurs. However, the rectangular hoops do produce a signifi-
cant increase in the ductility of the core as a whole.
Base and Read (Reference 18) agree that decreasing the brittleress of the
failure of some types of concrete members is an important consideration and
that close spacing of rectangular stirrups is one method of containing dilat-
ing concrete in the compression zone of a plastic hinge. One-point-loaded,
0/. simply supported beams indicated that under-reinforced concrete beams probably
have more than adequate plasticity at failure and should not need any special
secondary reinforcement at plastic hinge regions. Balanced-section reinforced
concrete beams failed in a brittle manner unless the compression zone was
"bound". Over-reinforced concrete beams without special secondary reinforce-
• .ment failed very brittle and failure was terminated by a shear collapse.
Closely spaced stirrups completely prevented shear collapse but eventually al-
lowed the compression zone to crush because they deformed outwards under the
bursting pressure of the concrete. It was concluded that a combination of
helices and close stirrups would be necessary to produce ideal
characteristics.
Shah and Rangan (Reference 19) investigated the use of stirrups in rein-
, forced concrete beams. For over-reinforced beams (P > Pb) it was found
that: (1) the addition of stirrups does not significantly influence the
load-deflection curves up to the maximum load, (2) the addition of stirrups
increases ductility, and (3) the addition of stirrups retards internal crack
* , . growth of compression concrete. For under-reinforced beams < Pb) it was
found that: (1) in agreement with Base and Read (Reference 18), the addition
of stirrups did not influence the rotation capacities, and (2) no volume dila-
tion of the compression zone was observed and the concrete compressive strains
were considerably lower than those for over-reinforced beams.
-- 9
- r r r. r m r . r . .
Shah and Rangan (Reference 19) also studied the relative efficiency of
compression reinforcement, rectangular ties, and randomly oriented short steel
fibers in improving ductility of compression concrete in flexural members.
Rectangular ties were by far the most efficient.
Yamashiro (Reference 20) varied axial load on beam columns. The deflec-
tion at ultimate load was quite sensitive to variations in the amounts of
transverse and compression reinforcement, whereas the deflection at crushing
was not. The deflection at ultimate load was from 2 to 12 times the crushing
deflections.
Based on beam data, Keenan and others (Reference 21) state that conven-
tional reinforced concrete members with compression steel can reliably main-
tain their ultimate moment resistance to maximum support rotations of
14 degrees, provided the compression bars are confined by effective ties and
q < 0.14 where q is the reinforcing index defined by:
q (pf- 'f )f;
where:
p tension steel ratio
f yield strength of tension steely
P' compressive steel ratio
f: yield strength of compression steel
f :compressive strength of concrete
The effectiveness of ties depends on the tie spacing, the size of the compres-
sion bars, and the applied moment gradient. Without ties but with q (0.14
the effectiveness of compression reinforcement is less reliable.
Mattock (Reference 22) tested 37 beams, demonstrating that the rotational
capacity of a part of a beam under loading producing a moment gradient is
greater than that of a similar beam under loading producing constant moment
• (zero shear). A method was proposed to calculate the rotational capacity of a
hinging region in reinforced concrete beams. Mattock states that if calcula-
tions are to be made of the total inelastic or plastic rotations, a knowledge
of moment-curvature relationships for the reinforced concrete sections is
necessary. It was shown that close estimates of moments and safe limiting es-timates of curvatures and rotations can be derived from well-known principles
of equilibrium of forces and compatibility of strains, provided that strain
10
~~~~~~..................'....'..l . . .... --
hardening of the reinforcement and variation of maximum concrete compressive
strain are taken into account. Mattock also found that maximum apparent con-
crete strain is often considerably in excess of the commonly assumed value of
0.0030 and that it increases as the shear span decreases.
Based upon tests on two beams and two columns, Sinha and Rane (Refer-
ence 23) concluded that the use of an ultimate concrete strain value of 0.0030
and the determination of the position of the neutral axis assuming linear
strain distribution provides a very conservative basis for determining the
total curvature developed in a reinforced concrete member. The data obtained
from the experiments showed that a concrete strain value of 0.0050 to 0.0060
for beams reinforced in tension and compression yields better results.
Mattock (Reference 22) points out that in the past, considerable effort
has been made to determine moment-curvature relationships experimentally and
to devise calculational methods. Curvature measurements have usually been
taken in the constant-moment region of a simply supported beam loaded at two
points. Rotations have been predicted with reasonable accuracy except for
plastic rotation calculations of the region adjacent to a support in a contin-
uous beam, in which calculated rotational capacity is less than the observed
rotation in the continuous beam.
Mattock did not investigate confinement of concrete in the beam tests.
Corley (Reference 24) tested 40 beams as an extension of Mattock's tests to
investigate the effects of specimen size and confinement of the concrete in
compression. Corley also studied the effects of moment gradient, percentage
of tensile reinforcement, and size of loaded area. All 40 beams had rectangu-
lar stirrups and were under-reinforced. Failure occurred due to crushing of
the concrete after the tension reinforcement had yielded. Corley concluded
that the direct effect of size of model on rotational capacity is not signifi-
cant, and that beams with a large number of closely spaced stirrups exhibit
considerably more rotational capacity than beams with few stirrups.
Taylor, Maher, and Haynes (Reference 25) used axial test data on rein-
forced concrete cylinders to conclude that confinement is found to be effec-
tive only when the pitch 6f the ties is less than the least lateral dimension
of the confined specimen.
Bachman (Reference 26) tested two groups of five symmetrical two-span
beams and observed two types of plastic hinges: (1) flexural crack hinges and
(2) shear crack hinges. Flexural crack hinges develop in a beam zone in which
............. ............. ...,, .... .. ............................ ..-..-...
the bending moment is predominant. The shear stress is small and only ver-
tical flexural cracks occur. When the plastic deformations are concentrated
mainly to one or a few cracks, the rotational capacity of such a flexural
crack hinge may be very small. At a shear crack hinge, diagonal flexural-
shear cracks are produced due to a relatively large shear stress accompanied
by a bending moment, improving the behavior of the hinge. It was shown that
the plastic deformations in a shear crack hinge occur over a much wider zone
than with flexural crack hinges, allowing a much greater rotational
capacity.
Bachman stated that in flexural crack hinges with ultimate failure due to
the rupture of the reinforcement, the ultimate rotations are found to decrease
with: (1) better bond properties, (2) smaller bar diameter, (3) less strain-
hardening, (4) smaller permanent steel strain, (5) greater crack spacing, and
(6) greater shear force.
Cohn and Ghosh (Reference 27) recognize ductility as a factor governing
*: the rotation capacity of hinging zones and the redistribution of moments in a
* structure. The researchers state that members are sufficiently ductile, for
all practical purposes, when they resist only transverse loads, are moderately
reinforced in tension, moderately to heavily reinforced in compression and
shear, use mild- or intermediate-grade steels, and use high-grade concretes.
Cohn and Ghosh believe that ductility can be increased somewhat by reducing
. the spacing and increasing the diameter of the ties. They also believe that
ductility decreases with increasing amounts of tension steel, but can be im-
proved considerably by the addition of suitable amounts of compression steel.
Srinivasa Rao, Kannan, and Subrahmanyam (Reference 28) and Burnett (Ref-
erence 29) point o,'t ciat several authors including Corley (Reference 24),
Mattock (Reference 22), and Baker and Amarakone (Reference 30) disagree even
on the basic definition of what is to be taken as plastic rotation capacity.
Baker and Amarakone suggest that the rotation capacity under a concentrated
load acting at beam midspan increases with length of the beam. In contrast,
Mattock and Corley predict that rotation capacity will be larger in short
beams. Srinivasa Rao, Kannan, and Subrahmanyam loaded simply supported beams
with a concentrated load at midspan, varying span length. It was concluded
* that plastic rotation capacity increased as the spread of plasticity increased
with larger beam spans.
Burnett states that if research priorities are to be established, it is
12
evident that the support critical section is particularly important.
In any study investigating the effect of a parameter (for example, the
variation of shear stirrup shape and placement) on the load-response behavior
of reinforced concrete slabs, an understanding of the effects of boundary con-
ditions and loading conditions on the load-response behavior of slabs is bene-
ficial. In 1955, Ockleston (Reference 31) tested a slab in a dental hospital
building and found that the interior panel of the under-reinforced floor sys-
. tem, acting as a restrained slab, carried more than double the load predicted
by Johansen's yield-line theory (Reference 32).
In 1958, Ockleston (Reference 33) explained that the unexpected results
of his test in 1955 were not due to reinforcement strain hardening, tensile
strength of concrete, or catenary actions. It was concluded that the increase
in load capacity was due to the development of inplane compressive forces,
termed "arching" or "dome action."
Experimental research using uniformly loaded beams or one-way slabs is
very limited. Burnett (Reference 34) considered that the effect of applying a
uniformly distributed load rather than a point load to a simply supported beam
. would alter the moment distribution, the curvature distribution, and the
moment-rotation relation. Burnett concluded that the parameters involved in
the behavior of a member as a whole are many more than those affecting the be-
havior of an individual section within that member. Corley (Reference 24)
*. acknowledged that uniform loading was not investigated as a part of his exten-
sion of Mattock's work. Corley stated that although no significant change in
the results of tests with uniform loading should be anticipated, this respect
still remains to be studied. Iqbal and Derecho (Reference 35) stated that no
data are available for one-way slabs tested under uniformly distributed load.
During the same year that Iqbal and Derecho reported their work (1969),
*- Keenan (Reference 36) tested four laced reinforced concrete one-way slabs to
failure under a uniformly distributed load. All slabs spanned one direction
with ends clamped and longitudinally restrained to prevent rotation and longi-
tudinal movement at their supports. One slab was tested to the point of
failure with an increasing static load applied by water pressure. The other
three slabs were subjected to two or more short-duration dynamic loads. Prin-
cipal tension and compression reinforcement were placed to the interior of the
transverse reinforcement, and diagonal lacing bars were bent around the
U exterior face of the transverse reinforcement in a grid system. The lacing
13
Mbars distributed the load, resisted diagonal tension stresses, and confined
both the flexural steel and concrete separating the two layers of reinforce-
ment. The experimental rotation capacity of Keenan's slabs at the supports
was greater than 9.2 degrees.
Keenan (Reference 37) developed a theory for predicting the thrust, de-
* flection, and ultimate flexural resistance of uniformly loaded square slabs.
He then applied this theory to the tested one-way slabs (Reference 36) and
found good correlation between the theoretical and experimental resistance,
deflection, and steel stresses at stages of ultimate flexure and initial ten-
sile membrane action.
Keenan's theory considers that a slab spanning one direction is subjected
to combined bending and direct stress if the ends are restrained against
longitudinal movement. Deflections of the slab induce thrust on sections
along hinge lines which increases the moment resistance of sections along the
hinge lines, thereby significantly increasing the stiffness and ultimate flex-
ural resistance of the slab.
Park and Gamble (Reference 38) explain that Johansen's yield-line theory
only considers the presence of moments and shear forces at the yield lines in
the slab. Park and Gamble agree with Keenan that if the edges of slabs are
restrained against lateral movement by stiff boundary elements, inplane (com-
pressive membrane) forces are induced as the slab deflects and changes of
geometry cause the slab edges to tend to move outward and to react against the
bounding elements. The compressive membrane forces enhance the flexural
strength of the slab sections at the yield lines, which causes the ultimate
load of the slab to be greater than the ultimate load calculated using
Johansen's yield-line theory.
Kiger, Eagles, and Baylot (Reference 39) tested five one-way slabs pri-
-7- marily to investigate the effects of soil cover on the static and dynamic
capacity of earth-covered reinforced concrete slabs. One slab was loaded sur-
face flush with a slowly increasing uniform load. Compressive membrane forces
acted to almost triple the slab capacity predicted for the slab under unre-
strained conditions.
Roberts (Reference 40) tested 36 strips representing restrained one-way
slabs loaded by several point forces to simulate uniformly distributed load-
ing. The ratio of peak load to that given by Johansen's yield-line theory
varied from approximately 17 for strips with high concrete strength and a low
14
percentage of reinforcement to approximately 3 for beams with low concretestrength and a high percentage of reinforcement. Roberts concluded that the
deflection at maximum load is not a fixed proportion of the slab thickness,
and that it is not necessary for the restraint to have enormous stiffness to
develop enhanced peak loads.
Wood (Reference 41), Park (Reference 42), and Morley (Reference 43) as-
sume the central deflection at ultimate load to be 0.5 times the slab thick-
ness for fully restrained slabs. Hung and Nawy (Reference 44) use experi-
mental values of deflection at ultimate load and note that the ultimate load
is not always reached at a deflection equal to 0.5 times the slab thickness.
Instead, values ranging from approximately 0.4 to 1.0 times the slab thickness
are considered.
Work by Isaza (Reference 45) indicates that the maximum compressive mem-
brane effect occurs at a central deflection equal to approximately one-sixth
of the slab thickness.
Hopkins (Reference 46) points out that the absence of top steel at the
edges of laterally restrained slabs has little effect on the ultimate load.
The complete omission of top steel is not considered wise, but its length
could be reduced in slabs subjected to compressive membrane forces.
Brotchie, Jacobson, and Okubo (Reference 47) tested 45 two-way square
slabs in a highly rigid steel frame. It was observed that at small deforma-
tions, the compressive strength of the concrete governs and if the plate is
" restrained, arching or compressive membrane behavior occurs. However, at
large deformations, the concrete crushes, leaving only the tensile strength of
the reinforcement to resist loading. If the edge of the slab is restrained
- .iagainst inward displacement, the full strength of the reinforcement may be de-
veloped as a tensile net. It was also observed that tensile cracks increase
in number but decrease in width with the number of reinforcing bars.
Park (Reference 48) and Park and Gamble (Reference 38) discuss the ten-
sile net development known as tensile membrane behavior. After ultimate load
has been reached in a reinforced concrete slab, the supported load decreases
rapidly with further deflection. Eventually, membrane forces in the central
region of the slab change from compression to tension and the slab boundary
restraints begin resisting inward movement. Cracks in the central region
penetrate the whole thickness of the concrete and yielding of the steel
spreads throughout the region. The reinforcement may begin acting as a
15
S
v. .
tensile membrane with load-carrying capacity increasing with further
deflection until the reinforcement fractures.
From tests by Park (Reference 48), it was evident that pure tensile mem-
brane action did not occur in lightly reinforced two-way slabs, since the
cracking present at the end of the tests was little more than the cracking
which developed with the yield-line pattern at the ultimate flexural load.
Therefore, the load was carried by a stronger combined bending and tensile
membrane action. Heavily reinforced slabs cracked over much of their area and
therefore approached pure tensile membrane action.
1.2 OBJECTIVES
In considering the use of stirrups in one-way reinforced concrete slabs,
it is important to unddrstand the benefits which will be gained through the
use of the stirrups. Also, the effects which specific physical details will
* have on the efficiency of the stirrups should be understood. Figure 1.1 shows
three possible stirrup configurations. Figure 1.la shows a double-leg stirrup
(Type I) which might be expected to provide better confinement of concrete and
principal steel than the single-leg stirrup (Type I) in Figure l.b. The
135-degree bends on both ends of the Type II single-leg stirrup might be ex-
pected to confine concrete and principal steel better than the Type III
single-leg stirrup shown in Figure 1.1c which has a 90-degree bend on one
end. It is obvious that installation of both single-leg stirrups would be
labor-saving when compared to the installation of the Type I stirrup. The
Type III stirrup is also easier to install than the Type II stirrup, but the
question arises as to whether the 90-degree bend is as effective as the
135-degree bend against pullout. Type III stirrups used by Slawson (Refer-
ence 49) fractured under'large slab deflection, indicating that pullout may
not be a problem. In conjunction with specific details, the placement and
quantity of the stirrups required to achieve the desired benefits must be
known. This leads to an investigation of stirrup spacing.
Another important parameter to be considered is the interaction of the
stirrups with other reinforcement in the slab (for example, the transverse re-
inforcement or temperature steel). Much of the work explained above concerned
the use of closed rectangular hoops. The presence of stirrups and temperature
steel at the same location forms a closed hoop resembling a continuous
rectangular tie. Keenan and others (Reference 21) indicated that in order to
16
d ,d d., .'.,** * " - .. . . .
assure adequate confinement of concrete rubble under large deflections of a
slab, the principal steel bar spacing should not exceed the effective depth.The interaction of this parameter with the presence of stirrups should be
understood to insure that stirrups are not used ineffectively due to excessive
principal steel bar spacing.
Specifically, the objectives of this study were to investigate the ef-
fects of the following parameters on the ultimate load capacity and tensile
membrane behavior of a one-way reinforced concrete slab: (1) stirrup configu-
,i rations as presented in Figure 1.1; (2) stirrup spacing; (3) the interaction
of the stirrups with the transverse reinforcement (temperature steel) under
the two placement conditions shown in Figure 1.2; and (4) the interaction of
the stirrups with the two principal reinforcement bar spacings shown in
Figure 1.3.
1.3 SCOPE
Ten one-way reinforced concrete slabs were statically (slowly) loaded
with water pressure in the WES 4-foot-diameter blast load generator. Huff
(Reference 50) gives a detailed description of the test device, which is
capable of developing static loads up to 500 psi. The slabs had a span-to-
effective-depth (L/d) ratio of 12.4 with a clear span length of 24 inches.
Principal steel ratios were about 0.0075 and 0.0085 for the tension face and
compression face, respectively. Grade-60 reinforcement steel was used, and
the concrete had an average test-day compressive strength of 4,790 psi. The
slabs were supported in a reaction structure and were restrained at the ends.
Table 1.1 presents a test m trix demonstrating the variations of the
parameters required to accomplish the stated objectives. Each of the three
stirrup configurations was separately tested in three different slabs. An
analysis based upon three empirical relations developed by Baker and Amarakone
(Reference 30), Corley (Reference 24), and Mattock (Reference 51) was used to
determine the stirrup spacings to be investigated. Stirrup spacings of 0.75,
1.5, and 3.0 inches were selected with the anticipation that the behavior of
the slabs with the 0.75-inch spacings would be cor iderably different frr
slabs with the 1.5- or 3.0-inch spacings.
The temperature steel was spaced at 3.0 inches on center in both faces in
all slabs, giving a ratio of total temperature steel to total concrete area of
0.00326. Placing the temperature steel in the interior and the exterior
17.... .... .... . * - ** - - . .
*.- * *-... * -.. - *-
regions of the slab cross section, as shown in Figure 1.2, allows a variation
in the area of concrete confined between the temperature steel. Therefore,
two slabs were constructed with the temperature steel placed in the exterior
regions.
Two principal steel spacings, 1.75 and 3.75 inches, were used in the
slabs. The 3.75-inch spacing was used in order to allow correlation with
tests being performed by Slawson (Reference 52) on 1/4-scale box elements re-
presenting the HND-proposed roof slab design. The 1.75-inch spacing was used
to investigate the effect of the criteria given by Keenan and others (Refer-
ence 21) maintaining the bar spacing to a value less than the effective depth,
1.9375 inches.
Table 1.2 presents a more detailed description of each of the ten slabs.
18
Table 1.1. Test matrix.
Number ofSpacings,
Stirrup Number of Spacings to be Spacing InteriorConfig- Tested with Temperature Steel in of Principal anduration Interior Region Exterior Region Steel, in Exterior
Type I 1 -- 3.75 1
Type II 3 1 3.75 4. Type I 2 -- 1.75 2
Type III 1 1 3.75 2
No Stirrups 1 3.75 1
Total Number of Tests 10
Table 1.2. Slab characteristics.
Stirrup Stirrup PrincipalConfiguration Spacing Steel Spacing Temperature
Slab Type in in Steel Placement
1 No Stirrups -- 3.75 Interior
2 II 0.75 3.75 Interior
" 3 II 1.5 3.75 Interior
4 II 3.0 3.75 Interior
5 II 1.5 3.75 Exterior
6 I1 1.5 3.75 Interior
7 Il 1.5 3.75 Exterior
8 I 1.5 3.75 Interior
9 II 1.5 1.75 Interior
10 II 0.75 1.75 Interior
19
V- ) : " "-'-" i : - i - " " " " " ' " " " " "" " "
NN
~II+_______ D1 WIREL (db' 0. 11"1
I- 3.75"
4. 0"
4.22"
a. TYPE 1
D1 WIRE(ldb 0. 11"
b. TYPE 2
+
D1 WIRE
* c. TYPE 3
Figure 1.1. Stirrup details.
20
S7
00PRINCIPAL STEEL TEMPERA TURE STEEL
a. Temperature steel outside principal steel.
PRINCIPAL STEEL TEMPERA TURE STEEL---,.
0 01
b. Temperature steel inside principal steel.
Figure 1.2. Temperature steel placement.
24"
1- j -15/16-
~~~334 ~ 2LZ ~EPRTRE STEEL PRINCIPAL STEdb -O ll'd 0.25"
a. 3-3/4-inch spacing.
24"
1- 15,176"
518" TEMPERA TURF STEELdh -0. 11"l PRINCIPAL STEEL
(,-0. 179"
b. 1-3/Lb-inch spacing.
Figure 1.3. Principal steel spacing.
21
CHAPTER 2
TEST DESCRIPTION
2.1 TEST TIME PERIOD, LOCATION,AND GENERAL DESCRIPTION
Ten one-way reinforced concrete slabs were statically tested by WES in
Vicksburg, Mississippi, between 30 November 1983 and 3 February 1984.
The following sections describe test slab construction details, reaction
' structure details, instrumentation, photography, test procedure, and material
properties.
2.2 CONSTRUCTION DETAILS
Eight of the ten slabs (Slabs 1 through 8) were constructed of 0.25-inch-
diameter deformed wire (principal reinforcement) and D1 deformed wire (tem-
*- perature reinforcement). Slabs 2 through 8 were also reinforced with DI
deformed wire stirrups. Figure 2.1 shows a plan view of Slabs 1 through 8
* without stirrups. The total area of reinforcement in the compression face was
equal to the total area of reinforcement in the tension face. Due to the dif-
ferent thickness of concrete cover on compression and tension reinforce.cnt,
compression and tension reinforcement ratios were not equal. The effective
.* depth used in calculating the ratios was measured from the extreme tension
_ face for the compression reinforcement and from the compression face for the
tension reinforcement. Principal reinforcement percentages for Slabs 1
through 8 were 0.72 percent and 0.83 percent for the tension face and compres-
sion face, respectively.
Slabs 9 and 10 were constructed of D2.5 deformed wire (principal rein-
* forcement) and D1 deformed wire (temperature reinforcement). Figure 2.2 is a
plan view of Slabs 9 and 10 without stirrups. Stirrups in these two slabs
were made from 0.080-inch-diameter smooth wire. Principal reinforcement ,er-
centages for Slabs 9 and 10 were 0.75 percent and 0.86 percent for the tension
face and compression face, respectively.
The temperature steel was spaced at 3.0 inches on center in both faces in
all slabs, giving a ratio of total temperature steel to total concrete area of
0.00326. The effective depth (d) in each slab was 1.9375 inches, and the
span-to-effective depth (L/d) ratio was 12.4.
22
.- . .. .. . .- - . ... . -. .* - - . *7 * - . *, " - .* *
As discussed in Chapter 1 and shown in Figure 1.2, two temperature rein-
forcement placement conditions were investigated. Slabs 5 and 7 were con-
structed using the "exterior" placement condition presented in Figure 1.2a.
The remaining eight slabs were constructed using the "interior" placement con-
dition presented in Figure 1.2b.
Each slab, except Slab 1, contained stirrups as presented in Table 1.2.
Figure 2.3 shows typical placement details for slabs having single-leg (Type I
or Type II) stirrups. Figure 2.4 shows stirrup placement details for the slab
(Slab 8) containing double-leg stirrups. The stirrup spacing utilized in Fig-
ures 2.3 and 2.4 is 1.50 inches. The double-leg stirrups were staggered to
place only one leg at any location along the principal reinforcement, simulat-
ing the spacing of single-leg stirrups.
The slabs were constructed and cast at the Structures Laboratory of WES.
Figure 2.5 documents the steel reinforcement placement of Slab 2 (bottom side
up) prior to placement of concrete.
2.3 REACTION STRUCTURE DETAILS
The reaction structure used by Kiger, Eagles, and Baylot (Refer'ence 39)
at the WES Structures Laboratory in a previous test program was utilized in
the test series under discussion. Figure 2.6 shows a cross-sectional view of
the reaction structure. The reaction structure was modified with a removable
door to allow access as shown in Figure 2.7. Placement of a 36- by 24-inch
" slab in the reaction structure allowed 6 inches of the slab at each end to be
clamped by a steel plate bolted into position, thereby leaving a 24- by
24-inch one-way restrained slab for testing.
2.4 INSTRUMENTATION
Each slab was instrumented for strain, displacement, and pressure mea-
surement. The data were recorded on a Sangamo Sabre III FM magnetic tape
recorder, and digitized and plotted by computer. Figure 2.8 shows the instru-
mentation gage layout for a typical slab with stirrups. Two displacement
transducers were used in each test to measure vertical displacement of the
slab, one at one-eighth span (D1) and one at midspan (D2). The transducers
used were Trans-Tek Model 0246-0000, having a working range of 6.00 inches.
Two single-axis, metal-film, 0.125-inch-long, 350-ohm, strain gage pairs
were installed on principal reinforcement in each slab. Each pair consisted
23
.: " 4 ' - . *, •~. . ".* - " . " --. - - *.* * ' T i • . - - " T- -: . * * .'...".: w ....
", of a strain gage on a top bar and one on a bottom bar directly below. One
pair was located at one-fourth span (STI, SB1) and one was located at midspan
(ST2, SB2). The gages used were Micro-Measurements Model EA-06-125 BZ-350.
Strain gages were also installed on three stirrups in each of Slabs 2
through 10. The strain gages were located at mid-height of total stirrup
height. One instrumented stirrup was placed at 1.50 inches from the support
(S3), one at one-fourth span (S4), and one at midspan (S5). Figure 2.9 shows
that Slab 4 is an exception, with Gages S4 and S5 placed at 7.50 and
10.50 inches from the support, respectively.
One Kulite Model HKM-S375, 500-psi-range pressure gage (P1) was mounted
in the bonnet of the test chamber in order to measure the water pressure ap-
plied to the slab.
2.5 PHOTOGRAPHY
Photographic coverage was provided during construction of the slabs and
during posttest examination of each slab. The photographs helped document the
*. structural damage for comparative purposes.
Photographic coverage was also provided during the testing procedure. A
Cannon AE-1 35-mm camera was placed inside the reaction structure beneath the
slab and was remotely controlled. Therefore, photographs of the undersurface
. of the slab were obtained at several levels of damage.
- 2.6 TEST PROCEDURE
The 4-foot-diameter blast load generator (Figure 2.10) was used to stat-
ically load the slab with water pressure. The reaction structure was placed
. inside the test chamber and surrounded with compacted sand as shown in Fig-
ure 2.7. The slab was then placed on the reaction structure. The wire leads
from the instrumentation gages and transducers were connected, and the camera
- was placed into position. After placing the removable door in position, the
sand backfill was completed on the door side. A 1/4-inch-thick neoprene
, rubber membrane was placed over the slab, and 1/2- by 24-inch steel plates
were bolted into position as shown in Figure 2.11. Prior to the bolting of
the plates, Aqua Seal putty was placed between the rubber membrane and the
steel plates to seal gaps around the bolts and to prevent loss of water
pressure during testing. A torque wrench was used to achieve approximately
50 foot-pounds on each bolt, and a consistent sequence of tightening the bolts
24I[
was used for each slab. The bonnet was bolted into position with forty
1-1/8-inch-diameter bolts tightened with a pneumatic wrench. A commercial
waterline was diverted to the chamber's bonnet. The data tape recorder was
started immediately preceding the opening of the waterline valve. A time of
approximately 18 minutes was required to fill the bonnet volume of the test
chamber. A relief plug in the top of the bonnet indicated when the bonnet had
* -,been filled. At that time the waterline valve was closed to allow closing of
the relief plug. The waterline valve was again opened slowly, allowing a flow
of approximately 1.0 gal/min through the 1/4-inch-diameter waterline and
*" inducing a slowly increasing load to the slab's surface. A pneumatic water
pump was connected to the waterline to facilitate water pressure loading in
the case that commercial line pressure was not great enough to reach ultimate
resistance of the slab in any particular test. Only tests of Slabs 9 and 10
required use of the pump due to the lack of sufficient commercial waterline
pressure. Monitoring of the pressure gage and the deflection gage located at
midspan of the slab indicated the behavior of the slab during the test and
enabled the engineer to make a decision for test termination by closing the
waterline valve. Following test termination, the bonnet was drained and
removed. Detailed measurements and photographs of the slab were taken after
removal of the rubber membrane. Finally, the damaged slab was removed and the
* reaction structure was prepared for another slab test.
2.7 MATERIAL PROPERTIES
The 10 slabs were cast of concrete from one batch which was proportioned
for a 28-day design strength of 4,000 psi. The concrete was composed of
Type I portland cement and 3/8-inch-maximum-diameter pea gravel. The mix pro-
portion, by weight, given as cement:fine aggregate:coarse aggregate was
1:3.26:3.14. The water-cement ratio, by weight, was 0.67. !4
*" One test cylinder was cast for each slab and two cylinders were cast from
the batch for 28-day compression tests. The one cylinder per slab was tested
on test day for that particular slab. Results of the concrete cylinder tests
are presented in Table 2.1.
Five of the concrete cylinders were instrumented with strain gages.
Figure 2.12 is a typical plot of the strain gage data for a cylinder. The
average values of modulus of elasticity E and Poisson's ratio v for the
five instrumented cylinders were 4.4 x 10 psi and 0.22, respectively.
25
. . . I
*- ."Deformed wire was used as reinforcement in the slabs. The wire was heat-
treated in an oven at WES, producing a definite yield point at a yield stress
of approximately 60,000 psi. Before heat treatment, the wire had an approxi-
mate yield stress of 90,000 psi. Numerous trials with various oven tempera-
r- tures were required before satisfactory results were obtained. Table 2.2
-- presents results of tensile tests performed on specimens from heat-treated
batches used in construction.
26
Table 2.1. Results of concrete cylinder tests.
Concrete Age Compressive Corresponding
Batch days Strength, psi Slab Test
1 28 4,120
1 28 3,960
1 103 4,860 4
1 118 5,060 3
1 124 4,920 2
1 140 4 ,8 5 0a 6
S1 144 5 ,1 10a 8
1 154 5 ,0 2 0a 7
1 158 5 ,0 60a 5
1 163 4 ,700a 9
1 166 4,930 10
1 168 4,830 1
aStrain-gaged cylinder.
27
Table 2.2. Tensile test for steel reinforcement(deformed wire).
Wire Diameter Yield Stress Ultimate Stressin psi psi
0.11 68,500 69,400
Temperature steel, all slabs 57,760 61,580
Stirrup steel, Slabs 1 through 8 65,040 67,650
57,310 61,130
0.247 64,300 66,700
Principal steel, Slabs 1 58,000 65,500through 8 59,290 65,570
57,620 65,990
59F490 60,960
61,200 68,480
58,460 64,930
0.174 66,400 71,200
Principal steel, Slabs 9 65,600 72,000and 10 66,200 77,400
58,000 72,400
55,600 79,200
0.080 63,360 81,470
Stirrup steel, Slabs 9 and 10 64,360 82,040
63,650 80,620
62,660 80,600
28
- • ... "" --- "" - .- .*." .-. ... .•". ,:-.. .- ... ,. • -.. -. . . . . -. .. . .. .-. . - .- . ,. ..- .-. , ,> . ,. . . . . . '.. -. . . -. .. . . .. . . . .-. -, .... . .- A..- - N.,
6 U
at 4"a
0
__ -- -- -- -- -- -- -- -- --c IA. z
- r- co- - - - -- - - - - - - - - - - - - -- 4O
a)IV
t' r
-K 4-
CCI-
04.> 4.)tj4M :3k
C 0)
0 ) -
ccc
at a
* 00
14\
292
t.L-7
Twe Newt -,.. . . .
N~d UV79,' I I
I~ I IC U)
" ' I I I I I I I ~ -
CL ()
q cc : Q)Cc4
z ~ z -4
oI u
IC~
at
A~ IwL
Q)
I bo
at,
c0
- - 4
Nil J. ..- wKrwrwr-- "vr
Figure 2.5. Slab 2 construction.
6- i1r 0/A. 60 KSI THREADED
RODS 041, 0.C.
0 a
24
Z 24"4.
* *.112"- THICK STEEL
C * .4 La PLATE* ~J -.La
p
I... - ~ 38- 314'
Figure 2.6. Cross section of reaction structure.
31
Figure 2.7. Reaction structure.
24"
D2
* -STSB Figure 2.8. Instrumentation
D2S T S--gage
location.ST1, Sal.S4
DI
SI,1 12
LEGEND
0STRAIN GAGE ON TOP AND BOTTOM PRINCIPLE REINFORCED BARS
ASTRAIN GAGE ON STIRRUP
0 DISPL.ACEMENT GAGE BENEATH SLAB 3
4 24
ST2. SB2 D2
S5S4T ~
STI. SBI
01 L_ K.
_ 53
LEGEND
o STRAIN GAGE ON TOP AND BOTTOM PRINCIPLE REINFORCEMENT BARS
STRAIN GAGE ON STIRRUP
O DEFLECTION GAGE BENEATH SLAB
Figure 2.9. Instrumentation gage location, Slab 4.
W, w
Figure 2.10. Four-foot-diameter blast load generator.
33
,." -, ' ' ..'" ...-," -. .' .".. . . . ." ,- " . . ' "• . ,
Figure 2.11. Membrane in place.
3000
* o260 ____ Figure 2.12. Straingage data.
HI0 7S0 600 ISO 000 1250 1500 1750 2000 2250I IX 0 I1W) 4100 500 600 700 B00 0()
STN*IN MU *lfIN -N
34~
CHAPTER 3
TEST RESULTS
3.1 STRUCTURAL DAMAGE
Detailed posttest measurements and inspection provided a data check and
damage assessment of each slab prior to removal from the test device. Fig-
ures 3.1 and 3.2 show overviews of two of the slabs representing the range of
• .damage experienced in this test series. Similar views of each of the remain-
ing eight slabs are presented in Figures A.1 through A.8 in Appendix A. The
cracks were darkened with black ink markers for photographic purposes.
Figure 3.3 is a side view schematic of the general three-hinged mechanism
that was formed in each slab. The measured posttest midspan deflection repre-
sented by the variable A is also given in Figure 3.3 for each slab. Posttest
measurements also documented damage at the critical hinge regions of the
three-hinged mechanism. Tables 3.1 and 3.2 present the posttest data measured
at midspan and at the supports, respectively.
3.2 PHOTOGRAPHIC DATA
Figure 3.4 shows the underside of all 10 slabs after removal from the
* test device. It is evident that all slabs underwent the same general form of
response, but variations in the pattern of the smaller cracks are obvious.
Photography during the application of load resulted in documentation of
crack formation on the undersurface of eight slabs at several pressure
levels. Malfunctions of camera equipment prohibited the collection of photo-
graphic data during tests on Slabs 4 and 7. Figure 3.5 consists of photo-
* graphs taken during the testing of Slab 8, showing the crack formation
sequence typical of most of the slabs. The general view of the photographs is
from near the support (top of photograph) to slightly past midspan. The
displacement gage probe mounted to the undersurface of the slab indicates the
location of midspan, and the black dashed line is at the one-fourth span of
S the one-way slab.
Figure 3.6 shows the pressure and midspan displacement at the time eachof the photographs was taken. Points labeled 1 through 11 correspond to
Figure 3.5, a through k, respectively. Table 3.3 summarizes the data shown in
Figure 3.6.
35
* 2
-..
3.3 INSTRUMENTATION DATA
The electronically recorded data are presented in Appendix B. A summary
of the data is presented in this section, and a more detailed analysis is pre-
sented in Chapter 4.
Due to a water leak and pressure loss during the first loading of Slab 5
at a pressure of about 55 psi, the slab was reloaded (Test 5B). Data for
Test 5B are shown on pages 121 through 130.
In general, the quality of the recovered data was very good. Gages SB2
and S3 in Slab 7 and Gages D1 and S5 in Slab 10 failed to operate properly,
resulting in a 96-percent data recovery for the test series.
Figure 3.7 shows the general shape of the midspan load-deflection curve
for the slabs as measured with Gages P1 and D2. Values of load and deflection
* at points A through D in Figure 3.7 are given in Table 3.4. During the test-
ing procedure, the decision to terminate a test depended upon the trend of the
monitored load-deflection curve; therefore, the deflection at test termination
varied among slabs.
° .Maximum deflections measured at midspan (as presented in Figure 3.3)
-* differ from those in Table 3.4. Values presented in Figure 3.3 were physi-
cally measured after each test while those in Table 3.4 were electronically
,* recorded during each test. The data presented in Appendix B indicate a re-
bound in most of the slabs following pressure relief at test termination. A
comparison of the electronically recorded residual deflections with the post-
test measured deflections is presented in Table 3.5.
The posttest measured deflection was greater than or equal to the elec-
*i tronically recorded residual deflection for each slab. The discrepancies were
due to kinking of the displacemcnt transducer probe at large slab deflections.
The R/M ratio given in Table 3.5 is an indication of the discrepancies in
recorded and measured maximum deflections at midspan. In general, the re-
corded strain gage data appeared to be good. The gages on principal rein-
forcement indicated yielding and rupture of steel, and the gages on stirrups
indicated strains below yield.
36
Table 3. 1. Structural damage at midspan.
Measured Bottom Width of Width ofMidspan Bars Top Bars Crushed Crack on
Deflection Broken Broken Area UndersurfaceSlab in percent percent in in
1 3.5 86 0 3 to 9 1.5 to 2.0
2 4.5 100 43 1.75 to 10 1.25 to 2.5
3 3.0 100 0 0.5 to 4 0.25 to 2.0
4 2.8 100 0 1 to 4 0.5 to 1.5
5 3.25 86 0 2 to 8 1.25 to 1.5
6 3.0 71 0 1.25 to 6 0.5 to 1.0
7 3.1 86 0 1.5 to 8 1.0 to 1.5
8 3.0 71 0 1 to 7 1.0 to 2.5
* 9 3.5 100 0 1.5 to 4 0.5 to 1.25
10 4.0 100 57 2 to 7 1.5 to 4.0
Table 3.2. Structural damage at supports.
MeasurableTop Crack Top Crack Top BarsWidth Depth Broken
Slab in in percent
1 0.5 to 1 2.00 50
2 0.5 to 2 1.75 64
_ 3 0.1 to 0.5 0.90 43
4 0.1 to 0.75 0.90 29
5 0.1 to 0.6 1.25 14
6 0.25 to 0.5 1.00 14
7 0.1 to 0.6 1.10 14
8 0.1 to 0.5 0.75 14
9 0.1 to 1 1.50 39
'0 0.1 to 1 1.50 71
* .37
. . * °
Table 3.3. Photographic data summary for Slab 8.
Point Labeled Corresponding Pressure Displacement(Figure 3.6) Figure psi in
I 3.5a 23 0.12
2 3.5b 40 0.20
3 3.5c 53 0.37
4 3.5d 69 0.85 ;
5 3.5e 65 1.20
6 3.5f 53 1.90
7 3.5g 58 2.30
8 3.5h 54 3.10
9 3.5i 38 3.10
10 3.5j 12 2.90
11 3.5k 0 2.80
Table 3.4. Load-deflection summary.
Load-DeflectionPA AA PB AB PC AC PD AD
Slab psi in psi in Es in ps in
1 59.7 0.75 42 1.8 35 3.1 43 3.7
2 66.1 0.75 39 2.1 41 3.1 66 4.1
3 71.6 0.75 32 7.7 45 3.0 a a
4 76.0 0.75 52 1.7 45 2.8 a a
5 75.2 0.65 47 1.6 47 2.4 67 3.2
6 66.6 1.1 55 1.8 49 3.1 a a
7 65.5 0.85 42 1.8 .2 7 55 3.4
8 69.5 0.80 51 2.0 48 2.8 54 3.19 71.0 0.75 41 1.6 37 2.9 56 3.4
10 77.4 0.90 42 1.7 42 2.8 85 3.4
aNo increase in load-carrying capacity experienced.
38
Table 3.5. Residual midspan deflection.
Posttest ElectronicallyMeasured (M) Recorded (R)
Slab in in R/M
1 3.5 3.5 1.0
2 4.5 4.0 0.89
-3 3.0 2.7 0.90
14 2.8 2.5 0.89
*5 3.3 3.0 0.91
6 3.0 2.8 0.93
7 3.1 3.1 1.0
8 3.0 2.8 0.93
9 3*5 3.14 0.97
*.10 41.0 3.41 0.85
93
Figure 3.2. Posttest view of Slab 2.
44
Sj
SLAB NO. (INCHES)
2 4.53 3.0
4 2.85 3.256 3.0
7 3.1
8 3.0
24"9 3.52 "10 4 .0
Figure 3.3. General deformation.
Figre .4.Posttest view of undersurface of slabs.
41
2> 42
- - - - - - --I I J -- -* 5 l I I- 7--
AC'
e. 65 psi, 1.20 inches. f. 53 Psi, 1.90 inches.
g. 58 psi, 2.30 inches. h. 514 Psi, 3.10 inches.
Figure 3.5. (Sheet 2 of 3).
43
i. 38 psi, 3.10 inches. J. 12 psi, 2.90 inches.
44
90 --
80 - ___-
70 -- -- -
50
ww
U,
wj 30CL
20
10
0
-10 .1 -L__ ___ ______-0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5DISPLACEMENT, IN.
Figure 3.6. Slab 8 photographic sequence. Note: SeeTable 3.3. for data summary.
(psi)
(INCH ES)
* Figure 3.7. General load deflection.
145
CHAPTER 4
ANALYSIS
4.1 COMPARISON OF STRUCTURALDAMAGE AND RESPONSE
Table 3.4 presents a load-deflection summary of the 10 slabs. In order
to compare slab response and satisfy stated objectives, it is convenient to
categorize the data in Table 3.4 by parameter investigated. The following
discussion refers to points on the curve presented in Figure 3.7. Table 4.1
compares the results of tests on Slabs 3, 6, and 8 which were used to investi-
gate the effects of the three stirrup configurations presented in Figure 1.1.
Ultimate load capacity (PA) of Slab 6 was approximately 93 percent ofthat for Slab 3. Slab 8 had an ultimate load capacity that was approximately
97 percent of that for Slab 3. The load-deflection responses of the three
* slabs were similar except that a small increase in load-carrying capacity from
- Point C to Point D was experienced by Slab 8 but not by Slabs 3 and 6.
- Although Slabs 5 and 7 were primarily tested to investigate the effects
of temperature steel placement, they also provided data on the effects of
" stirrup Types II and III. As was the case for Slabs 3 and 6, the slab with
. Type III stirrups (Slab 7) had an ultimate load capacity less than the Type II
stirrup slab (Slab 5). Data for Slabs 5 and 7 are shown in Table 4.2.
Table 4.3 shows that Slabs 1, 2, 3, and 4 were used to investigate
stirrup spacing. The load capacity of Slab 2 at Point A was 8 percent and
13 percent less than Slabs 3 and 4, respectively. At Point B, the load capa-
city was 25 percent and 11 percent less than that of Slabs 3 and 4, respec-
tively. Slab 1 had no stirrups (simulating a very large spacing) and the
lowest value of PA " Slab 1 had a slightly higher capacity at Point B than
did Slab 2, but it had the lowest value at Point C. Slabs 2, 3, and 4 had
relatively similar values for PC Slab 2 (the closest stirrup spacing) was
the only slab of this group having PD approximately equal to P. Slab 1
did show an increase in load capacity from Point C to Point D, but PD was
approximately equal to PB (not PA).
Slabs 3 and 4 behaved similarly, having almost identical load-deflection
values at Point C.
Inconsistencies in the ultimate load capacity indicate scatter in thedata. The ultimate load capacity decreased as stirrup spacing decreased from
46
.'!
F:
-. 3.0 inches to 0.75 inch; however, the slab with the largest spacing (no stir-
rups) had the lowest value of PA instead of the highest.
Table 4.2 presents data for the two pairs of slabs used to investigate
the effects of the two temperature steel placement conditions shown in Fig-
ure 1.2. Slabs 3 and 5 investigate the parameter, as do Slabs 6 and 7. The
*region of the load-deflection curve affected by the steel placement was at
large deflections. Slabs 5 and 7 experienced an increase in load resistance
- from Point C to Point D, whereas Slabs 3 and 6 were constructed with the
-interior placement condition and experienced no significant increase in load
resistance beyond Point B.
Table 4.4 shows that two pairs of slabs were used to investigate the ef-
fects of the principal steel spacings shown in Figure 1.3. Slabs 2 and 10
- constituted one pair used to investigate the parameter, and the other pair
consisted of Slabs 3 and 9.
Slabs 3 and 9 in Table 4.4 had stirrups spaced at 1.5 inches. Slab 9 had
- a closer spacing of principal steel and exhibited an increase in load resist-
ance from Point C to Point D (PD 0.79 PA) , whereas Slab 3 did not. Slab 10
had a stirrup spacing of 0.75 inch and the closer principal steel spacing of
. 1.75 inches. It was observed from Table 4.3 that Slab 2 with a 0.75-inch
stirrup spacing was the only slab of that group with a significant increase in
load resistance at Point D (PD = P A Slab 10 exhibited a greater increase
in load resistance (PD = 1.10 PA) at large deflections than any of the slabs
T* in the test series. It is not clear whether the closer principal reinforcing
is totally responsible for the increased resistance, since the testing of
Slab 3 was terminated at a deflection of about 3.0 inches (the deflection at
which Slab 9 began increasing in load resistance).
4.2 YIELD-LINE THEORY
The method of limit analysis of reinforced concrete slabs known as the
yield-line theory was developed by Johansen (Reference 32). An assumed col-
lapse mechanism consistent with boundary conditions is used to estimate the
ultimate load capacity of t'he slab. Considering the moments of the plastic
hinge lines as the ultimate moments of resistance, the ultimate load is deter-
mined using the principle of virtual work or the equations of equilibrium. As
Park and Gamble (Reference 38) point out, Johansen's yield criterion is for
the case where in-plane (membrane) forces do not exist in the slab. The
47
-S. . < " " ' .
* yield-line theory assumes that the slab has sufficient shear strength to in-
*- sure a flexural collapse mode of failure.
*The results of applying the yield-line theory to the slabs in this study
are presented in Table 4.5 along with the experimental values of ultimate load
.- resistance. An average test-day concrete compressive strength of 4,790 was
* used in the yield-line calculations. The yield-line theory predicts from
[] approximately 57.8 to 73.5 percent of the experimental values for this test
. series. The greater percentage (73.5) was for Slab 1, which was the only slab
,X without stirrups.
The predicted yield-line values were based upon nominal moment capacities
of the slabs calculated in accordance with the ultimate strength method of the
1983 ACT Code (Reference 53). Slabs I through 8 had nominal moment capacities
* of aproximately 42.5 and 33.3 inch-kips at the midspan and the supports, re-
spectively. Slabs 9 and 10 had nominal moment capacities of approximately
43.6 and 34.3 inch-kips at the midspan and the supports, respectively.
Slabs 9 and 10 differed from Slabs 1 through 8 in this calculation due to the
use of fy = 62.4 ksi rather than 60.0 ksi.
The virtual-work method was used, whereby the work performed by the ex-
ternal loads during the displacement is equated to the internal work absorbed
- by the hinges. The ultimate load W for a uniformly loaded fixed beam or
one-way slab may be expressed as
(M + MM )W 8 s m (4.1)L
2
where:
W uniform load
Ms moment capacity at the support
Mm =moment capacity at midspan
L length of beam
- 4.3 COMPRESSIVE MEMBRANE EFFECT
As discussed in Chapter 1, compressive membrane forces are induced in
slabs whose edges are restrained against lateral movement. As the slab de-
flects, changes of geometry cause the slab edges to tend to move outward and
to react against the stiff boundary elements. The membrane forces enhance the
48
flexural strength of the slab sections at the yield lines.
- Table 4.6 presents the results of applying compressive membrane theory to
*the slabs at ultimate resistance along with the experimental values. An aver-
age test-day concrete compressive strength of 4,790 psi was used.
The approach utilized for compressive membrane theory was that developed
by Park (Reference 42) and discussed by Park and Gamble (Reference 38). A
- .fixed-end strip with plastic hinges and full restraint against rotation and
vertical translation is assumed by the theory. The ends of the strip are
* :considered to be partially restrained against lateral displacement. Other as-
sumptions include: (1) the tension steel has yielded at each plastic hinge,
(2) the compressed concrete has reached its strength with the stress distribu-
tion as defined by the 1983 ACI Code (Reference 53), (3) the tensile strength
of the concrete can be neglected, (4) the top steel at opposite supports has
the same area per unit width, (5) the bottom steel is constant along the
*O length of the strip, but the top and bottom steel may be different, (6) the
portions of the strip between plastic hinge sections remain straight, and
(7) the sum of the elastic creep and shrinkage axial strain have a constant
value along the length of the strip.
The compressive membrane values in Table 4.6 were calculated through the
use of a computer program at WES which utilizes Park's theory. The deflec--_
tion-thickness, (A/t)ult values in Table 4.6 are the experimental ratios of
midspan deflection at ultimate resistance to slab thickness. Wood (Refer-
-ence 41), Park (Reference 42), and Morley (Reference 43) assume a ratio of
0.5. Hung and Nawy (Reference 44) use experimental values to conclude that
ratios ranging between about 0.4 and 1.0 should be considered. Work by Isaza
(Reference 45) indicates a ratio of about 0.17.
Table 4.7 shows that compressive membrane theory is sensitive to the
7 (A/t)uit ratio. Deflection-thickness ratios suggested by the above research-
. ers are applied, resulting in considerable variation in predicted load
resistance. Experimental ultimate load resistance values are given for,
comparison.
Predicted resistance, assuming (A t)ul t of 0.5, corr6sponds more
closely to the predicted yield-line Lteiory values of Table L.5 than 1o the
experimental values. The trend ob., rved rrom Table 4.7 is that predicted
ultimate resistance increases with decreasing (A/t)uIt ratios. This trend
is also indicated in the experimental data. Slabs 1 through 8 had similar
L 49 .
principal steel spacings, although there were some differences among the
slabs. Of that group, Slabs 3, 5, 6, 7, and 8 had stirrup spacings of
1.5 inches, but did vary in stirrup type and temperature steel placement.
Table 4.8 lists the five slabs by order of increasing experimental (A/t)uit
ratios. Slab 6 had a slightly higher ultimate resistance than Slab 7, causing
an inconsistency in the trend.
It is evident from Table 4.7 that the compressive membrane theory closely
aproximates the experimental ultimate resistance for 60 percent of the slabs
(2, 3, 6, 7, 8, and 9) when a (A/t)ult ratio of 0.3 is used. Thirty percent
(Slabs 4, 5, and 10) are approximated by the criteria of (A/t)ult equal to
0.17, and the remaining slab (Slab 1) is approximated using a ratio of 0.4.
No correlation of the varying parameters of this investigation with the
(A/t)ult ratio was apparent, except that only the slab without stirrups had
an ultimate resistance more closely approximated by the use of a (A/t)ult
* ratio of 0.4.
Roberts (Reference 40) concluded that the deflection of maximum load is
not a fixed proportion of the slab thickness. Two slab strips in that study
had tensile steel percentages and compressive concrete strengths very similar
. to that of the current study, and a (6/t)ul t ratio of about 0.275 was
* observed. The 0.275 value is similar to the approximate value of 0.3 observed
in the majority of slab tests in this study.
14.4 ROTATION CAPACITY
Figure 4.1 shows the idealized behavior of a beam or one-way slab under
uniform loading. The structure initially undergoes elastic deflection. Under
continued loading, plastic hinges first form at the supports and later at mid-
span. The rotational capacity of the plastic hinges is directly related to
-. the ductility of the slab. The inelastic rotation that can occur in the
* - vicinity of the plastic hinge (critical section) may be expressed as
0 ( u- ¢y)p (4.2)pr u y p
where:
Op = plastic hinge rotation to one side of the critical section
"u = ultimate curvature of the section
o y = yield curvature of the sectionI p = equivalent plastic hinge length
50
S
as discussed by Park and Paulay (Reference 4).
Corley (Reference 24), Mattock (Reference 22), and Baker and Amarakone
(Reference 30) have proposed empirical expressions for pand the maximum
concrete strain (E ) at ultimate curvature. Based on tests on simply sup-c
ported beams, Corley proposed:
z 0.5d + 0.21d
2b + 0
where: c :.0o3 0.32 + 0\20 (4.3)~where :
d effective depth of beam
Z distance from the critical section to the point of contraflexure
b = width of beam
P = ratio of volume of confining steel (including compression steel) tovolume of concrete core
f = yield strength of the confining steel in kips per square inch.inch
Mattock modified Corley's work and suggested the following expressions:
: 0.5d + 0.05Zp
b
c 0.003 + 0.02 + 0.2p (4.4)
where Z, B, d, and o are defined as in Equation 4.2.
For members confined by transverse steel, Baker proposes the following:
9z 0.8 klk 3 (k )c
'. 0.0015 1 + 150 s + (0.7 - 10o) .0.01 (4.5)
where:
-k 7 or mild stee or 0.9 for cold-worKed noee
wn"' = 5, wr si or 0.9 when ," = )o0 psi,
assuming fC = 0.85 cube strength of concrete
c = neutral axis depth at the ultimate moment
0" = ratio of volume of the transverse confining reinforcementto the volume of the concrete core
ft
The effect of stirrup spacing on rotation capacity in the slabs in this
*study was investigated using the expressions by Corley, Mattock, and Baker.
*Values for curvature, strains, and neutral axis depth used in the calculations
were obtained by use of a computer program developed by Mahin and Bertero
called Reinforced Concrete Column Analysis (RCCOLA) (Reference 54). The
RCCOLA program evaluates general flexural characteristics of reinforced con-
crete cross sections subjected to axial forces and uniaxial bending moments.
- The stress-strain relationship for concrete utilized by the program was that
proposed by Kent and Park (Reference 17) for concrete confined by rectangular
hoops.
The results of the calculations are presented in Figure 4.2 for the
plastic hinge rotation to one side of the critical section at midspan.
Similar results were obtained at the support critical sections. Figure 4.2
shows that discrepancies pertaining to rotation capacity exist among re-
searchers. The significance of Figure 4.2 is that it shows an increase in ro-
- tation capacity when close stirrup spacings are used.
.*- The vertical dashed lines in Figure 4.2 indicate the spacings used in
this test series (0.75, 1.5, and 3.0 inches). The predicted increase in rota-
tion capacity induced by the 0.75-inch spacing compared to the 3.0-inch spac-
ing is slightly greater than 0.01 radian when using Corley's criterion. The
predicted enhancement is less when using Mattock's or Baker's criterion. The
predicted enhancement due to the 1.5-inch spacing is less than one-half of
that due to the 0.75-inch spacing. At the 3.0-inch spacing, an increase of
only about 0.0015 radian is predicted by Corley's criterion when compared to a
larger spacing of 6.0 inches. The slopes of all three curves in Figure 4.2
approach zero beyond the 6.0-inch spacing.
It should be noted that the empirical expressions are for design purposes
S and tend to be conservative. Considering the evaluation of rotation capacity,
*' the results may be questionable. In fact, Burnett (Reference 29) discusses
* -that both the concept and use of curvature are unrealistic for postyield re-
"-• sponse. Table 4.2 indicates that the stirrup spacing had no significant ef-
-- fect on the behavior of the slabs until the region of large deflections (2 to
4 inches). Having similar load-deflection curves up to ultimate load, Slabs 1
through 4 all reached ultimate load capacity at a midspan deflection of
0.75 inch.
Using the support plastic hinge rotation capacities determined from the
52
SL " " " " " " .[ .' " " " "• " " " " "
Corley, Mattock, and Baker criteria, midspan deflections at the predicted ro-
tations were computed for Slabs 2, 3, and 4, and are presented in Table 4.9.
The theory implies that the ductility of the slabs should be adequate to main-
tain the ultimate load capacity to the deflections in Table 4.9. Close exami-
nation of the experimental load-deflection curves shows that Slabs 2, 3, and 4
experienced sharp drops in load resistance of several pounds per square inch
at midspan deflections of about 1.25, 1.25, and 1.2, respectively. The load
resistances immediately prior to the sudden drops were 97, 92, and 89 percent,
respectively, of the ultimate load capacities for Slabs 2, 3, and 4. Deflec-
tions derived from Corley's criterion most accurately predict experimental de-
flections incurred prior to sharp decreases in load resistance. The validity
of this comparison is questionable since, as mentioned in the discussion com-
paring structural damage and response, there appear to be inconsistencies in
the ultimate load capacities for Slabs 1 through 4. Also, the calculations
based on Corley's criterion do not account for in-plane compressive membrane
thrusts. Slab 1 experienced a more gradual decline in load resistance past
the ultimate load and did not incur a sudden drop in resistance until a de-
flection of about 1.6 inches was reached.
Based on beam test data, Keenan and others (Reference 21) state that re-
inforced concrete members with compression steel can reliably maintain their
ultimate moment resistance to support rotations of up to 4 degrees, provided
the compression bars are confined by effective ties and q < 0.14 where q
is the reinforcing index defined by:
(Pf - P'f')q (4.6)
c
The slabs in this test series meet Keenan's criterion assuming the stirrups
act as effective ties. A support rotation of 4 degrees implies a midspan de-
flection of approximately 0.84 inch, which is 84 to 88 percent of that
-. predicted using Corley's criterion for Slabs 2, 3, and 4.
The rotational capacity of a plastic hinge, particularly for design pur-
poses, is limited to situations in which one of the following actions occurs:
1. Tension steel fractures.
2. The concrete compression block crushes.
53
S-
3. Compression steel buckles.
4. Ties fracture in tension.
In the case of the slabs in this study, a redistribution of forces at the
.. critical hinge sections allowed the slabs to continue carrying some load after
one or more of the above failure modes had occurred in portions of the crit-
ical sections. Considering the formation of a three-hinge mechanism, the ro-
tation of the hinges at the supports when the tests were terminated (antici-
pated incipient collapse) are presented in Table 4.10. Table 4.10 also gives
the percentage ratio of maximum attained midspan deflection (Amax) to the
clear span length (L).
4.5 TENSILE MEMBRANE EFFECT
It is generally known (Reference 38) that after the ultimate load resist-
ance has been reached in a reinforced concrete slab, the supported load de-
creases until membrane forces in the central region of the slab change from9compression to tension. In pure tensile membrane behavior, cracks penetrate
the whole slab thickness, and yielding of the steel spreads throughout the
* central region of the slab. The load is carried mainly by the reinforcing
bars acting as a tensile net or membrane.
Park (Reference 48) concluded that pure tensile membrane action did not
occur in lightly reinforced two-way slabs, since the cracking present at the
end of the tests was little more than the cracking which developed with the
*yield-line pattern at the ultimate flexural load. Therefore, the load was
carried by a combined bending and tensile membrane action. Similarly,
*Figure 3.5, d. and k. show little change in the crack pattern during testing
of Slab 8. The dominant cracks became larger in width and depth, but
significant spreading of the crack pattern was not evident. Table 3.4 shows
that Slabs 2 and 10 exhibited the most significant increases in load
resistance in the tensile membrane region. Figure 3.4 shows that Slabs 2 and
10 also experienced the greatest spread in crack patterns.
Park (Reference 48) gives criteria for predicting the slab response in
the tensile membrane region. For uniformly loaded one-way slabs, the rela-
tionship between the load and the midspan deflection is approximated as:
WL2
SA 8 T (4.7)
54S
where T = yield force of the reinforcement per unit width. Figures 4.3
.. through 4.12 show the linear regression proposed by Park plotted on the ex-
perimental load-deflection curves of Slabs 1 through 10, respectively. Most
of the slabs exhibited the tendency for an increase in load resistance at a
* midspan deflection between 1.75 and 2.0 inches (d = 1.9375 inches). The
curves for Slabs 1, 4, 5, 7, and 8 clearly indicate a transition into the
tensile membrane region near the intersection of the load-deflection curve and
- -the predicted regression. The slopes of the experimental curves also appear
to be similar to the predicted slope, particularly for Slabs 5 and 8. Though
not as obvious as in the case of these slabs, the curve for Slab 10 also has a
slight tendency to follow the predicted slope during initial stages of tensile
membrane behavior.
Keenan (Reference 37) shows that the slab resistance just prior to ten-
sile membrane behavior should nearly equal the computed yield-line resistance
corresponding to zero thrust in the plane of the slab (Johansen's yield-line
value). The yield-line resistance has been shown to be approximately 44 psi
for Slabs 1 through 8 and 45 psi for Slabs 9 and 10. The transition into the
tensile membrane region occurred at load resistances between about 42 and
45 psi for Slabs 1, 2, 4, 5, 7, 9, and 10, but the resistances of Slabs 3, 6,
and 8 were around 50 to 52 psi. Slabs 3 and 6 never indicated strong ten-
.' dencies for tensile membrane behavior, but rather gradually decayed in resist-
, ance from the ultimate load to nearly equal the yield-line value at a midspan
*deflection of about 3.0 inches.
Pure tensile membrane behavior did not occur in any of the slabs. Frac-
. ture of the tensile reinforcement (bottom steel at midspan and top steel at
supports) weakens the tensile membrane effect.
Table 3.1 shows that large percentages of bottom bars at midspan and top
* bars at supports fractured. Only Slabs 2 and 10 experienced rupture of top
bars at midspan. Table 3.2 shows that Slabs 2 and 10 also had the largest
percentage of steel to fracture at the supports.
Slabs 1 through 4 investigated the effects of stirrup spacing, and all
but Slab 1 incurred fracture of 100 percent of the bottom steel at midspan.
Slab 1 had one unbroken bar remaining. All five slabs also experienced frac-
ture of some top reinforcing at the supports.
Only the load-deflection curve for Slab 2 showed a steady increase in
load resistance past a midspan deflection of about 2.5 inches.
55
* *.** . .* *i*
A significant difference in the behavior of Slabs 3 and 5 was observed in
the tensile membrane region. At a midspan deflection of 3.0 inches, the load
. resistance of Slab 5 had climbed from the yield-line resistance of approxi-
mately 45 to 60 psi. The load resistance of Slab 3 gradually decayed from ul-
timate load and was approximately equal to the yield-Line resistance at the
midspan deflection of 3.0 inches. Slabs 3 and 5 investigated the effects of
temperature reinforcement placement in the "interior" and "exte ior" condi-
tions, respectively. Slabs 6 and 7 also investigated the paramefer of
t...orAture steel placement and yielded results similar to Slabs 3 and 5 but
*] a lesser degree.
Slabs 3, 5, 6, and 7 were all constructed with Tjpe IT or Type III
sing i-leg stirrups spaced at 1.5 inches. Slab 8 was constructed with the
Type I double-leg stirrup and temperature steel placed in the interior place-
ment condition. Unlike Slabs 3 and 6, Slab 8 exhibited strong tendencies for
* increasing load resistance in the tensile membrane region. However, Slab 8
could not maintain a steady climb in load resistance.
Slabs 9 and 10 were constructed with a close principal steel spacing of
1.75 inches and exerienced a sharper decay in load resistance after ultimate
loading than Slabs 1 through 8. After the decay, the load resistances of
Slabs 9 and 10 remained at or below the yield-line resistance until a deflec-
tion of about 3.0 inches was reached. A sharp increase in load resistance was
then experienced in Slabs 9 and 10. The testing of Slab 9 was terminated at a
- " lower pressure than Slab 10. It appears that the variation in stirrup spacing
in the slabs having close principal reinforcement had little effect on the
load-deflection behavior in the tensile membrane region.
The loading of Slabs 9 and 10 beyond a midspan deflection of 3.0 inches
revealed that at very large displacements under slowly applied load, the ten- -'
sion loading of the top steel at midspan induces an increase in load resist-
ance. It is not clear that this behavior would not have occurred in Slabs 3,
4, 6, and 8 since testing of these slabs was terminated at a midspan de-
flection of about 3.0 inches. Slab 1 had no stirrups and was tested to a
midspan deflection of about 3.75 inches. Slab 1 did exhibit an increase in
load resistance past the 3.0-inch deflection; however, the increase at the
3.75-inch deflection was significantly less than that in Slabs 9 and 10 at a
deflection less than 3.5 inches.
56
Table 4.1. Stirrup configuration.
Stirrup AStirrup Spacing PA A B AB C AC D AD
Slab Type in psi in psi in psi in psi in
- 8 I 1.5 69.5 0.80 51 2.0 48 2.8 54 3.1
3 II 1.5 71.6 0.75 52 1.7 45 3.0 a a
* 6 III 1.5 66.6 1.1 55 1.8 49 3.1 a a
- aTest was terminated due to large deflections and decreasing load-carrying
*;"" capacity.
Table 4.2. Temperature steel placement.
Temper-ature StirrupSteel Stirrup Spacing PA AA PB AB PC AC PD AD
Slab Placement Type in psi in psi in psi in psi in
* 3 Interior II 1.5 71.6 0.75 52 1.7 45 3.0 a a
5 Exterior II 1.5 75.2 0.65 47 1.6 47 2.4 67 3.2
6 Interior III 1.5 66.6 1.1 55 1.8 49 3.1 a a
7 Exterior 111 1.5 65.5 0.85 42 1.8 42 2.7 55 3.4
aTest was terminated due to large deflections and decreasing load-carrying
capacity.
Table 4.3. Stirrup spacing.
Stirrup A* Stirrup Spacing A A AB PC AC PD AD
Slab Type in psi in psi in psi in psi in
1 1 No stirrups -- 59.7 0.75 42 1.8 35 3.1 43 3.7
2 II 0.75 66.1 0.75 39 2.1 41 3.1 66 4.1
3 II 1.5 71.6 0.75 52 1.7 45 3.0 a a
4 II 3.0 76.0 0.75 44 1.7 45 2.8 a a
aTest was terminated due to large deflections and decreasing load-carrying
0*I. capacity.
57
* .--
Table 4.4. Principal steel spacing.
PrincipalSteel Stirrup
Spacing Stirrup Spacing PA A B B C C D DSlab in. Type in psi in psi in psi in psi in
2 3.75 II 0.75 66.1 0.75 39 2.1 41 3.1 66 4.1
10 1.75 II 0.75 77.4 0.90 42 1.7 42 2.8 85 3.4
3 3.75 II 1.5 71.6 0.75 52 1.7 45 3.0 a a
9 1.75 II 1.5 71.0 0.75 41 1.6 37 2.9 56 3.4
aTest was terminated due to large deflections and decreasing load-carrying
capacity.
Table 4.5. Yield-line theory versus experimentalultimate load resistance.
Yield-Line (YL) Experimental (E) YL/E
Slab psi psi percent
1 43.9 59.7 73.5
2 43.9 66.1 66.4
3 43.9 71.6 61.3
4 43.9 76.o 57.8
5 43.9 75.2 58.4
6 43.9 66.6 65.9
7 43.9 65.5 67.0
8 43.9 69.5 63.2
9 45.1 71.0 63.5
10 45.1 77.4 58.3
58 :i
-A
Table 4.6. Compressive membrane theory versus
experimental ultimate load resistance.
CompressiveMembrane CM Experimental (E) CM/E
Slab psi A/t psi percent
1 66.6 0.32 59.7 111.6
2 66.6 0.32 66.1 100.8
3 66.6 0.32 71.6 93.0
4 66.6 0.32 76.0 87.6
5 70.5 0.28 75.2 93.8
6 52.5 0.48 66.6 78.8
7 61.9 0.37 65.5 94.5
8 63.7 0.35 69.5 91.7
9 69.1 0.32 71.0 97.3
10 62.6 0.39 77.4 80.9
Table 4.7. Ultimate resistance versus (A/t)ult
Predicted Resistance
due to CompressiveMembrane Theory for
(A/t)ut -
Experimental '.-
Resistance (a) (b) (c) (d)
(E) 0.17 0.3 0.4 0.5 a/E b/E c/E d/ESlab psi psi psi psi psi____ _
1 59.7 80.7 67.1 57.5 48.9 135.2 112.4 96.3 81.9
2 66.1 80.7 67.1 57.5 48.9 122.1 101.5 87.0 74.0
3 71.6 80.7 67.1 57.5 48.9 112.7 93.7 80.3 68.3
4 76.0 80.7 67.1 57.5 48.9 106.2 88.3 75.7 64.3
5 75.2 80.7 67.1 57.5 48.9 107.3 89.2 76.5 65.0
6 66.6 80.7 67.1 57.5 48.9 121.2 100.8 86.3 73.4
7 65.5 80.7 67.1 57.5 48.9 123.3 102.4 87.8 74.6
8 69.5 30.7 67.1 57.5 48.9 116.1 96.5 82.7 70.4
9 71.0 82.8 69.3 59.7 51.2 116.6 97.6 84.1 72.1
10 77.4 82.8 69.3 59.7 51.2 107.0 89.5 77.1 66.1
59
7 7
Table 4.8. Increasing (A/t)ult.
Slab (A/t)ut Experimental UltimateSlab ___ _ Resistance, psi
5 0.28 75.2
3 0.32 71.6
8 0.35 69.5
7 0.37 65.5
6 0. 48 66.6
Table 4.9. Predicted midspan deflection.
StirrupSpacing Midspan Deflection, in
Slab in Corley Mattock Baker
2 0.75 1.0 0.62 0.11
3 1.5 0.95 0.61 0.10
4 3.0 0.95 0.60 0.094
Table 4.10. Maximum support rotations.
Rotation max
Slab degrees perent
1 16.3 14.6
2 20.6 18.8
3 14.0 12.5
4 13.1 11.7
5 15.4 13.8
6 14.0 12.5
7 14.5 12.9
8 14.0 12.5
9 16.3 14.6
10 18.4 16.7
U!
60
4
ELASTIC
ELASTIC- PLASTIC HINGE
PLASTIC HINGES
Figure 4.1. Formation of three-hinged* mechanism.
16
9
0 5s ORE
I Z
0'
STRU SPCIG INFigur 4.. Rtto aa it vess tirp pa ng
C- I62
-l 15sLRCFENr - IN
Figure 4-3. Slab 1 tensile membrane prediction.
DISPLACEMENT IN_____
o__
_ "
k " •"-Figure 4.4. Slab 2 tensile membrane prediction.
U63
b"IL
* __ - i
.-. _ __ - ---. __ __ -__
'-0..,0 . ¢
..- RCEE ,- /* iue4LSa tesilemmrepeition
-. ".63
S
0 - 4 , --." ./_ 5 I30.--
___ / -,-
. .' /
DISPLAlCEMENT -IN-.-- Figure 4.5. Slab 3 tensile membrane prediction.
. . /J,Ce
•- 5
.iSPLRCEMET
- ITFigure 4.6. Slab 4 tensile membrane prediction.
I _-
0 .°
",~-' ."64
3%
/?
Q-7---
OU) 0 1. 0 1.5 30 35 40 4. .
IIP RC MN IN
Fiur 4.7 Sla 5- tesl-eban rdcin
-0S0 0. 1 1. 1.5 2 0 2 3.0 3.5 4.0 4.55.
015PLRCEMENT IN
Figure 4.7. Slab 5 tensile membrane prediction.
7--
AK - -i
Ln
Figure
3 66
" I L-EMN - -- -N
.- 2.-Figure 14.10. Slab 8 tensile membrane prediction.
'..-< I 66
.5 0 3- -. - -0 -.
C- --
I -fl
l.A
n.. o , ...., -
0 - - -0 - 0 - - . - 4 -
//
//0 - - " - -"-
-- , ,------ ./ - -
S- -. r o s.A .0 .5 2.0 .<, .0 .5 4.3 4.5,
OlSPLPCEMFNT - IN
Figure 4.12. Slab 10 tensile membrane prediction.
67
" : '- . v - - .- - . -- . , . . . . . . - .... ._
t' ',=,- , ', ' .. . . . .- -- . - - "0 - .. ..- . .- " - -.. ___' "- "
r-, ., > :,< . . '. .' .'-. . .. '-.-- -',. -/ . . • • .. .'.. ." .. . ' - ; ' " ; '1 -:'.".-'[ .'. 'L' ";' i -:' .-. .. .-. .
CHAPTER 5
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
5.1 SUMMARY
Ten one-way reinforced concrete slabs were statically tested under a uni-
form load to large deflections to investigate the use of stirrups in the key-
worker shelter. These data significantly increase the current data base on
the large deflection behavior of one-way slabs under uniform loads.
The ultimate load resistance of the laterally restrained slabs in this
test series was approximately 1.4 to 1.7 times the yield-line value computed
from theory developed by Johansen (Reference 32). The experimentally attained
midspan-deflection-to-siab-thickness (A/t) ratios varied from about 0.32ult
to 0.48. Compressive membrane theory by Park (Reference 42) closely predicts
the ultimate load resistance of the slabs when a t/t ratio between about 0.2
- and 0.4 is used (0.3 is applicable to the majority of the slabs).
The following two observations were made pertaining to the effects of the
varied parameters on the ultimate load resistance:
(1) The lowest ultimate load capacity occurred in the slab having no
stirrups, and (2) slabs constructed with the Type III stirrups experienced ul-
timate resistances 88 to 93 percent of those for slabs having Type I or IIstirrups.
Rotation capacity calculations based on criteria from Corley (Refer-
ence 24), Mattock (Reference 22), and Baker and Amarakone (Reference 30) indi-
cate an enhancement in ductility in the slab having the closest stirrup spac-
ing (Slab 2). Support rotations between 13.1 and 20.6 degrees were observed.
The rotations correspond to maximum attained midspan-deflection-to-clear span
ratios (m/L) between 11.7 and 18.8 percent. The greatest support rotationmax
of 20.6 degrees was experienced by Slab 2 and appeared to be very near the
incipient collapse support rotation.
A three-hinged mechanism was formed in each slab, and significant spread-
ing of the cracking pattern on the underface of the slabs did not occur. The. greatest spreading of cracking was observed in Slab 2 which experienced a sig-
-" nificant increase in load resistance at large deflections.
Park (Reference 48) approximated the midspan deflection (approximately
equal to the effective depth of the slab) and the load resistance
7 68
(approximately equal to the yield-line value) at which the slabs exhibited
initial tensile membrane tendencies. Fracture of reinforcement in these
under-reinforced slabs (p < Pb) prohibited extensive load resistance en-
hancement in the tensile membrane region.
5.2 CONCLUSIONS
Conclusions for this test series are given below.
1. Slabs with a large number of closely spaced (spacing ( d/2) stirrups
exhibit increasing load resistance at large deflections.
2. Slabs with stirrups spaced at 1-1/2 inches (d/2 < spacing < d) be-
haved similar to those with stirrups spaced at 3.0 inches or without stirrups
at large deflections. The 1-1/2-inch stirrup spacing represented the prelim-
inary keyworker shelter design.
3. Slabs with temperature steel placed "exterior" to the principal rein-
forcement experience better tensile memebrane behavior than do slabs having
temperature steel placed "interior" to the principal reinforcement.
4. Slabs containing Type I double-leg stirrups have greater tendencies
toward tensile membrane behavior than do slabs containing the Type II or
Type III single-leg stirrup.
5. Slabs containing the Type III stirrup with a 90-degree bend at one
end have load response behavior similar to those containing the Type II
stirrup (up to at least the midspan deflections yielding a max /L ratio of
about 12.5 percent), except for a slight reduction in resistance at the
ultimate load.
6. The load-response behavior of slabs having a principal reinforcing
bar spacing slightly less than the effective depth (d) is not significantly
affected by close stirrup spacings.
In summary, ductile behavior is increased by construction details which
imply better confinement due to more confining steel (i.e., closely spaced
stirrups, Type I stirrups, and closely spaced principal reinforcing bars) or alarger area of the confined core (i.e., exterior placement of temperature re-
.- .inforcing). The effects of the same construction details on ultimate load
* capacity are not apparent from the data for these under-reinforced one-way
slabs.
69
• ." .".: :- -';- -', I' .I L- -'- , :' i -', '. i i' ' '- ." ", -' . " "i - - .'. ' * ": .- - -.. .' ' , . - , -- ' " " , i -." : - - -
5.3 RECOMMENDATIONS
The slabs tested in this series are among the very few one-way slabs that
have been tested under uniform loading conditions. An extension of the data
base is necessary to support the findings of these tests.L
Parameters similar to those varied in this series should be investigated .
for over-reinforced slabs (P > ) Also, the effects of these parameters
on slabs that have different span-to-thickness ratios, principal reinforcing
details, and end restraints remain to be investigated. In general, the large
number of investigations that have been performed on beams (usually simply
supported under concentrated loads) should be extended to the uniformly loaded
one-way slab.
Based upon these tests, recommendations to HND pertaining to the
deliberate-type Keyworker Blast Shelter roof design are given below.
1. The omission of stirrups is recommended unless the sustaining of a
reserve capacity (increasing load resistance at large deflections) is deemed a
criterion significant enough to justify the expense of a large number of
stirrups spaced at d/2 or less. The omission of stirrups in the roof and
floor of the keyworker shelter decreases the construction costs of the
preliminary design by 3.5 to 4 percent.
2. Consideration should be given to the development of alternate prin-
cipal reinforcement designs which may economically provide a reserve capacity.
3. If stirrups are included, the Type III stirrup should be used to pro-
vide economical benefits without significantly decreasing roof load capacity.
4. The placement of the transverse reinforcement (temperature steel)
should be in the "exterior" condition when stirrups are used, and should
probably have the same bar diameter as the stirrups in order to maintain
concrete cover. In the absence of stirrups, benefits from the exterior
placement may not be observed since a reduction in the principal reinforcement
effective depth would occur for a given slab thickness and concrete cover.
5. It is not clear that the closer spacing (less than d) of the prin-
cipal steel is responsible for an enhancement in load resistance at very large
deflections, but it has been suggested by other researchers (Keenan and
others, Reference 21) as a means to confine concrete rubble. Closer spacing
should be considered, particularly if the recommended amount of attention is
given to alternate principal reinforcing details.
- 70
;.i:"70
.6 A
REFERENCES
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2. S. P. Shah; "Micromechanics of Concrete and Fibet Reinforced Con-crete"; Proceedings, International Conference on Structure, Solid Mechanicsand Design in Civil Engineering, April 1969; University of Southampton,England.
3. P. R. Barnard; "The Collapse of Reinforced Concrete Beams"; Proceed-ings, International Symposium on Flexural Mechanics of Reinforced Concrete,November 1964, Pages 501-520; American Society of Civil Engineers and American
* Concrete Institute.
4. R. Park and T. Paulay; "Reinforced Concrete Structures"; 1975; JohnWiley & Sons, New York.
5. M. Z. Cohn; "Rotation Compatibility in the Limit Design of Rein-forced Concrete Continuous Slabs"; Flexural Mechanics of Reinforced Concrete,
* November 1964, Pages 359-382; American Society of Civil Engineers and AmericanConcrete Institute.
6. M. A. Cohn and V.A. Petcu; "Moment Redistribution and Rotation Capa-city of Plastic Hinges in Redundant Reinforced Concrete Beams"; The IndianConcrete Journal, August 1963, Vol. 37, No. 8, Pages 282-290.
7. H. E. H. Roy and M. A. Sozen; "Ductility of Concrete"; FlexuralMechanics of Reinforced Concrete, November 1964, Pages 213-236; AmericanSociety of Civil Engineers and American Concrete Institute.
. 8. W. L. Cnan; "The Ultimate Strength of Deformation of Plastic Hingesin Reinforced Concrete Frameworks"; Magazine of Concrete Research, November1955, Vol. 7, No. 2, Pages 121-132.
9. M. T. M. Soliman and C. W. Yu; "The Flexural Stress-Strain Relation-ship of Concrete Confined by Rectangular Transverse Reinforcement"; Magazineof Concrete Research, December 1967, Vol. 19, No. 61, Pages 233-238.
10. S. Stockl; Discussion of "Ductility of Concrete," by H. E. H. Royand M. A. Sozen; Proceedings, International Symposium on Flexural Mechanics ofReinforced Concrete, November 1964, Pages 225-227; American Society of CivilEngineers and American Concrete Institute.
11. V. V. Bertero and C. Felippa; Discussion of "Ductility of Concrete,"by H. E. H. Roy and M. A. Sozen; Proceedings, International Symposium on Flex-ural Mechanics of Reinforced Concrete, November 1964, Pages 227-234; AmericanSociety of Civil Engineers and American Concrete Institute.
12. J. E. McDonald; "The Effect of Confining Reinforcement on theDuctility of Reinforced Concrete Beams"; Technical Report C-69-5, March 1969;
.* US Army Engineer Waterways Experiment Station, Vicksburg, Miss.
13. M. Sargin, S. K. Ghosh, and V. K. Handa; "Effects of Lateral Rein-- forcement Upon the Strength and Deformation Properties of Concrete"; Magazine
of Concrete Research, June-September 1971, Vol. 23, No. 75-76, Pages 99-110.
71
" " . . . " - . . .. * " * * ... .. " . " " " " , * * ** . .. -* . .*
14. F. E. Richart, Z. Brandtzaeg, and R. L. Brown; "The Failure of Plainand Spirally Reinforced Concrete in Comopression"; Engineering Experiment Sta-tion Bulletin No. 190, 1929; University of Illinois, Urbana, Ill.
15. K. T. R. J. Iyengar, P. Desayi, and K. N. Reddy; "Stress-StrainCharacteristics of Concrete Confined in Steel Binders"; Magazine of ConcreteResearch, September 1970, Vol. 22, No. 72, Pages 173-284.
16. S. A. Sheikh and S. M. Uzumeri; "Analytical Model for ConcreteConfinement in Tied Columns"; Journal, American Concrete Institute, December1982, No. ST12, Pages 2703-2722.
17. D. C. Kent and R. Park; "Flexural Members with Confined Concrete;"Journal Structural Division, American Society of Civil Engineers, July 1971,Vol. 97, No. ST7, Pages 1969-1990.
18. G. D. Base and J. B. Read; "Effectiveness of Helical Binding in theCompression Zone of Concrete Beams"; Journal, American Concrete Institute,July 1965, Vol. 62, No. 7, Pages 763-780.
19. S. P. Shah and B. V. Rangan; "Effects of Reinforcements on Ductilityof Concrete"; Journal, Structural Division, American Society of Civil Engi-neers, June 1970, Vol. 96, No. ST6, Pages 1167-1184.
20. R. Yamashiro; "Moment-Rotation Characteristics of ReinforcedConcrete Members Subjected to Bending, Shear, and Axial Load"; November 1962;thesis submitted to Department of Civil Engineering, University of Illinois,Urbana, Ill.
21. W. Keenan and others; "Structures to Resist the Effects of Acci-dental Explosions" (Revision in preparation); Department of the Army TechnicalManual TM 5-1300, Department of the Navy Publication NAVFAC P-397, Departmentof the Air Force Manual AFM 88-22; Departments of the Army, the Navy, and the
*Air Force, Washington, DC.
22. A. H. Mattock; "Rotational Capacity of Hinging Regions in ReinforcedConcrete Beams"; Proceedings, International Symposium on Flexural Mechanics ofReinforced Concrete, November 19614, Pages 227-234; American Society of CivilEngineers and American Concrete Institute.
23. N. C. Sinha and V. S. Rane; "Computation of Curvature and Deflection* in Reinforced Concrete"; Journal, Institution of Engineers, India, July 1965,*.' Vol. 45, No. 11, Pages 826-836.
24. W. G. Corley; "Rotational Capacity of Reinforced Concrete Beams";Journal, Structural Division, American Society of Civil Engineers, October1966, Vol. 92, No. ST5, Pages 121-146.
25. R. Taylor, D. R. H. Maher, and B. Haynes; "Effect of the Arrangementof Reinforcement on the Behavior of Reinforced Concrete Slabs"; Magazine of
-." Concrete Research, June 1966, Vol. 18, No. 55, Pages 85-94.
26. H. Bachman; "Influence of Shear and Bond on Rotational Capacity ofReinforced Concrete Beams"; International Association for Bridge andStructural Engineering, Zurich, Vol. 30, Part II, Pages 11-28.
27. M. Z. Cohn and S. K. Ghosh; "Ductility of Reinforced Concrete Sec-
tions in Bending"; Symposium on Inelasticity and Non-Linearity in Structuralhi Concrete, January-June 1972, Pages 111-146; University of Waterloo, Waterloo,
Ontario, Canada.
72
" , . K§.".i"i i K:."- . -K . - " .-- ---'" -'" - • - " . . , - " . . ' .J-. .::. : •. .,- , . -.- , .. ,• ." .. .. - . " * " - *...** '-.* .* .- ,,. " -. ' *' *, " . . *- .,. - ' " ." -L "
28. P. Srinivasa Rao, P. R. Kannan, and B. V. Subrahmanyam; "Influenceon Span Length and Application of Load on the Rotation Capacity of PlasticHinges"; Journal, American Concrete Institute, 1971, Vol. 68, No. 6,Pages 468-471.
29. E. P. Burnett; "Rotation Capacity of Reinforced Concrete FlexuralElements"; Symposium on Inelasticity and Non-Linearity in Structural Concrete,January-June 1972, Pages 181-209; University of Waterloo, Waterloo, Ontario,Canada.
30. A. L. L. Baker and A. M. N. Amarakone; "Inelastic Hyperstatic FrameAnalysis"; Flexural Mechanics of Reinforced Concrete, 1965, SP-12, Pages 85-142; American Society of Civil Engineers and American Concrete Institute.
31. A. J. Ockleston; "Load Tests on a Three-Story Reinforced Building inJohannesburg"; Structural Engineer, October 1955, Vol. 33, No. 10,Pages 304-322.
32. K. W. Johansen; "Brudinie Teorier" ("Yield-Line Theory"); 1943;Gjellerups Forlag, Copenhagen; Page 191; Translated by Cement and ConcreteAssociation, London, 1962, page 181.
33. A. J. Ockleston; "Arching Action in Reinforced Concrete Slabs";Structural Engineer, June 1958, Vol. 36, No. 6, Pages 197-201.
34. E. Burnett; "Flexural Rigidity, Curvature and Rotation and TheirSignificance in Reinforced Concrete Design"; Magazine of Concrete Research,March-December 1964, Vol. 16, No. 46-49, Pages 67-72.
of 35. M. Iqbal and A. T. Derecho; "Design Criteria for Deflection Capacity
of Conventionally Reinforced Concrete Slabs--Phase I"; January-August 1979;Construction Technology Laboratories, Skokie, Ill.
36. W. A. Keenan; "Strength and Behavior of Laced Reinforced ConcreteSlabs Under Static and Dynamic Load"; R620, April 1969; US Naval CivilEngineering Laboratory, Port Hueneme, Calif.
37. W. A. Keenan; "Strength and Behavior of Restrained Reinforced Con-crete Slabs Under Static and Dynamic Loading"; R621, April 1969; US NavalCivil Engineering Laboratory, Port Hueneme, Calif.
38. R. Park and W. L. Gamble; "Reinforced Concrete Slabs"; 1980; JohnWiley & Sons, New York; Pages 562-609.
39. S. A. Kiger, P. S. Eagles, and J. T. Baylot; "Response of Earth-Covered Slabs in Clay and Sand Backfills"; Technical Report SL-84-18, October1984; US Army Engineer Waterways Experiment Station, Vicksburg, Miss.
40. E. H. Roberts; "Load-Carrying Capacity of Slab Strips RestrainedAgainst Longitudinal Expansion"; Concrete, 1969, Vol. 3, Pages 369-378.
41. R. H. Wood; "Plastic and Elastic Design of Slabs and Plates"; 1961;Thames & Hudson, London, England; Pages 225-261.
42. R. Park; "Ultimate Strength of Rectangular Concrete Slabs UnderShort-Term Uniform Loading with Edges Restrained Against Lateral Movement";Proceedings, Institution of Civil Engineers, June 1964, Vol. 28, Pages 125-150.
73
%
p7
43. C. T. Morley; "Yield Line Theory for Reinforced Concrete Slabs atModerately Large Deflections"; Magazine of Concrete Research, December 1967,Vol. 19, No. 61, Pages 211-222.
44. T. Y. Hung and E. G. Nawy; "Limit Strength and Serviceability Factorin Uniformly Loaded, Isotropically Reinforced Two-Way Slabs"; Cracking,Deflection and Ultimate Load of Concrete Slab Systems, 1971, Special Publica-tion 30, Pages 301-324; American Concrete Institute, Detroit, Mich.
45. E. C. Isaza; "Manual of Extensibility of Reinforcement for CatenaryAction"; August 1972; Concrete Structures Technology, Civil Engineering De-partment, London, England.
46. D. C. Hopkins; "Effects of Membrane Action on the Ultimate Strengthof Reinforced Concrete Slabs"; December 1969; thesis presented to the Depart-ment of Civil Engineering, University of Canterbury, Christchurch, New
" Zealand.
47. J. F. Bi tchie, A. Jacobson, and S. Okubo; "Effect of MembraneAction on Slab Behavior"; R-65-25, August 1965; US Naval Civil EngineeringLaboratory, Port Hueneme, Calif.
48. R. Park; "Tensile Membrane Behavior of Uniformly Loaded RectangularReinforced Concrete Slabs with Fully Restrained Edges"; Magazine of ConcreteResearch, March 1964, Vol. 16, No. 46, Pages 39-44.
49. T. R. Slawson; "Dynamic Shear Failure of Shallow-Buried Flat-RoofedReinforced Concrete Structures Subjected to Blast Loads"; December 1983;thesis presented to the Department of Civil Engineering, Mississippi StateUniversity, Mississippi State, Miss.
50. W. L. Huff; "Test Devices Blast Load Generator Facility"; Miscel-laneous Paper N-69-1, April 1969; US Army Engineer Waterways Experiment Sta-tion, Vicksburg, Miss.
51. A. H. Mattock; Discussion of "Rotational Capacity of Reinforced Con-crete Beams", by W. G. Corley; Journal, Structural Division, American Societyof Civil Engineers, April 1967, Vol. 93, No. ST2, Pages 519-522.
52. T. R. Slawson; "Structural Element Tests in Support of the KeyworkerBlast Shelter Program" (in preparation); US Army Engineer Waterways ExperimentStation, Vicksburg, Miss.
53. American Concrete Institute; "Building Code Requirements for Rein-forced Concrete"; ACI 318-83, November 1983; Detroit, Mich.
54. S. A Mahin and V. V. Bertero;; "RCCOLA (A Computer Program for Rein-forced Concrete Column Analysis), User's Manual and Documentation"; August1977; Department of Civil Engineering, University of California, Berkeley,Calif.
74
";'< ): ,i-,'' _." -, ?5 "i-';"2" ii'.L i.- ., ....i.;'? ,". . '
APPENDIX A
POSTTEST PHOTOGRAPHS AND DATA
75I
Figure A.1. Slab 1 posttest.
* Figure A.2. Slab 3posttest.
76j
K.K
LAi
00
Sw
Figure A.5. Slab 7 posttest.
* Figure A~.6. Slab 8 posttest.
78
1. - - ----- -- - 7
01
04
* i,-ir A.8. .St ib 10 post _.-
I.-
0
0
80
3
APPENDIX B
STIRRUP SLAB TEST DATA
81
-4 .
FE~1q STIEFXUF' ,LF5
59 7134 2,2 71 1 5 '
CHR'INII N C 2093
Oc 0/04,"94 £0597
- r
-' --------
C*)
f4 . 0 *_ _ _ __ _ _ _ _ _
04
I I"
Ci.) r,-I
. - _ _ _ _
0 /q
L- 0 0 iO 2,9 30 <0 5C, 'O ?0. 00 30.
.82
4" °.' 82
F EM TI F RUF U Lfl6ID -
0 ,14 72 -.3227
05/'4 /94 a r) 7
cr)
C)
JC,
C83
FEMR STIRRUF SLRB I0-2MRXIMUM SjGlr, rIRL CIL M L-
3.7510 2,13 2 5.2
CHRNNEL NO 3 20953 I
"05/0419 4 ROf, .7
C,(..-
030 3.5 4.0 4.5 5.0
D ISPLACMENT IN
84
, -o.".. . .°
FEMR STIRRUP SLRB I
MAXIMUM S $[ cmrl CA (il- VAL-4035.O45r6 2 .4 1tJ 16b 7
CHRNNEt NO.- 4 20 9 63 1
Ori'/4 /94 RO0 17
J0 ;*00 -6- -6- O. j '0 00 400G 50
____ _ __ __ _ ___iN____ ____W I
085
':) 4
.1
FEMc 51 1RRUP [5LR5 I -O[%5b- 1
r4'XMU1 C'1%i C r L CAiL Vp.1637.5jG2l -26347 .6 7
CHrINNL NC 5 tic .2035 93Or5/04 /94 Ra 7 ..
C)
-L r r
( r1 r-|
Q1 j.D ,Q Q -
(d T F, R| I I ( IN
-86
C ) " - -_ __ _ __ __ _ __ _
r..,t< - -
FEMq 5TIRRUF SLRB I"" ST-2
MFIXIMUM 5[GMF CpL CRL IAL193,3 L 2. ,0 5735 L 2
CHINJNEL NO 9 2095)3
05/O04/,4 R0517
C:;
C)
* U)
". j rr50
T Nr lICR01N
87
""o'7 -7
FEMR $-'TIRRFUF SR6
CPqNNE NO 20953O0'04I94 R9
LO
C)
c) _
C)
-j0vr'-CO 0 4 4 0 ,G ,I, oc)i rj jl
5TRtIF WIN
-'C) 88
(I7
1 7.
FEMR STIRRUP SLRB 2P-- IMAX IMUm SIOM CAL CRL RL67.5286 .128. 35 9
CHANNEL. NO. 1 13092 1
06/12/84 R0342
F,,
O0
or-0.. I
i t
Lo. 0 .o. ZO. 30. 40.- 50. s0. 0. 80. 90.
PRESSURE - PSI
89
-: U . * U . .
FEMq STIRRUP SLRB 20-1MAXIMUM SIGMA CRL CAL VAL0.0884 0.9772 1 .1
CHANNEL NO. 2 13092 1
06/12/84 R0342
0f)
09
FEfIR STIRRUP SLRB 2D-2MAXIMUM SIGMA CAL CRL VAL1.6610 1-8505 5.3
CI-INNEL NO. 4 13092 1
06/12/84 R0342
c:)
CD
-0
(191
FEMR STIRRUP SLRB 2
ST-iMRXIMUM SIGMA CAL CAL VAL24714,6999 1.0935 11666.7
CHANNEL NO. 5 13092 1
06/12/84 R0342
E -
on
(D
0)
",.
0
0-
) 0
a-C WI0_-_ _92
O o .... _ _.__ __.
"i', -?0000-15000-l0000 -5000 0 5000 10000 15000 20000 25000 30000:
4 STRRIN-MICRO IN/IN "
'" 92 2
* . -I
FEMR STIRRUP SLAB 2SB-MAX IMUM SIGMA CAL CAL VAL
-9591.32'49 1.1550 11666.7
CHANNEL p40. 7 13092 1
06/12/84 R0342
C2
(L
0tGO -80 600-0C-00 00 00 60 80 00
.f)I - IC O I
t93
FEMR STIRRUP SLAB 2ST-2MAXIMUM SIGMA CAL CA AL
11811.3075 1.1069 C 5766.1
CHANNEL NO. 8 13092 1
06/12/84 R0342
0*
c;
CD
0*v
C3
C:D
CD
.12
-J00 0 20 0060 00100 20 40 60 80STANMIR I
u-94
FEMR STIRRUP SLRB 2SB-2
SIGMA CAL LMAM960516 1.5889 5"66 A
CHANNEL NO 9 13092 1
06/12184 R0342
CY)
c;
co~
C.
too
0 __... "
- 0 / _ ___ ___ ____ _ -a
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
STRRIN-MICRO IN/IN
95
FEMR STIRRUP SLRB 2
5-3MAX MUM SIGMA CAL CAL VAL2432.6618 4.0873 5766.1
CHANNEL NO. 10 13092 1
06/12/84 R0342
0
c; /0,
C,
0*
c;-.
to
~0
"50O0 500 1000 1500 2000 2500 3000 3500 4000 4500Non STRIN-MICRO I/IN
• .960 *--- '__•
FEMR STIRRUP SLRB 2S-4MAXIMUM SIGMIA CAL CAL VAL-268.4668 1 .3558 2899.8
CHANNEL NO. 11 130921
06/12/84 R0342
0; -
LLA10::
'0 0 -2 0 -2 0 -10 -10 50- 0 5 . 10 15 . 2 .
U*)I -M R W IN
U97
FEMR STIRRUP SLAB 2S-5
MAXIHUM iGMAI CAL CALVLM2066212923 1.2231 57661
CHANNEL NO. 12 130921
06/12/84 R0342
0 -;-
In
CL
w
160 -50 001'0 '0 400 200 30 50 40
ST AI - IC O IN I
w9
F"EMq STIRRUP SLAB 3P-1
MqxIrUM SICMR C L CI c5V[L71 .907 2.753 3l 5.V
CHqNN.A. NO, i 13437 1
04/25034 R0434
(Cs0*
~2- .,j
S.CL
LU
S. • U
"L. O. 0 O 2. 3L 4. 0 0 0 0
R-'ESSURE rS,
99° . . .-
FEf1q STIRRUP SLRB 30-IM AXJIMSM Sl~GMAIAL CI ~LVAL
0. 1 4 2
CHANNEL NO. 2 13437104/25/94 R0434
0
(0
L&JCL~
LO.L0' 0 0.02 0.04 0.06 0.09 040O 02 1 0.-4 0416 0ig
OISPLRCEMENT -IN
100
V7
F:EMrl STIRRUP SLAB 3
mqxImum 'MG~q CflL CflL VAlL2')645 1.Y9 5.
CHA~NNE[ NO, 41 13437 i
0 4/23 9 4 R03 1h
010
F:Et1 STIRRUP SLAB 3ST-1mqximum SJGMRSC$L CAL VAL03i 1.-Oj39 -3i 99 11666.7
CHRNNEA. NO. - 13437 1
04/2t5/94 R0434
CL
Lu
10
U)7
FEMR STIRRUP SLAB 3SB-IMRXIMUM 5;CNQI CAL AVL2070,4159 Ir32Cq'L
CHANNEL NO. 7 134.371
04/25/54 R0434
(C
0 0 001_)_20 EO30 50 0040
10
FEMlR STIRRUP SL.RB 3ST-2MSXIMUM 31GM CAL CAL VAL5947.1935 5.i005 5759,i
CHqNNEL NO. 9 13437 1
04/2/94 R0434
c; --
0,
<'i.C,. (D
uj.
C,)
"
J100 0 1000 2000 3000 4000 5000 SOO 7000 9000 9000
STRRIN-MICRO IN/IN
1QS104
FE~1R STIRRUP SLAB 3SB-2mnxirIum siri CR(14 L CAL VAL12030.7947 4.41% 571914
CHflNNEA. NO. 9) 13437104/25/94 R0434
a-
co
CD
10
.1
,:i
FEMR STIRRUP SLAB 3S-3MAX6IMUM,, SIG MR CAL CAL R42 .4922 2 L 57981
CHqNNEL NO. jO 13437 i
04/23/94 R03-)5
C
C,4a,,
1i °1
ik-
b .r.
L500 -400 -300 -200 -100 0 100 200 300 400 500
STRRIN-MICRO IN/IN
106A Lt h. L C. U.-
;. .. .-~~~ .-- - S -
FEMR STIRRUP SLAB 35-4"M'QX IMUM SIOM CRL CqL VAL-309.2492 2.6140 2999 ,"
CHANNE[ NO. i I 13437 1
04/25/84 R0434
-3 r5
-) __ ____
.
Lij
(L
o"c ---
4
cJ350- -300 -2E0, -200 -150, -100, -50. 50 IGO ISO
F~rlSTRAIN-MICRO INIIN
0.
"1-"
... .......... ..... .. .. ....... . . ...... : ,:: . '.I " " ".., :. .• " " " " ":. , _ , C ,, -._,
W V W'V ~~~~~~~~~~~~~- - -- -~V -'-i --o r r r -wrv~-r-- -~--- --r w --- -~
FEMR~ STIRRUP SLAB 3
CH'INNEL NCW. a'2 13437
04/23/S4 R039S
;.-
L500 -600 -400 -200 0 20 400 SOC 900 1000 1200
5TRRiIN-MICRO WNIN
108
F'"! S .i, lP 5
X[1*C CAL VAL' ;C) ,. 3..V. 2 .3 3 '
c~qjtj71 tj r 46
I-
0 L o 94 5 i Ci
0F
--
Cin
In, 303 "
10
.J . ----
0.-- -__
C'..'
0*
109
.I
FEM1. STIRRUP' SLR 4
ii-
M-XI"UM S[G'M- CAL CAL VAL--. 72 2q., .5255 14]
CHRNNEL NO 2 345205/04/94 0 9
"+' C) _ _ _ _ _ _ __ _ _
0* C)
L.
-0 0 0 .2 .3 0.4 0.5 9. 7 0 019
DISPLAlCEMENT -INI
110
7 - . -. .*.-
[ STIRRUP 5LS 4
M.X3459 3rN' 3P)5 LL m
CHARNNEL NO 4 345s2
05/04!934 Rc
C-3
C -
C-
r-4 Ic L C-P T I
FE.'1q STIR~RUP 5.R6 45 T -
MGX [MUM 5[Cin CAL CRL VALi15CC 595 2.3331 S).
CH~qtlNFL NO 3492
0510O4194 SIr
* C, ____ ________________ ___or%_
L~
-tilvv 0 50 0O G 1t 0 v0 2GU 30CG ' Q 400P 5-
ST)I I R N
C11
FEMR STIRRUP SLAB 4
m1qX1MUM 1I' C R CQL VRL
CHqNNE[, No3 345,
05/1 /5 - -3
-400 -GO -0 -0S 0 CG of 4 5
cwR I -IR N I
0 _113
FF1 TIRRUF' 5L.S6 4
mqxImum 1t&1'1fl (Al CL'15S3O3.0733 3.410 555.
CI1~NNE1 NO (3 3452
05/04/94 r0 9 5
0 - -
r,__ _
Eu 4_ _ _ _ _ _ __G9G v Vv Q
0T R N II R /1-
C7,
U11
E Si ~T IRU F 5 LP. 54
*0 44 2 7 J0 3)
CWPJNNEI NO 1 3462
CD-r:NMIR IW
C) ______ ____115
FEMR STIRRUP 5LRB 45-3MAiXIMUM r~Acmq~ CAL CAL !AiL
99 - 22.5712 1 j
CHIVMMIL. NO. 0 3 452
051.04/94 R09S 5
Cl
CK
CL.
u-i
I DIV' 0 o.,_o
-0 0 0 200. 300 50 %0 0 00 70 O %- 9C- 300*5TRPIN-MICRO IN/IN
116
FEMR STIRRUP SLAB 4
S- 4
$IS. 3542 3.91 93
.& ''4-5
C•rNNEI. NO. 1 3462 105/11/94 R073i
Cy
C'
*- .|
4. .5- •.
-100 0 t00 20 0 300 400 500 500 700 S00 900
A STRRIN-rIICRO IN/IN
117
*..'" c' -7
FE'.q 'STIRRUP cOLR6 4
NMiXIMUM CSfG? 'l CRI CrL 'IFL7931.,570 2 7 4 Z4 5655.
CHI-TNt NO. . 345'
0*-
L3-)
0*_____
I, _____ ______ v___J______j 01 1 cP r, 30
C- TNMCOwII
U11
:0-2
STIRRUP SLRB 5BP-iMAXIMUM bIGMA CAL CRL VAL74.5348 4.7394 135.9
F2CHqNNEL NO. 1 13701
08/17/84 R0181
CL
. .-
0JO 0_ 10_0. 4 ._0_0. 7 . 80 _0
(119
0
i Do
. .'
"- 119
. . . . . . .. o . • .. . .
STIRRUP SLRB 550- 1MAX I mum SIGMA CAL CAL VAL
0.1461 2.7534 1.1F2
CHRNNEL NO. 2 13701 1
08/17.184 R~0181
C;
C)-
LJ)
D-
02
STIRRUP SLRB 58
0-2MAXIMUM SIGMA CAL CAL VAL3.2265 2.3787 5.2
F2CHANNEL NO. 3 13701 1
08/17/84 RO11
-.. ~V v Vv"" Vr-
0*to
U)
LuJ
Lu
CL.
'0 0.5 1.0 1 .5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
DISPLRCEMENT - IN
121
k~ .. .- -. :* .K . . ~ . * .j - $f. *.*
STIRRUP SLRB 58ST-1MRX;MUM03 SjGt1RJAL CAL IR~L
F2CHANNEL NO. 4 13701 1
08/17/84 R0181
0 - c
0
-J6000 -4000 -2000 0 2000 4000 6000 8000 10000 12000 14000
* STRRIN-tIICRO IN/IN
122
STIRRUP SLRB 55SB-IMAXIMUM S IGMA CAL CAL VAL2640.2470 2 .4200 11666.7
F2CHqNNEL NO. 5 13701 1
08/17/84 R0181
CD
C
L00 0 00 10 0020 0030 0040
0TRN-IR WIN_
(123
STIRRUP SLAB 5BST-2MAX I mum S IGMR A CAL VAL
10411.4495 3.0541 576.1F2
CHANNEL NO. 6 13701
*08/17/84 R0181
co
C3
0%
STT-2MCR "N/I
124
1071.49_.04_576_t_~
,(/
-U,tl " "ol
-J200O0 2000 4000 6000 8000 10000 12000 14000 16000 18000 .
KSTRAIN-MICRO IN/IN "
124 --
STIRRUP SLRB SBSB-2MAX6MUI SIGMR CRL CAL VRL12033.3612 3.0177 S"/66.1
CHANNEL. NO. 7 13701 1
08/17/84 ROIBI
Go1
,n ,
C : ..'...
-' o 'ii
-J4000 -2000 0 000 4000 6000 6000 10000 12000 14000 16000
.0 STRRIN-MA'CRO IN/!N
67~
'125
p0 -
I -'---- -
ii0 -
0i-- - - -
i£ 125
2 .O-".
STIRRUP SLRB 55S-3MAXIMUM SIGMA CAL CAL VAL-1074.8645 2.7431 5766.1
F2CHANNEL NO. 8 13701 1
08/17/84 R0181
C3
to
C
inD
-Ui
:)- . 0
C3
-00 10 80 -0 40 -0 0 0 0 o
STRI -M COI)I
U12
STIRRUP SLRB 5BS-4MAXIMUM SICMq CAL CAL VAR1155.0916 2.7508 2899.
F2CHANNEL NO. 9 13701 1
08/17/84 ROt18
0o
(L
U00
Ir-0i
U)
OL0
F4
L200 0 200 400 600 800 1000 1200 1400 1600 1800
STRRIN-MI'CRO IWIN
127
STIRRUP SLRB 58S-5MAXIMUM 3 1 MR CAL CA R5564.F2 56 2.7177 S66.1
CHqNNEL NO. 10 13701 1
08/17/84 R0181
.-.
Lu
0jOO 0 10 40 0040050 0070 CO90
128
I Fr 1 1 II R RUF ~L P5 9
I59 5554 LiY57
C HPNNEL NC. i 9z
04/2i)/94 ' 0432
10 4C) r_ F_ F E
______ t ___129
FFMq STIRRUP SLRE3 60-1MRXIMUM v~M R CAL VAL
04/'S/94 R0432I
0~on
LO _ _ _ _ __ _ _ _ _ _Lo
16_ __ _ __ _ _ _ _ _
* . c;
CD
13
FEMq STIRRUP' SLPB 5
C.INNE', NO.- 4 91,15
04/2,'4 ~O43
Crj
-03 0 4. *, > 25 Q 35 .0 4 5
* IJL R E.M.EN T I IN
131
FEMR STIRRUP SLRB 6ST-iMAXIMIUM SJCMtA CAL CAL VAL
CHflNNEL. NO. S 9 21 1
04/25/94 R0432
CD _ _ _ _ _ _C
C3 - -_ __ _ _
C'
.
50 i00 a'0 0 00 5030 SG 0G40
5TRNMIR I
1321
FEf1R siJiRru SLRf3 6SB-1mflximum 51CMq CAL CAL MfL239C.4110 43 C C S 11565.
CW1INNEL NO. 1 21
04/19/94 04
C1
C,
L3
C)3
5G) 10'C t ______ ______ ____3'_500___5G
5TRAI________WI
I133
FEM1R STIRRUP SLRB 6ST-2MAXIMUM SIGMA CAL CAL VAL
3930.7357 3.9,47 5766.1
CHAINNELt NC. 9 92 16
04/2S/9~4 "O4*32
CD
C)
C)
(134
FEMP STIRRUP' SLPRB 656-2MqX1I1UM S1CMRI CAL CAL IARL
11943 -3bl2 3.3006 57156
CHRqNNEL NO 9 52 151
04/19/84 R0347
C)
CD
V)
0 __
c) ;____ ____ ____ ________
IM 0 UG S O ,''r 2 " 1 0 C 1 ' 1 C e
5T RI - ICO)N I
013
FEMR STIRRUP SLRB 65-3MRXIMUM 1slmn CRL CRL vRl_
2 11.-7 422 2 .5994 576i
(JIRNNEL. NO. iO 916
04/2b/'94 R0432
C;
cr-
CD
0 . ____10 . M 00 - 30 , 30 40 5
STRNMIR I
U13
FEMR STIRRUP SLRB 6
mnx IM mum11 )Im RL cA w- n!-43L -'MO 3.4014 9
CI-flNNF1 NO. il 9131 1
04/2'j/94 R0432
C)
C.)
CL -
Cr:
2U -40 -0 -20 -100 0 0 G 2100 300G 40 5c)0 0
* 5TRRI!N-MICRO IN/IN
137
.3
FEMR STIRRUP SLRB 6
MA~XIMUMl SITcmfl AL CAL iRL3220-1750 2 .647 57/66.1
CHnNNEL. NO. 1 Z 9216 1
04/19/94 R0347
C3.LO
ci
0 ___ G__ -5c c 5G0 _G 15 G2G 2_C30 3 _
5TANMIR I
Cd) 138
FEPIR STIRRUP SLR;B 7
MGXIMUM j!CMr, CALI CAL. VAL54339 2 -39 34 135.3
CHnNNE', NO. 19442
0j/04/94
CL 1
r)
LC a 0 L0 9 3 4 )02
rw S5JRF-FS
U)139
FEMR STIRRUP SLAB 7D-111qxImum SIGMq CAL CAL VAL
0.I~ 2 - i iV3 1 .1
CHANNEL NO. Z 19442 105~/04/94 ROSIS
C3.
014
FEtIR STIRRUP SLRB 7
0-2mnximutI iiGmr CAL cfll L
3.-4423 2 -77 92 5.2
CMIJNEL NO 3 194421
0
C)
ci
C3.
C3
-- --17-
FEFAR STIRRUP SLR5 7
MfjXIMUM Sir-MR R CRI1c . v rL!I 155.3245 3.57164 1 15 95
CHRNNE1 NO. 4 193442
05/04/94 R0619
an
L)
C.)
C:)
LUJ
C),
C)
000 so 0 c G0 'OG c0 2060 2560 3000 3500 4000
5TRRIN-MTCRO IN/IN
142
FEMR STIRRUP SL.RB 75B-1MnXIMUM 5ICMq CRL CAL VRL19523 55043 2,7199 115967
CHqNNEL NO. ' 19442
O'5/04/94 R 0 59
C)
ulr^
¢,J• .
L..
JLJGGG 0 5000 10000 i5ir0U 20GGG -SG0G00000 3SOOG 40000 4-5r00
5 5TR R!TN-MIICRO IN/IN .
.. 143.
LAJ
U )". . . , - . . .'J . . L " ., , i . - ' . . i - , .- . - 2 '. , . -: '
1T
FEIIR STIRRUP SLRB 7ST-2mqX1mum SIG~MA CAL CAL ifll
4111 .5797 4.35763 5765 L
CINNEL NO. 6 1)3442 1
O'v'tJ4/94 R05i9
CD
C:)
Cr)
L5U0 50 10 j)2000 003G 0G45G
STRNMIR I
14
FEMR STIRRUF SLRB 7S-4mix IMU mum CM ll lL c- CR1. vflL
1237 .34293 3. 3959' 2933 93
CH.rNNE. NO. -9 19442Oc~i04/9 4 RO0 9 3
C-
C:)
-)
- T7
14~5
FEMRi STIRRUP SLRB 75-5MAXIMUM SJtGMR CAL CR!. VAL594-3943 54 a26 51,6J
CHANNEL NO. jO 19 4 4.2
05~/04/94 ROSi~
C2
C)
L3-
c;
uj
cJ
LGOo 0 100 200 300 400 5 00 Soo 7100 9C0, 300
5TRRIN-MICRO WNIN
FEMR cI.TIRRUF SLR i9
MflXIMUM IEM q C L cL m-1!,.. 59 4'452 2 j • 3 13 35 •
C NHqNNE NO I 470
04/24194 R0409
r".-"
C)
ct:
C-)
p.r
LL
- , - ,
. t ).* /bj
LL .I . t_ _ _ _ _ _ _ _
LIO 1 0 20 30 40 0. iC • 0. 1 0 . 3 ,
FSJFE -7F1 ISO:
FEM1R STIRRUP SLRB 8D-1MAXIMIUM STOMPR CAL CAL VAL
ClH'qNNEL NO. 2 147301
04/24/94 R04013
-L-n
QU)
u
L) 0 1 0 0-2 0.4 0.6 0.0 1 2 G-4 '5 0 IDIPUEMN
L14
* -. FE,%Iq STIRRUP SLAB 9
mqx [um r[GMR nL CI. JAL
c pqtjNEI N In 4 14730
04/13/94 R03413
c; - -
C3,
* C )
C -
C2 -
I- ___ b__ ___ ___ 3 ____
.0.3 isrLRCEMENT -IN
149
FEMRI STIRRUP 5LRB 85-1MAXIMUM OcIcMA CAL CAL VAL
-2244.3274 2 . 7433 1 1136 .7
CIJqNNEt NO. . 14730
04/24/94 'RO409
C,
U-,
uj
7-)cr.
c.J
~2~S 20 -~0-1000 -,,o G o G0 10,00 io 0!"0 2000 2
5TRRIN-MICRO IN/IN
150
FEMR~ STIRRUP SLAB 9SB-1MRXIMUM rjIG~q CAL CA1 JAL2S255Ocri 3.2043 11665 7
Cl'jqNNE( NO 7 14730
04/13/S34 R0346
0r
C3 _ _ _ _I_ _ __ _ _ _ _ _ _ _ _
0~ :j C:)* 1 _ __ _ _ _ _ _ _ _ _ _ _
C2~~ VI v- ______--_____
1(G 0.:G2)I 0w'' 'G 'w 4 G ' 4 G
0T A N- T R_ C -I N I
- .(A151
FF1 E.l TIRRUP SLAB 93
ST-mqx[mum 5rC~ CflL ClL 'JAL
1'2239.-0773 3 -CM7519
(Hrillit[ No- pi 14730 1
04/13/94 R'4
C3
LL;
CD _ _ _
ci) ~
Uol , 'p 0G C OG !on 12P 4P 5-r
Lu V w V v vv v v vi
- 152
!194 73 7534 3.$9'43 5 1 9
C H INJE [ r11C 1 473004/10/94 R03413
40" __C1 "_0 2 " 4 " sr r
T F R1N -M CFO IN/I N
153
FE~9R STIRRUP SLRB 65-3M'iXt1UM ~r qCL CAL'L
10 ~~ ~ ~ ~ 7.35 1-701
(H1NNF. NC 10 I1)3
04/10/54 R0346
or,
C3.,
L-33
( t. 0 4. _ _4__ _ _ _ _
',,
U))
" -V3 - 00
L O 0,C P_ _ fVI_3_ Q . , l t.10 vV 1 % r
'0'
.C ,I n 1 0 O 'GS n u r , r. rr
.... 2 0 ' ~ ~ O 00 :20.. o 40 , : oo t e,,
* 5TRRIN-MICRO IN/IN
154.
FEMfl STIPRUP SLABE 95-4mqxImumI s[C-Iq Cpl_ CW- IP.L
')5S5 4 i590 29911 9
U-IRNN t IJC 4 17 J .04!24 /94 0 4 0
C.-'
LAO2 __1"__GC__1 '
5TGI-MTROINI
C) -__ __ _155
FEMR STIRRUP 5LRB 8
S--|
MAXIMUM S[CMq CAL CAL /IL"734.400C 2,713 5 5756
(19NNEL. NO 2 14 730
04/24/94 R0409
mLD
C:)iu
U-1
U)
) -
2L-U
15J1OCC -5CC C 50C ,0 ,50C ,.0CC,., 2 O 30CC 350C 40CC,
* STRRIN-MI!CRO IN/IN
156
FEt1q FTIFFZU H P5 9
mqXImum S 1.Imi AL CrIL /JrL
1R~NNP NC. 97 1
04 /2S3/94 UO440
C')
Fr)
C157
MAX I mum Ic SEM rc P, CRL /Pli
CH9NNE, NC 2 9i
04/2S/934 R0440
CD
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APPENDIX C
NOTATION
175
n .
, *
c Neutral axis depth at the ultimate moment
b Beam width
d Depth from the compression face of the slab to the centroid of thetension steel (effective depth)
db Diameter of reinforcement bar
E Modulus of elasticity
fe Compressive strength of concrete
f Yield strength of steelyf' Yield strength of compression steel
I Equivalent plastic hinge lengthpL Clear span length
M Posttest measured deflection
Mm Moment capacity at midspan
Ms Moment capacity at the support
P Applied overpressure
q Reinforcing index
R Electronically recorded maximum deflection
t Slab thickness
- T Yield force of reinforcement per unit width
W Uniform load
Z Distance from critical section to point of contraflexure
A Deflection at midspan
' Concrete strain
e Plastic hinge rotation to one side of the critical sectionpv Poisson's ratio
p Tension steel ratio
" P' Compression steel ratio
Pb Balanced reinforcement ratio
- P5 Ratio of volume of confining steel to volume of concrete core
-u Ultimate curvature of the section
y Yield curvature of the section
.6 y
176
[ 176
,L ? '" . . --"*."* -° '- *--'-. . . . ." .'-- . . . " -" -' - .' ..... . ..*
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