Embed Size (px)
Citation preview
FEASIBILITY STUDIES OF TWO-WAY COMPOSITE STEEL-DECK SLAB
by
CHEE KHEONG WONG, B.S. in C.E.
A THESIS
IN
CIVIL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirement for
the Degree of
MASTER OF SCIENCE
IN
CIVIL ENGINEERING
Approved
Accepted
December, 1987
ACKNOWLEDGMENTS
The author wishes to express his thanks to Dr. James
R. McDonald for his guidance and encouragement throughout
the course of this research. Special thanks to Dr. Kishor
C. Metha, Dr. Y. C. Das, and Dr. W. Pennington Vann for
their helpful suggestions and constructive criticisms.
The author would like to express his deepest
gratitude to his parents for their support and
encouragement and for working so hard to give him a good
education.
The author expresses his utmost sincere thanks to
Mr. and Mrs. Koh Boon Chor for giving him the opportunity
to further his education. He is also heavily indebted to
them for their kindness, support and constant
encouragement for so many years.
In addition, the author also likes to thank his
girlfriend Soo Ying for her love, understanding and patience
for al1 these years.
Finally, thanks to Mr. IS for his help with LOTUS.
1 1
TABLE OF CONTENTS
t
ACKNOWLEDGMENTS i i
LIST OF TABLES v
LIST OF FIGURES vi i
CHAPTER
1. INTRODUCTION 1
Development of Light Gage
Steel-Concrete Floor System 3
Current Practice 4
Advantages of One-Way Composite Slabs 5
The Need for Two-Way Composite Slabs 7
Organization of Thesis 8
2. LITERATURE REVIEW 9
Early Developments 9
AISI Studies 10
Pushout and Beam Tests 10
Ful1-Scale Tests 14
3. CONCEPTS AND CONSTRUCTION FEASIBILITY 15
The Basic Concept 15
Feasibility of Manufacture 17
Dimensions Used in Feasibility Studies 20
Nodule Size 20
Deck Size 2 1
1 1 1
Feasibility of Construction 21
Analysis 25
Results 28
Conclusion 34
4. PERFORMANCE OF TWO-WAY COMPOSITE SLAB 35
Loadings On Slab 35
Plate Theory 37
Flexural Rigidity of Composite Slab 38
Deflections, Moments, And Shears 42
Deflection 47
Moment Capacity 55
Shear Capacity 62
Shear Strength of Slab 62
Sheai—Bond Capacity 63
Shear Flow 64 Bond Strength Between Concrete and Steel 66 Shear Strength of Nodules 69
5. CONCLUSIONS AND RECOMMENDATIONS 73
Is The Proposed Concept Feasible ? 73
Manufacturing Feasibility 73
Construction Feasibility 74
Performance Feasibility 75
Recommendations for Future Research 78
REFERENCES CITED 79
1 v
LIST OF TABLES
3.1 Capacity of Puddle Welds 27
3.2 Tensile Capacity of Metal Deck Sheet 27
4.1 Locations of Concentrated Load 36
4.2 Uncracked And Cracked Flexural Rigidities 43
4.3 Expressions for Maximum Deflection, Moment, and Shear 46
4.4 Deflections of Uniformly Loaded Two-Way Composite Slabs With 18 Gage Deck (in.) 49
4.5 Deflections of Uniformly Loaded Two-Way Composite Slabs With 20 Gage Deck (in.) 50
4.6 Deflections of Uniformly Loaded Two-Way Composite Slabs With 22 Gage Deck (in.) 51
4.7 Deflections of Two-Way Composite Slabs With 18 Gage Deck Produced by Four Concentrated Loads (in.) 52
4.8 Deflections of Two-Way Composite Slabs With 20 Gage Deck Produced by Four Concentrated Loads (in.) 53
4.9 Deflections of Two-Way Composite Slabs With 22 Gage Deck Produced by Four Concentrated Loads (in.) 54
4.10 Ultimate Moment Capacity of Beam Model 58
4.11 Ultimate Moment Produced by Uniform Loads 59
4.12 Ultimate Moment Produced by Concentrated Loads 60
4.13 Allowable Uniform And Concentrated Loads as Governed by Slab Moment Capacity 61
4.14 Shear Flow (lb/in.) Produced by Uniform Loads on 3 in. Slab With 18 Gage Deck 67
4.15 Shear Flow (lb/in.) Produced by Concentrated Loads 68
4.16 Total Shear Resistance at the Interface Between Deck and Concrete 72
5.1 Uniform Loads Capacity of Two-Way Composite Slab 76
5.2 Concentrated Load Capacity of Two-Way Compos ite SIab 77
VI
LIST OF FIGURES
1.1 Isometric View of Proposed Two-Way Composite Slab 2
1.2 Mechanical Shear Transfer Device in Metal Deck 6
2.1 Linear Regression Plot for Shear
Capacity of Slab 12
3.1 Arrangement of Modular Decks 16
3.2 Base Deck Arrangement
(Nodules Not Shown) 18 3.3 Top Deck Arrangement
(Nodules And Shoring Not Shown) 19
3.4 Dimensions And Shape of Proposed Modular Deck 22
3.5 Shore Used As Support 24
3.6 Tensile Force in Base Deck Versus Midspan Deflection, for 3 in. Slab 29
3.7 Tensile Force in Base Deck Versus Midspan Deflection, for 4 in. Slab 30
3.8 Tensile Force in Base Deck Versus Midspan Deflection, for 5 in. Slab 3 1
3.9 Tensile Force in Base Deck Versus Midspan Deflection, for 6 in. Slab 32
3.10 Tensile Force in Base Deck Versus Midspan Deflection, for 7 in. Slab 33
4.1 Locations of Concentrated Loads on Two-Way Composite Slab 36
4.2 Transformation of Two-Way Composite Slab to Equivalent Flat Slab 39
V 1 1
4.3 Beam Model Used In Determining Moment
Capacity of Composite Slab 56
4.4 Slab Model for Shear Flow Calculation 65
4.5 Nodule Dimension Used for Calculating Shear Resistance 71
VI 1 1
CHAPTER 1
INTRODUCTION
The objective of this research is to explore the
feasibility of constructing a new two-way action light
gage steel-concrete composite floor system. The feasi
bility study involves only theoretical analysis from first
principles of mechanics and material properties. No
experimental work was performed in this feasibilty study.
A secondary objective of the study was to determine if the
concept is worthy of a testing program.
The performance of existing composite floor systems
is acceptable in today's building industry despite their
limited two-way action. It is not the objective of this
study to provide a replacement for the current system
but simply to explore a new idea that might be workable
in providing true two-way action in a light gage composite
floor system.
The new concept is illustrated in Figure 1.1. It
consists of two layers of modular deck that are laid per
pendicular to each other and overlap to form a platform to
support the concrete. A uniform pattern of nodules is
spaced so the overlapping sheets interlock. The nodules
strengthen the sheai—bond between the metal deck and the
concrete to enable two-way composite action to take place.
V- \ \ \ \ ^ \»A \ \ \ \v / • / \ \ \ \ vV
J * 'j\7 // y \ \ ^ •» J ., X ^ // * \ \ \ y
\/W<^ < V / W ^ ^ V
/m7% ^ <»/\
m v ^ < < ^ \-lA^ * < //
M V * A / V'A / \/\// ///
- V-^V /A /// «/> \ ' • V • / / \ / //
«* X"* ^ / / \ / Z' -•-» X • S / / A / / « \""v^v / / / v y *-» \* S / / / /A
A" y // / // " A '»/ / / / // JS / • < / / / / / / * * *
/ • / / / / / / OO / * ^ / / / / / /
/• ,n,/ / / / //
Top
Deck
Pu
ddle
Vel
ds
^
Pudd
le V
elds
'yC ^\
Show
n To
p De
ck N
ot
IS C O
a>
0) (0
0 (D _ _ Q. in
O 4J
Vie
w
-np
osi
0 O (J •*-1_ 5K
>om
et
/o-W
a
•
0)
'ig
ur
L ^
.
Development of L ight Gage Stee1-Concrete F1oor System
Composite floor slabs constructed with light gage
metal deck and reinforced concrete are commonly used in
buildings. The terms "composite construction" and
"composite slabs" are sometimes confused. Thus, the
following definitions are used to describe composite floor
slab construction:
1) Composite construction consists of steel beams or girders supporting a reinforced concrete slab, so interconnected that the beam and slab act together to resist bending (one-way action).
2) A one-way composite floor or roof slab consists of conventional light gage metal deck supporting a concrete topping, so interconnected that the deck and concrete act together to resist bending in one di rection.
3) A two-way composite floor or roof slab consists of two layers of modular metal deck supporting a concrete topping, so interconnected that the deck and concrete act together to resist bending in mutually perpendicular directions.
The system investigated in this study is a two-way
composite slab.
One-way composite slabs using light gage metal
deck were first introduced by the Granco Steel Products
Company in 1950. Their "Cofar" deck precipitated rapid
development of other one-way deck systems by other
manufacturers. However, much of the early research on
one-way deck systems in terms of analysis, testing, and
development of design procedures was proprietary with each
deck manufacturer working independently. These early
proprietary developments produced negative effects on the
market owing to the lack of exchange of information
between various deck manufacturers. In 1967, the American
Iron And Steel Institute (AISI) sponsored a research
project at Iowa State University with the objective of
obtaining a unified design procedure for steel-deck
concrete composite floor systems (Sabnis, 1979). The test
results form the basis for current one-way composite slab
design.
Current Practice
In today's practice composite slab systems use metal
deck rolled to form channels running in one direction.
These corrugations produce one way slab action, which
leads to an uneven distribution of forces in the direction
perpendicular to the deck corrugations.
Indentations, embossements, and transverse wires are
used to provide a better transfer of shear between deck
and concrete. Although the current one-way composite deck
systems perform satisfactorily, tests from AISI sponsored
research indicate that shear-bond failure is the
predominant mode of failure (Schuster, 1972). A shear-
bond failure results in slippage between the concrete and
the metal deck, which can result in cancellation of the
composite action between deck and concrete. Two methods
are used to achieve acceptable shear-bond strength in the
current practice: mechanical devices and chemical bond.
Mechanical shear transfer devices, as shown in Figure 1.2^
lock the concrete slab to the deck. An alternative way to
achieve adequate shear-bond strength is strictly through a
chemical bond between the metal deck and the concrete.
In practice the deck spans in one direction across
floor beams or purlins. The deck sheets form a platform
that supports workmen and the wet concrete. Shoring may
or may not be required prior to setting of the concrete,
depending on span and strength of the metal deck. If the
slab is continuous across two or more supports, negative
reinforcement may be required at the interior supports.
Welded wire fabric or other forms of reinforcements may be
required to control shrinkage and temperature cracks.
Design procedures for one-way composite slabs are
similar to conventional reinforced concrete slab design.
The concrete in the slab is assumed to resist only
compressive stresses, while the metal deck resists tensile
forces. The design philosophy recognizes two limit states
based on shear-bond and flexural failure modes.
Advantages of One-Way Compos ite Slabs
There are many inherent advantages in one-way
composite floor slabs.
1) The metal deck serves as a form to support the wet concrete and remains permanently in place as part of the structure.
Indentations
Enbossenents
Indenta Eibosseients
Figure 1.2 Mechanical Shear Transfer Device in Metal Deck
2) The metal deck serves as a working platform for the workmen, their tools, materials, and equipment prior to casting the concrete.
3) The metal deck acts as positive reinforcement after the concrete sets.
4) The metal deck is easy to install.
5) A composite floor slab weighs less because it is thinner than a conventionally reinforced concrete slab.
The Need for Two-Way Compos ite Slabs
The choice of the type of slab construction for a
particular application depends on many factors. Economy
of construction is obviously an important consideration,
but other factors such as strength and serviceability may
come into play.
In situations where the long span to short span
ratio is less than two and where it is possible to support
the slab on all four sides, two-way action slabs may be
more desirable and more economical. The situation is true
with conventional reinforced concrete slabs, also.
However, in today's practice which utilizes a light gage
steel-concrete composite floor slab, the slab provides
only one-way action. In situations where two-way action
may be desirable, current practice provides an uneven
^1 g.j.plj3jj ,-on of forces in the so-called 'weak' direction
tranverse to the deck corrugations. This situation gives
rise to nonuniform size selection of the supporting beams
a
or girders around the perimeter of the slab. A one-way
composite slab has a limited span between the supporting
beams. In comparison, a two-way composite slab will pro
vide even distribution of forces to its edges and leads to
uniform sizing of the supporting structural members around
the slab perimeter. Larger spans in both directions of
the slab also may be possible with two-way action.
Organ ization of Thes i s
Chapter 2 reviews previous research on composite
slabs. Chapter 3 explores manufacture of the modular deck
and the constructabi1ity of the proposed two-way composite
slabs. Performance evaluation with respect to deflection,
moment, and shear capacities is found in Chapter 4. The
last chapter states conclusions regarding the feasibility
study and suggests the need for additional research.
CHAPTER 2
LITERATURE REVIEW
This chapter examines previous research on composite
slabs. Early developments were not published in the open
literature, because they were considered proprietary.
Because of extensive studies sponsored by the American
Iron and Steel Institute, the behavior of one-way
composite slabs is well understood. Only a limited
number of studies have considered two-way composite slab
action. Because the proposed two-way composite slab
system is a new idea, no previous work on its performance
is available. Research on one-way slabs is reviewed in
this chapter with the objective of showing how it leads to
the proposed two-way composite slab concept.
Early Developments
Cofar, the first metal deck for composite floor
slabs, was first marketed in 1950. Produced by Granco
Steel Products Company, St. Louis, Missouri, the steel
deck had transverse wires welded to the top of the
corrugations. A concrete topping completed the composite
system. Friberg, 1954, published the first significant
article on design of composite slabs using "Cofar."
10
The study also contained a cost comparison between
conventional concrete slabs and composite slabs.
Bryl, 1967, carried out investigations on different
deck cross section profiles. Results of his investiga
tions identified several important behavioral and design
characteristics of composite deck:
1) Brittle failure of the composite slab occurred when shear transfer devices were not used.
2) Large plastic deformations were accompanied by considerable increase in load-carrying capacity in slabs with shear transfer devices.
3) Composite slabs should be analyzed as cracked sections and should be designed using the criteria for bending and bond stresses.
Discussions by Friberg, 1954, and Bryl, 1967, were based
on the working stress principles.
AISI Studies
A project started in 1967 under sponsorship of AISI
at Iowa State University had as its objective the develop
ment of an ultimate strength design approach for composite
slabs. The work involved extensive testing of pushout and
beam specimens. Full-scale tests of composite slabs also
were conducted.
Pushout and Beam Tests
The objective of pushout and beam tests was to
secure data for determining the ultimate shear-bond
11
strength of composite slabs. Pushout tests are tests in
which the resistance to slippage due to a horizontal
force acting on the element is measured. The beam
element testing was focused primarily on the nature of
shear transfer between the steeI-deck and the concrete.
All beam elements were simply supported and subjected to
symmetrical concentrated loads. A total of 353 beam and
pushout elements were tested. The test programs were
conducted by Ekberg, Schuster, and Porter. Significant
publications by the above are cited in the references.
Data obtained from those tests led to the development of
the following expression for the ultimate shear capacity
of the slab in kips.
V^ = (bd)/s (mpd/L' + k(f'^)^^^} • (2.1)
Where
b = unit width of slab (in.)
d = effective depth of concrete slab (in.)
s = spacing of shear devices (in.)
p = reinforcement ratio
L' = shear span of slab (in.)
f = compressive strength of concrete (ksi)
k = parameter determined from Figure 2.1 (intercept on the ordinate)
m = slope of reduced regression line (see Figure 2.1).
12
«, X
Figure 2.1 Linear Regression Plot for Shear Capacity of Slab
13
Equation (2.1) is the basis for current composite slab
design specified by AISI. Values of m and k are
obtained from a plot of experimental data. The parameters
VgS/bd(f'^)^/^ and d/L'(f'^)^/2 ^^^ plotted as ordinate
and abscissa, respectively. A linear regression is then
performed to determine the slope, m, and the intercept, k.
Equation (2.1) indicates that the primary parameters
affecting shear capacity are as follows:
1) shear span length
2) concrete properties, including age, and compressive strength
3) metal deck cross section parameters, including cross-sectional area, location of the centroid, material thickness, and depth of metal deck
4) spacing of the mechanical shear transfer devices (if present)
5) material properties, including yield and tensile strength.
The most important conclusion from the tests was
that shear-bond failure is the most predominant type of
failure. Ekberg et al., 1976, defined shear-bond fail
ure as the formation of a diagonal tension crack in the
concrete, which results in slippage between the concrete
and deck that is observable at the end of the span.
It was not always clear from the tests if shear-bond
failure preceded yielding of the steel.
14
Ful I-SeaIe Tests
Five full-scale tests were performed in the Iowa
State Project. The test objective was to obtain informa
tion, which could lead to improved criteria for the design
of one-way composite floor systems. Four symmetrically
placed concentrated loads were applied to each slab.
The slabs were simply supported on all four sides. Even
though the ratio of the long span to the short span was
only 1.33, there was little indication of two-way action.
Results from the full-scale tests confirmed the early
conclusions drawn from the beam and pushout tests that
shear-bond is the predominant failure mode.
Porter, 1974, also used the above results to develop
a set of procedures that combine the principles of yield-
line theory and shear-bond regression formula for analysis
of the limited two-way action in the one-way composite
slabs.
From the literature review it can be seen that
little or no research has been done in developing a true
two-way concrete composite slab. However, a very good
understanding of one-way composite slab behavior has
been established.
CHAPTER 3
CONCEPTS AND CONSTRUCTION FEASIBILITY
This chapter discusses the feasibility of
manufacturing and constructing the proposed two-way
composite floor slab system.
The Bas i c Concept.
Developing the concept of a two-way composite slab
is an exercise in creativity that could lead to an
innovative new floor system. The concept requires a
modular deck that is not presently produced by U.S.
manufacturers.
The new modular deck will have uniformly spaced
nodules instead of parallel channels. The nodules will be
pressed in the deck by a cold rolling process. The geome
try and arrangement of the nodules will allow two layers
of deck to overlap at right angles to each other.
The shapes and sizes of the nodules that will
produce optimum performance have not yet been determined.
For the purpose of this study, the shape of the nodules is
assumed to be that of a frustrum. Figure 3.1 shows that
the modular deck overlaps when the sheets are placed at
right angles and parallel to each other.
15
16
Decks Overlap At Right AngM
Base Deck Top Deck
Decks Overlap Paral lel To Each Other
Top Deck
Top Deck
Figure 3.1 Arrangement of Modular Decks
17
The bottom and top layers are called the base deck
and the top deck, respectively. From the plan view in
Figure 3.2, the base deck spans in one direction and is
placed with a gap between each sheet. The ends of the
base deck are welded to the support beams with puddle
welds. As shown in Figure 3.3, a solid layer of the top
deck is placed over the base deck at right angles to it.
The ends of the top decks are also anchored with puddle
we Ids.
Shoring is required to prevent excessive deflection
of the deck during placement of the concrete. The number
of shores needed depends on the span of the composite
slab, the strength and the thickness of the metal deck,
and the thickness and type of concrete (regular or light
weight). Because the base and top sheets interlock, welds
are only needed at the ends of the sheets.
Feas i bi1 ity of Manufacture
Light gage metal deck in use today is manufactured
by a cold rolling process. Flat steel sheets are passed
through a series of rollers that impose the shape and
dimensions of the deck profile. Cold working during the
rolling process increases the strength of the steel while
reducing its ductility slightly.
The proposed modular deck could also be manufactured
by passing steel sheets through a series of rollers
IB
Base Deck (nodules and shores not shown)
Puddle Velds Bean
Plan View
Figure 3.2 Base Deck Arrangement (Nodules Not Shown)
19
hr
Beai
1 , > —. ^
1 . 1
B e a i — j
I
i-j-
r Top Deck (supported by base decks and nodules not shown)
\ ' •
\ 1.
\
• ' \
_ —
- —
^ ^
, 1
; •
1*
1 <
i f
^ — P u d d l e Velds flean 1
•TH
Bea • ^
_ _ j 1
PI an V i ew
Figure 3.3 Top Deck Arrangement (Nodules And Shoring Not Shown)
20
equipped with uniformly spaced protrusions on the
circumference of the rollers. The spacing of the
protrusion will be the same as the spacing of the nodules
on the deck. The protrusions on individual rollers will
be the same size and shape. However, the protrusions will
increase in size from the first roller to subsequent ones
until the size of the intended nodule is achieved.
A manufacturer would have to tool up to produce the
modular deck, but the general manufacture of the deck is
very similar to current practice. Informal discussions
with deck manufacturers did not reveal any major concern
about manufacturing the proposed modular deck.
D imens ions Used i n Feas ibi I ity Studi es
The feasibility study considered an isolated 20 ft
by 20 ft slab, simply supported on all four edges. This
particular size represents a typical span for floor
systems. The square slab lends itself to two-way action
NoduIe Size
For the purpose of this study, the shape of an
individual nodule is taken as a frustrum. There is no
special reason for choosing this shape. A cross-section
through the nodules is similar to conventional composite
metal deck. If actual tests are performed in the future,
the shape of the nodules can be optimized. The best
21
shape for the nodule may depend on the manufacturing
process. The following dimensions were adopted for the
nodules. (See Figure 3.4).
1) Nodule base = 2.5 in.
2) Nodule height = 1.55 in.
3) Nodule top = 1.8 fn.
Deck Size
Dimensions of the modular deck sheet assumed for
this study are shown in Figure 3.4. The sheets are 26
in. wide by 20 ft long. The nodules are spaced 3.5 in.
apart in both directions. Each sheet has four rows of
nodules in the longitudinal direction. Sections A-A and
C-C shown in Figure 3.4, define the 'strong' and 'weak'
cross section of the sheets, respectively. Distance to
the centroid of the strong cross section from the base of
the nodule is 0.63 in. The deck is assumed to be 18, 20,
or 22 gage for purposes of calculating tensile capacity.
The yield strength of the material is assumed to be
36 ks i.
Feas ibi1ity of Construction
The proposed two-way composite slab will not be
feasible unless it can be constructed with reasonable ease
by methods familiar to the construction trade.
0 *
22
I
Li
SI
m - ^ H 11 EJ E
0 0 I
0 0 EH E
11 0 0 B
Bi 1 sa E
0 1 0 El B
E 0 0 0 0
5 Q)
C (0 4 5 1
lO
o —
4-O
0) u a 01 (Q Q r in
T3 c <
c o (n c E
u tD D T) 0
r T3 0) in O
a 0 L
Q.
cn
(U u D
h t o
23
The construction process consists of first placing
the base deck sheets and anchoring their ends to the
support beams with puddle welds. Because of the weak
cross section (section C-C in Figure 3.4), the modular
deck is not capable of supporting its own weight.
The shores that will be needed later to help to support
the weight of the wet concrete can be used to assist in
supporting the base deck. One end of a sheet is welded
in place while the sheet is supported by the shores.
The other end is then welded. A slight pretension may be
required before welding the sheet in place.
Once the base deck sheets are in place, the top
deck sheets can be laid in place. The nodules of the top
deck interlock with the nodules of the base deck. The two
ends of the top deck are welded in place to complete the
installation. The working platform is then safe for work
men, equipment, and the wet concrete. Placement of shores
is shown in Figure 3.5. The base deck is supported in the
number of locations dictated by design requirements. The
modular deck has virtually no rigidity and is not capable
of supporting its own weight. Therefore, the puddle welds
are essential if the deck is to carry the required loads.
The deck must achieve its load carrying capacity from
membrane action. The intermediate shores are required to
limit deflection of the modular deck and to reduce the
tensile forces in the deck under vertical loads.
24
^ V e l d e d
Seal Support
e£r^-^ Steel Deck As Cable Velded;7-
^ , ^ j ' > « ' — _ ^ ^ ^ ^ ^ g *
4 A Vood Shore Supports
Slab Span
Seal Support
Base Deck
Vood Shore Support
/ / y / y y / / / ^ y r /' y y y ^ y y y / ,> r / ^ y r y y r /• ^ y y ^ / ' ^ ^
Section A-A
F i g u r e 3 . 5 S h o r e Used As S u p p o r t
25
Analysi s
In order to determine the number of shores and the
required weld capacity, the base deck is assumed to
behave as a parabolic cable. Analyses are performed to
determine the deck capacity for up to four shores and
three different gage thicknesses. Loads used in the
analysis are those anticipated during the construction
stage. Estimated loads include the dead load due to the
weight of the concrete (150 pcf) and the steel deck
(5 psf). The AISI design criteria requires a construction
live load of 20 psf (Sabnis, 1979).
For purposes of comparison, slab thicknesses
of 3, 4, 5, 6, 7 in. were considered. Analysis was
carried out on a single base deck sheet spanning 20 ft
between two steel beams. In order to calculate the in-
plane tensile forces in the deck due to dead plus live
construction loads, the maximum deflection between any
two shores was set to 0.35 in. The limitation is
arbitrary based on judgment. It represents a 1 imitation
on the variation of the slab thickness. For a 5 ft shore
spacing the deflecting span ratio is approximately L/180,
where L is 5 ft.
The equation for tensile force in a parabolic cable
under uniform load (Sandor, 1983) is given as follows:
T = (V^ + H^)'/2 (3.1) max
26
where V and H are the vertical and horizontal cable force
components at the supports, respectively.
V = W/2 . (3 2)
H = Wl/8f . (3.3)
Where
W = total dead load plus live load between the two supports (lbs)
1 = clear span between supports (in.)
f = midspan deflection (in.).
A proper design must find the right combination of
material thickness (gage), shore spacing and puddle welds
capacity to satisfy Equation (3.1) within an acceptable
deflection limitation. Puddle welds are typically 5/8,
11/16 or 3/4 inches in diameter. Assuming E70 XXX
electrode and the shielded metal arc welding process, the
weld capacity R in kips/weld is
R = A X 0.30 Fu (3.4) w w
where 2
A is area of weld (in. ) w
Fu is tensile strength of the E70 XXX electrode, which is 70 ksi.
Table 3.1 gives the capacities of three weld sizes.
A minimum edge distance must be specified for the puddle
weld locations in order to prevent the deck material
from tearing around the weld. The tensile capacity of the
metal deck tabulated in Table 3.2 is given by
T = (0.6Fy) X Ag (3.5) max
27
Tab 1e 3.1
Capacity of Puddle Welds
Weld Diameter
(in.)
5/8
1 1/16
3/4
Weld Area
(in.^)
0.31
0.37
0.44
'weld
(k
Capacity
ips)
6.5
7.8
9.2
Note : (1) Calculated using Equation (3-4) with shielded metal arc weld and E70 XXX Electrode (Fu = 70 ksi).
Tab Ie 3.2
Tensile Capacity of Metal Deck Sheet
Deck gage
18
20
Deck Thi ckness
(in.)
0.0516
0.0396
Tensile Capacity Number of per sheet 5/8 in. Dia. (kips) Puddle Welds
29
22
22 0.0336 19
Note : (1) Calculated using Equation (3-5) with material yield strength Fy = 36 ksi and Ag = 26 in. x deck thickness (ins. ).
28
where
Fy is yield strength of the material (ksi)
Ag is the cross sectional area of deck (in.^).
The tensile capacity of base deck sheets of 18, 20, and 22
gage is tabulated in Table 3.2.
Results
From Table 3.2, it is clear that the puddle welds
are capable of resisting the tensile load capacity
developed in the deck. A series of calculations were
performed to study the effects of deck gage and the number
of shores in the assumed 20 ft clear slab span. Slab
thicknesses of 3, 4, 5, 6, and 7 in. were considered in
the calculations. The number of shores ranges from one to
four. The midspan deflection was limited to 0.35 in. The
construction loads (dead plus live) were not factored for
deflection calculations. The results of the calculations
are presented for each slab thickness in Figure 3.6 to
Figure 3.10. Each curve represents a different number of
shores. The limiting midspan deflection is indicated by a
vertical dotted line drawn on each graph.
The three horizontal Iines on each graph represent
the allowable tensile capacity of the deck material for
18, 20, and 22 gage thick respectively. The horizontal
lines are projected to meet with the vertical dotted line,
which is the limiting deflection. The minimum number of
eo
29
<Q
O
«>
«1
fio -
40
s30
20 -
10
\ \.
18 gage
20 gage
22 gage
\
k N \ VT
N
•*<.
-^..
\.
.IW.
^ I shores
^ i ^ shores
I -^ 3 shores
4 shores
3 in. Slab
— r -0.1 0.2
HIdspan Deflection (In.)
O.J 0.4
F i g u r e 3.6 T e n s i l e F o r c e in B a s e D e c k V e r s u s M i d s p a n D e f l e c t i o n , for 3 in. S l a b
30
o o u. u
7Q
eo -
ao -
40 -
30 -
20
10 -
T—\ I
\
I
\ s.
\ \
18 gage
20 gage
22 gage
\ \ \ \.
\ '•••
\
\
1
\
s
\ • <
\
\
V
4 In . Slab
s. • X .
%.. N»,
•^T y 1 shores I
s. Jii J -4 2 shores
'A.. i : : : ^ _
: ^ : = ^ •-^ 3 shores
~ - | 4 shores
I
—r-Q.t
— I — O.J . 0 0.2
Hidspan Deflection (In.)
0.4
Figure 3.7 Tensile Force in Base Deck Versus Midspan Deflection, for 4 in. Slab
31
7Q
eo -
so -
AO -
u 1 -o
c
30 -
20 -
iO -
18 gage
20 gage
22 gage
5 i n . Slab
\ \
\
V
V. \ .
^
\ . \
• • • ^
V .
X. I ' ^ 2 shores
-A
^2lr^_
I ^ 1
_ -3 ' 3 shores
"I 4 shores
I
— I — 0-3 O.i 0.2
HIdspan Deflection (in.)
0.4
F i g u r e 3.8 T e n s i l e F o r c e in Base Deck Versus Midspan D e f l e c t i o n , for 5 in. Slab
32
w u o
7 0
00 -
•:: so
4 0 -
30
20 -
10 -
18 gage
20 gage
22 gage
\
\
6 in . Slab
\ \
\
\ \ .
•^_
V N.
\ .
+ 2 shores
\ - ^ < -\
^ ^ ^ .
— P -
0.1 0.2
Hidspan Deflection (In.)
= ^ ^ • - 3 shores
— I 4 shores
I
0.3 0.4
Figure 3.9 Tensile Force in Base Deck Versus Midspan Deflection, for 6 in. Slab
33
u
U
o
01
eo -
ao -
40 -
30 -
20 -
10 -
o -
18 gage
20 gage
22 gage
/
7 in. Slab
J
1
•i 1
K \
... ,
" "I
1
\
\
,
\ A.
N
1
\
\ V
\ V \
X .
\
X
" ^ " ^ A — -
I " I I • ••
1 1 1 1 1 1
1 1
S 2 shores
1 1
1 1
•^4 3 shores
1 '-{ 4 shores
1
1
-4 0.1 0.2
Hidspan Deflection (in.)
0.3 0.4
Figure 3.10 Tensile Force in Base Deck Versus Midspan Deflection, for 7 in. Slab
34
shores needed to support the decks during construction of
the slab is indicated on the graph. The last curve to be
cut by each horizontal line before reaching the vertical
line is the minimum number of shores needed.
From the graphs in Figure 3.6, a 3 in. thick
concrete slab on a 20 gage modular deck needs a minimum
of 3 shores equally spaced in the 20 ft span of the
composite slab. The maximum deflection between any two
shores due to the construction loads is approximately
0.20 in.
Conclus ion
Analyses presented in this section show that
construction of the proposed two-way action composite
slab, using modular deck, is possible with the required
number of shores. The number of shores needed depends
on the concrete thickness and the gage of the modular
deck used.
CHAPTER 4
PERFORMANCE OF TWO-WAY COMPOSITE SLAB
The studies conducted on the performance of the
proposed two-way composite slab include deflections,
moment capacity, and shear capacity.
Since no experimental tests were performed, the
analytical studies were based only on thin plate theory
and the concepts of basic mechanics.
Loadings On Slab
Both uniform and concentrated loads were considered
in the performance studies. Uniform loads were considered
to act over the entire surface of the slab. In the
concentrated loading case, four concentrated loads were
placed as shown in Figure 4.1 and tabulated in Table 4.1.
A single load at the center of the slab gives the worst
case of deflection and moment, but the four concentrated
loads are more practical representations of actual loads
than a single concentrated load.
As in usual practice, unfactored loads are used
in the deflection calculations and factored loads are
used in the calculation of moments and shears. A load
factor of 1.55 was used throughout, which is the average
of 1.7 (live load) and 1.4 (dead load). Using a load
35
36
o
1/1
Q . • cn
SInply Supported
Concentrated Loads
1
B "" To
i 1 J 1 1 1
Siaply Supported
i, 4'
20'
Sii
ply
Sup
port
ed
I (
T\
CSI
1
j 1
Figure 4 .1 Locations o f Concentrated Loads on Two-Way Composite Slab
Tab 1e 4.1
Locations of Concentrated Load
Point Loads (Kips)
B
C
D
(Ft)
8
8
12
12
(Ft)
8
12
8
12
37
factor of 1.55 is equivalent to assuming that the ratio
of dead load to live load is 1.0. Maximum deflections,
moments, and shears in the slab were calculated for the
two loading cases.
Plate Theory
At first glance, the two-way composite slab appears
to have orthotropic properties. However, because the
material properties are identical in all directions, the
proposed slab can be analyzed by considering it as a thin
plate with small deflections.
The differential equation for behavior of thin
plates is
4 4 4 9 w 5 w g w
D { 2~ •*• 2 2 2 " T ^ " P(x»y)- (4.1) 9x ax" ay av
Where
D = flexural rigidity of the plate
P(x,y) = applied loads
w = deflection of the plate
x,y = coordinates on the plate.
Equation (4.1) is used to obtain expressions for deflec
tions resulting from application of loads. Once the
expressions for deflections are obtained, they are then
used to obtain expressions for moments and shears. Before
considering the expressions for deflection, moment, and
38
shear, discussion of the flexural rigidity of the
composite slab is required.
F1exura1 Ri qidity of Compos ite Slab
In order to facilitate analysis of the proposed two-
way composite slab, the steel deck is transformed to rebar
in an equivalent flat slab as shown in Figure 4.2. The
thicknesses of the two slabs are the same. The area of
steel in the composite slab is equal to the area of steel
in the flat slab. The steel in the flat slab is located
at the centroid of the steel deck cross section.
With these simplifications, expressions for flexural
rigidities of a two-way reinforced concrete slab can be
obtained. The expressions for the flexural rigidities of
a two-way reinforced concrete slab (Timoshenko and
Woinowsky-Krieger, 1959) are
^x = V^^-^c>' ^^cx^ ^^s/^c - ^^Ux> (4.2)
\ = ^c^^'^\^^ ^^cy ^ ^^s/^c - ^>Uy> ^^'^^
H = (D D ) ^ / ^ . (4.4) X y
Where
D ,D = flexural rigidity in the x-direction and ^ ^ y-direction
1 , 1 = moment of inertia of concrete in the x-^^ ^^ and y-directions respectively
1 , 1 = moment of inertia of steel in the x- and ^^ ^^ y-directions respectively
3 9
Slab Thickness
Slab Thickness
Deck Centroid
Assuaed Transformation
Deck Centroid
Equivalent Reinforceient
F i g u r e 4.2 T r a n s f o r m a t i o n o f Two-Way C o m p o s i t e S l a b t o E q u i v a l e n t F l a t S l a b
40
E^ = modulus of elasticity of concrete
E^ = modulus of elasticity of steel
"0^ = Poiss ion's ratio of concrete.
However, since the composite slab and the
equivalent flat slab are symmetrical about the x and y
axes, I = I , = I and I = 1 = I . Hence, D = D ex cy c sx sy s x y
= D, indicating that the flexural rigidity of the equi
valent flat slab D is the same in the x and y directions.
Thus, Equations (4.2) and (4.3) can both be expressed as
D = E ^ / d - ' O ^ ) ^ {I^ + ^^s/^c " ^^'s^ ^"^-^^
where the term (I + (E /E -1)1 }, which is a moment of c s c s^
inertia term, can be replaced by any one of the following:
1) uncracked moment of inertia (I )
2) effective moment of inertia (I )
3) cracked moment of inertia (I^p)«
With the above substitutions, the flexural rigidity D of
the composite slab becomes 1) uncracked flexural rigidity
D = EI /(I- 1)^^) (4.6) g g c
2) effective flexural rigidity
D = EI /U-'O ^^) (4.7) e e c
3) cracked flexural rigidity
D = EI /( I- "0 ) cr cr^ c ^ ) . (4.8)
Expressions for cracked and uncracked moments of inertia
used above are
I = (b(x)^}/3 4 n(As) X (d - x ) ^ (4.9) cr
41
Where
b = unit width of the slab (in.)
X = distance from the neutral axis to the extreme compressive fiber of concrete (in.)
d = effective depth of concrete (in.)
n = modular ratio of concrete and steel
As = area of steel deck (in.^)
h = thickness of concrete slab (in.).
The expression for effective moment of inertia (I ) e
where
M^P = cracked moment (ft-kips)
f^ = modulus of rupture of concrete (ksi)
y. = distance from neutral axis to the extreme tension fiber of concrete in tension (in.)
M = maximum moment in slab produced by unfactored ^ loads (ft-kips)
was developed by Branson, 1963, and adopted by AC I.
The effective moment of inertia, I , is a smooth e
transition between the cracked and uncracked moment of
inertia. Hence, the effective moment of inertia lies
between the lower and upper bound values represented by
cracked and uncracked moments of inertia, respectively.
The relationship holds true for flexural rigidities.
Uncracked and cracked flexural rigidities are tabulated in
42
Table 4.2, for a range of slab thicknesses and deck gages.
Because the effective flexural rigidity is a function of
the loading it cannot be easily tabulated, but its value
always lies between values of cracked and uncracked
flexural rigidities.
A decision was made not to use flexural rigidity,
based on uncracked section for deflection calculations.
Because the loading magnitude to cause maximum permissible
deflection is being determined, the concrete likely will
crack under these circumstances. Thus, only the effective
flexural rigidity (D^) and the cracked flexural rigidity
(D^^) from Equations (4.7) and (4.8), respectively, are
used for deflection calculations.
Def1ect ions, Moments, And Shears
In solving Equation (4.1) for the deflection of
simply supported plates subjected to uniform and concen
trated loads, Navier's solution is used. Solutions for
moment and shear are then obtained from the known
deflections. The solutions can be found in Timoshenko and
Woinowsky, 1959, and also in Ugural, 1967. The general
expressions for deflection, moment, and shear are
1) Uniform loading case
16P oo oc Sin(m7:x/a) Sin(n7Cy/b)
7C D m n mn [ (m/a)"^ + (n/h)^ ]^
43
Table 4.2
Uncracked And Cracked Flexural Rigidities
Steel Deck
Thickness
18 gage
20 gage
22 gage
Concrete Slab
Thi ckness h
(in.)
3 4 5 6 7
3 4 5 6 7
3 4 5 6 7
Effecti ve Depth
d
(in.)
2.37 3.37 4.37 5.37 6.37
2.37 3.37 4.37 5.37 6.37
2.37 3.37 4.37 5.37 6.37
2 Cracked F1exura1 R i g i d i ty
D cr
(ft-kip)
387 896 1647 2651 3916
329 753 1371 2191 3219
297 672 1218 1938 2839
^Unc Fl Ri
racked exura1 gidity
''g
(ft-kip)
630 1493 2917 4834 7676
630 1493 2917 4834 7676
630 1493 2917 4834 7676
Notes :
(1) d = h - 0.63 in. (Distance to deck centroid).
(2) Calculated using Equation (4.8).
(3) Calculated using Equation (4.6)'
44
16P « « ( m / a ) ^ + D ( n / b ) ^ V —7-EE
7C m n mn [ ( m / a ) ^ + ( n / b ) ^ ] ^
X S i n ( m 7 U x / a ) S i n ( n 7 c y / b ) . ( 4 . 1 3 )
1 6 P Q « « D ( m / a ) ^ + ( n / b ) ^
^ 7C m u mn [ ( m / a ) ^ + ( n / b ) ^ ] ^
X S i n ( m 7 c x / a ) S i n ( n 7 c y / b ) . ( 4 . 1 4 )
16P^ ^ ^ ' ^ C o s ( m 7 : x / a ) S i n ( n 7 u y / b ) x~ 3~ Z-/Z-/ 2 2 2
K ra n [ ( m / a ) ^ + ( n / b ) ^ ] ^
X [ { ( m ^ ) / ( a ^ n ) } + ( 2 - - 0 ) ( n / a b ^ ] . ( 4 . 1 5 )
16P oo oo S i n ( m 7 : x / a ) C o s ( n 7 c y / b ) V = —?-EE
^ n^ m n [ ( m / a ) ^ + ( n / b ) ^ ] ^
X C { ( n ^ ) / ( b ^ m ) ) + ( 2 - 1 ) ) ( m / b a ^ ] . ( 4 . 1 6 )
2) C o n c e n t r a t e d l o a d i n g case
4P oo 00 S i n ( m 7 : ^ / a ) S i n ( n TU T i / b ) }
w= EE TC^abD "* « { ( m / a ) ^ + ( n / b ) ^ } ^
X S i n ( m 7 c x / a ) S i n ( n 7 t y / b ) . ( 4 . 1 7 )
4P oo oo { S i n ( m 7 C ^ / a ) S i n ( n 7 t T l / b ) }
7C^- m n { ( m / a ) ^ + ( n / b ) ^ ) } M. = — ^ E E — — 2 . . . . 2 . , 2 5 i n ( m T t x / a )
X S i n ( n 7 C y / b ) { ( m ^ / a ^ b ) i- i j ( n ^ / a b ^ ) } . ( 4 . 1 8 )
4P oo oc { S i n ( m 7 r ^ / a ) S i n ( n 7 iT | /b) ) M = p - E E 2 2 ~ 2 S i n ( m 7 l x / a )
y Tt^ m n { ( m / a ) ^ + ( n / b ) " ^ ) } ^
X S i n ( n 7 : y / b ) ( ( n ^ / b ^ a ) + "U ( m ^ / b a ^ ) } . ( 4 . 1 9 )
45
4P °g °2, {Sin(m7t^/a) Si n(n T:?]/a )} X ~ jr ^ ^ ' " ~" 7-3 'Cos{m7Ux/a)
" - {(m/a)^ + (n/b)"^)^
X Sin(n7ty/b) { (m^/a'^b) + (2-1)) (mn^/a^ta^ )) . (4.20)
4P ii,^ (Sin(m7c5/a) Sin(n7r T]/a )) ^y ~ Z 2-^2^ — Sin(m7:x/a)
^ " « {(m/a)^ + (n/b)"^}^
X Cos(n7cy/b) ((n^/b'^a) + (2- 0) (nm^/b^a^)}. (4.21)
Where
w = vertical deflection at any point of the slab
M ,M = moments in the x-direction and y-direction.
V ,V = Kirchoff shear in the x-direction X y . ..
and y-direction
P = uniform loads o
P = single concentrated point load
a,b = length and width of the slab
m,n = odd indexes for summations
= 1, 3, 5, (for Equations (4.11) to (4.21))
D = flexural rigidity of the slab (depends on the moment of inertia assumed, i.e., effective or uncracked)
x,y = coordinates which define the location of the deflection, moment or shear
% ' ^ = X and y coordinates for the location of the concentrated loads
Table 4.3 shows simplified expressions for maximum
deflection, moment, and shear for the two loading
conditions on a square slab (a=b) with Poisson's ratio of
Table 4.3
Expressions for Maximum Deflection, Moment, and Shear
Un i form Load i ng Concentrated Loading
46
Maximum Deflection :
w = 0.00406-- (4.22) D i
Maximum Deflection :
2
w = 0.03898-D,
(4.23)
Maximum Moment : Maximum Moment :
M or M X y
= 0.04203P a' o (4.24)
M or M X y
= 0.5904P- (4.25)
Maximum Kirchoff's Shear Maximum Kirchoff's Shear
V or V X y
= 0.4361P a o (4.26)
V or V , X y
T = 2.683 1—-- (4.27) a
P = uniform loads.(kips) o
p = total concentrated loads on slab (P j = 4P) (kips)
a = dimension of square slab (ft)
D. = flexural rigidity of slab (i = e, for effective ^ flexural rigidity or i = cr for cracked flexural
rigidity) (ft-kip)
p = single concentrated load on slab (kips)
Note : The above expressions are for a square slab and Poisson's ratio of 0.15.
47
0.15. Location of the maximum deflection is at the
center of the slab for both loading cases. The maximum
moment for the uniformly loaded slab also occurs at the
center of the slab, but for the slab with concentrated
loads, the maximum moment occurs under the loads.
However, the maximum moment expression is singular
at the exact location of the concentrated load. To
overcome this problem, the moments are calculated close to
the point load rather than exactly at the location. After
some experimentation it was found that moments evaluated
within 0.2 ft of the point load give reasonable results.
The location of maximum Kirchoff shear is at the center of
the slab edge for both loading cases.
Computer programs were written by the author to
solve for the maximum deflections, moments, and shears for
different uniform and concentrated load cases.
The following values are used in the evaluation of
composite slab performance. The modular ratio is 9.
Compressive strength of concrete f'^ is 3000 psi and
Poisson's ratio is 0.15. The modulus of elasticity for
concrete E is 3.15 x 10^ and the tensile yield strength c
of equivalent reinforcement f is 36,000 psi.
Def1ect ion
Equation (4.22) and (4.23) from Table 4.3 are used
to calculate the maximum deflections for various deck gages
48
and slab thicknesses. Calculations were made using the
cracked flexural rigidity and effective flexural rigidity.
Tables 4.4, 4.5. and 4.6 give deflections for
uniformly loaded two-way composite slabs constructed with
18, 20. and 22 gage deck, respectively. The upper set of
deflections for slab thicknesses that range from 3 to 7 in.
are determined using a cracked flexural rigidity (Equation
4.22). The lower set is based on effective flexural
rigidity. The loads for deflection calculations are not
factored.
Table 4.7. 4.8. and 4.9 give deflections of the two-
way composite slabs produced by four concentrated loads;
the slabs have 18, 20, and 22 gage deck, respectively.
Deflections are tabulated for cracked flexural rigidity
and effective flexural rigidity. The limiting deflection
is L/180. The loads are not factored.
As expected deflections calculated on the basis of
cracked flexural rigidity are larger than those based on
effective effective flexural rigidity. Experimental tests
are required to determine which approach gives the more
realistic values. Based on experience with conventional
reinforced concrete slabs, use of the effective flexural
rigidity is justified.
Comparison of the results also reveals that
composite slabs with heavier gage deck are able to support
larger loads.
>» «u 15 I 0 i
c "->^
K- j«:
TD u Q) (U Q T) (D 0 -J
>v ^-E L.
lU 0) (D (3
CO -<
0 r «^ -p • » •#— C 3 D
(A * - JD 0 (D
— W (/)
c 0 ••--p u (U — *4-Q)
0) •P •— (/) 0 a E 0
Q U
n
cvi so
u-»
V O
fVJ
o
CVI
4-> «« L .
o c o
in <n
c . K
u .»« . c
_ . c=
. w »
.«.^
CO •*-'
X — ta <u O) a>
CVI
i n
s o
o o CSJ CVI as
oo
s o CVI
o o CVI s o CVI CO u ^
^ CVI CO o o CVI
u^ s o i~»
— > . •a to *-» a> L- — CJ X — IO a> en »_ — —
<_> i . - o c
CVI
s o u- l CVi o o
CVI VO
o o CVI CO u- l
CVI ^ » CVI CVI r . . •<»
^ so m
CV4
•
1.04
as so
0.95
0.
76
0.57
oo en
0.59
0.
47
0.35
C V i
0.40
0.
32
0.24
so
1.25
0.
96
m wo
0.87
0.
65
0.40
r»"» CVI
0.45
0.
29
0.20
rr»
0.21
0.
17
0.13
OS C 3
r~ C3 SO C V i
—
oo
<=> e»
wo
=> wo rrt
«=» r—
CVI
C 3
as
«=»
s
— c»
CVI
«= S O
— «= C O
a
^r
^ — r— wo
^ so CVI
m
«=> CVI CVI
«=» ~
— =>
zz «»
C 3
•^ = r—
«=»
^ «=» •"*
^ CVI
m ' v wo so r »
a> » — >>
— IO ^-» 4 j i _ — a« >< '—
WW- O l CD
4 9
=1 er
wn
c o .^ «n c= O l
^ .. ca J 3 IT>
^ B «
w/>
u a i —.• ^ 4 .
a» ca a> c •*— 4 -> • * *
• • ^ H
•^
> c (D 3 1 0 J
•— V i i ^
H ^
"D U (U
Q) Q T3 fl] 0 -J
X r - >
0) 0) (D C3
O Ec\j L oi: ^ 4J
• t — •»-C 3 D
(0 "^-iD 0 CD
U) I/)
c 0 •.-4-» U (U ^-«*-Q)
0) +J — (0 0 a E 0
Q U
in
5 (D
CVI
a.
- O CO <TJ CVI O
O CVI
so
i n « i «n
4-> OJ —^ (U c • w- .»£ e O CJ — c — — o .c
m
X •— "o
Lk. oc =3
oo CVI
rvi
oo CVI
CO wo oo CVI o o u-l
m CVI ^ » . ^ w o
• » wo *o r—
"O ID •4-» Ol C- — CJ X •— CD ai o>
(_> Lk. QC
CVI CVI
oo
as
CVI o > C 3 u- l
1.24
.8
3
•
0.90
0.
68
.45
0.57
0.
43
G O
•
•
0.39
0.
29
•
1.09
u-l •
•
0.72
0.
42
m CVI •
0.5
0.29
0.
20
.13
CVI
0.17
0.
12
C O
t-» ^ so C V I
—
I O as ea
r—
V O
=
•^r
•=
C V i
rrs
C 3
m CSJ
«=»
—
C V I
^
z «=»
^
— «=»
s ^
wo
CVI
—
as u-> C 3
S O CVI
r r i
^
CS4 CVI
•=».
—
— ^
—
«=•
so C3
— «=»
so
«=»
C 3
O
C 3
C 3
«=
CVI
wo VO r ~
> — >. . — CO 4.J 4_i l _ —
o 3 -a Oi X —
W W . — — LU U . Of
50
cr 1/1
c o m c a> e cs J 3 (O
o OJ
^^ ww-Oi
ex O l
c • — 4-»
• — ^ e CO
> c (D 3 1 0 5
'— \.y
K .^
13 U 0
0) O TJ (0 0
- J
> N ^-
0) 0) (D a CVJ
E cvj (-
0 r *i- -P w - w—
C 15 D
(0 ti- £1 0 CD
(A I/)
c 0 •— -p u Q)
r—
^ Qi
0) 4-> •^
(n 0 a E 0
Q U
VO
•^
Q)
i3 fO H
51
s o
i n
a. T 3 IO o
s o
CVI
CO CSJ
CVI
CVi
. ~ VO
CV4
0.93
•—•
CO CVI
.
1.02
0.
77
0.51
oo m
1.29
1.
13
0.97
0.
60
0.64
0.
48
0.32
c ^
1.26
1.
11
0.98
0.
88
0.77
0.
66
0.55
0.
44
0.33
0.
22
s o
1.19
0.
58
CO r n CVI m
1.29
l.
iO
0.78
0.
43
0.23
r~-
as CVI •
1.13
0.
93
0.73
0.
51
0.30
0.
20
0.13
C 3
1.11
o^
0.77
0.
63
0.48
0.
34
0.21
0.
17
0.12
0.
08
VO
w o s o s o s o ^ ' ^ CVI —
CVI
« l •*•» OJ w. o c o (_>
i n O l c:
.aiC CJ
.— .ez t—
•-..* . c
•^ • .
X — - o a> o> o)
^— .— <n u- oe ^
CSJ m *rt CVJ
m oo wo
ui so r»
— >» •^ to •*•* Oi w- —
. ^ 3 - a <J X •—
as CVI w o CVI
so • r
so CVI
s o 0-» CVJ
•^r u"» v ^ r-"-
OI > > v
. — ro 4-> 4-> W- • — o 3 - a OJ X —
wi_ Ol OS
01 c eo
CO
c o i n c Ol
• . -<—> . a (T>
CJ Ol
.—. «*-at a
en c
• " - « - • • *-s
tn n CD .— {fi
0) 0 4J U. '0—
V) > 0 n a E T3 0
u (U u D
>sT} «D 5 1 0
0 L Q.
f^
• c •.-v . ^
v\ 5 .i^ T3 H- U
0) M- Q 0
in c
ID 0 -J
(U T3 0) CD
0 (J ••—
0) •p CD L
•P 00 4J U 0) .—
»—«
r ^ -P (U •.-
C (U u c 0
Q 3 U
P*-
"^
0)
z (D
1 -
so CSJ
CSi CSi
a.
II
so
o
"S d IQ
c: « i CJ c o
c_>
OO
so
CSJ
Ol .J.J Oi 1—
o c o
C J
I D i -3 X Oi
"•»
i n i n OJ C
.a< CJ
• .— J =
^-
> s 4 . J
.^ T D • M >
o> • ^ —
«•*« « e
•.« .
" O Oi an
W O
—
o r i
^
OO
C 3
r n
1.25
0.84
m so
«= CVI
=»
CVI
-
Crac
ked
1.31
1.08
0.91
0.68
0.45
rrt
ca
r n CVI
=»
ZZ
*£S
Flex
ural
1.27
1.13
0.99
0.85
0.67
0.56
0.42
0.28
CVI
«=
z «=»
C O
s o
Rigi
dity
0.96
1.05
1.
15
1.24
0.86
0.76
0.67
0.57
0.48
0.38
0.29
0.19
^»
=»
2 ca
r».
CVI
—
ea a>
^
CVI
ca
m
1.20
0.79
m
«= as CVI
^
._
".»
Effe
ctiv
e 1.35
•
0.88
0.63
0.36
oo
«=
m
«=»
^
u ^
Flex
ural
1.26
1.11
0.97
0.62
0.67
0.51
0.33
0.15
S ^
r—
•=»
^
so
Rigi
dity
0.94
1.03
1.
13
1.23
0.83
0.73
0.63
0.52
0.41
0.29
0.16
0.
10
so
«=»
U 1 ca ^
-
r—
52
3 o-CO
c o in c Ol
en
CJ Ol
Ol
ex O l
in n CD
S u to 0 •p u.
W > i
0 13
a E T3 0 Q) U U
3 M J CD 0
L CL
3 I 0
I - u (U
U- Q
in ID CD 0 - J
in c 0
CU "D 0) Q) CD
•P O U CVJ CD
- r QJ . -Q 15
00
0)
4J CD 1 -4J C 0) u c 0 u
CD
r s i CSJ
^ so
CVI
IO O
at
m
a> o
CVI
Ol i n 4- t a t « -« Oi c • W- .ac C CJ CJ — c — >— o .c
C J »—
ID 4-» I . — 3 T3 X — " o Qt at Qi
_ •— «n
CVI
s o
t o
m ON
as —
CVI C 3
^ wo oo m oo IO
. . .
OS CO s o
•^r CVI —» wo CSJ oo wo r n
OS wo •«» m OS wo m CVI
•^» — v ^ r>~ •.»• CSJ
wo CVI
rrt CO
VO w o
OS VO
m o» r—
as — u-l m
53
CSi CSJ
r~» w o ^ OS s o u - l CVI ^ ^ ^
••• wo v^ r~~
• ^ ID .*J a i I - •—
. ^ 3 - 0 CJ X —
(O OJ at
CJ o - oc
CVJ as c a CSJ
rrt r— as CSJ — ^
• ^ wo so r—
> — >» . — CD •«-*
I D
CO -~«
I I
3 0 0
X O l C7I
<= 0
•n c O l
^ ..— < — ' XJ <o
CJ a> ..— u-« i C 3
0 1 c • w
- * - » ••— e
U l
54
in n CD
0) L 3
(D 0
In >s
a^ ET3 0 (U u o
3
CD 0 (-
Q. J^ O Q)
O
2 I 0
I -
o in c 0
in U CD 0
_ J
QJ 1 3
ID CD
•P CVJ U t\J 0)
- JZ M--P lU . -Q 3
*
Q)
(D L
•P C (U u c 0 o
CD I -
wo CVi CSJ
s o
a. II
CVi
t 3 to O
O l
CO
O i CJ
o
CSJ
wo
s o CVJ CV«i O S
s o OS
s o s o
CVJ r— w o
s o r s i o o ^ CVJ as w o '«v
— ' —> O S s o — s o m CV.J
m s o o« ^ o o ' ^ <VJ CSJ
s o s o CVI U-)
•^ as rrt
OS
CSJ o o
OS r~~ C 3 s o
o o w o
s o ""• m ^^ s^ rn
m .^ as r^ CSJ o o m —
CVi s o
^ » OS — r ~
. » w o o o w o
s o CVI
m Oi
( J CJ c — o .c CJ >—
ID
X — - o OJ o > a>
— — «n
i r t v « r »
— >. • O ID 4>> ai c —
.atf 3 T 3 CJ X — CO a t O l w_ . — —
C J w ^ o c
•^ u> so f~-
>• — > s — CD 4-« 4 J I - — O 3 " O OJ X —
wi - a t a >
Ol c I D 3 er
CO
4-1 w»_ ca CVI
. . a o «n c: a> a
(=» X3 ID
• • I I I
CO
I I
^a oo —^ "*.*» _ j
• • c o . " 4-> CJ at — wt-OJ
o O l c •^ 4 ^
••— a • « _ i
55
Moment Capacity
In calculating the flexural capacity of two-way
composite slabs, the following assumptions are made
1) No slippage occurs between the modular deck and the concrete
2) The predominant mode of failure is flexure
3) Slab behavior can be simulated as a series of individual beams acting together in resisting bending in perpendicular directions
4) The modular deck cross section is transformed to equivalent concrete area
Based on these assumptions, the beam model shown in
Figure 4*3 is used to calculate ultimate moment capacity
of the slab. The steel area is equal to the area of
modular deck within the width of the beam. The effective
depth d is measured from the top of the concrete to the
centroid of the deck area. Ultimate strength concepts of
AC I-318-83 are used in the calculations.
The ultimate moment capacity of the beam model is
M^ = (j)(C or T) (d-a/2) . (4.28)
Where
C = compressive force in the concrete, (kips)
T = tensile force in the steel (kips)
d = effective depth of the beam (in.)
a = depth of the stress block (in.)
(|)= strength reduction factor according to AC!-9.3. (ACI-318-83).
u 0
CD
56
(0 in 0) L -P
OJ CJ
E CD L Oil CD
in in 0) u -p tn
c 0
•p o
(/)
"D d) E i-0 in c CD l -
C 0
4J O Q)
CO
in in O L
U
QJ
0
n CD
CD in C ..-c ..— E L Q;
• p Q)
0) +J •.— tn 0 a E 0
Q U
c <*. *-*
D
0
>v 0) 4J in 3
r -
Q)
— o CO a CD
X) U 0 z: E CD Q)
• p
c 0) E 0
CQ 2 :
m
^
Q) U 3 0)
ssau>|3mi qeis
57
Ductile behavior of the slab is assured by limiting the
percentage of reinforcement to a maximum of 0.75 o , but ^ b
requiring at least 200/fy, as specified by the ACI-10.3.3
and ACI-10.5.1, respectively (ACI-318-83). The balanced
reinforcement ratio is given by
0.85B f 87,000 Pb= ; - - - - ( ) .
f^, 87,000 + f
y y
Where
Pl= 0.85 for f'j, < 4000 psi f - 4000
B, = 0.85 - 0.05(— ) for f > 4000 psi 1000 ^
as referenced by ACI-10.2.7.3.
Ultimate moment capacities calculated using Equation
(4.28) are tabulated in Table 4.10. The uniform and
concentrated loads associated with the ultimate moment
capacities are obtained from Equation (4.24) and Equation
(4-25), respectively. A load factor of 1.55 is used as
explained earlier. The ultimate moments produced by
various uniform and concentrated loads are tabulated in
Table 4.11 and Table 4.12, respectively. Table 4.13
summarizes the allowable (service) load capacity of
two-way composite slabs with various deck gages and slab
thicknesses. Note that the loads above the solid line in
the table produce deflection greater than L/180.
58
Tab 1e 4.10
Ultimate Moment Capacity of Beam Model
Steel Deck
Thickness
18 gage
20 gage
22 gage
•
Concrete Slab
Thickness (in.)
3 4 5 6 7
3 4 5 6 7
3 4 5 6 7
Moment Capacity
(ft-kip)/ft
5 a 10 13 16
4 6 8 10 12
3 5 7 9 1 1
Notes :
The above results are calculated using Equation (4.28)#
f = 3000 psi c
f = 36,000 psi y
59
Tab Ie 4.11
Ultimate Moment Produced by Un i form Loads
Unfactored Un i form Loads (psf)
50 100 150 200 250 300 350 400 450 500 550 600
Notes :
Factored Un i form Loads (psf)
77.5 155.0 232.5 310.0 387.5 465.0 542.5 620.0 697.5 775.0 852.5 930.0
^Ultimate Moments
(ft-kip)/ft
1 3 4 5 7 8 9 10 12 13 14 16
(1) Load factor assumed to be 1.55»
(2) Calculated by using Equation (4.24) from Table 4.3.
60
Tab 1e 4.12
Ultimate Moment Produced by Concentrated Loads
Unfactored Concentrated
Loads (kips)
2 4 6 8 10 12 14 16 18 20
Notes :
Factored Concentrated
Loads (kips)
3. 1 6.2 9.3 12.4 15.5 18.6 21.7 24.8 27.9 31 .0
"^Ultimate Moments
(ft-kip)/ft
2 4 5 7 9 1 1 13 15 16 18
(1) Unfactored load is P^, the sum of four concentrated loads,
(2) Load factor assumed to be 1.55.
(3) Calculated using Equation (4.25) from Table 4.3
61
Tab 1e 4.13
Allowable Uniform And Concentrated Loads as Governed by Slab
Moment Capacity
Steel Deck
Thickness
18 gage
20 gage
22 gage
Concrete Thi ckness
(in.)
3 4 5 6 7
3 4 5 6 7
3 4 5 6 7
Moment Capac ity
(ft -kip)/ft
5 8 10 13 16
4 6 8 10 12
3 5 7 9 1 1
^Uniform ( Unfactored
Loads (psf)
200.0 300.0 400.0
^ 500.0 600.0 1
150.0 240.0 300.0 400.0 450.0
100.0 200.0 250.0 350.0 425.0
Concentrated Unfactored
Loads (kips)
6.0 9.2 11.1 14.0 18.0
4.0 7.2 9.2 11.1 13.0
^.n 6.0 8.0 10.0 12.0
Notes
(1) Extracted from Table 4.10-
(2) Interpolated from Table 4.11'
(3) Interpolated from Table 4.12.
(4) Loads above solid lines produce deflection greater than L/180.
62
Shear Capacity
The shear strength of two-way composite slabs and the
shear-bond resistance at the interface between concrete
and deck are discussed in this section.
Shear Strength of Slab
The shear strength of the proposed composite slab is
provided by the shear strength of the concrete alone,
since there is no shear reinforcement in the composite
slab. Hence,
<I>V > V^. (4.29)
Where
V = shear strength of concrete (kips)
V = maximum ultimate shear on slab using Equation (4.26) and (4.27) from Table 4.3, for uniform and concentrated loads, respectively (kips)
({) = strength reduction factor of 0.85 as defined by ACI-9.3. (ACI-318-83).
The shear strength of the concrete V as mentioned above
is calculated by the following expression, which comes
from ACI-11.3.1. (ACI-318-83).
V = 2(f' )^^^bd. (4.30) c c
Where
f = compressive strength of concrete (ksi) c
b = unit width of slab (in.)
d = effective depth of the slab (measured from the top of the concrete to the centroid of the steel deck cross section) (in.).
63
From Equation (4.30), a 3 in. thick composite slab
provides a shear strength of 3.1 kips. Solving for P and o
P- . from Equations (4.26) and (4.27) with V = V = 3 1 X y
kips, the unfactored loads that can be carried by the slab
are P^ = 230 psf and P^ = 14 kips. If the loads are
governed by limiting deflection to L/180, then P = 60 psf o
and P^ = 3 kips (from Table 4.4 and 4.7, respectively). If limiting moment capacity governs, then P = 200 psf and
o P^ = 6 kips (from Table 4.13) for the same slab thickness.
Equation (4.30) also indicates that the shear
strength of the composite slab increases with an increase
in slab thickness. Thus, if similar calculations were
performed on a thicker slab, the same conclusion regarding
shear strength would be drawn.
Shear-Bond Capac ity
Sheai—bond capacity of the slab is important because
without it, composite action between the concrete and
modular deck cannot take place. If slippage occurs at the
interface, the load carrying capacity of the slab is re
duced drastically and as such a shear-bond failure occurs.
The resistance to the horizontal shear stresses at
the interface between the concrete and metal deck is
achieved by the bond strength between concrete and deck
and by the nodules, which act as individual shear
connector.
64
The above can be studied in equation form
^b - sc > ^ • (4.31)
Where
q = shear flow produced by loads (lb/in.)
= VQ/I
V|_ = bond strength of concrete and deck (lb/in.)
Vg^ = shear resistance of the nodules acting as individual connectors (lb/ins.)
V = Kirchoff shear in slab due to loads (kips)
Q = first moment of area above or below concrete -deck interface about the neutral axis (in. )
I = moment Inertia of the transformed composite section (in. ).
The three terms in Equation (4.3 1) are discussed in
the following paragraph.
Shear Flow
In order to calculate the shear flow, a unit width
of the slab as shown in Figure 4.4 is considered. The
steel deck area is transformed to equivalent concrete area
by multiplying by the modular ratio n. The concrete-deck
interface is assumed to be located at the centroid of the
deck cross section (line A-A, in Figure 4.4). The shear
flow of interest is obtained by using the expression
VQ/I. The neutral axis used in calculating Q is that of
an uncracked section. The maximum Kirchoff shear is
calculated using Equations (4.26) and (4.27) for uniform
<n X
65
<o 4-1 3 Ol
1 CVI
o
a* ( J
C 0
-p u Q)
If)
" D QJ E L 0
M -in c CD L h-
C 0
•p
U
CO in in 0 L
U
.QJ TD 0
z :
L CO Q) iZ to t . 0 ^
— Q) T3 0
c 0 .^ •p CD — 3 U — ID
:E U D CD
5 0
I/)
Q)
L cn
ss3U)|3|i|i qeis
66
loads and concentrated loads, respectively. The loads are
factored. Table 4.14 tabulates the shear flow due to
uniform loads for a 3 in. slab and an 18 gage deck.
Results in Table 4.14 represent the worst case among all
of the slabs parameters. Other cases are not tabulated.
Shear flow produced by concentrated loads are presented in
Tab1e 4.15.
Bond Strength Between Concrete and Steel
The bond strength between the modular deck and
concrete can be determined only by tests. However, a
literature review of bond strength reveals that the
natural surface bond strength between steel and concrete
is proportional to its contact area and also varies with
the character of the surfaces and the nature of the con
crete. The C i V i1 Engineering Handbook, Urquhart, 1974,
states that the bond strength between concrete and steel
can range from 5 to 40 percent of the ultimate compressive
strength of concrete at 28 days, depending on the steel
and concrete characteristics. The Mechanical Engineers
Handbook, Marks, 1955, states that previous testing
indicates a 2000 psi compressive strength concrete
at 28 days has a bond strength that ranges from 18 to 23
percent of the ultimate compressive strength.
For the purpose of this study, the surface bond
strength (v. ) between concrete and deck is assumed to be
67
Table 4.14
Shear Flow (lb/in.) Produced by Uniform Loads on 3 in. Slab
With 18 Gage Deck
Unfactored Un i form Loads (psf)
20 40 60 80 120 160 200 240 280 320 360 400 460 500 540 580 620
Factored Uni form Loads (psf)
31 62 93 124 186 248 310 372 434 496 558 620 713 775 837 899 961
2 Shear Flow In Slab
(lbs/in.)
6 13 19 26 39 52 65 78 91 103 1 16 129 149 162 175 188 201
Notes :
(1) Load factor assumed to be 1.55.
(2) Calculated using VQ/I from Equation (4-3 1)
Tab 1e 4 . 1 5
Shear F low ( l b / i n . ) Produced by C o n c e n t r a t e d Loads
68
Concentrated load (kips) K * *f
Unfactored 1.0 2.0 3.0 4.0 (.1 8.0 10.0 12.0 14.0 K.O 18.0 21.0
Factored l.( 3.1 4.7 (.2 9.3 12.4 15.S 18.( 21.7 2i.O 27.9 31.0
18 gage Deck
20 gage Deck
22 gage Deck
Concrete Thickness
(In.)
(0 37 2S 18 14
SI 31 21 IS II
47 28 19 13 10
119 73 50 36 27
102 (2 42 30 27
93 56 37 27 20
179 110 75 54 41
154 93 (2 45 34
140 84 5( 40 30
239 147 100 72 55
205 125 84 (0 45
187 112 74 53 40
359 220 150 108 02
308 167 125 90 U
279 169 112 00 60
477 293 175 144 109
412 250 167 120 90
373 224 149 107 00
597 367 250 180 137
514 312 210 150 113
466 280 186 133 100
716 441 300 217 164
617 375 251 100 136
559 336 224 lit 119
036 514 350 253 192
720 437 293 211 158
(53 392 261 186 139
955 587 400 289 219
023 500 336 240 181
746 449 299 213 159
1074 (61 4SI 325 246
926 5(2 377 270 203
893 505 3]( 240 179
1193 734 SOI 361 274
1029 625 419 301 226
932 5(1 373 266 199
69
10 percent of the 3000 psi concrete ultimate compressive
strength at 28 days. This assumption is conservative
because the nodules on the deck greatly increase the
contact area between the concrete and the steel deck.
Shear Strength of Nodules
A portion of the horizontal shear strength is
contributed by the nodules, which act as shear connectors.
The actual strength is hard to determine without a large
test program. Shear resistance of the shear connector
depends on the concrete strength, the shape of the
connector, the size of the connector, the attachment of
connector to its base, and deformations of the connector
during loading.
Expressions for the ultimate shear strength of the
various connectors, such as spiral, stud, and channel,
have been determined by experimental tests. However, none
of them are even approximately equivalent to the nodules
of the proposed modular deck.' Only a rough estimate can
be made based on the assumption that the nodules shear off
at their base. The shear resistance of a single nodule is
F = F X (c ) x (t .) . (4.32) r vy P a
Where
F = ultimate shear resistance of a single nodule ^ (lbs)
70
F^y = allowable shear yield stress of material (psi)
Cp = perimeter ABCD around base of nodule, as shown in Figure 4.5 (in.)
t^ = thickness of deck (in.).
The shear flow resistance provided by the nodules over the
entire surface of the deck is given by
F V sc "• • (4.33)
s Where
^sc - uniform shear flow resistance provided by nodules (lbs/in.)
s = center-to-center distance between two nodules (8.5 in. as shown in Figure 4.5).
Based on Equations (4.32) and (4.33) and an assumed
natural bond strength of 300 psi, the total shear
resistance at the interface between the concrete and steel
can be obtained. These values tabulated in Table 4.16
represent a crude estimate of the actual shear resistance
at the interface. However, it gives an indication that
sheai—bond failure is not likely to be a predominant
failure mode in the two-way composite slab.
Based on the shear capacity studies, it is clear
that shear capacity does not control the load capacity of
the two-way composite slabs.
tn at
71
IO
CO
h - 8.5 ins
Model C r o s s S e c t i o n
Nodule Side View
2.5 In.
N o d u l e D i m e n s i o n
Plan VIev
Figure 4.5 Nodule Dimension Used for Calculating Shear Resistance
72
Tab Ie 4.16
Total Shear Resistance at the Interface Between Deck and Concrete
Shear Flow Resistance Steel Deck ^ r j Thickness By By Total
Natural Nodules Bond
(lbs/in.) (lbs/in.) (lbs/in.)
18 gage 300 1262 1562
20 gage 300 968 1268
22 gage 300 822 1122
Notes :
(1) Terms on the left side in equation (4.31).
(2) Assumed to be of 10 percent of f'^ = 3000 psi
(3) Caculated using Equations (4.32) and (4-.3). with F = 36,000 psi, c^ = 10 in., and s ^ 8.5 in.
(4) Total = (2) + (3).
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
The concept of a two-way composite slab is described
in this document. Preliminary studies were carried out to
determine the feasibility of manufacturing the modular
deck and constructing the slabs. The overall performance
of the slabs in terms of deflections, moment capacity, and
shear capacity was evaluated. All studies are based on
theorectical analysis. Many basic assumptions are
required. No experimental testing was performed.
Is The Proposed Concept F ea s i b 1 e 1_
Based on the results from the various calculations
and evaluations, conclusions on the feasibility are
presented.
Manufactur i ng Feas ibi1ity
Discussions regarding maufacturing feasibility in
Chapter 3 indicated that it is possible to produce the
proposed new modular decks through a cold form process.
It could be accomplished by passing flat steel sheets
through a series of rollers equipped with regularly spaced
protrusions, to form the nodules.
73
74
The most predominant problems in manufacturing
these modular decks are the possibility of high stress
concentration and material yielding around the edges of
the nodules during the forming process. One way to
prevent this, is by limiting the depth of the nodules.
Experimental tests would be required to optimize the
nodule depth.
Because the cnanufacture of the modular deck is not
that different from current practices, the cost of tooling
for the new type of deck may be minimal.
All points mentioned above give a strong indication
that it is possible and feasible to manufacture the
proposed modular deck, a pilot program will be required to
verify these conclusions.
Construction Feas ibi1ity
It is possible to install the modular deck to serve
as a platform for workmen and wet concrete during
construction. Shores and puddle welds will be required to
limit the deflection and to provide the membrane action
required to support construction loads.
Results from the calculations performed on the 20 ft
by 20 ft isolated slab indicated that in the proposed
concept, shorings will be required at about a 5 ft
spac ing.
75 Performance Feasibi1ity
Results from the performance evaluation suggested
that the amount of allowable uniform and concentrated load
capacities is governed by the deflection or moment
capacity of the slab. The high shear capacity of the slab
is mainly due to the increase in bond surface area between
the deck and concrete by the nodules. The assumption that
each individual nodule will act as a shear connector also
further increases the value of the shear resistance of
the slab.
Tables 5.1 and 5.2 show the comparisons of the
allowable applied uniform and concentrated loads as
governed by deflections, moments, and shear capacity of
the slab. It was found that for slabs with a concrete
thickness of 4 in. or less, the applied loads, both
uniform and concentrated are governed by deflections.
For slabs with a concrete thickness greater than 4 in.
the controlling factor on allowable loads is the
slab moment capacity. Based on the above, we now can
speculate that the limiting capacity of the proposed two-
way composite slabs is either by deflections or moment
capac ity.
76
Table 5.1
Uniform Loads Capacity of Two-Way Composite Slab
Uniform Unfactored Loads (psf)
Steel Concrete *By ^By ^By Deck Slab Deflections Moments Shear
Thickness Thickness Capacity Capacity Capacity (Inches)
18 gage 3 60 200 4 160 300 5 280 400 6 460 500 7 620 600
20 gage 3 60 150 4 120 240 5 240 300 6 360 400 7 540 450
22 gage 3 40 100 4 120 200 5 200 250 6 320 350 7 460 425
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
620 620 620 620 620
540 540 540 540 540
460 460 460 460 460
Notes :
(1) Extracted from Table 4.4, 4.5, & 4.6.
(2) Extracted from Table 4.13.
(3) Shear capacity of the proposed composite slab is not a problem.
The above are for a 20ft by 20ft proposed composite slab.
77
Table 5.2
Concentrated Load Capacity of Two-Way Composite Slab
Steel Deck
Thickness
18 gage
20 gage
22 gage
Notes :
Concret Slab
Thickne (Inche
3 4 5 6 7
3 4 5 6 7
3 4 5 6 7
Unfactored Concentrated Loads (kips)
:e
JSS
'By Deflections Capacity
3.0 6.0 1 1 .0 18.0 25.0
2.0 5.5 9.5 15.0 21.0
1.5 5.0 7.0 13.5 19.0
^By Moments Capacity
6.0 9.2 11.1 14.0 18.0
4.0 7.2 9.2 11.1 13.0
3.0 6.0 8.0 10.0 12.0
(P^ = 4P)
^By Shear
Capacity
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
25.0 25.0 25.0 25.0 25.0
21 .0 21 .0 21 .0 21 .0 21 .0
19.0 19.0 19.0 19.0 19.0
(1) Extracted from Table 4.7, 4.8, & 4.9.
(2) Extracted from Table 4.13.
(3) Shear capacity of proposed composite slab is not a problem
The above are for a 20ft by 20ft proposed composite slab
78
Recommendat i ons for Future Research
The studies reported herein do not constitute an
exhaustive evaluation of the performance of the proposed
composite slab. Rather, this research is only the first
step in introducing the idea and demonstrating its
potential performance. Most of the work done in this
study can be verified only by full-scale experimental
tests. However, the conclusions reached to date suggest
that further studies be conducted to prove or disprove the
merits of the proposed two-way composite slab concept.
These studies should include manufacture of the modular
deck, construction of slabs, testing of slabs, economic
analysis of slabs, and marketability of the concept to the
construction industry.
REFERENCES CITED
'• Concrete^'Ac?''^,'fl'2? ^°?^ Requirements for Reinforced A S I ? Mi^Aigan. " • *™"'"'"' "" ^°""'-^*^ Institute.
2. AISC. 1980: "Manual of Steel Construction. 8th A^^r ?:• *'"^'""=^" Institute of Steel Construction. AIbC, Chicago.
^* tQ«9 " c ''''' 2! Co^^c'J of Codes and Standard Division, 1982: Specifications for Design and Construction of Composite Slabs," American Society of Civil Engineers, ASCE, New York.
4. Bryl, S. , 1967: "The Composite Effect of Profiled Steel Plate and Concrete in Steel Deck Slabs," Acier Stahl Steel, October.
5. Ekberg, C. E, Jr., Elleby, H. A., Greimann, L. F., and Porter, M. L., 1976: "Shear Bond Analysis of Steel Deck Reinforced Slabs," Journal of the Structural Division, ASCE, Paper 12611, Vol. 102, No. STI2, December, pp 2255-2268.
6. Ekberg, C. E, Jr., and Porter, M. L., 1971: "Investigation of Cold-Formed Steel Deck Reinforced Concrete Floor Slabs," Proceedings of the 1st Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, Missouri, August, PP 179-185.
7. Ekberg, C. E, Jr., and Porter, M. L., 1972: "Summary of Full-Scale Laboratory Tests of Concrete Slabs Reinforced With Cold-Formed Steel Decking," Preliminary Report, International Association for Bridge and Structural Engineering, 9th Congress, Zurich, Switzerland, May, pp 173-183.
8. Ekberg, C. E, Jr., and Porter, M. L., 1975: "Design vs. Test Results for Steel Deck Floor Slabs," Proceedings of the 3rd International Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, Rolla, Missouri, pp 792-812.
79
80
9. Ekberg, C. E, Jr., and Porter, M. L., 1976: "Design Recommendations for Steel Deck Floor Slabs," Journal ?n^ L e^?!^''T' Division, ASCE, Paper 12826, Vol. luo, iNo. bill, November, pp 2121-2136.
10. Ekberg, C. E, Jr., and Schuster. R. M., 1968: "Floor Systems With Composite Form-Reinforced Concrete blabs. Final Report, International Association for Bridge and Structural Engineering, 8th Congress, New York, September, pp 385-394.
11. Friberg, B. F., 1954: "Combined Form and Reinforcements for Concrete Slabs," Journal of the American Concrete Institute, Vol. 50, May, pp 697-716.
12. Johnson, J. E., and Salmon, C. G., 1980: "Steel Structures Design And Behaviour," 2nd edition. Harper & Row, Publishers., New York.
13. Mark, F., 1974: "Handbook of Concrete Engineering," Van Nastrand Reinhold Co., New York.
14. Marks, L. S. , 1955: "Mechanical Engineer's Handbook," 5th edition, McGraw Hill Book Co., New York.
15. Porter, M. L. , 1968: "Investigation of Light Gage Steel Forms as Reinforcement for Composite Slabs," M. S. Thesis, Department of Civil Engineering, Iowa State University, Ames, Iowa.
16. Porter, M. L. , 1974: "The Behavior and Analysis of Two-Way Simply Supported Concrete Floor Slabs Constructed With Cold-Formed Steel Decking," Ph. D. Dissertation, Department of Civil Engineering, Iowa State University, Ames, Iowa.
17. Porter, M. L., 1979: "Compendium of ISU Research Conducted On Cold-Formed Steel Deck Reinforced Slab Systems," Bulletin No. 200, Engineering Research Institute, Iowa State University, Ames, Iowa.
18. Sabnis, G. M., 1979: "Handbook of Composite Construction Engineering," Van Nostrand Reinhold Co., New York.
19. Salmon, C. G., and Wang, C. K., 1985: "Reinforced Concrete Design," 1st edition. Harper & Row, Publishers., New York.
81
20. Sandor, B. l', 1983: "Engineering Mechanics: Statics," 1st edition, Prentice-Hall Co., New York.
21. Schuster, R. M., 1970: "Strength and Behavior of Cold-Rolled Steel Deck Reinforced Concrete Floor Slabs," Ph. D. Dissertation, Department of Civil Engineering, Iowa State University, Ames, Iowa.
22. Schuster, R. M., 1972: "Composite Steel Deck Reinforced Concrete Systems Failing in Shear-Bond," Preliminary Report, International Association for Bridge and Structural Engineering, 9th Congress, Amsterdam, Netherlands, May, pp 185-191.
23. Timoshenko, S., and Woinowsky, K., 1959: "Theory of Plates and Shells," 2nd edition, McGraw Hill Book Co., New York.
24. Ugural, A. C. , 1985: "Stresses In Plates and Shells," 1st edition, McGraw Hill Co., New York.
25. Urquhart, L. C 1959: "Civil Engineering Handbook," 4th edition, McGraw Hill Book Co., New York.
PERMISSION TO COPY
In presenting this thesis in partial fulfillment of the
requirements for a master's degree at Texas Tech University, I agree
that the Library and my major department shall make it freely avail
able for research purposes. Permission to copy this thesis for
scholarly purposes may be granted by the Director of the Library or
my major professor. It is understood that any copying or publication
of this thesis for financial gain shall not be allowed without my
further written permission and that any user may be liable for copy
right infringement.
Disagree (Permission not granted) Agree (Permission granted)
Student's signature
Date
dho/s^-Date
