Design vs. Test Results for Steel Deck Floor Slabs
Transcript of Design vs. Test Results for Steel Deck Floor Slabs
Missouri University of Science and Technology Missouri University of Science and Technology
Scholars' Mine Scholars' Mine
International Specialty Conference on Cold-Formed Steel Structures
(1975) - 3rd International Specialty Conference on Cold-Formed Steel Structures
Nov 24th, 12:00 AM
Design vs. Test Results for Steel Deck Floor Slabs Design vs. Test Results for Steel Deck Floor Slabs
Max L. Porter
C. E. Ekberg Jr.
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Recommended Citation Recommended Citation Porter, Max L. and Ekberg, C. E. Jr., "Design vs. Test Results for Steel Deck Floor Slabs" (1975). International Specialty Conference on Cold-Formed Steel Structures. 9. https://scholarsmine.mst.edu/isccss/3iccfss/3iccfss-session3/9
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DESIGN VS. TEST RESULTS FOR STEEL DECK FLOOR SLABS
M. L. Portera and C. E. Ekberg, Jr.b
INTRODUCTION
An extensive experimental and theoretical investigation of steel-deck-
reinforced floor slabs was undertaken in 1967 at Iowa State University
(ISU) under the sponsorship of the Arne an Iron and Steel Institute (AISI).
To date, 353 full-scale specimens have been tested. See Ref. 3 for a
summary of tests. An over-view of the types of specimens tested was
presented at the First Specialty Conference on Cold-Formed Steel Structures
[41- The majority of tests have been one-way slab elements as shown in
Fig. 1. The results of some of these full-scale experimental tests will
be utilized in this paper for illustrating a comparison with design
recommendations.
Design recommendations for steel-deck-reinforced floor slabs are
contained in the latest American Iron and Steel Institute's draft entitled
"Tentative Recommendations for the Design of Composite Steel Deck Slabs"
and Commentary. Another paper by the same authors at this Third Specialty
Conference presents some of these tentative design recommendations [5],
and an additional paper by T. J. McCabe presents an example design utilizing
the recommendations L2J. The purpose of this paper is to present results
aAssistant Professor, Civil Engineering Dept., Iowa State Univ., Ames, Iowa.
bProfessor & Head, Civil Engineering Dept., Iowa State Univ., Ames, Iowa.
793
794 THIRD SPECIALTY CONFERENCE
of the computations utilizing the design predictions recommended for the
shear-bond capacity of steel deck slabs as compared with experimental
data. In addition, end-slip and deflection behavioral characteristics
associated with a shear-bond failure mode are presented.
L
Fig. 1. Typical arrangement for testing one-way slab elements.
SHEAR-BOND END-SLIP BEHAVIOR
Most steel-deck-reinforced floor slabs fail by the shear-bond mode
of failure. This failure mode is characterized by the formation of a
diagonal tension crack in the concrete at or near one of the load points
followed by end-slip at one end of a one-way slab element as described
previously LS~. A photograph illustrating this displacement between
the steel decking and concrete at one end-face is shown in Fig. 2. The
shear-bond failure observed from the experimental tests was typically
rather sudden, with the concrete moving horizontally, overriding or
TEST RESULTS FOR SLABS 795
Fig . 2 . Photograph of end-slip after failure of a one-way slab element .
failing the shear transferring device, which consisted of embossments,
spot-welded wires, or concrete protruding through holes in the steel
deck.
Typical load -displacement relationships for end-slip are given in
Fig. 3. Most steel deck systems do not experience end-slip until reaching
the ultimate load, as illustrated by the relationship on the left in
Fig. 3. However, some systems may experience end-slip prior to ultimate,
as shown by the load-displacement plot on the right in Fig . 3.
Additional behavioral displacement information will be presented
later in this paper.
796 THIRD SPECIALTY CONFERENCE
.02 .04 .06 .08 . 10 DISPLACEMENT - inches
.~a .:>£
I
o6 <{
94 0 w ::i Q. 0-~ . 02 . 04 . 06 . 08 . 1 0
DISPLACEMENT - inches
~ig. 3. Typical load-displacement relationships for end-slip .
SHEAR-BOND DESlGN FORMULATION
As previously described L; j , a series of perforn~nce tests, like
those in Fig. l, is necessary to properly establish a relationship for
strength involving significant: parameters affecting the shear-bond capacity.
Since the above described slippage be~een the concrete and the steel
deck occurs a long the region of the shear-span length, r.' , as shown in
Fig. l, a primary parameter for shear-bond computation is L1
• Other
important parameters include the following:
TEST RESULTS FOR SLABS
1. ultimate experimental end shear, Ve = Pe/2bd;
2. reinforcement percentage, p = As/bd;
3. cross-sectional area of steel deck, As;
I
4. concrete strength, fc;
5. specimen width, b, and effective depth, d; and
6. center-to-center spacing of shear transferring devices, s,
797
where such devices are variable from one deck section to another, such as holes or transverse wires. For those devices having a fixed pattern, such as embossments, s is taken as unity.
Utilizing the shear formulation as contained in the ACI Building
Code [1], the above parameters can be combined to form the terms V s/bdVfO e c
and pd/L'Vf', plotted as y- and x-coordinates, respectively, for the c
performance test series as demonstrated in Fig. 4. To obtain the neces-
sary strength relationship, a linear regression is obtained for the
plotted points.
v s e
k
t
To account for differences between field conditions and
REGRESSION LINE Y
/
q';Y' /
/ m =SLOPE OF REDUCED
REGRESSION LINE
REDUCED REGRESSION LINE
Fig. 4. V es pd
Relationship between bdJf' and ~ c c
798 THIRD SPECIALTY CONFERENCE
those in the laboratory, the regression line is reduced by -15 percent
to obtain the design slope, m, and intercept, k. Thus the computed shear-
bond capacity, Vu' is found from
V us mPd bdY£7 = l:Vf' + k
c c (l)
where the non-reduced value of the slope of the regression line is given
by
m nL:xy -L:x.Cy
nL:x 2 - (L:x) 2
and the non-reduced value of the regression line intercept is given by
k L:y :c:x2
- L:x iXY
ni:x2- (I: X)
2
Equation (1) has been found to be valid for all the various means
of shear transfer for steel decks currently manufactured. Since each
steel deck configuration has a different regression plot, a separate
determination of m and k in Eq. (1) is a necessity for each different
steel deck cross section.
Examples of the plot from Fig. 4. for Eq. (1), utilizing strength
data from tests of slabs constructed with various deck types, are shown
in Figs. S-8. Each of these figures represents a linear regression for
a different steel deck type. Lines representing plus or minus 15 percent
deviation intervals from the regression line are shown as an aid in
determining the spread of the data. Figures 5-8 are representative of
results obtained from Eq. (l) and provide a quantitative measure of the
accuaracy of this equation in predicting the ultimate shear force for
slab elements where the shear-bond mode of failure governs.
4.0. DECK 1 / /
/ /
0 f- / 20 GAGE x':/ / I / o -i
/o :<1 /0 v:
v s 3.0f- /_ ,<~lo 1._<0'- ~ zo ~1 // o o / ~ e I -...;./ • ' i / / 8 / V,
i / /r,}\o / 0 / C I / /,' / ~ ~ / /~ ~ I / n 0/ 'Tl
o_..a o / ~
~
24 GAGE r- /<:f- / , t L t L , t:?/ o 20 GAGE :;;:
I/ ~ w_'_J "I - -· _., __ I 1 • 5 ______lL___
0.0 0.1 0.2 0.0
Fig, 5. Example shear-bond regression for deck type 1.
o:l ~
--.1 -D -D
800
v s e
brif; 0.5
THIRD SPECIALTY CONFERENCE
DECK 2
6 16 GAGE 0 20 GAGE + 22 GAGE
O.OL---------~---------L--------~--------~ 0.0 0.2 0.4
~X 10-4
L'Fc 0.6 0.8
Fig. 6. Example shear-bond regression for deck type 2.
v s e
b~
DECK 3
0.4
0.1 0.2 0.3
~X 10-4
L~
6 16 GAGE 0 18 GAGE 0 20 GAGE
0.4 0.5 0.6
Fig. 7. Example shear-bond regression for deck type 3.
v s e
bdtr \/'cl.O
DECK 4
TEST RESULTS FOR SLABS
6 16 GAGE o 18 GAGE + 22 GAGE
O.OL_ ____ J_ ____ ~ ______ L_ ____ _L_ ____ J_ ____ _i ____ ~
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Fig. 8. Example shear-bond regression for deck type 4.
801
802 THIRD SPECIALTY CONFERENCE
In some instances, a significantly different equation determination
can be made for each gage thickness of the same steel deck cross section.
The diagrams in Fig. 5 indicate there is a definite change in the re
gression constants m and k as gage thickness changes. A composite dia
gram shown in Fig. S(c) illustrates a much greater scatter for a regres
sion of the combined gage thickness. This greater scatter (to a lesser
degree) is illustrated in Figs. 6 and 8. Figure 7 indicates litt'le or
no influence of gage thickness on the constants m and k. For those
steel decks where gage thickness significantly influences the regression
constants m and k, separate equation determinations should be made for
each gage thickness to more accurately predict the ultimate shear capacity.
In addition to the steel deck configuration and gage thickness, a
separate regression equation determination may be needed for other significant
variables not accounted for in Eq. (1). For example, the shear-bond
capacity is dependent upon the surface coating of the steel deck. If more
than one coating is used, then an additional equation determination is
necessary unless the m and k constants for the more conservative (lower)
shear values are used. An additional example of where a separate
determination may be needed is for lightweight versus normal weight
concretes, unless the more conservative results are used for both concrete
types.
SHEAR-BOND DESIGN EQUATIONS
As previously described .s", Eq. (l) can be re-written for design in
the following form to give the calculated ultimate shear, Vu in pounds
TEST RESULTS FOR SLABS 803
per foot of width:
v ¢ [ l;d (!"Pd + k./£7---) + ~lL J (2) u L' c
where ¢ shear-bond capacity reduction factor = 0.80
y portion of dead load added upon removal of shear, see Ref. 2
wl slab dead load, psf
Utili?:inG the load ~actors in the ACI Building Code [ 1], the allowaale
superimposed live load (LL) in pounds per square foot is:
LL (3)
where L span length, feet
dead load applied to· slab exclusive of w1
, psf.
EXAMPLE RESULTS OF SHEAR-BOND PREDICTIONS
Based upon design Eqs. (2) and (3), several illustrative examples
will be presented. As a means of indicating the validity of the predicted
results, the experimental load-deflection relationships for slab elements
constructed with 16, 18, and 20 gage deck will be utilized. See Figs. 9
and 10. The experimental deflections were measured at midspan and
represent the maximum vertical displacement at each applied loading
increment. Indicated on each curve is a horizontal line corresponding to
the allowable live load (ALLOW LL) as obtained from Eq. (3). The constants
m and k in Eq. (2) were obtained from linear regressions shown in Fig. 11,
where data from tests on slab elements is plotted separately according to
gage thickness. All specimens in Figs. 9-11 were reinforced with a
B.. -"'
0 UJ
-' -<{ 1-
0 1-
L' =24in. L' =48in. L' = 70 in. L' =86in. L =5ft8in. L = 9 ft 8 in. L =11ft8in. L = 15 ft 8 in. W
1= 52.9 psf w( 53.3 psf w( 53.4 psf w,= 53.0 psf
I y = 0.0 y = 0.0 y = 0.625 y = 0.625 A = 0.745 sq .in. A = 0 .7 45 sq . in . A = 0. 7 45 sq . in . As= 0.745 sq.in. bs =36.25in. bs=35.75in. b s = 35 . 88 in . b = 36.00 in. d =5.62in. d = 5.69 in. d = 5.75 in. d = 5.69 in. m = 11,764 m = 11,764 m = 11,764 m = 11,764
1/ k = 0.2512 k = 0.2512 k = 0.2512 k = 0.2512 f~ = 3505 psi f' = 3505 psi f' = 3540 psi f' = 3540 psi
. c c c
F ~ALLOW LL lf:r-ALLOWLL I VALLO~LL I ~LLOWLLi I 1
' --":"""":"'
1.0 2.0 0 1.0 2.0 0 1.0 2.0 0
MIDSPAN DEFLECTION- inches
Fig. 9. Example load-deflection relationships of various shear spans and span lengths showing the allowable live load for specimens reinforced with 18 gage steel deck.
1.0 2.0
00
:i2
...., :::; :::0 t:l Vl '"t:l tT1 (j
;; l' ...., ....:: (j
0 z ., tTl :::0 tTl z (j tTl
16 GAGE 18 GAGE 20 GAGE
L' =70in. L' = 70 in. L' = 70 in. L = 11 ft. 8 in. L = 11 ft 8 in. L = 11 ft 8 in. w1 = 53.2 psf w( 53.4 psf W1=51.7psf y =0.625 'Y = 0.625 'I = 0.625 a_ A = 0. 979 sq . in • A = 0.745 sq.in. As= 0.575 sq.in. ~
I 20 b s = 36.00 in. b s = 35, 88 in . b = 35.75 in.
d =5.75in. d = 5.56 in. 0 d = 5.50 in. <! 0 -' 0 UJ
:::; c._ c._
<! -' <! f-
0 f-
m = 0,2723 m = 11,764 m=14,272 k = 0.2723 k = 0.2512 k = 0.1597 f' = 3700 psi c
rc = 3540 psi f~ = 4452 psi
10
0ALL~Wll ~ALLOWLL bALLOWll ~1 1
360 O I I I
0 1.0 2.0 0 1.0 2.0 0
MIDSPAN DEFLECTION- inches
Fig. 10. Example load deflection relationships showing the effects of specimens reinforced with different gage thicknesses of steel deck.
-l m Vl -l
"' m Vl c: r -l Vl ., 0
"' Vl r > O:J Vl
00 0 Uo
;~j ~u '0 ..0
>-
16 GAGE 18 GAGE 20 GAGE
1.0~ I ~~~~~~---·· 0 / q\c/
o.sf- I:~ /
/ o~:;
8 / "~ / / o'?j § / ot ;j/ ~ I
;7 I
0 / I I 0/ I 0.4 r--; / / y
/ / 'l
REDUCED m = 11,059 r REDUCED m = 11,764 REDUCED m = 14,272 REDUCED k = 0.2723 REDUCED k = 0.2512 REDUCED k = 0.1597
OL---~----~-----L-----L----~----~----~----~--~--~ 0 2 4 6 0 2 4
X= _o_d_ x 10-4
L'-/P c
0 2
Fig, 11. Linear regression relationships for obtaining design live loads indicated in Figs. 9 and 10.
4
00 0 C7'
...., :r: ~
::0 u Vl 't)
tT1 n :; L' ...., -< n 0 z "!']
tT1 ::0 tT1 z n tT1
TEST RESULTS FOR SLABS 807
three-inch deep steel deck having embossments as the means of shear
transfer between the deck and concrete. The nominal width and out-to-
out depth of all specimens was 36 in. by 5-l/2 in. and the lengths varied
from 6 to 16 feet. The concrete had an average compressive strength
of approximately 4,000 psi. Other pertinent data used in Eqs. (2) and
(3) is indicated in Figs. 9-ll.
As can be seen, each of the predicted allowable live load values in
Figs. 9 and 10 falls just above the upper limit of the straight-line
portion of the load-deflection curves. Thus, the computed live load in
all cases provides good results in comparison to the ultimate and
behavioral test data and provides a consistant and reasonable margin of
safety for all the test members.
Figure 9 gives examples of load-deflection behavior for specimens
reinforced with the same gage thickness of steel deck, but with varying
shear spans and span lengths. It is evident that the behavior changes
considerably from a short shear span to a long shear span. The slab
elements exhibit considerable stiffness with little nonlinearity when the
shear-span is short. However, the long shear-span ( and span length)
induces much more ductility and considerable nonlinearity. It is
significant that the computer allowable live load (ALLOW LL) provides
consistent results for each type of load-deflection relationship, i.e.,
decreasing load with increasing shear span and span length.
Figure 10 gives load-deflection relationships for specimens reinforced
with three different gage thicknesses of steel deck, but having the same
shear span and span length. As expected, the ultimate load decreases
808 THIRD SPECIALTY CONFERENCE
with decreasing thickness of steel deck reinforcing. Also, the nonlinearity
increases slightly with decreasing thickness of the steel. Again, it is
significant that the predicted live load provides consistent results, i.e.
decreasing load with decreasing steel thickness.
Figures 9 and 10 include a vertical line indicating the allowable
1 deflection limitation of
360 of the span length. As can be seen the
load-deflection behavior is a fairly straight-line relation to the left
of this allowable deflection limitation. In addition, the 3~0 of the
span length limitation is significant in comparison with the computed
allowable live load. In most cases the allowable LL value was close to
or within the 3 ~0 limitation, indicating somewhat of a "balanced" design
with respect to deflections.
CONCLUSIONS
1. All simple span slab elements failing by a shear-bond mode of failure exhibit end-slip between the steel deck and concrete.
2. Most steel-deck-reinforced slab systems exhibit end-slip upon reaching the ultimate failure load.
3. Plots of the terms V s/bdJ~ and pd/L'Jf~ reasonable linear re~ressiog relati0nship~ equation can be written for predicting the shear-bond.
give consistent and from which a design maximum load for
4. On the basis of load-deflection data, it is apparent that the recommended design equations for shear-bond provide a consistent margin of safety.
TEST RESULTS FOR SLABS 809
ACKNOWLEDG'MENTS
The proposed design criteria presented in this paper are part of
the American Iron and Steel Institute's (AISI) latest draft of "Tentative
Reconunendations for the Design of Composite Steel Deck Slabs and Commentary."
The design criteria is based upon an extensive theoretical and experimental
research program sponsored by AISI and conducted by the Engineering
Research Institute of Iowa State University. Valuable guidance in the
conduct of the research was provided by the AISI's Task Committee on
Composite Construction of the Joint Engineering Subcommittee of the
Conunittees of Hot Rolled and Cold Rolled Sheet and Strip Producers and
Galvanized Sheet Producers under chairmanship of Mr. T. J. McCabe and
past chairman Mr. A. J. Oudheusden.
810
REFERENCES
1. American Concrete Institute, Building Code Requirements for Reinforced Concrete (ACI 318-71). Detroit, Michigan: American Concrete Institute, 1971.
2. McCabe, T. J., "Design Example of Steel Deck Reinforced Floor Slabs," Proceedings of Third Specialty Conference of Cold-Formed Steel Structures, Dept. of Civil Engineering, University of Missouri-Rolla, November 1975.
3. Porter, M. L., and Ekberg, C. E., Jr., Discussion of paper by the Subcommittee on the State-of-the-Art Survey of the Task Committee on Composite Construction of the Committee on Metals of the Structural Division entitled "Composite Steel-Concrete Construction," ASCE Journal of the Structural Division, Vol. 101, No. ST3, March 1975.
4. Porter, M. L., and Ekberg, C. E., Jr., "Investigation of Cold-Formed Steel-Deck-Reinforced Concrete Floor Slabs," Proceedings of First Specialty Conference on Cold-Formed Steel Structures, Dept. of Civil Engineering, University of Missouri-Rolla, August 19-20, 1971.
5. Porter, M. L., and Ekberg, C. E., Jr., "Tentative Design Recommendations for Steel Deck Reinforced Floor Slabs," Proceedings of Third Specialty Conference on Cold-Formed Steel Structures, Dept. of Civil Engineering, University of Missouri-Rolla, November 1975.
b
d
f. c
k
L
LL
L'
m
s
v u
y
p
TEST RESULTS FOR SLABS
APPENDIX - NOTATION
Cross-sectional area of steel deck where used as tension reinforcement, in.2/ft of width
Width of slab
811
Effective slab depth (distance from extreme concrete compression fiber to centroidal axis of the full cross-sectional area of the steel deck), in.
28-day compressive test cylinder strength, psi
Intercept of regression line
Length of span, ft.
Allowable superimposed live load for service conditions, psf
Length of shear span, in.
Slope of regression line
Center-to-center spacing of shear transfer devices other than embossments, in.
Calculated ultimate shear based on shear-bond failure, lb/ft of width
Weight of slab (concrete plus steel deck), psf
Dead load applied to slab, exclusive of w1 , psf
Coefficient depending on support during curing
Capacity reduction factor
Reinforcement ratio, A /bd s