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Flexural behavior of prestressed composite beams with corrugated web: Part II. Experiment and verification
Composites: Part B 42 (2011) 1617–1629
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Flexural behavior of prestressed composite beams with corrugated web: Part II. Experiment and verification Kang Su Kim 1, Deuck Hang Lee ⇑ Department of Architectural Engineering, The University of Seoul, 90 Jeonnong-dong, Dongdaemun-gu, Seoul 130-743, Republic of Korea
a r t i c l e
i n f o
Article history: Received 7 September 2010 Received in revised form 14 February 2011 Accepted 8 April 2011 Available online 27 April 2011 Keywords: B. Strength C. Analytical modeling C. Computational modeling D. Mechanical testing Corrugated web
a b s t r a c t This paper presents an experimental study on the flexural behavior of three full scaled non-prestressed and prestressed composite beams with corrugated web, which had been developed by authors in their previous study. Also, the performance of the proposed flexural behavior model considering the accordion effect was examined, comparing to the test results. The test result showed that, due to the accordion effect before composite with the concrete, the introduced prestress in the top and bottom flanges of the steel beam has drastically increased, and that after composite with concrete, the flexural strength and stiffness of the prestressed specimens were superior to those of the non-prestressed specimen. It was verified that the proposed flexural behavior model accurately estimated the flexural behavior, before and after the composite with concrete, of the prestressed composite beams with corrugated web. Also, the horizontal shear strengths of the composite members, summing the average shear bond strength between steel plate and concrete and the direct shear strength of concrete, were evaluated considering the horizontal shear failure observed in the test specimens. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The authors, in their previous study, proposed a prestressed composite beam with corrugated web that is advantageous for a long span and saving story height. The corrugated web utilized in the proposed composite beam enhances the efficiency of prestressing by making full use of the stress to the top and bottom flanges utilizing the accordion effect, and additional web stiffener is not required due to its great local and out-of plane buckling strength. The proposed composite beam with corrugated web has excellent performance on the composite action between concrete and steel beam, and provides good flexural rigidity and strength [1]. The authors, in their previous paper [1], proposed the concept of effective sectional area and effective moment of inertia to reflect the accordion effect that occurs on the steel beam with corrugated web before composite with concrete and also developed an analysis method on the behavior of the composite beam. While there have been some experimental researches on the externally prestressed composite beams [2–6], there has been no such study on the encased prestressed composite beam, which is presented in this study. Therefore, this paper, following the previous paper by the authors, presents experimental results on two encased pre⇑ Corresponding author. Tel.: +82 2 2210 5354, fax: +82 2 2248 0382. E-mail addresses: [email protected] (K.S. Kim), [email protected] (D.H. Lee). 1 Tel.: + 82 2 2210 5707, fax: +82 2 2248 0382. 1359-8368/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2011.04.019
stressed composite beams with corrugated web and a non-prestressed composite beam, in which the effect of prestressing is analyzed and the proposed analysis method for the accordion effect and the flexural behavior of the composite beam are verified. On the other hand, most of the composite beams in previous experimental researches [7–9] had a narrow flange width of the concrete slab and the top flange of the steel beam extended to the height of the center of the slab, resulting in the neutral axis being located lower than the top flange of the steel beam. However, the effective width of the actual T-shaped concrete section may be larger than that of previously studied specimens. In fact, in the construction site, it is quite common that the neutral axis locates in the slab due to the relatively wide effective width of slab. In such a case, it is possible to have a shear failure between slab and beam, which may occur before the composite beam reaches its ultimate flexural capacity. Therefore, this study also includes the analysis on the horizontal shear strength that reflects the actual failure mode observed in this experiment. 2. Experimental program A total of three full-scaled specimens have been fabricated to evaluate the flexural strength and behavior of the prestressed composite beams with corrugated web. As shown in Table 1, two specimens, FPCE1 and FPCE2, were prestressed, whereas the specimen FNC was not. Fig. 1a and b shows the tendon profiles and geometry of the steel beam specimens before composite. The tendon was
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Nomenclature Aeff Aflange Ag Aweb a bf bft C d dp Es Est e Fs Fy fc0 fpy fpe fpu fsb fy hw Ieff Ig
effective sectional area considering accordion effect sectional area of top and bottom flange gross sectional area of wide flange steel beam with corrugated web area of corrugated web web panel width bottom flange width top flange width compression force wave height of corrugate web distance from extreme top fiber to tendon centroid elastic modulus of steel reinforcement elastic modulus of steel plate eccentricity of tendon from the centroid of gross section at maximum moment region stress in steel plate yield stress of steel plate ultimate compressive strength of concrete yield strength of tendon effective stress of tendon ultimate strength of tendon average shear bond strength yield stress of reinforcing bar height of web effective moment of inertia moment of inertia based on gross section
arranged in a way that a drape point was at the center of FPCE1 and two drape points were near the center of FPCE2. All details of the specimen FNC is identical to those of FPCE1 and FPCE2 except that no tendon was placed. All the specimens were 7240-mm long. As shown in Fig. 1c, the corrugated web and flanges were 6 mm, 12 mm thick, respectively. The widths of top and bottom flanges were different, and they were 200 mm, 300 mm, respectively. The wide bottom flange was used to provide easy installation of precast slab or form, if applicable. Also, as shown in Fig. 1d in detail, the wave height of the corrugated web was 60 mm with the angle of 28.7°. No additional stiffener was installed on the web. As shown in Fig. 2a and b, the corrugated web and the top and bottom flanges were separately manufactured and welded together. It should be noted that the flanges and the corrugated web were welded only in parts, as shown in Fig. 2c, except the wave angle—that is, the inclined web—so as to maximize the accordion effect. Also, in order to ensure the safety against axial stress at ultimate, the welding size (s) and the thickness of the welding neck (a) were set to 12 mm and 8.4 mm, respectively, according to the standard on AISC J 2.2 [10]. Moreover, after the completion of welding, it was checked by an ultrasonic test [10,11]. In the specimens FPCE1 and FPCE2, four tendons were prestressed to 75% of tensile strength (fpu). As the jacking force of each tendon (Pj) was 137 kN, the total force by four tendons was 548 kN. Fig. 2d shows the jacking operation and Fig. 2e describes the jacking order. After prestressing the steel beam, forms were installed as shown in Fig. 3, and concrete was cast after the slab bars is placed. Fig. 4 shows the sectional details and geometry of the prestressed composite beams. The total height of the composite beam was 470 mm, and the distances from the top fiber of the section to the centroid of the tendon (dp) were 205 mm, 420 mm at the end and at the center of the member, respectively. The slab was 1100 mm wide and 140 mm thick, in which 10-D16 steel bars were placed in two layers with the spacings of 100 mm. As shown in Table 2, the water-to-cement ratio was 43.4%, and crushed granite
jd La Md,steel Pe Pj tw v Vdir Vh Vu
vdir
yb yt
eb ecu e0c epe epe,st,b epe,st,t et ga gf
distance of moment lever arm at critical section length of shear span dead load moment before composition effective force of tendon jacking force of tendon web thickness shear slip direct shear force of concrete horizontal shear force vertical shear force direct shear strength of concrete distance from bottom fiber of section to the centroid of gross section distance from top fiber of section to the centroid of gross section strain of bottom flange of steel plate maximum compressive strain of the concrete concrete compressive strain at maximum compressive stress effective prestrain in tendon effective prestrain in bottom flange of steel beam effective prestrain in top flange of steel beam strain in top fiber of section coefficient of effective web area coefficient of effective moment of inertia
with the maximum size of 25 mm was used as coarse aggregate. The design compressive strength of the concrete was 45 MPa, and the actual compressive strength was 48 MPa. The compressive strain at the maximum strength of the concrete (e0c ) was measured as about 0.0025. The D16 deformed bars used in the slab was SD400, as shown in Table 3, and the average yield strength was 410 MPa. The steel plate used in the beams with corrugated web was SS400, and the average yield strengths 278–292 MPa. Sevenwired low-relaxation tendons with 12.6 mm-diameter were used for all specimens and their ultimate tensile strength was 1860 MPa. As shown in Fig. 5, the test specimens were simply supported with a span length of 5720 mm, and subjected to two points loading. As shown in Fig. 5b, four LVDT were installed under the specimen to measure deflection of specimens. LVDTs were installed at
Table 1 Variables of test specimens. Variables Specimen
Web
Prestress
Drape point(s)
FPCE1 FPCE2 FNC
C C C
s s
1 2 –
*F
P
C
E1
P
S S: member with shear connecter P: partial welding, G: gross welding E1: 1 drape point, E2: 2 drape points C: corrugated web P: prestressed member F: flexural member
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• See details in (d)
1619
A
A
(a) FPCE1
• See details in (d)
A
A
(b) FPCE2
(c) A-A section
(d) Details of corrugated web Fig. 1. Details of steel beam with corrugated web before composite (units: mm).
both ends of the member to measure the slippage during the loading history as also shown in Fig. 6a. As shown in Fig. 6b, the load cell was installed at the end of the specimens to observe the stress change of the tendon, if any. To measure the longitudinal strains of the specimens, strain gauges were attached, as shown in Fig. 6c–e, on the concrete slab, the top and bottom flanges of the steel beam, web, and tendon. All data from the measuring devices were collected by the main computer, and by each loading stage, crack patterns and crack width were observed and recorded.
when the specimens FPCE1 and FPCE2 were prestressed. It can be observed that there is no or little strain on the corrugated web whereas the top and bottom flanges have very large strains. In these specimens, the prestress on the bottom flange is about 18% greater than the case of the typical I-shaped beam, and of course, this efficiency rate of prestress depends on the sectional characteristics of the steel beam, as mentioned in the previous study [1].
3.2. Load–deflection behavior 3. Test results 3.1. Accordion effect As reported in the authors’ previous paper [1] and existing studies [3,12–15], it is known that the prestress introduced to the top and bottom flanges increases because there is little stress introduced to corrugated web due to the accordion effect. Fig. 7 shows the strain distribution along the height of the section at midspan
The initial camber measured after the composite with concrete was 4 mm for FPCE1 and 3 mm for FPCE2. Fig. 8a is the measured load–deflection curves of specimens including the initial camber, and Fig. 8b shows the horizontal displacement of slab resulting from the horizontal shear force that seperates the top slab from beam. In the specimen FNC, the initial flexural cracking was observed near the midspan at the load of about 50 kN. As the applied force
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Fig. 2. Fabrication of steel beam with corrugated web.
Fig. 3. Fabrication of prestressed composite beam with corrugated web.
exceeds about 450 kN, the lower flange began to yield, and as cracks propagated to the slab, the flexural stiffness began to decrease. As the applied force exceeds 500 kN, the slope of the load–displacement curve began to decline rapidly, at which the deflection in the midspan was about 30 mm. Later at 520 kN of the applied load, horizontal shear cracks were observed from the end regions, and at 600 kN, they extended to the maximum mo-
ment region. Eventually, the horizontal shear failure occurred as the concrete slab was separated from the top surface of the steel beam. Unfortunately, however, the relative horizontal displacement between the slab and the steel beam of the specimen FNC was not measured due to malfunctioning of the measuring device. The specimens FPCE1 and FPCE2, to which prestressing was introduced, showed an almost identical load–deflection behavior,
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A
A
(a) FPCE1 A
A
(b) FPCE2
(c) Composite section at end of the beam
(d) Composite section at A-A
Fig. 4. Detail of prestressed composite beam with corrugated web.
Table 2 Concrete mixture proportion. Design strength (MPa)
Gmax (mm)
W/C (%)
S/A (%)
45
25
43.3
46.3
Weight per unit volume (kg/m3) W
C
S
G
AD
162
373
830
981
1.87
Table 3 Characteristics of reinforcing bars, tendons and steel plates. Specimen
Rebar
Tendon
D13
FPCE1 FPCE2 FNC
D16
D19
/12:6
Es (MPa)
fy (MPa)
Es (MPa)
fy (MPa)
Es (MPa)
fy (MPa)
fpu (MPa)
2.0 105 2.0 105 2.0 105
410 410 410
2.0 105 2.0 105 2.0 105
410 410 410
2.0 105 2.0 105 2.0 105
410 410 410
1855 1855 1855
Steel Thickness 6 mm
FPCE1 FPCE2 FNC
Thickness 12 mm
Fy (MPa)
Est (MPa)
Fy (MPa)
Est (MPa)
278 278 278
1.9 105 1.9 105 1.9 105
292 292 292
2.0 105 2.0 105 2.0 105
and compared with that of FNC in which prestressing was not introduced, the flexural rigidity and the ultimate strength increased by about 20% and 25%, respectively. The load–deflection curves of the specimens FPCE1 and FPCE2 show only little decrease of flexural rigidity even at the yield strength of FNC, which increase almost linearly until the load increased up to about 650 kN, showing the reinforcing effect of the prestressed tendons. The initial
flexural cracking strength of these specimens also increases by about 40%, at near 70 kN of loading, compared to the specimen FNC. The specimen FPCE1 showed horizontal shear cracks between the slab and the beam near the end of member at around 420 kN, and the flexural cracks progressed gradually toward the midspan as the load increased. Later, at 680 kN, the bottom steel
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UTM (10000 kN)
L5
: LVDT
specimen
L1L1
L2L2
L3L3
(b) Description of test set-up and location of LVDT
(a) Test set-up and loading frame
Fig. 5. Test set-up.
(a) LVDT for measuring end slip
(b) Load cell at the end of test specimen
Concrete strain gauge : see details in (e) Strain gauge : see details in (d) Tendon strain gauge
Center point
(c) Location of strain gauges
slab top fiber d/ 4
concrete gauge strain gauge
d/ 4 d/ 4 d/ 4
(d) Detailed location of strain gauges along the member height
C5
L4L4
C4
C1 C2 C3
(e) Location of concrete strain gauges (top view) Fig. 6. Location of measurement.
L6
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373
η f f = 0.91 ηa = 0.39
700
93
600
Load (kN)
187
Beam height (mm)
280
500
FNC FPCE1 FPCE2
400 300
Ultimate load Observed horizontal shear crack Tendon yielding Tension flange yielding Flexural cracking
200 100 0 -20
0 -600
-500
-400
-300
Compressive strain
-200
-100
0
0
20
40
60
80
100
120
Deflection (mm)
(x106)
(a) Load vs. deflection
Fig. 7. Longitudinal strains along the height of steel section immediately after prestressing.
800 700
3.3. Crack patterns and failure modes The crack patterns of each specimen are shown in Fig. 10. In the specimen FNC, the flexural cracks in midspan propagated deeply to the top slab at 550 kN, and the horizontal shear cracks propagated from the right end of the specimen to the center of the member. The deformation was concentrated on a small number of cracks, and thus the crack widths were very large, developed up to 3.0 mm at ultimate. As opposed to the specimen FNC, the flexural
600
Load (kN)
flange began to yield, and at 719 kN, the tendon stress reached near the yielding strength (fpy ). At 737 kN, the ultimate load, the lower part of the corrugated web also yielded, and the horizontal shear cracks propagated to the center of the member length. The horizontal shear failure was observed at between the concrete slab and the top steel flange, at which the load rapidly decreased by 12%. Although no load increase appeared after the separation of slab, the specimen maintained a certain level of load, and the vertical deflection increased by up to 110 mm, at which the applied force was removed. In the specimen FPCE2, the horizontal shear cracks were observed at 450 kN, and the lower flange yielded at 691 kN. The tendon stress reached near the yield strength (fpy ) at 725 kN, and the horizontal shear failure occurred at 745 kN. Fig. 8b shows the slip between the concrete slab and the top steel flange at the end of FPCE1 and FPCE2. The loads at which the horizontal shear cracks were observed were almost identical to the load at which the end slip increased rapidly. At 420 kN where the end slip increased rapidly, the flexural moment at the center of FPCE1 specimen was 456 kN m. If the moment lever arm is assumed to be about 0:9dp (378 mm), the corresponding horizontal shear force is about 1206 kN. The bond stress at the initial slip, calculated based on the bonded perimeter area shown in Fig. 8c, was about 0.48 MPa. This is somewhat lower than 0.6 MPa, which is the average bond strength (fsb ) between steel plate and concrete proposed by Mullett [8]. However, the average bond stress based on the maximum load was about 0.85 MPa, which was higher than what Mullet had proposed. As aforementioned, the stress change in the tendon was measured by the load cells installed at the ends of the specimens FPCE1 and FPCE2. However, there was no change in tension forces during all loading stages, implying that tendons and concrete were perfectly bonded. Fig. 9 shows the deflections along the member length measured by LVDTs installed. Due to the increased rigidity by the prestressing, FPCE1 and FPCE2 showed about 3/4 of the deflection compared to that of the specimen FNC at the same load. This means that the proposed composite beam is considerably advantageous to control deflections, and thus it is suitable for a long-span structure.
500 400 300 200
FPCE1
100
FPCE2
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
End slip (mm)
(b) Load vs. horizontal displacement of slab at ends
(c) bond perimeter Fig. 8. Load vs. deflection and load vs. slip relationships.
crack on the concrete slab is little progressed even at the ultimate load. This is because of the effect of prestressing tendons. In FPCE1, compared to the specimen FNC, only little cracks progressed on the top slab even at the ultimate load, and a large number of flexural cracks were distributed in wider regions. Thus, the maximum crack width was only 0.6 mm at 550 kN, which is relatively smaller as it was 2.5 mm in case of FNC. The maximum crack width of and FPCE2 at the failure load was only 1.0 mm, whereas that of FNC was only 3.0 mm. This supports that the proposed composite beam is advantageous for controlling cracks due to the effect of tendons. The horizontal shear failure between the concrete slab and the top steel flange, observed in every specimen, was because there was no shear connector. Thus, it is, of course, believed that the specimen would have somewhat higher flexural strength if shear connectors were installed. Fig. 11 shows the compressive strains on the extreme top fiber of slab measured from the concrete strain gauges installed as shown in Fig. 6c. In all specimens, the compressive strains were evenly distributed along the slab width of 1100 mm. As shown in Fig. 11a, the specimen FNC had the compressive stain of 0.0025 at failure, which is the same as the maximum compressive strain measured from the concrete cylinder test. Therefore, it is considered that the specimen FNC almost reached its flexural strength. In cases of FPCE1 and FPCE2 as shown in Fig. 11b and c, however,
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(a) FNC
(b) FPCE1
(c) FPCE2 Fig. 9. Deflection along the span.
the measured maximum strains reached only around 0.0015, showing that horizontal shear failure occurred considerably before their flexural strength.
epe;st;b ¼
4. Verification of the proposed analysis model Authors, in their previous research, proposed an approach utilizing the concept of effective section for the analysis of the accordion effect by the corrugated web [1]. As concretized by the effective moment of inertia (Ieff) and the effective area (Aeff), the concept of effective section is expressed by:
Ieff ¼ gf Ig
ð1Þ
Aeff ¼ Aflange þ ga Aweb
ð2Þ
where Ig is the gross moment of inertia, Aflange is the sum of the sectional areas of the top and bottom flanges, and Aweb is the sectional area of web. gf and ga are the coefficients of the effective moment of inertia and the effective sectional area, respectively, which are proposed by:
gf ¼ 0:70
d a bf t w hw hw
0:15
" 0:56 # 0:19 0:19 bf d a ga ¼ 0:30 tw hw hw
epe;st;t ¼
ð3Þ
ð4Þ
where d is the wave height of the corrugated web, tw is the thickness of web, a is the panel width of web, hw is the height of web, and bf is the thickness of bottom flange. By substituting the coefficients calculated by Eqs. (3) and (4) to Eqs. (1) and (2), the axial strains of the top and bottom flanges (epe;st;t ; epe;st;b ) are given by:
rt Es
rb Es
¼
Pe Pe e M d;steel þ y y Es Aeff Es Ieff t Es Ieff t
ð5aÞ
Pe Pe e M d;steel y þ y Es Aeff Es Ieff b Es Ieff b
ð5bÞ
¼
where Pe is the effective prestressing force, Es is the elastic modulus of steel plates (2.0 105 MPa), Ag is the gross sectional area of steel beam, Ig is the gross moment of inertia of steel beam, e is the eccentricity from the cenroid of section to the centroid of tendons, Md;steel is the flexural moment of steel beam by self-weight, yt is the distance from the centroid of section to the top fiber of steel beam, and yb is the distance from the centroid of section to the bottom fiber of steel beam. In Fig. 7, the measured axial strains from experiments are compared to the strains calculated by Eq. (5), considering the accordion effect by the proposed concept of effective section. It should be noted that the values of gf and ga were 0.91 and 0.39, respectively, for the top and bottom strains of the specimens FPCE1 and FPCE2, and that the strains of web were assumed to be zero. The proposed approach well estimated the strains of top and bottom flanges with marginal errors of 1% and 8%, respectively, which shows that the proposed method reflects the accordion effect reasonably good but rather simply. Fig. 12 is the layered sectional model for the flexural behavior of the prestressed composite beams with corrugated web proposed in the authors’ previous study [1]. In this analysis, Collins model [16] was used for the compressive stress–strain relationship of concrete, the bilinear model for steel bars and plates, and modified Ramberg–Osgood model [17] for tendons. The moment–curvature response can be obtained by the proposed approach, which involves a few iteration procedures to find the strain, the stress, and the force of each element that satisfy the equilibrium
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(a) FNC
(b) FPCE1
(c) FPCE2
1625
were pretty closely caught by the analysis. The reason that the difference of member stiffness between the test and analysis was the largest among all specimens is considered that the specimen FNC was not prestressed, in which the composite web also has a weak accordion effect like the corrugated steel web. For the specimens FPCE1 and FPCE2, however, as shown in Fig. 13b and c, the proposed model accurately evaluated the flexural behavior from the initial curvature to the point just before the horizontal shear failure. Furthermore, as shown in Fig. 14, the tendon stresses of the specimens FPCE1 and FPCE2 near mid-span were well estimated by the proposed method. When the top steel flange of the composite beam is encased deep into the center of slab, the location of the neutral axis becomes lower than the top steel flange. In this case, there is little possibility of horizontal shear failure. However, when the effective width of composite beam with the T-shaped section—for example, as defined in ACI 318-08 [18]—is large enough to locate the neutral axis above the top steel flange, there is high possibility of horizontal shear failure in case there is no shear connector. In this case, the horizontal shear failure plane may develop as shown in Fig. 15. In most laboratory tests, however, the slab part is often not fabricated or its width is not that large due to the difficulty of fabrications and other limitations. Thus, it is pretty hard to observe such a horizontal shear failure. In this study, therefore, all specimens were planned in such a way that, as shown in Fig. 4c and d, the neutral axis is located above the top steel flange at the ultimate. This was intentionally done by placing a heavy amount of compression steel bars, instead of making the slab width wide. As a result, as aforementioned, all specimens had, as in Fig. 10d, the horizontal failure showing the separation between the slab and the steel beam, which is interesting to examine in more detail. The horizontal shear resistance (Vb) by the bond stress between the top surface of steel flange and the concrete, in Fig. 15a and b, is given by:
V b ¼ fsb bft La
ð6Þ
where bft is the width of the top steel flange, La is the shear span length. And, fsb is the average bond strength, for which this study used 0.6 MPa as suggested by Mullett [8]. Also, the shear strength (Vdir) against the failure surface in the direction of the length, whose width and depth are defined by tw in Fig. 15a and shear span La in Fig. 15b, is expressed by:
V dir ¼ v dir ðtw La Þ
ð7Þ
where vdir is the direct shear stress on the surface considered, which is suggested by Mattock [19] as:
(d) Horizontal shear failure Fig. 10. Crack patterns of test specimens.
condition. The analysis for flexural behavior is completed when the strain of the top fiber of section (et reached the maximum compressive strain of the ecu concrete). It should be mentioned that the horizontal shear strength were considered in a separate procedure as explained later. It should be also noted that neither concrete elements nor the corrugated web element had prestrain or prestress. For the compression flanges, tension flanges, and tendons, however, the strains by prestressing and the strains increased after the composite with the concrete were accumulated and calculated accordingly. Fig. 13 shows the moment–curvature responses of the specimens. The specimen FNC, as shown in Fig. 13a, showed somewhat smaller stiffness than the analysis results, though the overall behavior including stiffness degradation near the yielding point
v dir ¼ 0:1fc0 ðpsiÞ
ð8Þ
where fc0 is the compressive strength of concrete, and based on Eq. (8), the direct shear strength (vdir) is 4.79 MPa. Li and Maekawa [20] and Li et al. [21] also proposed, by simplifying the contact density model, the direct shear (v dir ) as:
v dir ¼ 3:83fc01=3
m2 m2 þ w2
ð9Þ
where m is the shear displacement and w is the crack width. By substituting 0.5 mm, the amount of slip at the maximum load of the specimens FPCE1 and FPCE2, to the shear displacement (m), and 0.5 mm, the crack width measured just before the maximum load, to the crack width (w), the direct shear stress (vdir) by Eq. (9) becomes 6.95 MPa. Meanwhile, as shown in Fig. 16, Paulay and Leober [22] presented the direct shear strength as a bilinear relationship based on test results. Based on the measured data— concrete compressive strength, crack width, and amount of slip at ultimate load—in this study, therefore, the shear strength can approximately estimated at 4.5 MPa. In addition, AASHTO LRFD
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Bridge Design Specifications [23] defined the horizontal shear strength as 2.8 MPa for the specimens. The horizontal shear force (Vh) on the failure section is given by:
Vh ¼
X
C¼
V ua jd
to be 7.24 MPa, 6.42 MPa, and 6.66 MPa, respectively. In other words, the average direct shear strength (vdir) of the specimens is about 6.77 MPa, which is similar to the value calculated by the Eq. (9) and higher than the other methods aforementioned. Then, by summing the horizontal shear resistance Vb and Vdir, the horizontal shear strength of the member (Vhn) can be calculated as:
ð10Þ
P where C is the sum of the compression forces at the corresponding section, Vu is the vertical shearing force, and jd is the length of moment lever arm. Thus, the direct shear stress of the concrete (vdir) at the failure surface can be inversely estimated by:
v dir ¼
ðV h V b Þ tw La
V hn ¼ fsb bft La þ v dir ðt w La Þ
ð12Þ
In Fig. 13, the horizontal shear strengths (Vhn) of the member, calculated by Eq. (12) applying the aforementioned approaches for the direct shear stress (vdir), are expressed with horizontal lines in different types. The ratios of the calculated horizontal shear strengths to the test results (Vpred/Vtest) were also summarized in Table 5. The horizontal shear strengths by Mattock [19] and AASHTO LRFD [23] were considerably lower than the test results for all
ð11Þ
Table 4 shows the direct shear strengths (vdir) of the specimens at concrete failure surface calculated by Eq. (11). The direct shear strengths of the specimens FNC, FPCE1, and FPCE2 were shown
(a) FNC
(b) FPCE1
(c) FPCE2 Fig. 11. Measured concrete strains at top fiber of member.
Steel reinforcing bar element
Concrete element
d web, layer, i
d s 2 d s1 d st,b
dp
d st, t
εt
ε st,t
d web, layer, i +1
ε pe, st, t
Steel flange element Steel web element Tendon element
Δε ps
Steel flange element
ε st,b
Ns1
ε st, web,i ε st, web,i+1
Nst, web,i
Nc,tens
ε pe, st,b
(b) Strains
Fig. 12. Description of the proposed method for flexural behavior.
Nc
Nst, web, i+1
εps
εb
(a) Layered elements of section
Ns 2
Nst, t
Nst, web, n
Nst ,b
(c) Sectional forces
N ps
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K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629 1000
900
Horizontal shear strength
900
Horizontal shear strength
800
800
Moment (kN·m)
600 500 400
FNC Test Results Flexural behavior model
300
Matook Eq. 8
200 100
700 600 500
300 200
AASHTO-LRFD
100
Eq. 11
0
0 0
10
20
30
Curvature
40
(x10-3
FPCE1 Test Results Flexural behavior model Mattok Eq. 8 Li and Maekawa Eq. 9 AASHTO-LRFD Eq. 11
400
Li and Makawa Eq. 9
50
-5
60
0
5
10
15
20
25
30
Curvature (x10-3 rad/m)
rad/m)
(b) FPCE1
(a) FNC 1000 Horizontal shear strength
900
Moment (kN·m)
800 700 600 500
FPCE2 Test Results
400
Flexural behavior model
300
Mattok Eq. 8 Li and Maekawa Eq. 9
200
AASHTO-LRFD
100
Eq. 11
0 -5
0
5
10
15
20
25
30
35
Curvature (x10-3 rad/m)
(c) FPCE2
Tendon stress (MPa)
Tendon stress (MPa)
Fig. 13. Comparison of analysis results and test results.
Vertical deflection (mm)
(b) Tendon stress vs. Vertical deflection for FPCE1
Tendon stress (MPa)
Applied load (kN)
(a) Tendon stress vs. Applied Load for FPCE1
Tendon stress (MPa)
Moment (kN·m)
700
Applied load (kN)
(c) Tendon stress vs. Applied Load for FPCE2
Vertical deflection (mm)
(d) Tendon stress vs. Vertical deflection for FPCE2
Fig. 14. Comparison of tendon stresses by analysis and test results.
35
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K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629
Shear bond area
(a) Example of horizontal shear failure
(b) Horizontal shear failure plane
Fig. 15. Description of horizontal shear failure.
(psi)
(MPa)
1200 w = 0.005in
w = 0.001in
(0.13mm)
(0.25mm)
8
Shear stress
1000
crack width w = 0.002in (0.51mm)
7 6
800
±7%
5 ±20%
600
4
±20%
400
3
±20%
±30% ±40%
200
f c' = 37.0 MPa
±45%
specimens FNC and FPCE2, respectively, and 3% larger strength for the specimen FPCE1, which are considered to be pretty good estimation of the horizontal strength of the composite members. It would not be possible to estimate the horizontal shear strength of the composite members accurately based on the only small numbers of test results examined in this study. However, it can be inferred from the results of several researchers and code [19– 23], as well as the test result from this study, that the horizontal shear strength (Vhn) of the member can be safely estimated when about 6.0 MPa of the direct shear strength (vdir) is used.
2
5. Conclusion 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 (mm)
4.0
8.0
12.0
16.0
20.0
24.0
28.0
32.0
0 0
( 10-3 in)
Shear displacement (slip) Fig. 16. Typical mean shear stress–shear displacement relationship [19].
Table 4 Analysis results from the proposed method. Specimens
Flexural moment (kN m)
Compressive force P sum, C (Vh) (kN)
Moment lever arm, jd (mm)
vdir (MPa)
FNC FPCE1 FPCE2
677 787 810
2531 2176 2249
280.0 364.4 360.3
7.24 6.42 6.66
Table 5 Horizontal shear strength using various approaches. Approaches
Vhn Vhn Vhn Vhn
(using (using (using (using
Eq. (8) by Mattock) Eq. (9) by Li et al.) AASHTO LRFD approach) Eq. (11) by test results)
FNC
FPCE1
FPCE2
Vpred/Vtest
Vpred/Vtest
Vpred/Vtest
0.704 0.954 0.448 0.932
0.906 1.053 0.495 1.029
0.753 1.020 0.479 0.996
specimens, which means that these approaches provides a large margin of safety. The horizontal shear strengths by Li and Maekawa [20] and Li et al. [21] provided very close estimation to the test results, with the small difference within less than about 5% for all specimens. On the other hand, using the average direct shear strength (vdir) of all specimens calculated by Eq. (11) based on the test results, 6.77 MPa as explained earlier, the horizontal shear strength (Vhn) of the specimens also can be estimated. Compared to the test results, it provides 7% and 1% smaller strength for the
In this study, a non-prestressed and two prestressed composite beams with corrugated web have been fabricated in full scale and experimental tests were conducted to examine their flexural behavior. In addition, the flexural behavior model, reflecting the accordion effect, proposed for the prestressed composite beam with corrugated web in the previous study, was verified. The study resulted in the following conclusions: 1. The steel beam with corrugated web was very efficient to introduce larger prestress into the top and bottom flanges, compared to the typical I-shaped steel beam, due to the accordion effect. 2. The use of the effective moment of inertia (gf ) and the effective web area factor (ga ), proposed in this study, resulted not only in easy consideration of the accordion effect, but also provided very accurate estimation close to the test results. 3. Compared to the non-prestressed specimen FNC, the flexural stiffness and strength of the prestressed specimen FPCE1 and FPCE2 increased by about 20% and 25%, respectively, which verifies the good structural performance, in the view point of span length and story height, of the prestressed composite beam with corrugated web, proposed in the previous paper. 4. The proposed model very accurately estimated the flexural behavior of the prestressed composite beams with corrugated web including the tendon stress during the loading history. 5. Based on the test results and other studies on the horizontal shear strength of composite beams, it is considered that about 6 MPa of direct shear strength of concrete can be used for safe evaluation of the horizontal shear strength of such members.
Acknowledgments This work (Grants No. 00041190) was supported by Business for Cooperative R&D between Industry, Academy and Research Institute funded by the Korea Small and Medium business Administration in 2010.
K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629
References [1] Kim KS, Lee DH, Choi SM, Choi YH, Jung SH. Flexural behavior of prestressed composite beams with corrugated web: part I. Development and analysis. J Compos Part B: Eng; in preparation. [2] Lorenc W, Kubica E. Behavior of composite beams prestressed with external tendons: experimental study. J Constr Steel Res 2006;62(12):1353–66. [3] Metwally AE, Loov RE. Corrugated steel webs for prestressed concrete girders, RILEM. Mater Struct 2003;36(3):127–34. [4] Ayyub BM, Sohn YG, Saadatmanesh H. Prestressed composite girders under positive moment, ASCE. J Struct Eng 1990;116(11):2931–51. [5] Ayyub BM, Sohn YG, Saadatmanesh H. Prestressed composite girders. I: experimental study for negative moment, ASCE. J Struct Eng 1992;118(10):2743–62. [6] Ayyub BM, Sohn YG, Saadatmanesh H. Prestressed composite girders. II: analytical study for negative moment, ASCE. J Struct Eng 1992;118(10):2763–83. [7] Lawson RM, Mullett DL, Rackham JW. Design of asymmetric slimfloor beam using deep composite decking. The Steel Construction Institute, Publication No. 175; 1997. [8] Mullett DL. Composite floor system. Blackwell Science Ltd.; 1998. p. 72–3. [9] Heo BYW, Kwak MK, Bae KW, Jeong SM. Flexural capacity of profiled steel composite beams: deep deck plate. J Korean Soc Steel Constr 2007;19(3):247–58. [10] AISC. Manual of steel construction-load and resistance factor design, 3rd ed. Chicago, IL: American Institute of Steel Construction; 2001. [11] Drury JC. Ultrasonic flaw detection for technicians, 3rd ed. Silverwing Ltd.; 2004. p. 250.
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[12] Huang L, Hikosaka H, Komine K. Simulation of accordion effect in corrugated steel web with concrete flanges. Comput Struct 2004;82(23–26): 2061–9. [13] Elgaaly M, Seshadri A, Hamilton RW. Bending strength of steel beams with corrugated webs, ASCE. J Struct Eng 1997;123(6):772–82. [14] Khalid YA, Chan CL, Sahari BB, Hamouda AMS. Bending behavior of corrugated web beam. J Mater Process Technol 2004;150(3): 242–54. [15] Driver RG, Abba HH, Sause R. Shear behavior of corrugated web bridge girders, ASCE. J Struct Div 2006;132(2):195–203. [16] Collins MP, Mitchell D. Prestressed concrete structures. Prentice Hill; 1991. 766pp. [17] Mattok AH. Flexural strength of prestressed concrete sections by programable calculator. PCI J 1979;24(1):32–54. [18] ACI Committee 318. Building code requirements for structural concrete (ACI 318-05) and commentary (318R-05). Farmington Hills, MI: American Concrete Institute; 2005, 430pp. [19] Mattock AH. Shear friction and high-strength concrete. ACI Struct J 2001;98(1):50–9. [20] Li B, Maekawa K. Contact density model for cracks in concrete. IABSE Rep 1987;54:52–62. [21] Li B, Maekawa K, Okamura H. Contact density model for stress transfer across cracks in concrete. J Fac Eng, Univ Tokyo 1989;XL(1):9–59. [22] Paulay T, Loeber PJ. Shear transfer by aggregate interlocking. ACI SP-42 1974;1:1–15. [23] American Association of State Highway and Transportation Officials. AASHTO LRFD bridge design specifications, 3rd ed. AASHTO, Washington, DC; 2004. 1450pp.
Contents lists available at ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Flexural behavior of prestressed composite beams with corrugated web: Part II. Experiment and verification Kang Su Kim 1, Deuck Hang Lee ⇑ Department of Architectural Engineering, The University of Seoul, 90 Jeonnong-dong, Dongdaemun-gu, Seoul 130-743, Republic of Korea
a r t i c l e
i n f o
Article history: Received 7 September 2010 Received in revised form 14 February 2011 Accepted 8 April 2011 Available online 27 April 2011 Keywords: B. Strength C. Analytical modeling C. Computational modeling D. Mechanical testing Corrugated web
a b s t r a c t This paper presents an experimental study on the flexural behavior of three full scaled non-prestressed and prestressed composite beams with corrugated web, which had been developed by authors in their previous study. Also, the performance of the proposed flexural behavior model considering the accordion effect was examined, comparing to the test results. The test result showed that, due to the accordion effect before composite with the concrete, the introduced prestress in the top and bottom flanges of the steel beam has drastically increased, and that after composite with concrete, the flexural strength and stiffness of the prestressed specimens were superior to those of the non-prestressed specimen. It was verified that the proposed flexural behavior model accurately estimated the flexural behavior, before and after the composite with concrete, of the prestressed composite beams with corrugated web. Also, the horizontal shear strengths of the composite members, summing the average shear bond strength between steel plate and concrete and the direct shear strength of concrete, were evaluated considering the horizontal shear failure observed in the test specimens. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The authors, in their previous study, proposed a prestressed composite beam with corrugated web that is advantageous for a long span and saving story height. The corrugated web utilized in the proposed composite beam enhances the efficiency of prestressing by making full use of the stress to the top and bottom flanges utilizing the accordion effect, and additional web stiffener is not required due to its great local and out-of plane buckling strength. The proposed composite beam with corrugated web has excellent performance on the composite action between concrete and steel beam, and provides good flexural rigidity and strength [1]. The authors, in their previous paper [1], proposed the concept of effective sectional area and effective moment of inertia to reflect the accordion effect that occurs on the steel beam with corrugated web before composite with concrete and also developed an analysis method on the behavior of the composite beam. While there have been some experimental researches on the externally prestressed composite beams [2–6], there has been no such study on the encased prestressed composite beam, which is presented in this study. Therefore, this paper, following the previous paper by the authors, presents experimental results on two encased pre⇑ Corresponding author. Tel.: +82 2 2210 5354, fax: +82 2 2248 0382. E-mail addresses: [email protected] (K.S. Kim), [email protected] (D.H. Lee). 1 Tel.: + 82 2 2210 5707, fax: +82 2 2248 0382. 1359-8368/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2011.04.019
stressed composite beams with corrugated web and a non-prestressed composite beam, in which the effect of prestressing is analyzed and the proposed analysis method for the accordion effect and the flexural behavior of the composite beam are verified. On the other hand, most of the composite beams in previous experimental researches [7–9] had a narrow flange width of the concrete slab and the top flange of the steel beam extended to the height of the center of the slab, resulting in the neutral axis being located lower than the top flange of the steel beam. However, the effective width of the actual T-shaped concrete section may be larger than that of previously studied specimens. In fact, in the construction site, it is quite common that the neutral axis locates in the slab due to the relatively wide effective width of slab. In such a case, it is possible to have a shear failure between slab and beam, which may occur before the composite beam reaches its ultimate flexural capacity. Therefore, this study also includes the analysis on the horizontal shear strength that reflects the actual failure mode observed in this experiment. 2. Experimental program A total of three full-scaled specimens have been fabricated to evaluate the flexural strength and behavior of the prestressed composite beams with corrugated web. As shown in Table 1, two specimens, FPCE1 and FPCE2, were prestressed, whereas the specimen FNC was not. Fig. 1a and b shows the tendon profiles and geometry of the steel beam specimens before composite. The tendon was
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Nomenclature Aeff Aflange Ag Aweb a bf bft C d dp Es Est e Fs Fy fc0 fpy fpe fpu fsb fy hw Ieff Ig
effective sectional area considering accordion effect sectional area of top and bottom flange gross sectional area of wide flange steel beam with corrugated web area of corrugated web web panel width bottom flange width top flange width compression force wave height of corrugate web distance from extreme top fiber to tendon centroid elastic modulus of steel reinforcement elastic modulus of steel plate eccentricity of tendon from the centroid of gross section at maximum moment region stress in steel plate yield stress of steel plate ultimate compressive strength of concrete yield strength of tendon effective stress of tendon ultimate strength of tendon average shear bond strength yield stress of reinforcing bar height of web effective moment of inertia moment of inertia based on gross section
arranged in a way that a drape point was at the center of FPCE1 and two drape points were near the center of FPCE2. All details of the specimen FNC is identical to those of FPCE1 and FPCE2 except that no tendon was placed. All the specimens were 7240-mm long. As shown in Fig. 1c, the corrugated web and flanges were 6 mm, 12 mm thick, respectively. The widths of top and bottom flanges were different, and they were 200 mm, 300 mm, respectively. The wide bottom flange was used to provide easy installation of precast slab or form, if applicable. Also, as shown in Fig. 1d in detail, the wave height of the corrugated web was 60 mm with the angle of 28.7°. No additional stiffener was installed on the web. As shown in Fig. 2a and b, the corrugated web and the top and bottom flanges were separately manufactured and welded together. It should be noted that the flanges and the corrugated web were welded only in parts, as shown in Fig. 2c, except the wave angle—that is, the inclined web—so as to maximize the accordion effect. Also, in order to ensure the safety against axial stress at ultimate, the welding size (s) and the thickness of the welding neck (a) were set to 12 mm and 8.4 mm, respectively, according to the standard on AISC J 2.2 [10]. Moreover, after the completion of welding, it was checked by an ultrasonic test [10,11]. In the specimens FPCE1 and FPCE2, four tendons were prestressed to 75% of tensile strength (fpu). As the jacking force of each tendon (Pj) was 137 kN, the total force by four tendons was 548 kN. Fig. 2d shows the jacking operation and Fig. 2e describes the jacking order. After prestressing the steel beam, forms were installed as shown in Fig. 3, and concrete was cast after the slab bars is placed. Fig. 4 shows the sectional details and geometry of the prestressed composite beams. The total height of the composite beam was 470 mm, and the distances from the top fiber of the section to the centroid of the tendon (dp) were 205 mm, 420 mm at the end and at the center of the member, respectively. The slab was 1100 mm wide and 140 mm thick, in which 10-D16 steel bars were placed in two layers with the spacings of 100 mm. As shown in Table 2, the water-to-cement ratio was 43.4%, and crushed granite
jd La Md,steel Pe Pj tw v Vdir Vh Vu
vdir
yb yt
eb ecu e0c epe epe,st,b epe,st,t et ga gf
distance of moment lever arm at critical section length of shear span dead load moment before composition effective force of tendon jacking force of tendon web thickness shear slip direct shear force of concrete horizontal shear force vertical shear force direct shear strength of concrete distance from bottom fiber of section to the centroid of gross section distance from top fiber of section to the centroid of gross section strain of bottom flange of steel plate maximum compressive strain of the concrete concrete compressive strain at maximum compressive stress effective prestrain in tendon effective prestrain in bottom flange of steel beam effective prestrain in top flange of steel beam strain in top fiber of section coefficient of effective web area coefficient of effective moment of inertia
with the maximum size of 25 mm was used as coarse aggregate. The design compressive strength of the concrete was 45 MPa, and the actual compressive strength was 48 MPa. The compressive strain at the maximum strength of the concrete (e0c ) was measured as about 0.0025. The D16 deformed bars used in the slab was SD400, as shown in Table 3, and the average yield strength was 410 MPa. The steel plate used in the beams with corrugated web was SS400, and the average yield strengths 278–292 MPa. Sevenwired low-relaxation tendons with 12.6 mm-diameter were used for all specimens and their ultimate tensile strength was 1860 MPa. As shown in Fig. 5, the test specimens were simply supported with a span length of 5720 mm, and subjected to two points loading. As shown in Fig. 5b, four LVDT were installed under the specimen to measure deflection of specimens. LVDTs were installed at
Table 1 Variables of test specimens. Variables Specimen
Web
Prestress
Drape point(s)
FPCE1 FPCE2 FNC
C C C
s s
1 2 –
*F
P
C
E1
P
S S: member with shear connecter P: partial welding, G: gross welding E1: 1 drape point, E2: 2 drape points C: corrugated web P: prestressed member F: flexural member
K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629
• See details in (d)
1619
A
A
(a) FPCE1
• See details in (d)
A
A
(b) FPCE2
(c) A-A section
(d) Details of corrugated web Fig. 1. Details of steel beam with corrugated web before composite (units: mm).
both ends of the member to measure the slippage during the loading history as also shown in Fig. 6a. As shown in Fig. 6b, the load cell was installed at the end of the specimens to observe the stress change of the tendon, if any. To measure the longitudinal strains of the specimens, strain gauges were attached, as shown in Fig. 6c–e, on the concrete slab, the top and bottom flanges of the steel beam, web, and tendon. All data from the measuring devices were collected by the main computer, and by each loading stage, crack patterns and crack width were observed and recorded.
when the specimens FPCE1 and FPCE2 were prestressed. It can be observed that there is no or little strain on the corrugated web whereas the top and bottom flanges have very large strains. In these specimens, the prestress on the bottom flange is about 18% greater than the case of the typical I-shaped beam, and of course, this efficiency rate of prestress depends on the sectional characteristics of the steel beam, as mentioned in the previous study [1].
3.2. Load–deflection behavior 3. Test results 3.1. Accordion effect As reported in the authors’ previous paper [1] and existing studies [3,12–15], it is known that the prestress introduced to the top and bottom flanges increases because there is little stress introduced to corrugated web due to the accordion effect. Fig. 7 shows the strain distribution along the height of the section at midspan
The initial camber measured after the composite with concrete was 4 mm for FPCE1 and 3 mm for FPCE2. Fig. 8a is the measured load–deflection curves of specimens including the initial camber, and Fig. 8b shows the horizontal displacement of slab resulting from the horizontal shear force that seperates the top slab from beam. In the specimen FNC, the initial flexural cracking was observed near the midspan at the load of about 50 kN. As the applied force
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Fig. 2. Fabrication of steel beam with corrugated web.
Fig. 3. Fabrication of prestressed composite beam with corrugated web.
exceeds about 450 kN, the lower flange began to yield, and as cracks propagated to the slab, the flexural stiffness began to decrease. As the applied force exceeds 500 kN, the slope of the load–displacement curve began to decline rapidly, at which the deflection in the midspan was about 30 mm. Later at 520 kN of the applied load, horizontal shear cracks were observed from the end regions, and at 600 kN, they extended to the maximum mo-
ment region. Eventually, the horizontal shear failure occurred as the concrete slab was separated from the top surface of the steel beam. Unfortunately, however, the relative horizontal displacement between the slab and the steel beam of the specimen FNC was not measured due to malfunctioning of the measuring device. The specimens FPCE1 and FPCE2, to which prestressing was introduced, showed an almost identical load–deflection behavior,
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K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629
A
A
(a) FPCE1 A
A
(b) FPCE2
(c) Composite section at end of the beam
(d) Composite section at A-A
Fig. 4. Detail of prestressed composite beam with corrugated web.
Table 2 Concrete mixture proportion. Design strength (MPa)
Gmax (mm)
W/C (%)
S/A (%)
45
25
43.3
46.3
Weight per unit volume (kg/m3) W
C
S
G
AD
162
373
830
981
1.87
Table 3 Characteristics of reinforcing bars, tendons and steel plates. Specimen
Rebar
Tendon
D13
FPCE1 FPCE2 FNC
D16
D19
/12:6
Es (MPa)
fy (MPa)
Es (MPa)
fy (MPa)
Es (MPa)
fy (MPa)
fpu (MPa)
2.0 105 2.0 105 2.0 105
410 410 410
2.0 105 2.0 105 2.0 105
410 410 410
2.0 105 2.0 105 2.0 105
410 410 410
1855 1855 1855
Steel Thickness 6 mm
FPCE1 FPCE2 FNC
Thickness 12 mm
Fy (MPa)
Est (MPa)
Fy (MPa)
Est (MPa)
278 278 278
1.9 105 1.9 105 1.9 105
292 292 292
2.0 105 2.0 105 2.0 105
and compared with that of FNC in which prestressing was not introduced, the flexural rigidity and the ultimate strength increased by about 20% and 25%, respectively. The load–deflection curves of the specimens FPCE1 and FPCE2 show only little decrease of flexural rigidity even at the yield strength of FNC, which increase almost linearly until the load increased up to about 650 kN, showing the reinforcing effect of the prestressed tendons. The initial
flexural cracking strength of these specimens also increases by about 40%, at near 70 kN of loading, compared to the specimen FNC. The specimen FPCE1 showed horizontal shear cracks between the slab and the beam near the end of member at around 420 kN, and the flexural cracks progressed gradually toward the midspan as the load increased. Later, at 680 kN, the bottom steel
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K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629
UTM (10000 kN)
L5
: LVDT
specimen
L1L1
L2L2
L3L3
(b) Description of test set-up and location of LVDT
(a) Test set-up and loading frame
Fig. 5. Test set-up.
(a) LVDT for measuring end slip
(b) Load cell at the end of test specimen
Concrete strain gauge : see details in (e) Strain gauge : see details in (d) Tendon strain gauge
Center point
(c) Location of strain gauges
slab top fiber d/ 4
concrete gauge strain gauge
d/ 4 d/ 4 d/ 4
(d) Detailed location of strain gauges along the member height
C5
L4L4
C4
C1 C2 C3
(e) Location of concrete strain gauges (top view) Fig. 6. Location of measurement.
L6
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K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629 800
373
η f f = 0.91 ηa = 0.39
700
93
600
Load (kN)
187
Beam height (mm)
280
500
FNC FPCE1 FPCE2
400 300
Ultimate load Observed horizontal shear crack Tendon yielding Tension flange yielding Flexural cracking
200 100 0 -20
0 -600
-500
-400
-300
Compressive strain
-200
-100
0
0
20
40
60
80
100
120
Deflection (mm)
(x106)
(a) Load vs. deflection
Fig. 7. Longitudinal strains along the height of steel section immediately after prestressing.
800 700
3.3. Crack patterns and failure modes The crack patterns of each specimen are shown in Fig. 10. In the specimen FNC, the flexural cracks in midspan propagated deeply to the top slab at 550 kN, and the horizontal shear cracks propagated from the right end of the specimen to the center of the member. The deformation was concentrated on a small number of cracks, and thus the crack widths were very large, developed up to 3.0 mm at ultimate. As opposed to the specimen FNC, the flexural
600
Load (kN)
flange began to yield, and at 719 kN, the tendon stress reached near the yielding strength (fpy ). At 737 kN, the ultimate load, the lower part of the corrugated web also yielded, and the horizontal shear cracks propagated to the center of the member length. The horizontal shear failure was observed at between the concrete slab and the top steel flange, at which the load rapidly decreased by 12%. Although no load increase appeared after the separation of slab, the specimen maintained a certain level of load, and the vertical deflection increased by up to 110 mm, at which the applied force was removed. In the specimen FPCE2, the horizontal shear cracks were observed at 450 kN, and the lower flange yielded at 691 kN. The tendon stress reached near the yield strength (fpy ) at 725 kN, and the horizontal shear failure occurred at 745 kN. Fig. 8b shows the slip between the concrete slab and the top steel flange at the end of FPCE1 and FPCE2. The loads at which the horizontal shear cracks were observed were almost identical to the load at which the end slip increased rapidly. At 420 kN where the end slip increased rapidly, the flexural moment at the center of FPCE1 specimen was 456 kN m. If the moment lever arm is assumed to be about 0:9dp (378 mm), the corresponding horizontal shear force is about 1206 kN. The bond stress at the initial slip, calculated based on the bonded perimeter area shown in Fig. 8c, was about 0.48 MPa. This is somewhat lower than 0.6 MPa, which is the average bond strength (fsb ) between steel plate and concrete proposed by Mullett [8]. However, the average bond stress based on the maximum load was about 0.85 MPa, which was higher than what Mullet had proposed. As aforementioned, the stress change in the tendon was measured by the load cells installed at the ends of the specimens FPCE1 and FPCE2. However, there was no change in tension forces during all loading stages, implying that tendons and concrete were perfectly bonded. Fig. 9 shows the deflections along the member length measured by LVDTs installed. Due to the increased rigidity by the prestressing, FPCE1 and FPCE2 showed about 3/4 of the deflection compared to that of the specimen FNC at the same load. This means that the proposed composite beam is considerably advantageous to control deflections, and thus it is suitable for a long-span structure.
500 400 300 200
FPCE1
100
FPCE2
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
End slip (mm)
(b) Load vs. horizontal displacement of slab at ends
(c) bond perimeter Fig. 8. Load vs. deflection and load vs. slip relationships.
crack on the concrete slab is little progressed even at the ultimate load. This is because of the effect of prestressing tendons. In FPCE1, compared to the specimen FNC, only little cracks progressed on the top slab even at the ultimate load, and a large number of flexural cracks were distributed in wider regions. Thus, the maximum crack width was only 0.6 mm at 550 kN, which is relatively smaller as it was 2.5 mm in case of FNC. The maximum crack width of and FPCE2 at the failure load was only 1.0 mm, whereas that of FNC was only 3.0 mm. This supports that the proposed composite beam is advantageous for controlling cracks due to the effect of tendons. The horizontal shear failure between the concrete slab and the top steel flange, observed in every specimen, was because there was no shear connector. Thus, it is, of course, believed that the specimen would have somewhat higher flexural strength if shear connectors were installed. Fig. 11 shows the compressive strains on the extreme top fiber of slab measured from the concrete strain gauges installed as shown in Fig. 6c. In all specimens, the compressive strains were evenly distributed along the slab width of 1100 mm. As shown in Fig. 11a, the specimen FNC had the compressive stain of 0.0025 at failure, which is the same as the maximum compressive strain measured from the concrete cylinder test. Therefore, it is considered that the specimen FNC almost reached its flexural strength. In cases of FPCE1 and FPCE2 as shown in Fig. 11b and c, however,
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(a) FNC
(b) FPCE1
(c) FPCE2 Fig. 9. Deflection along the span.
the measured maximum strains reached only around 0.0015, showing that horizontal shear failure occurred considerably before their flexural strength.
epe;st;b ¼
4. Verification of the proposed analysis model Authors, in their previous research, proposed an approach utilizing the concept of effective section for the analysis of the accordion effect by the corrugated web [1]. As concretized by the effective moment of inertia (Ieff) and the effective area (Aeff), the concept of effective section is expressed by:
Ieff ¼ gf Ig
ð1Þ
Aeff ¼ Aflange þ ga Aweb
ð2Þ
where Ig is the gross moment of inertia, Aflange is the sum of the sectional areas of the top and bottom flanges, and Aweb is the sectional area of web. gf and ga are the coefficients of the effective moment of inertia and the effective sectional area, respectively, which are proposed by:
gf ¼ 0:70
d a bf t w hw hw
0:15
" 0:56 # 0:19 0:19 bf d a ga ¼ 0:30 tw hw hw
epe;st;t ¼
ð3Þ
ð4Þ
where d is the wave height of the corrugated web, tw is the thickness of web, a is the panel width of web, hw is the height of web, and bf is the thickness of bottom flange. By substituting the coefficients calculated by Eqs. (3) and (4) to Eqs. (1) and (2), the axial strains of the top and bottom flanges (epe;st;t ; epe;st;b ) are given by:
rt Es
rb Es
¼
Pe Pe e M d;steel þ y y Es Aeff Es Ieff t Es Ieff t
ð5aÞ
Pe Pe e M d;steel y þ y Es Aeff Es Ieff b Es Ieff b
ð5bÞ
¼
where Pe is the effective prestressing force, Es is the elastic modulus of steel plates (2.0 105 MPa), Ag is the gross sectional area of steel beam, Ig is the gross moment of inertia of steel beam, e is the eccentricity from the cenroid of section to the centroid of tendons, Md;steel is the flexural moment of steel beam by self-weight, yt is the distance from the centroid of section to the top fiber of steel beam, and yb is the distance from the centroid of section to the bottom fiber of steel beam. In Fig. 7, the measured axial strains from experiments are compared to the strains calculated by Eq. (5), considering the accordion effect by the proposed concept of effective section. It should be noted that the values of gf and ga were 0.91 and 0.39, respectively, for the top and bottom strains of the specimens FPCE1 and FPCE2, and that the strains of web were assumed to be zero. The proposed approach well estimated the strains of top and bottom flanges with marginal errors of 1% and 8%, respectively, which shows that the proposed method reflects the accordion effect reasonably good but rather simply. Fig. 12 is the layered sectional model for the flexural behavior of the prestressed composite beams with corrugated web proposed in the authors’ previous study [1]. In this analysis, Collins model [16] was used for the compressive stress–strain relationship of concrete, the bilinear model for steel bars and plates, and modified Ramberg–Osgood model [17] for tendons. The moment–curvature response can be obtained by the proposed approach, which involves a few iteration procedures to find the strain, the stress, and the force of each element that satisfy the equilibrium
K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629
(a) FNC
(b) FPCE1
(c) FPCE2
1625
were pretty closely caught by the analysis. The reason that the difference of member stiffness between the test and analysis was the largest among all specimens is considered that the specimen FNC was not prestressed, in which the composite web also has a weak accordion effect like the corrugated steel web. For the specimens FPCE1 and FPCE2, however, as shown in Fig. 13b and c, the proposed model accurately evaluated the flexural behavior from the initial curvature to the point just before the horizontal shear failure. Furthermore, as shown in Fig. 14, the tendon stresses of the specimens FPCE1 and FPCE2 near mid-span were well estimated by the proposed method. When the top steel flange of the composite beam is encased deep into the center of slab, the location of the neutral axis becomes lower than the top steel flange. In this case, there is little possibility of horizontal shear failure. However, when the effective width of composite beam with the T-shaped section—for example, as defined in ACI 318-08 [18]—is large enough to locate the neutral axis above the top steel flange, there is high possibility of horizontal shear failure in case there is no shear connector. In this case, the horizontal shear failure plane may develop as shown in Fig. 15. In most laboratory tests, however, the slab part is often not fabricated or its width is not that large due to the difficulty of fabrications and other limitations. Thus, it is pretty hard to observe such a horizontal shear failure. In this study, therefore, all specimens were planned in such a way that, as shown in Fig. 4c and d, the neutral axis is located above the top steel flange at the ultimate. This was intentionally done by placing a heavy amount of compression steel bars, instead of making the slab width wide. As a result, as aforementioned, all specimens had, as in Fig. 10d, the horizontal failure showing the separation between the slab and the steel beam, which is interesting to examine in more detail. The horizontal shear resistance (Vb) by the bond stress between the top surface of steel flange and the concrete, in Fig. 15a and b, is given by:
V b ¼ fsb bft La
ð6Þ
where bft is the width of the top steel flange, La is the shear span length. And, fsb is the average bond strength, for which this study used 0.6 MPa as suggested by Mullett [8]. Also, the shear strength (Vdir) against the failure surface in the direction of the length, whose width and depth are defined by tw in Fig. 15a and shear span La in Fig. 15b, is expressed by:
V dir ¼ v dir ðtw La Þ
ð7Þ
where vdir is the direct shear stress on the surface considered, which is suggested by Mattock [19] as:
(d) Horizontal shear failure Fig. 10. Crack patterns of test specimens.
condition. The analysis for flexural behavior is completed when the strain of the top fiber of section (et reached the maximum compressive strain of the ecu concrete). It should be mentioned that the horizontal shear strength were considered in a separate procedure as explained later. It should be also noted that neither concrete elements nor the corrugated web element had prestrain or prestress. For the compression flanges, tension flanges, and tendons, however, the strains by prestressing and the strains increased after the composite with the concrete were accumulated and calculated accordingly. Fig. 13 shows the moment–curvature responses of the specimens. The specimen FNC, as shown in Fig. 13a, showed somewhat smaller stiffness than the analysis results, though the overall behavior including stiffness degradation near the yielding point
v dir ¼ 0:1fc0 ðpsiÞ
ð8Þ
where fc0 is the compressive strength of concrete, and based on Eq. (8), the direct shear strength (vdir) is 4.79 MPa. Li and Maekawa [20] and Li et al. [21] also proposed, by simplifying the contact density model, the direct shear (v dir ) as:
v dir ¼ 3:83fc01=3
m2 m2 þ w2
ð9Þ
where m is the shear displacement and w is the crack width. By substituting 0.5 mm, the amount of slip at the maximum load of the specimens FPCE1 and FPCE2, to the shear displacement (m), and 0.5 mm, the crack width measured just before the maximum load, to the crack width (w), the direct shear stress (vdir) by Eq. (9) becomes 6.95 MPa. Meanwhile, as shown in Fig. 16, Paulay and Leober [22] presented the direct shear strength as a bilinear relationship based on test results. Based on the measured data— concrete compressive strength, crack width, and amount of slip at ultimate load—in this study, therefore, the shear strength can approximately estimated at 4.5 MPa. In addition, AASHTO LRFD
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Bridge Design Specifications [23] defined the horizontal shear strength as 2.8 MPa for the specimens. The horizontal shear force (Vh) on the failure section is given by:
Vh ¼
X
C¼
V ua jd
to be 7.24 MPa, 6.42 MPa, and 6.66 MPa, respectively. In other words, the average direct shear strength (vdir) of the specimens is about 6.77 MPa, which is similar to the value calculated by the Eq. (9) and higher than the other methods aforementioned. Then, by summing the horizontal shear resistance Vb and Vdir, the horizontal shear strength of the member (Vhn) can be calculated as:
ð10Þ
P where C is the sum of the compression forces at the corresponding section, Vu is the vertical shearing force, and jd is the length of moment lever arm. Thus, the direct shear stress of the concrete (vdir) at the failure surface can be inversely estimated by:
v dir ¼
ðV h V b Þ tw La
V hn ¼ fsb bft La þ v dir ðt w La Þ
ð12Þ
In Fig. 13, the horizontal shear strengths (Vhn) of the member, calculated by Eq. (12) applying the aforementioned approaches for the direct shear stress (vdir), are expressed with horizontal lines in different types. The ratios of the calculated horizontal shear strengths to the test results (Vpred/Vtest) were also summarized in Table 5. The horizontal shear strengths by Mattock [19] and AASHTO LRFD [23] were considerably lower than the test results for all
ð11Þ
Table 4 shows the direct shear strengths (vdir) of the specimens at concrete failure surface calculated by Eq. (11). The direct shear strengths of the specimens FNC, FPCE1, and FPCE2 were shown
(a) FNC
(b) FPCE1
(c) FPCE2 Fig. 11. Measured concrete strains at top fiber of member.
Steel reinforcing bar element
Concrete element
d web, layer, i
d s 2 d s1 d st,b
dp
d st, t
εt
ε st,t
d web, layer, i +1
ε pe, st, t
Steel flange element Steel web element Tendon element
Δε ps
Steel flange element
ε st,b
Ns1
ε st, web,i ε st, web,i+1
Nst, web,i
Nc,tens
ε pe, st,b
(b) Strains
Fig. 12. Description of the proposed method for flexural behavior.
Nc
Nst, web, i+1
εps
εb
(a) Layered elements of section
Ns 2
Nst, t
Nst, web, n
Nst ,b
(c) Sectional forces
N ps
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K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629 1000
900
Horizontal shear strength
900
Horizontal shear strength
800
800
Moment (kN·m)
600 500 400
FNC Test Results Flexural behavior model
300
Matook Eq. 8
200 100
700 600 500
300 200
AASHTO-LRFD
100
Eq. 11
0
0 0
10
20
30
Curvature
40
(x10-3
FPCE1 Test Results Flexural behavior model Mattok Eq. 8 Li and Maekawa Eq. 9 AASHTO-LRFD Eq. 11
400
Li and Makawa Eq. 9
50
-5
60
0
5
10
15
20
25
30
Curvature (x10-3 rad/m)
rad/m)
(b) FPCE1
(a) FNC 1000 Horizontal shear strength
900
Moment (kN·m)
800 700 600 500
FPCE2 Test Results
400
Flexural behavior model
300
Mattok Eq. 8 Li and Maekawa Eq. 9
200
AASHTO-LRFD
100
Eq. 11
0 -5
0
5
10
15
20
25
30
35
Curvature (x10-3 rad/m)
(c) FPCE2
Tendon stress (MPa)
Tendon stress (MPa)
Fig. 13. Comparison of analysis results and test results.
Vertical deflection (mm)
(b) Tendon stress vs. Vertical deflection for FPCE1
Tendon stress (MPa)
Applied load (kN)
(a) Tendon stress vs. Applied Load for FPCE1
Tendon stress (MPa)
Moment (kN·m)
700
Applied load (kN)
(c) Tendon stress vs. Applied Load for FPCE2
Vertical deflection (mm)
(d) Tendon stress vs. Vertical deflection for FPCE2
Fig. 14. Comparison of tendon stresses by analysis and test results.
35
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K.S. Kim, D.H. Lee / Composites: Part B 42 (2011) 1617–1629
Shear bond area
(a) Example of horizontal shear failure
(b) Horizontal shear failure plane
Fig. 15. Description of horizontal shear failure.
(psi)
(MPa)
1200 w = 0.005in
w = 0.001in
(0.13mm)
(0.25mm)
8
Shear stress
1000
crack width w = 0.002in (0.51mm)
7 6
800
±7%
5 ±20%
600
4
±20%
400
3
±20%
±30% ±40%
200
f c' = 37.0 MPa
±45%
specimens FNC and FPCE2, respectively, and 3% larger strength for the specimen FPCE1, which are considered to be pretty good estimation of the horizontal strength of the composite members. It would not be possible to estimate the horizontal shear strength of the composite members accurately based on the only small numbers of test results examined in this study. However, it can be inferred from the results of several researchers and code [19– 23], as well as the test result from this study, that the horizontal shear strength (Vhn) of the member can be safely estimated when about 6.0 MPa of the direct shear strength (vdir) is used.
2
5. Conclusion 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 (mm)
4.0
8.0
12.0
16.0
20.0
24.0
28.0
32.0
0 0
( 10-3 in)
Shear displacement (slip) Fig. 16. Typical mean shear stress–shear displacement relationship [19].
Table 4 Analysis results from the proposed method. Specimens
Flexural moment (kN m)
Compressive force P sum, C (Vh) (kN)
Moment lever arm, jd (mm)
vdir (MPa)
FNC FPCE1 FPCE2
677 787 810
2531 2176 2249
280.0 364.4 360.3
7.24 6.42 6.66
Table 5 Horizontal shear strength using various approaches. Approaches
Vhn Vhn Vhn Vhn
(using (using (using (using
Eq. (8) by Mattock) Eq. (9) by Li et al.) AASHTO LRFD approach) Eq. (11) by test results)
FNC
FPCE1
FPCE2
Vpred/Vtest
Vpred/Vtest
Vpred/Vtest
0.704 0.954 0.448 0.932
0.906 1.053 0.495 1.029
0.753 1.020 0.479 0.996
specimens, which means that these approaches provides a large margin of safety. The horizontal shear strengths by Li and Maekawa [20] and Li et al. [21] provided very close estimation to the test results, with the small difference within less than about 5% for all specimens. On the other hand, using the average direct shear strength (vdir) of all specimens calculated by Eq. (11) based on the test results, 6.77 MPa as explained earlier, the horizontal shear strength (Vhn) of the specimens also can be estimated. Compared to the test results, it provides 7% and 1% smaller strength for the
In this study, a non-prestressed and two prestressed composite beams with corrugated web have been fabricated in full scale and experimental tests were conducted to examine their flexural behavior. In addition, the flexural behavior model, reflecting the accordion effect, proposed for the prestressed composite beam with corrugated web in the previous study, was verified. The study resulted in the following conclusions: 1. The steel beam with corrugated web was very efficient to introduce larger prestress into the top and bottom flanges, compared to the typical I-shaped steel beam, due to the accordion effect. 2. The use of the effective moment of inertia (gf ) and the effective web area factor (ga ), proposed in this study, resulted not only in easy consideration of the accordion effect, but also provided very accurate estimation close to the test results. 3. Compared to the non-prestressed specimen FNC, the flexural stiffness and strength of the prestressed specimen FPCE1 and FPCE2 increased by about 20% and 25%, respectively, which verifies the good structural performance, in the view point of span length and story height, of the prestressed composite beam with corrugated web, proposed in the previous paper. 4. The proposed model very accurately estimated the flexural behavior of the prestressed composite beams with corrugated web including the tendon stress during the loading history. 5. Based on the test results and other studies on the horizontal shear strength of composite beams, it is considered that about 6 MPa of direct shear strength of concrete can be used for safe evaluation of the horizontal shear strength of such members.
Acknowledgments This work (Grants No. 00041190) was supported by Business for Cooperative R&D between Industry, Academy and Research Institute funded by the Korea Small and Medium business Administration in 2010.
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