- Open Access
Alternatives to Enhance Flat Slab Ductility
- Mohamed Husain^{1},
- Ahmed S. Eisa^{1}Email author and
- Ramy Roshdy^{1}
https://doi.org/10.1007/s40069-016-0180-5
© The Author(s) 2017
- Received: 23 January 2016
- Accepted: 17 November 2016
- Published: 28 February 2017
Abstract
Flat slab systems are vastly used in multi-story buildings because of their savings in story height and construction time, as well as for their flexibility in architectural remodeling. However, they frequently suffer brittle punching-shear failure around columns, especially when subjected to lateral loads. Therefore, seismic codes labeled flat slabs as non-ductile systems. This research goal is investigating some construction alternatives to enhance flat slab ductility and deformability. The alternatives are: adding different types of punching-shear reinforcement, using discreet fibers in concrete mixes, and increasing thickness of slab around columns. The experimental study included preparation and testing of seven half-scale interior slab-column connections up to failure. The first specimen is considered a reference, the second two specimens made of concrete mixes with different volumetric ratios of polymer fibers. Another three specimens reinforced with different types of punching-shear reinforcement, and the last specimen constructed with drop panel of inverted pyramidal shape. It is found that using the inverted pyramid-shape drop panel of specimen, increases the punching-shear capacity, and the initial and the post-cracking stiffnesses. The initial elastic stiffnesses are different for all specimens especially for the slab with closed stirrups where it is experienced the highest initial stiffness compared to the reference slab.
Keywords
- flat slab
- punching-shear
- stud-rails
- ductility
- punching reinforcement
- fibers
1 Introduction
Flat slabs are preferred in multi-story construction due to its economical and architectural benefits. These benefits include; reducing the construction time and reducing story height, which results in more stories for the same building, as well as their flexibility in architectural remodeling. However, they have been discredited by many seismic codes for less ductile behavior, and poor energy absorption (IBC 2009; Eurocode 8 2004; ACI 421-1R 2008).
The capacity design method has been widely adopted by a majority of modern seismic codes, since its introduction in the New Zealand code in mid-1970s (Park and Paulay 1974; Paulay and Priestley 1992; Dovich and Wight 1996; Robertson and Johnson 2004). The method uses ductility and energy absorption characteristics of structures to dissipate large amount of the seismic imparted energy, which boosts the structural safety and reliability. It requires flexural yielding at many locations of the building and provides them with adequate ductility. At the same time prevent any possibility of brittle failure, such as, shear and bond failures.
Hawkins (1974), Dam and Wight (2015) and Matzke et al. (2015) published a paper presenting an overview of tests performed with different punching-shear reinforcement systems such as steel heads, bent-up bars, and stirrups. During the 1980s and 1990s, Regan started his research on punching with and without shear reinforcement at the Polytechnic of Central London (Regan 1981, 1985). In the UK at the beginning of the 1990s, Chana and Desai have performed extensive experimental investigations on punching-shear tests with shear reinforcement (Chana and Desai 1992). Oliveira et al. (2000) have carried out experimental punching investigations on the effects of vertical or inclined stirrups on flat slab behavior. Carvalho (2011) also have conducted investigations on the same subject.
Another way to increase shear strength is to add fiber to concrete as shear reinforcement. Dinh et al. (2010) have tested 28 simply supported beams with 3.5 shear span/depth ratio, with different fiber volumetric ratio. They concluded that fiber concrete with appropriate fiber volumetric ratio can provide shear reinforcement to concrete beams. Meisami et al. (2013) have investigated the shear strengthening of flat slab by using fibers-reinforced concrete. In the early 1990s, a team of researchers from University of California, at Berkeley, has assessed the seismic performance of 14-story-non ductile-reinforced concrete built in middle 1960s. The building was termed non-ductile, because it was designed on code provisions prior to the 1976 seismic code (Graf and Mehrain 1992). The building has survived two major seismic events—San Fernando Valley in 1971, and Loma Prieta 1989—only by slab column framing action. It is concluded that the building exceptional behavior has to do with its inverted pyramid-shaped drop-panels. The ductility of flat plates: comparison of shear reinforcement systems have been studied (Broms 2007).
2 Experimental Program
Experimental studies were designed to achieve the objectives of this research. The experimental study included construction and testing of seven half-scale interior slab-column connections reinforced with the same steel bars in two direction top and bottom. The first specimen is considered a reference, the second two specimens made of concrete mixes with different volumetric ratios of polymer fibers. Another three specimens reinforced with different types of punching-shear reinforcement, and the last specimen constructed with drop panel of inverted pyramidal shape. Each specimen had a square plan of side length dimension of 1500 mm and a central column stub of cross section (200 mm × 200 mm) extending 600 mm beyond the top surface of the slabs. The test specimens were supported along all four edges. A concentric load was applied to the slabs through the column stub. Through the experimental program, the effects of the following parameters were investigated: (i) type of additional punching shear reinforcement; (ii) concrete with polymer fiber; (iii) slab thicknesses of 120 and 180 mm by adding pyramidal drop panel. All slabs were designed based on the ACI-421.IR two-way slab systems.
Characteristics and dimensions of the specimens.
Specimen | S1 | S2 | S3 | S4 | S5 | S6 | S7 |
---|---|---|---|---|---|---|---|
Effect | Control | Fiber 0.2% | Fiber 0.3% | Stud-rails | Multi-leg stirrups | Closed stirrups | Drop panel |
Thickness (mm) | 120 | 120 | 120 | 120 | 120 | 120 | 180 |
Effective depth (mm) | 95 | 95 | 95 | 95 | 95 | 95 | 155 |
Top reinforcement spacing (mm) | 200 | ||||||
Bottom reinforcement spacing (mm) | 167 | ||||||
Steel studs spacing (mm) | N/A | N/A | N/A | 60 | N/A | N/A | N/A |
Closed stirrups spacing (mm) | N/A | N/A | N/A | N/A | N/A | 60 | N/A |
Steel studs have a head diameter of 300 mm, shear stud’s shaft diameter of 100 mm, the steel base rail has a thickness of 60 mm with a length of 400 mm and the thickness of 10 mm whereas the total height is 106 mm. The shear studs have a yield strength of 360 N/mm^{2}. The multiple-leg stirrups arranged every 60 mm, and the height of the stirrup is 100 mm and the diameter is 6 mm. The closed stirrups used in slab S6, arranged every 60 mm with a diameter of 6 mm. All slabs have 5ϕ8/m as a top reinforcement and 6ϕ12/m as a bottom reinforcement. The shear studs and stirrups are arranged at a distance of 0.5 d from the column face.
2.1 Material Properties
Concrete mix proportions of 1.0 m^{3}.
Ingredient | Cement (kg) | Fine aggregate (m^{3}) | Coarse aggregate (m^{3}) | Water (kg) |
---|---|---|---|---|
350 | 0.4 | 0.8 | 250 |
Different ratio of polymer fiber on specimen S2 and S3 | |||
---|---|---|---|
Cement (kg) | Cement per specimen (kg) | Fiber per specimen | |
S2 | 350 | 103 | 0.2% = 206 g |
S3 | 350 | 103 | 0.3% = 309 g |
The characteristic yield strength of steel bars was 360 MPa and the mean yield strength of the steel bars was f _{ y } = 382 MPa (obtained from direct tension tests on three specimens). The ultimate strength of the steel bars was f _{ u } = 532 MPa and the average uniform elongation of bars at f _{ u } was ε _{ u } = 11%.
2.2 Test Setup
A vertically oriented hydraulic actuator, connected to a steel reaction frame, is used for application of the load to the slab specimens that shown in Fig. 3. This setup helps to subject the connection to horizontal and vertical loads to create unbalanced moment typical of lateral loads.
3 Results and Discussion
3.1 Load Deflection
Specimen’s cracking load, failure load, and deflection.
Specimens | Cracking load (kN) | Failure load (kN) | Deflection at failure (mm) | Failure mode |
---|---|---|---|---|
S1 | 20 | 130 | 13 | Brittle |
S2 | 22 | 135 | 15.5 | Brittle |
S3 | 23 | 141 | 17 | Brittle |
S4 | 25 | 200 | 22 | Ductile |
S5 | 27 | 220 | 28 | Ductile |
S6 | 30 | 244 | 35 | Ductile |
S7 | 35 | 300 | – | N/A |
3.2 Crack Pattern
Load deflection at different load stages and shear strength.
Slabs | P_{cr} (kN) | Δ_{cr} (mm) | P_{y} (kN) | Δ_{y} (mm) | P_{u} (kN) | Δ_{u} (mm) | V_{u} (measured shear strength) ACI 421-1R (N/mm^{2}) | V_{n} (nominal shear strength) ACI 421-1R (N/mm^{2}) |
---|---|---|---|---|---|---|---|---|
S1 | 20 | 0.5 | 112 | 10.5 | 130 | 13 | 3.00 | 1.83 |
S2 | 22 | 0.5 | 120 | 7.5 | 135 | 15.5 | N/A | N/A |
S3 | 23 | 0.6 | 120 | 8 | 141 | 17 | N/A | N/A |
S4 | 25 | 0.7 | 138 | 7.2 | 200 | 22 | 3.69 | 4.16 |
S5 | 27 | 0.6 | 140 | 6.4 | 220 | 28 | 5.08 | 1.1 |
S6 | 30 | 0.6 | 145 | 9 | 244 | 35 | 5.63 | 1.57 |
S7 | 35 | 0.8 | 185 | 14.5 | 300 | – | 2.97 | 1.83 |
V _{ u } is the factored shear force and M _{ ux } is the unbalanced moment, A _{ c } is the concrete area resisting shear, J _{ c } is the polar moment of inertia. Y is the location where the maximum shear stress is calculated. More details could be found in the ACI 421.1R.
While the nominal shear strength in slabs S1, and S7, where shear reinforcement is not provided, were taken the smallest value of Eqs. 4–7b, 4–8b, and 4–9b in ACI421.1R. The shear strength of slabs with stirrups (S5 and S6) is calculated based on Eq. 4–11 in ACI 421.1R, and finally the nominal shear strength of slab S4 is calculated based on Sec. 4.3.3 in the same document.
3.2.1 Example Slab S4 (Shear Studs Provided)
The critical section perimeter = c + d = 200 + 95 = 295 mm.
Column height = 600 mm.
P _{ u } = 200,000 N.
Table 4 shows the shear strength resisted by concrete for all the slabs except S2, and S3. The predicted values based on the ACI 421-1R (2008) and it is noticed that the percentages of actual/predicted shear strength are varied. The closest prediction was for slab S7 where the actual-to-predicted shear strength was 0.96 and the worst prediction was for slab S4 where the percentage of difference was 0.65.
3.3 Slabs Ductility
Ductility ratio of all specimens.
Slab | Δ _{ y } (mm) | Δ _{ u } (mm) | μ _{ Δ } = Δ _{ u } /Δ _{ y } |
---|---|---|---|
S1 | 10.5 | 13 | 1.238 |
S2 | 7.5 | 15.5 | 2.067 |
S3 | 8 | 17 | 2.125 |
S4 | 7.2 | 22 | 3.056 |
S5 | 6.4 | 28 | 4.375 |
S6 | 9 | 35 | 3.888 |
S7 | 14.5 | – | N/A |
4 Energy Absorption Index (EAI)
EAI and stiffness of all slab specimens.
Slab | A1 | A2 | A1 + A2 | EAI | K _{ i } | K _{ s } |
---|---|---|---|---|---|---|
S1 | 5.88 | 3.25 | 9.13 | 1.55 | 40.0 | 10.7 |
S2 | 4.5 | 10.8 | 15.3 | 3.40 | 44.0 | 16.0 |
S3 | 4.8 | 12.69 | 17.49 | 3.64 | 38.3 | 15.0 |
S4 | 4.97 | 29.6 | 34.57 | 6.96 | 35.7 | 19.2 |
S5 | 4.48 | 47.52 | 52 | 11.61 | 45.0 | 21.9 |
S6 | 6.53 | 63.44 | 69.97 | 10.72 | 50.0 | 16.1 |
S7 | 13.41 | NA | NA | NA | 43.8 | 12.8 |
4.1 Slab Stiffness
Table 6 shows the initial stiffness for all specimens. It is observed that all specimens have almost the same elastic stiffness except S5 (due to stirrups legs) and S7 (due to the larger depth).
5 Conclusions
- 1.
The addition of the pyramid-shaped drop panel in specimen (S7), has led to the increased strength, initial stiffness, and secant stiffness.
- 2.
The initial stiffness of specimens reinforced with stud-rail have increased by about 12.5% compared to the control slab.
- 3.
The secant stiffness for specimens made of fiber concrete S2, and S3 have increased by about 49.5 and 40% relative to the control specimens.
- 4.
In terms of ductility provided by the shear studs layout improved the ductility by a significant percentage (246%) compared to the control slab. Both the shear legs and the closed stirrups provided outperformance of ductility where it was observed to be 353, and 314% respectively.
- 5.
Specimens S5 has the highest energy absorption index (energy dissipation), about 7.5 times of the value of the control specimen S1. Specimens S4 and S6 exhibited energy absorption about 3.8, and 7 times of the value of S1.
- 6.
Finally, the following conclusions on ductility shall be emphasized: The use of fiber concrete has increased the post-crack stiffness only with no ductility, deformability, or energy dissipation enhancements.
- 7.
Good ductility enhancements obtained by using multi-leg and closed stirrups as punching-shear reinforcements, even better than the ductility of the famous stud-rail reinforcement.
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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