www.iiece.org GJESR RESEARCH PAPER VOL. 1 [ISSUE 1] FEBRUARY, 2014
ISSN:- 2349–283X
Behavior of Reinforced Concrete Skew Slab under Different Loading Conditions *Kanhaiya Lal Pandey
Dept. of Civil Engineering MMM. Engineering College Gorakhpur, India Email: pandeystr@gmail.com ABSTRACT- Behavior of reinforced concrete skew slab under different loading condition is reported in this paper a total of three slabs were tested in structure and concrete laboratory of Madan Mohan Malviya Engineering College Gorakhpur, Uttar Pradesh, India. All the test slabs were full scale model of prototype skew slab having opposite edges simply supported. For all the slabs same steel arrangement was used, Main steel was parallel to free edge and distribution steel was parallel to support line. Aspect ratios 0.625 were selected for study. Centrally and +300 and -300 eccentrically located four point load test with reference to IRC Class B loading were studied, and uniformly distributed load test also carried out. For study skew angle 30° is selected for slab. The experimental observation were limited to observation of vertical displacement at various nodal point, and crack pattern and observing the cracking and ultimate loads Keywords: Skew, Reinforced Concrete, Slabs, Four point loads, Uniformly Distributed load. Ultimate load. Crack pattern INTRODUCTION Skew slab can be defined as a four-sided slab having equal opposite angles other than 90°. Skew angle α is usually measured clockwise from the vertical line perpendicular to the support line of the skew slab. Aspect ratio (r) is defined as the ratio of span to width of the supports. Due to skewness of the structure, the stress and deflection characteristics are quite different from those observed in right bridge deck slabs. Laboratory test facility prescribe that a full scale model be selected which was also found be adequate from dimensional analysis of the model with respect to the prototype The constitutive relation of the model materials was geometrically similar to the one of the prototype, which is important for taking into account the material similitude. For the purpose of geometric similitude between the prototype and the model, all the linear dimensions of the model were scaled from the corresponding dimensions of the prototype by a constant ratio. The four point load was applied on the model through a 20mm thick steel plate to spread the load over an area of 11250mm2 (75×150) at four points with reference to IRC Class B loading. This was done to approximate the tyre effect of the vehicles wheel on prototype with reference to IRC Class B loading. Reinforced concrete skew slabs are widely used in bridge construction when the roads cross the streams and canals at angles other than 90 degrees. They are also used in floor system of reinforced concrete building as well as load
bearing brick buildings where the floors and roofs are skewed for architectural reasons or space limitations. [1] Due to increasing population in India, the demand for more roads and highways are increasing and more of them would require more intersections of roads and highways. To maintain steady flow of traffic in these intersections it will be necessary that they be designed with grade separation, which indicates that more skew slab and deck bridges will be constructed in future. This investigation is an attempt to study the physical behavior of skew slabs more closely and characterize the response observed.
Figure 1; Skew Slab with Four Point Loading Arrangement
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2. REVIEW OF PREVIOUS WORK In 1965 a paper is published by A. COULL, Dept. of Civil Engineering the University of Southampton, England. In this paper a method is presented for the direct stress analysis of orthotropic skew bridge slabs. The method of analysis employs the Principle of Least Work, in conjunction with the assumption that the stress resultants may be expressed as Fourier series in the chord wise coordinate, the coefficients being functions of the span wise position only. A system of oblique co-ordinates is used to simplify the analysis. A paper published By Baidar Bakht In 1988 in ASCE he analyzed a skew bridge of less than 20° skew angle. By the method of bridge analysis that are developed basically for right bridges. He give the procedure for obtaining longitudinal moments with good accuracy in skew slab-ongirder bridges. He obtained that the errors in analyzing skew slab-on-girder bridges as right are not characterized by the angle of skew but by two dimensionless parameters, which depend upon the angle of skew, the spacing and span of girders, and their flexural rigidities relative to the flexural rigidity of the deck slab. He proposed that bridges having (S tan α/L,) less than 0.05 can be analyzed as equivalent right bridges, where S, L, and α are the girder spacing, bridge span, and angle of skew, respectively.[2] In 1990 a paper is presented by Mohammad A. Khaleel and Rafik Y. Itani, Member, ASCE In This paper they presents a method for determining moments in continuous normal and skew slab-and-girder bridges due to live loads. Using the finite element method, 112 continuous bridges are analyzed, each having five pretensions I- girders. The spans vary between 24.4 and 36.6 m (80 and 120 ft.), and are spaced between 1.8 and 2.7 m (6 and 9 ft.) on center. The angle of skew α varies between 0 and 60°. A convergence study is also performed on a control bridge to ensure reliable results. Design parameters are identified and their influence on the load distributions studied. For a skew angle of 60°, maximum moment in the interior girder is approximately 71% of that in a normal bridge; and reduction in maximum bending moment is 20% in the exterior girders, which control the design for a bridge with long span, small girder spacing, and small relative stiffness of girders to slab. It is concluded that the AASHTO distribution of wheel loads for exterior girders in normal bridges underestimates the bending moments by as much as 28%. In august 2001 a paper is presented by A Kabir, S M Nizamud-Doulah, and M Kamruzzaman at 27th Conference on OUR WORLD IN CONCRETE & STRUCTURES Singapore. In this paper he presents empirical formulae for the determination of deflections and design moments in reinforced concrete skew slabs. The formulae are derived from numerical results of finite element analysis based on layered Mindlin plate element formulations. An eight-node isoperimetric Mindlin plate
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element that accounts for transverse shear deformations is used to develop the numerical model. The layered technique is adopted to allow for the progressive development of cracks through the thickness at different sampling points. The non-linear effects due to cracking and crushing of concrete and yielding of steel reinforcement are included in the numerical model. However, the empirical relations are derived on the basis of numerical results up to about 50% of the ultimate loads. This means that the proposed formulae represent the serviceability limit state values during which the overall response is somewhat linear except for the non-linearity effects due to the cracking of concrete. A Kabir, S M Nizamud-Doulah, and M Kamruzzaman presented a paper at 27th Conference on OUR WORLD IN CONCRETE & STRUCTURES Singapore. In this paper both experimental and numerical study has been carried out to investigate the effects of reinforcement arrangements on the ultimate behavior of skew slabs. A total of four skew slabs were experimentally tested in the laboratory. All the slabs were identical in dimension except the reinforcement arrangements. Three types of reinforcement style were used. The reinforcing bars for three slabs were hooked at the ends except in the case of the fourth slab. The main bars for this slab ending at the free edges were welded to an extra bar provided and laid parallel to the two free edges of the slab. The load displacement behavior of these slabs were carefully studied both numerically and experimentally to determine effective reinforcement scheme for skew slabs. Finite element layered Mindlin plate formulation was used to study the numerical response of these slabs. In august 2002 a paper is published by S M NizamudDoulah, A Kabir, Md Kamruzzaman at 27th Conference on OUR WORLD IN CONCRETE & STRUCTURES Singapore on “Behavior of RC skew slabs - finite element model and validation”. And in this paper Numerical material models incorporated in finite element method for the nonlinear analysis of reinforced concrete slabs are briefly described. The model is based on a layered Mindlin plate formulation in which the crosssection is divided into steel and concrete layers with nonlinear properties. Mindlin plate element is used to account for transverse shear deformations. Concrete and steel layers are simulated with eight-node quadrilateral plane stress element. The non-linear effects due to cracking and crushing of concrete and yielding of steel reinforcement are included Experiments on reinforced concrete skew slabs are carried out for validation of the numerical models. Comparison with experimental results indicates good performance of the numerical model. In December 2005 Md. Khasro Miah and Ahsanul Kabir from BUET present a paper in journal of civil engineering. IEB. And they present about the behavior of reinforced concrete skew slabs under vertical
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concentrated loads. A total of six slabs were tested in the Concrete Laboratory of Bangladesh University of Engineering and Technology (BUET), Dhaka. All the test slabs were 1/6th scale models of prototype skew slabs having opposite edges simply supported. The same steel arrangement was used for all the slabs. Main steel was parallel to free edges and distribution steel was parallel to support line. Two aspect ratio viz., 0.85 and 1.50 were selected for the study. Centrally located single concentrated load and four point loads equally spaced across the mid-span were the two types of loading condition studied. Two different skew angles viz., = α 25° and 45° were the other parameters of study. The experimental observations were limited to measurement of deflection at different nodal points, concrete fiber strains at some top and bottom points of the slabs, steel strains, cracking patterns and observing the cracking and ultimate loads. Numerical analysis was also carried out for the test slabs to verify the experimental results. In august 2006 a paper is published by S. N. Tande in 31st Conference on OUR WORLD IN CONCRETE & STRUCTURES Singapore. This paper presents a critical analysis of reinforced concrete skew slabs with clamped edges under different types of loads such as uniformly distributed, concentrated and patch loads. A simplified finite strip approach with higher order function for better accuracy has been used to develop the results for skew slabs in bending. The results are presented both numerically and graphically in the form of distribution coefficients for deflections and bending moments, for aspect ratios 1, 1.5, and 2. The effect of skew has been investigated on behavior of skewed slab subjected to various types of loads. The slabs having skew angles 0 to 60 with increment of 150 are considered. Hence the motivation herein was to find results, which would still yield reasonable accuracy, and find immediate applications. In 2007 a bulletin is published by The University of Illinois named as “Engineering Experiment Station Bulletin Series’’ on the “STUDIES OF HIGHWAY SKEW SLAB-BRIDGES WITH CURBS’’. This bulletin contains studies being made of highway slab- bridges with curbs. Designs, and analyses, based on a difference equation method made for a range of bridges. Normal span lengths range up to about 30 ft., skew angles up to 60 deg. Only a single standard curb and handrail detail is considered in all designs. Tables and curves are given which show the variation of design moments with the bridge dimensions. These moments are compared with the corresponding moments in similar right slab- bridges with curbs. And their test result contains: Maximum Dead Load Moment at Center of Slab, Minimum Dead Load Moment at Center of Slab , Maximum Live Load Moment at Center of Slab ,Secondary Live Load Moment at Center of Slab , Maximum Dead Load Moment in Curb ,.
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Maximum Live Load Moment in Curb. Moments at the centers of skew Slab-bridges of short span. A. Vasseghi, F. Nateghi and M. Pournadaf Haghi In May 2008 published a paper in IJE In this paper Highway bridges are frequently constructed as simple span structures with steel or concrete girders and a cast-inplace concrete deck, spanning from one pier to another. At each end of the simple span deck, a joint is provided for deck movement due to temperature, shrinkage, and creep Bridge deck joints are expensive and pose many problems with regard to bridge maintenance. Elimination of deck joints at the support of multi-span bridges has been the subject of recent studies. Recent researches have led to the development of a design concept and approach for joint less bridges where the expansion joints are replaced with continuous link slabs. Further studies have indicated the proper performance of such bridges under service loading conditions. This paper presents analytical study of seismic behavior and response of a two span bridge connected by link slabs. Three dimensional finite element analyses of straight and skew bridges with skew angles varying from 15 to 60 degrees is performed. Both linear time history and response spectrum analyses method are carried 60 degrees is performed. Both linear time history and response spectrum analyses method are carried displacement demands of the interior bent maybe reduced considerably, if link slab is used in the middle of the bridge instead of an expansion joint. In 2012 Patrick Théoret ; Bruno Massicotte; and David Conciatori present a paper in journal of bridge engineering, ASCE and they aimed to determine bending moments and shear forces, required to design skewed concrete slab bridges using the equivalent-beam method. Straight and skewed slab bridges were modeled using grillage and finite-element models to characterize their behavior under uniform and moving loads with the objective of determining the most appropriate modeling approach for design. A parametric study was carried out on 390 simply supported slabs with geometries covering one to four lane bridges of 3- to 20-m spans and with skew angles ranging from 0 to 60°. The analysis showed that no orthogonal grillages satisfactorily predict the amplitude and the transverse distribution of longitudinal bending moments and shear forces, and can be used for the analysis of skewed slab bridges. Results of the parametric study indicated that shear forces and secondary bending moments increase with increasing skew angle while longitudinal bending moments diminish. Equations are proposed to include, as part of the equivalent-beam method for skew angles up to 60°, the increase of shear forces and the reduction of longitudinal bending moments. Equations are also given for computing secondary bending moments. A simplified approach aimed at determining the corner forces for straight and skewed bridges is proposed as an alternative to a more-refined analysis. The analyses indicated the presence of high vertical shear stresses in the
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vicinity of free edges that justifies suggesting to provide shear reinforcement along the slab free edges. 3. EXPERIMENTAL WORK Three model skew slabs have been experimentally tested in the Concrete and structure Laboratory of Madan Mohan Malviya Engineering College Gorakhpur Uttar Pradesh, India. These investigations have been carried out to study the behavior of reinforced concrete skew slabs subject to four point load with reference to IRC Class B Loading The test slabs are designated as slab SS01 through slab SS03.skew slabs first tested with uniformly distributed load up to the elastic limit and then the same slab were tested with four point loading arrangement with centrally applied load and +300mm and -300mm eccentrically applies load. All the slab which is tested was a constant skew angle of 30°. The size and specification of the slab is given below and the slab thickness was 100 mm for all the test slabs. Skew span of the slab = 1600mm Right span of the slab = 1385.6mm Skew angle = 30° 3.1 Casting of slabs The test slabs were cast using Ordinary Portland Cement, Fine aggregate (F. M. = 2.85) and stone chips 20-mm and 10mm mixed by a constant ratio of 6:4 as coarse aggregate. The aggregate gradation conforms to the zone–III recommendations [IS 546-2000]. The flexural reinforcements used in the test slabs were Fe 5000D and diameter 06 mm. properties viz. actual
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the formwork. Fresh concrete was prepared manually. Immediately after mixing of fresh concrete, the fresh concrete was placed in the form and compacted manually. The top surface was leveled using a wooden float. A total of nine cubes and three prisms of standard size were cast simultaneously as a control specimen for determining the compressive and tensile strength of slab concrete. [3] 3.2 Testing of Slabs Three reinforced concrete skew slabs were tested, each of which was loaded with either uniformly distributed load or four concentrated loads. All the slabs were simply supported on two opposite edges. The test slab was placed on its supports. After checking for any possible damage, all the deflection dial gauges are placed at various nodal points for checking deflection precisely. After all the primary checks, initial zero load readings for the load cell, deflection dial gauges and strain gauges were taken. The test was then continued applying the load at suitable increments, so as to reach the ultimate load in about twelve installments. Loading arrangement for the application of four point loads is shown in Fig. 3 The readings of the load cell, deflection dial gauges were simultaneously read and printed out at 500 kg (5 KN) interval as indicated by dial reading of the testing machine. The process was repeated until the failure load was reached. The ultimate stage was assumed to have been reached when the deflection readings continuously moved on without any significant change in the applied load. The crack widths of some of the prominent cracks were measured at failure. An optical crack measuring device was used for such measurements with accuracy of up to 0.02 mm
The water cement ratio of concrete mix was 0.48 and the concrete mix ratio was 1: 2.30: 2.65 (by weight) of Cement: Sand: Stone Chips. The form works for the test slabs were made of brick wall and boundaries formed with cement, fine sand mixed paste. Boundary angle is precisely formed by the cement paste to make the desired skew slab dimensions. Steel reinforcement was calculated for 1.6 m span prototype slab. Steel for the 1.6 m span models were then appropriately scaled. Typical reinforcement layout of the Slab SS01 is given in Fig. 2. The reinforcement assembly was placed on the base of the prepared formwork for the respective model. Wooden block 20 mm thick were used between the form base and the reinforcement to maintain desired clear cover. The slab models were cast in the concrete laboratory. The formwork for casting was placed on the floor of the laboratory with proper arrangement. Lubricating oil was used to smear the bottom and side of the shutter for its easy removal after hardening of the concrete. The reinforcement mesh was then properly positioned inside
Figure 2. Reinforcement Layout of Skew Slab At the end of every slab test, the accompanying cube cast as control specimens were tested to assess the compressive strengths of concrete respectively. Nine cubes were tested for compression and three prism for flexural
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strength and their respective average value was considered as the representative value of slab concrete strengths. The average test results of the control cube specimens are summarized in Table.1 for the test slabs. Table. 1. Crushing Strength of Cubes
S.
Crushing
Crushing
Remark
No.
Load
Strength
(KN)
(MPa)
1.
790
35.11
2.
800
35.55
All values
3.
710
31.55
greater
4.
738
32.80
than
5.
725
32.22
The
6.
706
31.37
target
7.
730
32.44
mean
8.
718
31.91
strength
9.
714
31.73
31.37 MPa
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4. OBSERVATION AND DISCUSSION ON TEST RESULTS Some basic behavioral observations of the test slabs as noticed and recorded during the experimental investigations are briefly discussed and presented in the following articles: 4.1 Deflection The deflections were measured at some selected location for all the test slabs with the help of deflection dial gauges. The load-deflection response at the central point and +300mm and -300mm eccentric point of all the test slabs for the entire loading history up to failure is shown in Fig. 4-6. This includes slabs supporting both uniformly distributed and four point loads. As expected, the deflection recorded at central nodal point is found to be more in slabs as compared to the other nodal point. Slab thickness remaining constant. Comparing the two types of loading, it was observed that skew slabs supporting four point loads across the mid span deflected less at the centre span than the slabs supporting than slab supporting four points at eccentricity. This is expected as the four point load at centre are somewhat distributed over a central band line compared to the four point load at some eccentricity, thus reducing the point deflection at the centre. The maximum deflection of slabs SS01, SS022, SS03 having identical aspect ratio was found to depend on the loading type. As can be observed from Table 2-4, the deflections at obtuse zones were found to be more than acute zones in slabs SS01, SS02 and SS03 all having aspect ratios less than unity this indicates that the aspect ratio of skew slabs influences the flexibility of acute and obtuse angled zones . 4.1.1. Load Displacement tables Table .2 Load Deflection Table In Case Of Uniformly Distributed Load D/ L
D1
D2
D3
D4
D5
D6
D7
D8
D9
0
8.79
3.55
14.3 1
3.8 3
4.00
1.7 5
5.25
4.10
0.1 3
3.80
8.74
3.85
14.1 0
4.0 1
4.20
2.2 0
5.42
4.20
0.3 5
7.6
8.60
3.94
13.9 0
4.6 3
4.58
2.6 0
5.60
4.45
0.5 0
11.40
8.52
4.11
13.7 6
4.8 6
4.84
2.8 2
5.65
4.60
0.7 2
Figure 3. Load Position -300mm Eccentric
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Table 4. Load Deflection Table In Case of Four Point Load Test (Load Position Is Centric)
Table .3 Load Deflection Table In Case of Four Point Load Test (Load Position Is -300mm Eccentric) D
D1
D2
D3
D4
D5
D6
D7
D8
D9
5.11
8.48
6.17
0.79
10.1
3.53
1.32
1.50
8.68
/L 0
0 5
5.00
8.48
6.24
0.75
10.2
3.68
1.43
1.65
4.90
8.48
6.34
0.70
10.2
4.63
1.45
1.70
4.76
8.48
6.45
0.65
10.5
5.74
1.67
1.90
9.58
5.82
1.88
2.55
9.76
5.98
2.06
2.80
9.93
6.05
2.45
2.90
10.0
0 20
4.64
8.47
6.55
0.60
10.8 5
25
4.61
8.46
6.65
0.56
11.2 1
30
4.58
8.45
6.76
0.50
11.3 0
35
4.53
8.45
6.90
0.48
12.0
4.51
8.45
7.06
0.42
12.9
6.57
2.56
3.70
4.45
8.44
7.26
0.38
13.1
7.03
4.69
4.80
4.30
8.43
7.54
0.28
55
4.20
8.43
7.78
0.24
60
4.11
8.42
7.94
0.21
13.6
D5
D6
D7
D8
D9
0
11.69
3.92
14.15
1.83
4.00
2.40
11.33
5.6
0.77
5
11.65
3.83
14.11
1.84
4.5
2.70
11.40
5.8
1.00
10
11.59
3.79
14.07
1.83
4.55
3.00
11.70
6.00
1.25
15
11.48
3.75
14.06
1.83
4.80
3.20
11.70
6.40
1.43
20
11.39
3.72
14.06
1.83
5.60
3.50
11.70
6.66
1.65
25
11.27
3.70
14.06
1.83
6.25
4.77
12.20
6.90
1.80
30
11.18
3.60
14.04
1.83
6.40
4.80
12.50
7.15
2.00
35
11.07
3.60
14.01
1.83
7.10
4.85
12.90
7.80
3.00
10.6
40
11.04
3.60
13.98
1.83
8.50
4.97
13.55
9.25
3.65
11.8
45
10.84
3.60
13.95
1.86
9.95
5.00
14.22
9.80
4.30
50
10.69
3.57
13.93
1.86
10.70
5.90
14.60
10.30
5.05
55
10.59
3.57
14.01
1.88
11.40
6.30
14.85
10.35
5.25
60
10.35
3.57
14.10
1.88
12.30
6.50
16.10
10.20
7.00
3 7.55
5.67
4.95
5 50
D4
3
0 45
D3
6
0 40
D2
9.10
0 15
D1
8.86
5 10
D/ L
12.9 2
8.52
7.19
4.98
17.7
10.4
8.96
8.98
0
4
22.1
15.0
17.6
14.5
23.5
5
2
5
5
3
0
12.9 6 14.7 8
Figure 5. Load Position +300mm Eccentric Figure 4. Load Position -Centric
These tables show the displacement in vertical direction with respect to the incremental load,
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First of all layer of cube is placed on the skew slab for checking the deflection at uniformly distributed load three layers of cubes is placed on the slab in three steps for checking deflection under uniformly distributed load,
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4.1.2. Load displacement curve
Four point centric load
After that all the cubes is unloaded and four point load testing arrangement is placed on slab as shown in figure 3 for applying load. Manually operated hydraulic jack is used to apply incremental load.
18
DEFLECTION(mm)
16
Load is applied at an increment of 5KN. Table 5. Load Deflection Table In Case Of Four Point Load Test (Load Position Is +300mm eccentric)
14 12 10 8 6 4 2
D/ L
0
D1
D2
D3
D4
D5
D6
D7
D8
D9
0.00
11.40
5.41
1.29
8.55
6.55
5.65
10.35
3.80
0
10
20
30
40
50
D5
60
Load()KN 0
5
0.10
11.44
5.40
1.30
8.68
7.75
5.70
10.40
3.95
10
0.50
11.47
5.39
1.32
8.70
8.15
5.81
10.45
4.20
15
0.60
11.48
5.16
1.33
8.75
8.45
5.90
11.47
5.00
20
0.70
11.48
4.54
1.34
8.78
8.70
6.14
11.50
5.40
25
0.72
11.49
3.95
1.34
8.85
8.85
6.20
12.15
5.55
D1
D2
D3
D4
D6
D7
D8
D9
Figure 6. Load Deflection Curve for U.D.L
Four point load test , eccentricity -300mm 25
30
35
0.75
0.75
11.49
11.50
3.90
3.89
1.35
1.36
9.10
1025
9.00
10.10
6.50
7.00
12.50
13.40
6.00
7.05
40
0.77
11.52
3.85
1.36
12.15
10.40
8.03
13.80
8.55
45
0.78
11.53
3.80
1.40
14.05
11.95
10.55
15.60
10.18
50
1.05
11.53
3.72
1.49
14.15
27.85
11.50
16.95
12.55
55
1.50
11.60
3.65
1.50
16.68
29.45
13.40
17.65
12.95
Deflectiodn(mm)
20
15
10
5
0 0
10
20
30
40
50
D6
60
Load(KN)
60
2.05
11.70
3.50
1.65
16.98
30.64
14.50
29.15
16.25
D1
D2
D3
D4
D7
D8
D9
D5
Figure 7. Four Point Load Test Eccentricity -300mmm
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Load deflection curve for UDL
Load position/ Slab designation SS01 SS02 SS03
25 20
Axis Title
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Tables 6.Cracking Load for Skew Slabs for Four Point Loading
15 10 5
centric
Eccentric -300mm
Eccentric +300mm
37 40 38
33 32 35
32 35 34
0 0
2
4
6
8
10
12
Axis Title D1
D2
D3
D4
D6
D7
D8
D9
The load at failure condition recorded for each test slab is defined as the ultimate load shown in Table
D5
7.The ultimate loads of the slabs with centric loading were also higher compared to slabs with eccentric loading for the same skew angle
Figure 8. Four Point Load Test -Centric
Tables 7. Ultimate Load for Skew Slabs for Four Point Loading
Four point load test .eccentricity +300mm
Load position/ Slab designation SS01 SS02 SS03
25
20
Deflection (mm)
4.3 Ultimate Load Carrying Capacity
15
centric
Eccentric -300mm
Eccentric +300mm
77 75 79
71 74 70
69 72 74
4.4 Cracking patterns
10
5
0 0
10
20
30
40
50
D5
60
Load(KN) D1
D2
D3
D4
D6
D7
D8
D9
Figure 9. Four Point Load Test Eccentricity +300mmm 4.2 cracking load The load at the first visible crack termed as cracking load was recorded for each test slab and are furnished in Table 6... Cracks were observed in the test slabs between 40-50 percent of the respective ultimate loads. For the same skew angle, the cracking load of the slabs with centric four point loading were higher compared to slabs with eccentric four point loading.
The cracking patterns of all the test slabs were observed and photograph taken after test. Loading system on the skew slabs appears to have significant influence on the crack patterns. The first crack was always observed at concrete bottom surface near the mid span. For four point loading, a number of cracks originated from the bottom of mid span area and propagated nearly parallel to the support lines towards the free edges like a mesh crack. In case of four-point loading representing an area load at four points, the cracks were limited within a narrow band of centre span. The widths of the major cracks were measured at failure load by an optical crack-measuring device. The cracking patterns at the bottom surface of two test slabs are shown in Fig. 8 and Fig. 9. The crack widths of the prominently visible cracks at failure were measured. Crack width as large as 7 mm was recorded for slabs SS03 and SS02 and 6mm for SS01.It may be noted that relatively wider cracks were observed in case of four-point loading representing knife-edge loading.
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(ii)
The deflection at obtuse zone is more than acute zone in slabs with lower aspect ratio (r = 0...625) uplift of acute corners also occurred when aspect ratio is low as in this case.
(iii)
Cracks propagate toward free edges like a mesh crack and somewhat parallel to support line in case of a four point loading condition.
(iv)
Cracks are limited within a small bandwidth parallel to support line along centre span for multiple point loads placed across the centre span. REFERENCES
1.
AASHTO (1983). ″Standard Specification for Highway the
Figure 10.Crack at Mid-Point Parallel to the Supports
Figure 11.Failure at Mid-Point Parallel to the Supports 5. CONCLUSIONS The following conclusions may be drawn based on the observations of the present experimental study: (i)
For the same aspect ratio and skew angle, the ultimate (total) load carrying capacity of skew slabs are higher in case when the loads are distributed across the width like that of four point centric loads as compared to the four point eccentric loading.
Bridges″ 13 edition, American Association of State Highway and Transportation Officials, Washington. 2. ASTM C 136 (1988). Test method for Sieve Analysis of Fine and Course Aggregates, Vol. 04.02, Section-4, American Society of Testing Materials, Philadelphia, pp. 76. 3. Cope, R. J. and Rao, P. V. (1983). Moment Redistribution in Skewed Slab Bridge, Proc. Instn. Of Civil Engineers, Part 2, Vol. 75, September, pp. 419451. 4. Desayi, P. and Probhakara, A. (1981). load Deflection Behavior of Restrained R/C Skew Slabs, Journal of the Structural Division ASCE, 107, No. ST5, May, pp. 873 – 887. 5. Doullah, Sk. Md. Nizam-ud and Kabir A. (1997). Analysis of Reinforced Concrete Skew Slabs using Layered Mindlin Plate Element, J. of Inst. of Engineers (India), 78, pp. 97-102, Nov. 6. Doullah, Sk. Md. Nizam-ud (2000). Nonlinear Finite Element Analysis of Reinforced Concrete Skew Slabs, Ph. D. Thesis, Department of Civil Engineering, BUET, Dhaka. 7. El-Hafez, L.M.A., (1986). Direct Design of Reinforced Concrete Skew Slabs, Ph.D. Thesis, University of Glasgow, UK. 8. Islam, N. M. (1996). Ultimate Load Behaviour of Skew Slab Bridge Deck, M. Sc. Engineering Thesis, Department of Civil Engineering, BUET, Dhaka. 9. Engineering Thesis, Department of Civil Engineering, BUET, Dhaka. 10. Zia, P., White, R. N. and Vanhorn, D. A. (1970). Principles of Model Analysis, ACI Special Publication SP-24, American Concrete Institute, Detroit, Michigan, pp. 19-39 11. Jahan, S. M. (1989). Investigation of Skew Slab Bridge, M. Sc. Engineering Thesis, Department of Civil Engineering, BUET, Dhaka. 12. Miah, M. K. (2000). Behavior of Reinforced Concrete Skew Slab under Vertical Loads, M. Sc.
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ISSN:- 2349–283X
13. Jeanty, P.R. et al. 1988. Investigation of ‘‘Top Bar’’ Effects in Beams. ACI Structural Journal, Proceedings Vol. 85, No. 3, Detroit, Michigan, February 1988. 14. ECP 203-2007. Egyptian Building Code for Structural Concrete Design and Construction. Ministry of Housing, 2007. 15. ACI 318-05, 2005. Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute, Michigan, 2005.
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