Effective reinforcement layout for skew slabs

A Kabir Bangladesh University of Engineering amp Technology Bangladesh S M Nizamud-Doulah Bangladesh Institute of Technology Bangladesh

M Kamruzzaman Bangladesh Institute of Technology Bangladesh

27th Conference on OUR WORLD IN CONCRETE amp STRUCTURES 29 - 30 August 2002

Singapore

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2m Conference on OUR WORLD IN CONCRETE amp STRUCTURES 29 - 30 August 2002 Singapore

Effective reinforcement layout for skew slabs

A Kabir Bangladesh University of Engineering amp Technology Bangladesh S M Nizamud-Doulah Bangladesh Institute of Technology Bangladesh

M Kamruzzaman Bangladesh Institute of Technology Bangladesh

Abstract

Both experimental and numerical study has been carried out to investigate the effects of reinforcement arrangements on the ultimate behaviour 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 behaviour 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

Keywords Skew slabs reinforcement layout reinforced concrete experimental study

1 Introduction Reinforced concrete skew slabs are used in bridges and building floor systems The objective of

this study is to determine the effect of different arrangement of steel reinforcement on the behaviour of reinforced concrete skew slabs For two-way rectangular slabs a typical reinforcement pattern is parallel to the edges i e supports Depending on the geometry and boundary conditions this may not be the best reinforcement orientation especially so in case of skew slabs For skew slabs the sides are not orthogonal and so it is a matter of interest to study the effect of different types of reinforcement schemes to arrive at the best arrangement An experimental investigation was undertaken by Desayi and Prabhakara [1] to predict the load-deflection behaviour of restrained reinforced concrete skew slabs Non-linear analysis of reinforced concrete skew slab bridges has been carried out by Johnarry [2] Cope and Rao (3] EI-Hafez (4] They have also performed experimental investigations in order to provide experimental data and to validate the numerical formulations But none of the researchers studied the effect of reinforcement layout on the load displacement behaviour of reinforced concrete skew slabs In order to get an idea in this regard an investigation was undertaken to study the performance of different types of reinforcement layout Three types of reinforcement scheme were used in this study In type-1 main reinforcement is parallel to the free edge and the transverse reinforcement is parallel to the supported edge In typeshy2 main reinforcement is perpendicular to the supported edge and the transverse is parallel to the supported edge In type-3 main reinforcement is parallel to the free edge and the transverse is perpendicular to the free edge Three slabs were reinforced with these three types of reinforcement and all the bars were hooked at the ends The fourth slab was reinforced with type-2 reinforcement but the main bars for this slab ending at the free edges were welded with additional two bars provided at the free edges The reinforcement types are shown in Fig1

271

-----------------

----------------- ------------ --------------

------------ ------------- - --------------

-- - - - - - - - - - -- - -- ---------------

- --------------- -------------------

- --------------- ------------------- - --------------

III Type 1 Type 2 Type 3

Fig1 Types of Reinforcement

2 Slab Designation The test slabs were designated as S1-501 S2-502 S3-503 and S9-502W All the slabs were

identical in dimension except the reinforcement arrangements The slab S1-501 was reinforced with type-1 reinforcement slab S3-503 with type-3 and slab S2-502 and S9-502W with type-2 The reinforcing bars for slabs S1-501 S2-502 and S3-503 were hooked at the ends and for slab S9-502W the main bars ending at the free edges were welded with two additional bars provided at the free edges Table 1 gives the details of slab dimension angle of skew type of reinforcement and thickness of slab Skew angle is measured between the free edge and the line nonmal to the support A single point load was applied from top at the centre point of the slabs All the slabs had simple supports on two opposite edges Steel ratio in longitudinal direction was 086 percent and that in the transverse direction was 048 percent for all the slabs

Table 1 Details of Test Slabs with Designation

Slab Slab Dimension Type of SlabAngle of Type of Designation (mm) Skew Reinforcement ThicknessLoading

(degree) (mm)Span Width

I IS1-501 1200 1000 40 Type 1One Point 75 ----------------shy------------ I - - - - - - - - - - - - -- ------------shy

S2-502 1200 1000 Type 2 40 One Point 75 _---_-----shy-------------

S3-503 1200 1000 40 One Point Type 3 75 ----------------

S9-502W 1200 1000 40 Type 2 One Point 75i

llote For all slabs clear cover d =15 mm Aspect Ratios r =12 for all slabs

3 Constituent Materials The constituent materials used for the concrete were ordinary Portland cement sand and crushed

stone The fineness modulus of sand was 284 and its specific gravity and unit weight were 261 and 144 kNm 3 (898 Ibft3

) respectively The stone that passed through 191 mm (34) sieve and retained on No4 sieve was used The unit weight and the specific gravity of stone chips were 157 kNm 3 (97 Ibft3) and 270 respectively Defonmed bar reinforcement of 8 mm in diameter were used A number of randomly taken samples were tested in a tensile testing machine following the recommendations of ASTM A 370-88 [5] The average yield strength 0 y was 461 Nmm2 and ultimate strength was 705 Nmm2

272

4 Fabrication of Test Slabs The concrete mix proportion used was 1 21 25 by weight of cement sand and crushed stone

The reinforcing mesh was assembled and properly positioned so that 15-mm clear concrete cover was maintained The concrete was then placed in the formwork and compacted with a nozzle vibrator The control cylinder specimens were cast in a similar way simultaneously with the slab The test slab thus prepared was cured under wet burlaps The formwork was removed after seven days Curing of the slabs and the control specimens were continued for about 5 weeks after casting

5 Experimental Setup The simple support system consisted of two I-joists placed 1200 mm apart on centre The slab

along the support line was held down with the help of clamps specially made to prevent uplifting at the acute angled corners For single point loading the load was spread over a square loading area of 50shymm sides using 12-mm thick steel plates Underneath the steel plate a 15-mm thick hard rubber pad was glued On the top surface of the steel plate a hemispherical groove was formed right at its centre A high strength steel ball of 35-mm diameter was placed into the groove to apply load directly from the piston of the jack to the slabs through the ball The loading arrangement is shown in Fig2 Deflections were recorded at some selected points by means of electrical displacement transducers positioned at the bottom surface of the test slabs

6 Test Procedure The test slab was placed on its supports All the strain gauges were connected to the data logger

through a scanner junction box The deflection transducers were placed at the proper grid pOint locations The test was started applying the load at equal increment of half ton Deflection and strain gauge readings were recorded and stored in the data logger for every load increment The load initiating the first visible crack was recorded The load increment continued and the corresponding data were recorded until the failure load was reached The ultimate stage was assumed to have been reached when the deflection readings were found to increase without any change in the applied load At the end of every slab test the accompanying cylinders were tested for compressive and tensile strengths respectively

Fig 2 Loading Arrangement

273

7 Test Results and Discussion The data recorded for each of the test slabs during experiment were (i) Deflections at some

selected points (ii) Cracking loads and (iii) Failure loads The experimental records of deformations against progressive loading for all the slabs were used to plot the load versus deflection curves The load at the instant of sighting the first crack tenrned as cracking load and the ultimate load at failure were recorded for each test slab and are furnished in Table 2 The representative compressive and tensile strength of concrete obtained from cylinder crushing strengths and the split cylinder tensile strengths respectively are provided in the same table As the load increased the first crack for all the test slabs was found to fonrn on the bottom surface under the load The cracks were more or less confined in the bottom mid-span area and propagated gradually somewhat parallel to the support lines towards the free edges The crack directions were observed to be largely independent of the reinforcement directions The load-deflection behaviour at the centre point for all the slabs is shown in Fig3 The finite element model developed by Nizamud-doulah [6] and also described elsewhere [7] was used to determine the numerical response of these slabs having three types of reinforcement The experimental and the numerical results are compared in Figs4 Sand 6

Table 2 Comparison of Cracking and Failure Loads of the Test Slabs

I Slab Concrete Strength Cracking Load Per Failure Load Pu

Nmm2Designation (kN)I Ir-- ---- --- (kN)

NumericalNumerical ExperimentalExperimentalCompressive I Tensile

378S1-S01 308 29 11S 90 376i I I

I

468S2-S02 I 30S I 29 90 372124 - - --__----shy

I----I 420S3-S03 I 299 29 41S124 90

468474S9-S02W 312 I 31 124 90I I

The four test slabs were ide ntical in all respect except that they differed in the reinforcement arrangements only The experimental results in the form of load-deflection response for these slabs are shown in Fig3 It can be seen from the figure and the Table 2 that the failure load for the slabs S1-S01 S2-S02 and S3-S03 are fairly close Slab S3-S03 with type-3 reinforcement has slightly higher ultimate load compared to the other two This observation indicates that Type-1 Type-2 and Type-3 reinforcements with conventional hooks at the ends are perhaps equally effective and comparable from ultimate load consideration In spite of identical dimension and reinforcement pattern the failure load for slab S9-S02W is about 27 percent higher than the failure load of slab S2-S02 It is also interesting to see from Fig6 that the expe~imental behaviour of the slab S9-S02W correlates better with the numerical response having Type-2 reinforcement compared to the experimental response of slab S2-S02 The main bars ending at the free edges for the slab S2-S02 were merely hooked while the main bars for slab S9-S02W were welded with an extra bar of same size provided along the edge The hooked bars ending at the free edges of slab S2-S02 could not provide enough bond length to develop the required stress level This has resulted in premature failure Welding has provided sufficient bonding of the main steel of slab S9-S02W compared to slab S2-502 and hence the improved performance The lack of bonding of the main bars of type-2 reinforcement at the free edges is also demonstrated comparing the load-deflection response of test slabs S2-S02 and S9-S02W Response of the former (S2-S02) is flexible compared to the latter

Type-1 reinforcement arrangement is most widely used layout in practice and is a natural choice over the other two This is because it is simple and can be fabricated easily The test slab reinforced with type-2 reinforcement layout without any extra care to prevent slip of the main bars at the free edges perfonrns as good as the type-1 in respect of ultimate load carrying capacity Type-3 reinforcement

274

50

40

Z 30 Jt

0 Cl 200

J --- S1-501 -=-S2-502

10 - -(l S3-503 --ltJ- S9-502W

0 0 10 20 30 40 0 10

Deflection mm Deflection mm

Fig3 Load-Deflection Curves for Slabs FigA Load-Deflection Curves for at the Centre (Experimental) Slab S1-501 at the Centre

50

40

30Z Jt

0 Cl 200

J

10

0

----EXP -=-NUM

20 30 40

50

40

Z 30 Jt

0 Cl 200

J

10 ---EXP --NUM

0

50

40

Z Jt 30

0 Cl 0

J 20

10

- shy EXP-S2-502 -NUM U--Q M EXP-S9-502W

o 1

0 10 20 30

Deflection mm 40 0 10 20

Deflection mm 30

Fig5 Load-Deflection Curves for Slab S3-503 at the Centre

Fig6 Load-Deflection Curves for Reinforcement Type-2

layout appears to be more effective compared to type-1 and type-2 without welding However the type-2 layout with provision for sufficient end anchorage of the main bars ending at the free edges is perhaps the most effective steel arrangement for skew slabs The end anchorage may easily be achieved by welding the main bars ending at the free edge to another reinforcing bar or flat bar Thus if reinforcement pattern-2 (ie main reinforcement perpendicular to the support) is selected then sufficient end anchorage should be provided along the free edge lines in order to get the best result

275

8 Conclusion From the present study of skew slabs with pOint loading the following conclus ions may be drawn

(i) Type-1 reinforcement layout is the most common and widely used steel layout in practice even for skew slabs Its preference over the other two types is more because of its ease of fabrication than performance

(ii) Any of the three possible reinforcement layouts (including type-2 without proper anchorage of main steel at free edge lines) performs almost equally well for skew slabs from ultimate strength consideration However slab with type-3 reinforcement fails at slightly higher load and may be considered to have an edge over the other two

(iii) Type-2 reinforcement layout with the main bar tips welded to an extra bar at the free edges is perhaps the most effective and desirable reinforcement layout from both serviceability (load-deflection behavior) and ultimate strength requirement

(iv) Reinforcement layout type-2 should always be used with provision for sufficient end anchorage of the main bars ending at the free edges to get the best performance of skew slabs subject to point loading system An extra bar at the free edges welded to the main bars ensures sufficient anchorage

References [1] Desayi P And Prabhakara A Load Deflection Behaviour of Restrained Reinforced Concrete

Skew Slabs Journal of Structural Div Proceedings of the ASCE May 1981 Vol 107 No ST5 pp 873-888

[2] Johnarry T Elast ic-Plastic Analysis of Concrete Structures Using Finite Elements PhD Thesis University of Strathclyde May 1979

[3] Cope R J and Rao P V Nonlinear Response of Reinforced Concrete Skewed Slab Bridges University of Liverpool 1 Research Report 1981

[4] EI-Hafez LMA Direct Design of Reinforced Concrete Skew Slabs Ph D Thesis University of Glasgow 1986

[5] ASTM A 370 Methods and Definitions for Mechanical Testing of Steel Products American Society of Testing Materials VoI0104 Section-1 Philadelphia 1988 pp 198

[6] Nizamud-doulah S M Nonlinear Analysis of Reinforced Concrete Skew Slabs PhD Thesis Dept of Civil Engineering Bangladesh University of Engineering amp Technology Dhaka June 2000

[7] Nizamud-doulah S M and Kabir A Analysis of Reinforced Concrete Skew Slabs Using Layered Mindlin Plate Element Journal of the Institution of Engineers India Civil Engineering Division Vol 78 November 1997

276

2m Conference on OUR WORLD IN CONCRETE amp STRUCTURES 29 - 30 August 2002 Singapore

Effective reinforcement layout for skew slabs

A Kabir Bangladesh University of Engineering amp Technology Bangladesh S M Nizamud-Doulah Bangladesh Institute of Technology Bangladesh

M Kamruzzaman Bangladesh Institute of Technology Bangladesh

Abstract

Both experimental and numerical study has been carried out to investigate the effects of reinforcement arrangements on the ultimate behaviour 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 behaviour 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

Keywords Skew slabs reinforcement layout reinforced concrete experimental study

1 Introduction Reinforced concrete skew slabs are used in bridges and building floor systems The objective of

this study is to determine the effect of different arrangement of steel reinforcement on the behaviour of reinforced concrete skew slabs For two-way rectangular slabs a typical reinforcement pattern is parallel to the edges i e supports Depending on the geometry and boundary conditions this may not be the best reinforcement orientation especially so in case of skew slabs For skew slabs the sides are not orthogonal and so it is a matter of interest to study the effect of different types of reinforcement schemes to arrive at the best arrangement An experimental investigation was undertaken by Desayi and Prabhakara [1] to predict the load-deflection behaviour of restrained reinforced concrete skew slabs Non-linear analysis of reinforced concrete skew slab bridges has been carried out by Johnarry [2] Cope and Rao (3] EI-Hafez (4] They have also performed experimental investigations in order to provide experimental data and to validate the numerical formulations But none of the researchers studied the effect of reinforcement layout on the load displacement behaviour of reinforced concrete skew slabs In order to get an idea in this regard an investigation was undertaken to study the performance of different types of reinforcement layout Three types of reinforcement scheme were used in this study In type-1 main reinforcement is parallel to the free edge and the transverse reinforcement is parallel to the supported edge In typeshy2 main reinforcement is perpendicular to the supported edge and the transverse is parallel to the supported edge In type-3 main reinforcement is parallel to the free edge and the transverse is perpendicular to the free edge Three slabs were reinforced with these three types of reinforcement and all the bars were hooked at the ends The fourth slab was reinforced with type-2 reinforcement but the main bars for this slab ending at the free edges were welded with additional two bars provided at the free edges The reinforcement types are shown in Fig1

271

-----------------

----------------- ------------ --------------

------------ ------------- - --------------

-- - - - - - - - - - -- - -- ---------------

- --------------- -------------------

- --------------- ------------------- - --------------

III Type 1 Type 2 Type 3

Fig1 Types of Reinforcement

2 Slab Designation The test slabs were designated as S1-501 S2-502 S3-503 and S9-502W All the slabs were

identical in dimension except the reinforcement arrangements The slab S1-501 was reinforced with type-1 reinforcement slab S3-503 with type-3 and slab S2-502 and S9-502W with type-2 The reinforcing bars for slabs S1-501 S2-502 and S3-503 were hooked at the ends and for slab S9-502W the main bars ending at the free edges were welded with two additional bars provided at the free edges Table 1 gives the details of slab dimension angle of skew type of reinforcement and thickness of slab Skew angle is measured between the free edge and the line nonmal to the support A single point load was applied from top at the centre point of the slabs All the slabs had simple supports on two opposite edges Steel ratio in longitudinal direction was 086 percent and that in the transverse direction was 048 percent for all the slabs

Table 1 Details of Test Slabs with Designation

Slab Slab Dimension Type of SlabAngle of Type of Designation (mm) Skew Reinforcement ThicknessLoading

(degree) (mm)Span Width

I IS1-501 1200 1000 40 Type 1One Point 75 ----------------shy------------ I - - - - - - - - - - - - -- ------------shy

S2-502 1200 1000 Type 2 40 One Point 75 _---_-----shy-------------

S3-503 1200 1000 40 One Point Type 3 75 ----------------

S9-502W 1200 1000 40 Type 2 One Point 75i

llote For all slabs clear cover d =15 mm Aspect Ratios r =12 for all slabs

3 Constituent Materials The constituent materials used for the concrete were ordinary Portland cement sand and crushed

stone The fineness modulus of sand was 284 and its specific gravity and unit weight were 261 and 144 kNm 3 (898 Ibft3

) respectively The stone that passed through 191 mm (34) sieve and retained on No4 sieve was used The unit weight and the specific gravity of stone chips were 157 kNm 3 (97 Ibft3) and 270 respectively Defonmed bar reinforcement of 8 mm in diameter were used A number of randomly taken samples were tested in a tensile testing machine following the recommendations of ASTM A 370-88 [5] The average yield strength 0 y was 461 Nmm2 and ultimate strength was 705 Nmm2

272

4 Fabrication of Test Slabs The concrete mix proportion used was 1 21 25 by weight of cement sand and crushed stone

The reinforcing mesh was assembled and properly positioned so that 15-mm clear concrete cover was maintained The concrete was then placed in the formwork and compacted with a nozzle vibrator The control cylinder specimens were cast in a similar way simultaneously with the slab The test slab thus prepared was cured under wet burlaps The formwork was removed after seven days Curing of the slabs and the control specimens were continued for about 5 weeks after casting

5 Experimental Setup The simple support system consisted of two I-joists placed 1200 mm apart on centre The slab

along the support line was held down with the help of clamps specially made to prevent uplifting at the acute angled corners For single point loading the load was spread over a square loading area of 50shymm sides using 12-mm thick steel plates Underneath the steel plate a 15-mm thick hard rubber pad was glued On the top surface of the steel plate a hemispherical groove was formed right at its centre A high strength steel ball of 35-mm diameter was placed into the groove to apply load directly from the piston of the jack to the slabs through the ball The loading arrangement is shown in Fig2 Deflections were recorded at some selected points by means of electrical displacement transducers positioned at the bottom surface of the test slabs

6 Test Procedure The test slab was placed on its supports All the strain gauges were connected to the data logger

through a scanner junction box The deflection transducers were placed at the proper grid pOint locations The test was started applying the load at equal increment of half ton Deflection and strain gauge readings were recorded and stored in the data logger for every load increment The load initiating the first visible crack was recorded The load increment continued and the corresponding data were recorded until the failure load was reached The ultimate stage was assumed to have been reached when the deflection readings were found to increase without any change in the applied load At the end of every slab test the accompanying cylinders were tested for compressive and tensile strengths respectively

Fig 2 Loading Arrangement

273

7 Test Results and Discussion The data recorded for each of the test slabs during experiment were (i) Deflections at some

selected points (ii) Cracking loads and (iii) Failure loads The experimental records of deformations against progressive loading for all the slabs were used to plot the load versus deflection curves The load at the instant of sighting the first crack tenrned as cracking load and the ultimate load at failure were recorded for each test slab and are furnished in Table 2 The representative compressive and tensile strength of concrete obtained from cylinder crushing strengths and the split cylinder tensile strengths respectively are provided in the same table As the load increased the first crack for all the test slabs was found to fonrn on the bottom surface under the load The cracks were more or less confined in the bottom mid-span area and propagated gradually somewhat parallel to the support lines towards the free edges The crack directions were observed to be largely independent of the reinforcement directions The load-deflection behaviour at the centre point for all the slabs is shown in Fig3 The finite element model developed by Nizamud-doulah [6] and also described elsewhere [7] was used to determine the numerical response of these slabs having three types of reinforcement The experimental and the numerical results are compared in Figs4 Sand 6

Table 2 Comparison of Cracking and Failure Loads of the Test Slabs

I Slab Concrete Strength Cracking Load Per Failure Load Pu

Nmm2Designation (kN)I Ir-- ---- --- (kN)

NumericalNumerical ExperimentalExperimentalCompressive I Tensile

378S1-S01 308 29 11S 90 376i I I

I

468S2-S02 I 30S I 29 90 372124 - - --__----shy

I----I 420S3-S03 I 299 29 41S124 90

468474S9-S02W 312 I 31 124 90I I

The four test slabs were ide ntical in all respect except that they differed in the reinforcement arrangements only The experimental results in the form of load-deflection response for these slabs are shown in Fig3 It can be seen from the figure and the Table 2 that the failure load for the slabs S1-S01 S2-S02 and S3-S03 are fairly close Slab S3-S03 with type-3 reinforcement has slightly higher ultimate load compared to the other two This observation indicates that Type-1 Type-2 and Type-3 reinforcements with conventional hooks at the ends are perhaps equally effective and comparable from ultimate load consideration In spite of identical dimension and reinforcement pattern the failure load for slab S9-S02W is about 27 percent higher than the failure load of slab S2-S02 It is also interesting to see from Fig6 that the expe~imental behaviour of the slab S9-S02W correlates better with the numerical response having Type-2 reinforcement compared to the experimental response of slab S2-S02 The main bars ending at the free edges for the slab S2-S02 were merely hooked while the main bars for slab S9-S02W were welded with an extra bar of same size provided along the edge The hooked bars ending at the free edges of slab S2-S02 could not provide enough bond length to develop the required stress level This has resulted in premature failure Welding has provided sufficient bonding of the main steel of slab S9-S02W compared to slab S2-502 and hence the improved performance The lack of bonding of the main bars of type-2 reinforcement at the free edges is also demonstrated comparing the load-deflection response of test slabs S2-S02 and S9-S02W Response of the former (S2-S02) is flexible compared to the latter

Type-1 reinforcement arrangement is most widely used layout in practice and is a natural choice over the other two This is because it is simple and can be fabricated easily The test slab reinforced with type-2 reinforcement layout without any extra care to prevent slip of the main bars at the free edges perfonrns as good as the type-1 in respect of ultimate load carrying capacity Type-3 reinforcement

274

50

40

Z 30 Jt

0 Cl 200

J --- S1-501 -=-S2-502

10 - -(l S3-503 --ltJ- S9-502W

0 0 10 20 30 40 0 10

Deflection mm Deflection mm

Fig3 Load-Deflection Curves for Slabs FigA Load-Deflection Curves for at the Centre (Experimental) Slab S1-501 at the Centre

50

40

30Z Jt

0 Cl 200

J

10

0

----EXP -=-NUM

20 30 40

50

40

Z 30 Jt

0 Cl 200

J

10 ---EXP --NUM

0

50

40

Z Jt 30

0 Cl 0

J 20

10

- shy EXP-S2-502 -NUM U--Q M EXP-S9-502W

o 1

0 10 20 30

Deflection mm 40 0 10 20

Deflection mm 30

Fig5 Load-Deflection Curves for Slab S3-503 at the Centre

Fig6 Load-Deflection Curves for Reinforcement Type-2

layout appears to be more effective compared to type-1 and type-2 without welding However the type-2 layout with provision for sufficient end anchorage of the main bars ending at the free edges is perhaps the most effective steel arrangement for skew slabs The end anchorage may easily be achieved by welding the main bars ending at the free edge to another reinforcing bar or flat bar Thus if reinforcement pattern-2 (ie main reinforcement perpendicular to the support) is selected then sufficient end anchorage should be provided along the free edge lines in order to get the best result

275

8 Conclusion From the present study of skew slabs with pOint loading the following conclus ions may be drawn

(i) Type-1 reinforcement layout is the most common and widely used steel layout in practice even for skew slabs Its preference over the other two types is more because of its ease of fabrication than performance

(ii) Any of the three possible reinforcement layouts (including type-2 without proper anchorage of main steel at free edge lines) performs almost equally well for skew slabs from ultimate strength consideration However slab with type-3 reinforcement fails at slightly higher load and may be considered to have an edge over the other two

(iii) Type-2 reinforcement layout with the main bar tips welded to an extra bar at the free edges is perhaps the most effective and desirable reinforcement layout from both serviceability (load-deflection behavior) and ultimate strength requirement

(iv) Reinforcement layout type-2 should always be used with provision for sufficient end anchorage of the main bars ending at the free edges to get the best performance of skew slabs subject to point loading system An extra bar at the free edges welded to the main bars ensures sufficient anchorage

References [1] Desayi P And Prabhakara A Load Deflection Behaviour of Restrained Reinforced Concrete

Skew Slabs Journal of Structural Div Proceedings of the ASCE May 1981 Vol 107 No ST5 pp 873-888

[2] Johnarry T Elast ic-Plastic Analysis of Concrete Structures Using Finite Elements PhD Thesis University of Strathclyde May 1979

[3] Cope R J and Rao P V Nonlinear Response of Reinforced Concrete Skewed Slab Bridges University of Liverpool 1 Research Report 1981

[4] EI-Hafez LMA Direct Design of Reinforced Concrete Skew Slabs Ph D Thesis University of Glasgow 1986

[5] ASTM A 370 Methods and Definitions for Mechanical Testing of Steel Products American Society of Testing Materials VoI0104 Section-1 Philadelphia 1988 pp 198

[6] Nizamud-doulah S M Nonlinear Analysis of Reinforced Concrete Skew Slabs PhD Thesis Dept of Civil Engineering Bangladesh University of Engineering amp Technology Dhaka June 2000

[7] Nizamud-doulah S M and Kabir A Analysis of Reinforced Concrete Skew Slabs Using Layered Mindlin Plate Element Journal of the Institution of Engineers India Civil Engineering Division Vol 78 November 1997

276

-----------------

----------------- ------------ --------------

------------ ------------- - --------------

-- - - - - - - - - - -- - -- ---------------

- --------------- -------------------

- --------------- ------------------- - --------------

III Type 1 Type 2 Type 3

Fig1 Types of Reinforcement

2 Slab Designation The test slabs were designated as S1-501 S2-502 S3-503 and S9-502W All the slabs were

identical in dimension except the reinforcement arrangements The slab S1-501 was reinforced with type-1 reinforcement slab S3-503 with type-3 and slab S2-502 and S9-502W with type-2 The reinforcing bars for slabs S1-501 S2-502 and S3-503 were hooked at the ends and for slab S9-502W the main bars ending at the free edges were welded with two additional bars provided at the free edges Table 1 gives the details of slab dimension angle of skew type of reinforcement and thickness of slab Skew angle is measured between the free edge and the line nonmal to the support A single point load was applied from top at the centre point of the slabs All the slabs had simple supports on two opposite edges Steel ratio in longitudinal direction was 086 percent and that in the transverse direction was 048 percent for all the slabs

Table 1 Details of Test Slabs with Designation

Slab Slab Dimension Type of SlabAngle of Type of Designation (mm) Skew Reinforcement ThicknessLoading

(degree) (mm)Span Width

I IS1-501 1200 1000 40 Type 1One Point 75 ----------------shy------------ I - - - - - - - - - - - - -- ------------shy

S2-502 1200 1000 Type 2 40 One Point 75 _---_-----shy-------------

S3-503 1200 1000 40 One Point Type 3 75 ----------------

S9-502W 1200 1000 40 Type 2 One Point 75i

llote For all slabs clear cover d =15 mm Aspect Ratios r =12 for all slabs

3 Constituent Materials The constituent materials used for the concrete were ordinary Portland cement sand and crushed

stone The fineness modulus of sand was 284 and its specific gravity and unit weight were 261 and 144 kNm 3 (898 Ibft3

) respectively The stone that passed through 191 mm (34) sieve and retained on No4 sieve was used The unit weight and the specific gravity of stone chips were 157 kNm 3 (97 Ibft3) and 270 respectively Defonmed bar reinforcement of 8 mm in diameter were used A number of randomly taken samples were tested in a tensile testing machine following the recommendations of ASTM A 370-88 [5] The average yield strength 0 y was 461 Nmm2 and ultimate strength was 705 Nmm2

272

4 Fabrication of Test Slabs The concrete mix proportion used was 1 21 25 by weight of cement sand and crushed stone

The reinforcing mesh was assembled and properly positioned so that 15-mm clear concrete cover was maintained The concrete was then placed in the formwork and compacted with a nozzle vibrator The control cylinder specimens were cast in a similar way simultaneously with the slab The test slab thus prepared was cured under wet burlaps The formwork was removed after seven days Curing of the slabs and the control specimens were continued for about 5 weeks after casting

5 Experimental Setup The simple support system consisted of two I-joists placed 1200 mm apart on centre The slab

along the support line was held down with the help of clamps specially made to prevent uplifting at the acute angled corners For single point loading the load was spread over a square loading area of 50shymm sides using 12-mm thick steel plates Underneath the steel plate a 15-mm thick hard rubber pad was glued On the top surface of the steel plate a hemispherical groove was formed right at its centre A high strength steel ball of 35-mm diameter was placed into the groove to apply load directly from the piston of the jack to the slabs through the ball The loading arrangement is shown in Fig2 Deflections were recorded at some selected points by means of electrical displacement transducers positioned at the bottom surface of the test slabs

6 Test Procedure The test slab was placed on its supports All the strain gauges were connected to the data logger

through a scanner junction box The deflection transducers were placed at the proper grid pOint locations The test was started applying the load at equal increment of half ton Deflection and strain gauge readings were recorded and stored in the data logger for every load increment The load initiating the first visible crack was recorded The load increment continued and the corresponding data were recorded until the failure load was reached The ultimate stage was assumed to have been reached when the deflection readings were found to increase without any change in the applied load At the end of every slab test the accompanying cylinders were tested for compressive and tensile strengths respectively

Fig 2 Loading Arrangement

273

7 Test Results and Discussion The data recorded for each of the test slabs during experiment were (i) Deflections at some

selected points (ii) Cracking loads and (iii) Failure loads The experimental records of deformations against progressive loading for all the slabs were used to plot the load versus deflection curves The load at the instant of sighting the first crack tenrned as cracking load and the ultimate load at failure were recorded for each test slab and are furnished in Table 2 The representative compressive and tensile strength of concrete obtained from cylinder crushing strengths and the split cylinder tensile strengths respectively are provided in the same table As the load increased the first crack for all the test slabs was found to fonrn on the bottom surface under the load The cracks were more or less confined in the bottom mid-span area and propagated gradually somewhat parallel to the support lines towards the free edges The crack directions were observed to be largely independent of the reinforcement directions The load-deflection behaviour at the centre point for all the slabs is shown in Fig3 The finite element model developed by Nizamud-doulah [6] and also described elsewhere [7] was used to determine the numerical response of these slabs having three types of reinforcement The experimental and the numerical results are compared in Figs4 Sand 6

Table 2 Comparison of Cracking and Failure Loads of the Test Slabs

I Slab Concrete Strength Cracking Load Per Failure Load Pu

Nmm2Designation (kN)I Ir-- ---- --- (kN)

NumericalNumerical ExperimentalExperimentalCompressive I Tensile

378S1-S01 308 29 11S 90 376i I I

I

468S2-S02 I 30S I 29 90 372124 - - --__----shy

I----I 420S3-S03 I 299 29 41S124 90

468474S9-S02W 312 I 31 124 90I I

The four test slabs were ide ntical in all respect except that they differed in the reinforcement arrangements only The experimental results in the form of load-deflection response for these slabs are shown in Fig3 It can be seen from the figure and the Table 2 that the failure load for the slabs S1-S01 S2-S02 and S3-S03 are fairly close Slab S3-S03 with type-3 reinforcement has slightly higher ultimate load compared to the other two This observation indicates that Type-1 Type-2 and Type-3 reinforcements with conventional hooks at the ends are perhaps equally effective and comparable from ultimate load consideration In spite of identical dimension and reinforcement pattern the failure load for slab S9-S02W is about 27 percent higher than the failure load of slab S2-S02 It is also interesting to see from Fig6 that the expe~imental behaviour of the slab S9-S02W correlates better with the numerical response having Type-2 reinforcement compared to the experimental response of slab S2-S02 The main bars ending at the free edges for the slab S2-S02 were merely hooked while the main bars for slab S9-S02W were welded with an extra bar of same size provided along the edge The hooked bars ending at the free edges of slab S2-S02 could not provide enough bond length to develop the required stress level This has resulted in premature failure Welding has provided sufficient bonding of the main steel of slab S9-S02W compared to slab S2-502 and hence the improved performance The lack of bonding of the main bars of type-2 reinforcement at the free edges is also demonstrated comparing the load-deflection response of test slabs S2-S02 and S9-S02W Response of the former (S2-S02) is flexible compared to the latter

Type-1 reinforcement arrangement is most widely used layout in practice and is a natural choice over the other two This is because it is simple and can be fabricated easily The test slab reinforced with type-2 reinforcement layout without any extra care to prevent slip of the main bars at the free edges perfonrns as good as the type-1 in respect of ultimate load carrying capacity Type-3 reinforcement

274

50

40

Z 30 Jt

0 Cl 200

J --- S1-501 -=-S2-502

10 - -(l S3-503 --ltJ- S9-502W

0 0 10 20 30 40 0 10

Deflection mm Deflection mm

Fig3 Load-Deflection Curves for Slabs FigA Load-Deflection Curves for at the Centre (Experimental) Slab S1-501 at the Centre

50

40

30Z Jt

0 Cl 200

J

10

0

----EXP -=-NUM

20 30 40

50

40

Z 30 Jt

0 Cl 200

J

10 ---EXP --NUM

0

50

40

Z Jt 30

0 Cl 0

J 20

10

- shy EXP-S2-502 -NUM U--Q M EXP-S9-502W

o 1

0 10 20 30

Deflection mm 40 0 10 20

Deflection mm 30

Fig5 Load-Deflection Curves for Slab S3-503 at the Centre

Fig6 Load-Deflection Curves for Reinforcement Type-2

layout appears to be more effective compared to type-1 and type-2 without welding However the type-2 layout with provision for sufficient end anchorage of the main bars ending at the free edges is perhaps the most effective steel arrangement for skew slabs The end anchorage may easily be achieved by welding the main bars ending at the free edge to another reinforcing bar or flat bar Thus if reinforcement pattern-2 (ie main reinforcement perpendicular to the support) is selected then sufficient end anchorage should be provided along the free edge lines in order to get the best result

275

8 Conclusion From the present study of skew slabs with pOint loading the following conclus ions may be drawn

(i) Type-1 reinforcement layout is the most common and widely used steel layout in practice even for skew slabs Its preference over the other two types is more because of its ease of fabrication than performance

(ii) Any of the three possible reinforcement layouts (including type-2 without proper anchorage of main steel at free edge lines) performs almost equally well for skew slabs from ultimate strength consideration However slab with type-3 reinforcement fails at slightly higher load and may be considered to have an edge over the other two

(iii) Type-2 reinforcement layout with the main bar tips welded to an extra bar at the free edges is perhaps the most effective and desirable reinforcement layout from both serviceability (load-deflection behavior) and ultimate strength requirement

(iv) Reinforcement layout type-2 should always be used with provision for sufficient end anchorage of the main bars ending at the free edges to get the best performance of skew slabs subject to point loading system An extra bar at the free edges welded to the main bars ensures sufficient anchorage

References [1] Desayi P And Prabhakara A Load Deflection Behaviour of Restrained Reinforced Concrete

Skew Slabs Journal of Structural Div Proceedings of the ASCE May 1981 Vol 107 No ST5 pp 873-888

[2] Johnarry T Elast ic-Plastic Analysis of Concrete Structures Using Finite Elements PhD Thesis University of Strathclyde May 1979

[3] Cope R J and Rao P V Nonlinear Response of Reinforced Concrete Skewed Slab Bridges University of Liverpool 1 Research Report 1981

[4] EI-Hafez LMA Direct Design of Reinforced Concrete Skew Slabs Ph D Thesis University of Glasgow 1986

[5] ASTM A 370 Methods and Definitions for Mechanical Testing of Steel Products American Society of Testing Materials VoI0104 Section-1 Philadelphia 1988 pp 198

[6] Nizamud-doulah S M Nonlinear Analysis of Reinforced Concrete Skew Slabs PhD Thesis Dept of Civil Engineering Bangladesh University of Engineering amp Technology Dhaka June 2000

[7] Nizamud-doulah S M and Kabir A Analysis of Reinforced Concrete Skew Slabs Using Layered Mindlin Plate Element Journal of the Institution of Engineers India Civil Engineering Division Vol 78 November 1997

276

4 Fabrication of Test Slabs The concrete mix proportion used was 1 21 25 by weight of cement sand and crushed stone

The reinforcing mesh was assembled and properly positioned so that 15-mm clear concrete cover was maintained The concrete was then placed in the formwork and compacted with a nozzle vibrator The control cylinder specimens were cast in a similar way simultaneously with the slab The test slab thus prepared was cured under wet burlaps The formwork was removed after seven days Curing of the slabs and the control specimens were continued for about 5 weeks after casting

5 Experimental Setup The simple support system consisted of two I-joists placed 1200 mm apart on centre The slab

along the support line was held down with the help of clamps specially made to prevent uplifting at the acute angled corners For single point loading the load was spread over a square loading area of 50shymm sides using 12-mm thick steel plates Underneath the steel plate a 15-mm thick hard rubber pad was glued On the top surface of the steel plate a hemispherical groove was formed right at its centre A high strength steel ball of 35-mm diameter was placed into the groove to apply load directly from the piston of the jack to the slabs through the ball The loading arrangement is shown in Fig2 Deflections were recorded at some selected points by means of electrical displacement transducers positioned at the bottom surface of the test slabs

6 Test Procedure The test slab was placed on its supports All the strain gauges were connected to the data logger

through a scanner junction box The deflection transducers were placed at the proper grid pOint locations The test was started applying the load at equal increment of half ton Deflection and strain gauge readings were recorded and stored in the data logger for every load increment The load initiating the first visible crack was recorded The load increment continued and the corresponding data were recorded until the failure load was reached The ultimate stage was assumed to have been reached when the deflection readings were found to increase without any change in the applied load At the end of every slab test the accompanying cylinders were tested for compressive and tensile strengths respectively

Fig 2 Loading Arrangement

273

7 Test Results and Discussion The data recorded for each of the test slabs during experiment were (i) Deflections at some

selected points (ii) Cracking loads and (iii) Failure loads The experimental records of deformations against progressive loading for all the slabs were used to plot the load versus deflection curves The load at the instant of sighting the first crack tenrned as cracking load and the ultimate load at failure were recorded for each test slab and are furnished in Table 2 The representative compressive and tensile strength of concrete obtained from cylinder crushing strengths and the split cylinder tensile strengths respectively are provided in the same table As the load increased the first crack for all the test slabs was found to fonrn on the bottom surface under the load The cracks were more or less confined in the bottom mid-span area and propagated gradually somewhat parallel to the support lines towards the free edges The crack directions were observed to be largely independent of the reinforcement directions The load-deflection behaviour at the centre point for all the slabs is shown in Fig3 The finite element model developed by Nizamud-doulah [6] and also described elsewhere [7] was used to determine the numerical response of these slabs having three types of reinforcement The experimental and the numerical results are compared in Figs4 Sand 6

Table 2 Comparison of Cracking and Failure Loads of the Test Slabs

I Slab Concrete Strength Cracking Load Per Failure Load Pu

Nmm2Designation (kN)I Ir-- ---- --- (kN)

NumericalNumerical ExperimentalExperimentalCompressive I Tensile

378S1-S01 308 29 11S 90 376i I I

I

468S2-S02 I 30S I 29 90 372124 - - --__----shy

I----I 420S3-S03 I 299 29 41S124 90

468474S9-S02W 312 I 31 124 90I I

The four test slabs were ide ntical in all respect except that they differed in the reinforcement arrangements only The experimental results in the form of load-deflection response for these slabs are shown in Fig3 It can be seen from the figure and the Table 2 that the failure load for the slabs S1-S01 S2-S02 and S3-S03 are fairly close Slab S3-S03 with type-3 reinforcement has slightly higher ultimate load compared to the other two This observation indicates that Type-1 Type-2 and Type-3 reinforcements with conventional hooks at the ends are perhaps equally effective and comparable from ultimate load consideration In spite of identical dimension and reinforcement pattern the failure load for slab S9-S02W is about 27 percent higher than the failure load of slab S2-S02 It is also interesting to see from Fig6 that the expe~imental behaviour of the slab S9-S02W correlates better with the numerical response having Type-2 reinforcement compared to the experimental response of slab S2-S02 The main bars ending at the free edges for the slab S2-S02 were merely hooked while the main bars for slab S9-S02W were welded with an extra bar of same size provided along the edge The hooked bars ending at the free edges of slab S2-S02 could not provide enough bond length to develop the required stress level This has resulted in premature failure Welding has provided sufficient bonding of the main steel of slab S9-S02W compared to slab S2-502 and hence the improved performance The lack of bonding of the main bars of type-2 reinforcement at the free edges is also demonstrated comparing the load-deflection response of test slabs S2-S02 and S9-S02W Response of the former (S2-S02) is flexible compared to the latter

Type-1 reinforcement arrangement is most widely used layout in practice and is a natural choice over the other two This is because it is simple and can be fabricated easily The test slab reinforced with type-2 reinforcement layout without any extra care to prevent slip of the main bars at the free edges perfonrns as good as the type-1 in respect of ultimate load carrying capacity Type-3 reinforcement

274

50

40

Z 30 Jt

0 Cl 200

J --- S1-501 -=-S2-502

10 - -(l S3-503 --ltJ- S9-502W

0 0 10 20 30 40 0 10

Deflection mm Deflection mm

Fig3 Load-Deflection Curves for Slabs FigA Load-Deflection Curves for at the Centre (Experimental) Slab S1-501 at the Centre

50

40

30Z Jt

0 Cl 200

J

10

0

----EXP -=-NUM

20 30 40

50

40

Z 30 Jt

0 Cl 200

J

10 ---EXP --NUM

0

50

40

Z Jt 30

0 Cl 0

J 20

10

- shy EXP-S2-502 -NUM U--Q M EXP-S9-502W

o 1

0 10 20 30

Deflection mm 40 0 10 20

Deflection mm 30

Fig5 Load-Deflection Curves for Slab S3-503 at the Centre

Fig6 Load-Deflection Curves for Reinforcement Type-2

layout appears to be more effective compared to type-1 and type-2 without welding However the type-2 layout with provision for sufficient end anchorage of the main bars ending at the free edges is perhaps the most effective steel arrangement for skew slabs The end anchorage may easily be achieved by welding the main bars ending at the free edge to another reinforcing bar or flat bar Thus if reinforcement pattern-2 (ie main reinforcement perpendicular to the support) is selected then sufficient end anchorage should be provided along the free edge lines in order to get the best result

275

8 Conclusion From the present study of skew slabs with pOint loading the following conclus ions may be drawn

(i) Type-1 reinforcement layout is the most common and widely used steel layout in practice even for skew slabs Its preference over the other two types is more because of its ease of fabrication than performance

(ii) Any of the three possible reinforcement layouts (including type-2 without proper anchorage of main steel at free edge lines) performs almost equally well for skew slabs from ultimate strength consideration However slab with type-3 reinforcement fails at slightly higher load and may be considered to have an edge over the other two

(iii) Type-2 reinforcement layout with the main bar tips welded to an extra bar at the free edges is perhaps the most effective and desirable reinforcement layout from both serviceability (load-deflection behavior) and ultimate strength requirement

(iv) Reinforcement layout type-2 should always be used with provision for sufficient end anchorage of the main bars ending at the free edges to get the best performance of skew slabs subject to point loading system An extra bar at the free edges welded to the main bars ensures sufficient anchorage

References [1] Desayi P And Prabhakara A Load Deflection Behaviour of Restrained Reinforced Concrete

Skew Slabs Journal of Structural Div Proceedings of the ASCE May 1981 Vol 107 No ST5 pp 873-888

[2] Johnarry T Elast ic-Plastic Analysis of Concrete Structures Using Finite Elements PhD Thesis University of Strathclyde May 1979

[3] Cope R J and Rao P V Nonlinear Response of Reinforced Concrete Skewed Slab Bridges University of Liverpool 1 Research Report 1981

[4] EI-Hafez LMA Direct Design of Reinforced Concrete Skew Slabs Ph D Thesis University of Glasgow 1986

[5] ASTM A 370 Methods and Definitions for Mechanical Testing of Steel Products American Society of Testing Materials VoI0104 Section-1 Philadelphia 1988 pp 198

[6] Nizamud-doulah S M Nonlinear Analysis of Reinforced Concrete Skew Slabs PhD Thesis Dept of Civil Engineering Bangladesh University of Engineering amp Technology Dhaka June 2000

[7] Nizamud-doulah S M and Kabir A Analysis of Reinforced Concrete Skew Slabs Using Layered Mindlin Plate Element Journal of the Institution of Engineers India Civil Engineering Division Vol 78 November 1997

276

7 Test Results and Discussion The data recorded for each of the test slabs during experiment were (i) Deflections at some

selected points (ii) Cracking loads and (iii) Failure loads The experimental records of deformations against progressive loading for all the slabs were used to plot the load versus deflection curves The load at the instant of sighting the first crack tenrned as cracking load and the ultimate load at failure were recorded for each test slab and are furnished in Table 2 The representative compressive and tensile strength of concrete obtained from cylinder crushing strengths and the split cylinder tensile strengths respectively are provided in the same table As the load increased the first crack for all the test slabs was found to fonrn on the bottom surface under the load The cracks were more or less confined in the bottom mid-span area and propagated gradually somewhat parallel to the support lines towards the free edges The crack directions were observed to be largely independent of the reinforcement directions The load-deflection behaviour at the centre point for all the slabs is shown in Fig3 The finite element model developed by Nizamud-doulah [6] and also described elsewhere [7] was used to determine the numerical response of these slabs having three types of reinforcement The experimental and the numerical results are compared in Figs4 Sand 6

Table 2 Comparison of Cracking and Failure Loads of the Test Slabs

I Slab Concrete Strength Cracking Load Per Failure Load Pu

Nmm2Designation (kN)I Ir-- ---- --- (kN)

NumericalNumerical ExperimentalExperimentalCompressive I Tensile

378S1-S01 308 29 11S 90 376i I I

I

468S2-S02 I 30S I 29 90 372124 - - --__----shy

I----I 420S3-S03 I 299 29 41S124 90

468474S9-S02W 312 I 31 124 90I I

The four test slabs were ide ntical in all respect except that they differed in the reinforcement arrangements only The experimental results in the form of load-deflection response for these slabs are shown in Fig3 It can be seen from the figure and the Table 2 that the failure load for the slabs S1-S01 S2-S02 and S3-S03 are fairly close Slab S3-S03 with type-3 reinforcement has slightly higher ultimate load compared to the other two This observation indicates that Type-1 Type-2 and Type-3 reinforcements with conventional hooks at the ends are perhaps equally effective and comparable from ultimate load consideration In spite of identical dimension and reinforcement pattern the failure load for slab S9-S02W is about 27 percent higher than the failure load of slab S2-S02 It is also interesting to see from Fig6 that the expe~imental behaviour of the slab S9-S02W correlates better with the numerical response having Type-2 reinforcement compared to the experimental response of slab S2-S02 The main bars ending at the free edges for the slab S2-S02 were merely hooked while the main bars for slab S9-S02W were welded with an extra bar of same size provided along the edge The hooked bars ending at the free edges of slab S2-S02 could not provide enough bond length to develop the required stress level This has resulted in premature failure Welding has provided sufficient bonding of the main steel of slab S9-S02W compared to slab S2-502 and hence the improved performance The lack of bonding of the main bars of type-2 reinforcement at the free edges is also demonstrated comparing the load-deflection response of test slabs S2-S02 and S9-S02W Response of the former (S2-S02) is flexible compared to the latter

Type-1 reinforcement arrangement is most widely used layout in practice and is a natural choice over the other two This is because it is simple and can be fabricated easily The test slab reinforced with type-2 reinforcement layout without any extra care to prevent slip of the main bars at the free edges perfonrns as good as the type-1 in respect of ultimate load carrying capacity Type-3 reinforcement

274

50

40

Z 30 Jt

0 Cl 200

J --- S1-501 -=-S2-502

10 - -(l S3-503 --ltJ- S9-502W

0 0 10 20 30 40 0 10

Deflection mm Deflection mm

Fig3 Load-Deflection Curves for Slabs FigA Load-Deflection Curves for at the Centre (Experimental) Slab S1-501 at the Centre

50

40

30Z Jt

0 Cl 200

J

10

0

----EXP -=-NUM

20 30 40

50

40

Z 30 Jt

0 Cl 200

J

10 ---EXP --NUM

0

50

40

Z Jt 30

0 Cl 0

J 20

10

- shy EXP-S2-502 -NUM U--Q M EXP-S9-502W

o 1

0 10 20 30

Deflection mm 40 0 10 20

Deflection mm 30

Fig5 Load-Deflection Curves for Slab S3-503 at the Centre

Fig6 Load-Deflection Curves for Reinforcement Type-2

layout appears to be more effective compared to type-1 and type-2 without welding However the type-2 layout with provision for sufficient end anchorage of the main bars ending at the free edges is perhaps the most effective steel arrangement for skew slabs The end anchorage may easily be achieved by welding the main bars ending at the free edge to another reinforcing bar or flat bar Thus if reinforcement pattern-2 (ie main reinforcement perpendicular to the support) is selected then sufficient end anchorage should be provided along the free edge lines in order to get the best result

275

8 Conclusion From the present study of skew slabs with pOint loading the following conclus ions may be drawn

(i) Type-1 reinforcement layout is the most common and widely used steel layout in practice even for skew slabs Its preference over the other two types is more because of its ease of fabrication than performance

(ii) Any of the three possible reinforcement layouts (including type-2 without proper anchorage of main steel at free edge lines) performs almost equally well for skew slabs from ultimate strength consideration However slab with type-3 reinforcement fails at slightly higher load and may be considered to have an edge over the other two

(iii) Type-2 reinforcement layout with the main bar tips welded to an extra bar at the free edges is perhaps the most effective and desirable reinforcement layout from both serviceability (load-deflection behavior) and ultimate strength requirement

(iv) Reinforcement layout type-2 should always be used with provision for sufficient end anchorage of the main bars ending at the free edges to get the best performance of skew slabs subject to point loading system An extra bar at the free edges welded to the main bars ensures sufficient anchorage

References [1] Desayi P And Prabhakara A Load Deflection Behaviour of Restrained Reinforced Concrete

Skew Slabs Journal of Structural Div Proceedings of the ASCE May 1981 Vol 107 No ST5 pp 873-888

[2] Johnarry T Elast ic-Plastic Analysis of Concrete Structures Using Finite Elements PhD Thesis University of Strathclyde May 1979

[3] Cope R J and Rao P V Nonlinear Response of Reinforced Concrete Skewed Slab Bridges University of Liverpool 1 Research Report 1981

[4] EI-Hafez LMA Direct Design of Reinforced Concrete Skew Slabs Ph D Thesis University of Glasgow 1986

[5] ASTM A 370 Methods and Definitions for Mechanical Testing of Steel Products American Society of Testing Materials VoI0104 Section-1 Philadelphia 1988 pp 198

[6] Nizamud-doulah S M Nonlinear Analysis of Reinforced Concrete Skew Slabs PhD Thesis Dept of Civil Engineering Bangladesh University of Engineering amp Technology Dhaka June 2000

[7] Nizamud-doulah S M and Kabir A Analysis of Reinforced Concrete Skew Slabs Using Layered Mindlin Plate Element Journal of the Institution of Engineers India Civil Engineering Division Vol 78 November 1997

276

50

40

Z 30 Jt

0 Cl 200

J --- S1-501 -=-S2-502

10 - -(l S3-503 --ltJ- S9-502W

0 0 10 20 30 40 0 10

Deflection mm Deflection mm

Fig3 Load-Deflection Curves for Slabs FigA Load-Deflection Curves for at the Centre (Experimental) Slab S1-501 at the Centre

50

40

30Z Jt

0 Cl 200

J

10

0

----EXP -=-NUM

20 30 40

50

40

Z 30 Jt

0 Cl 200

J

10 ---EXP --NUM

0

50

40

Z Jt 30

0 Cl 0

J 20

10

- shy EXP-S2-502 -NUM U--Q M EXP-S9-502W

o 1

0 10 20 30

Deflection mm 40 0 10 20

Deflection mm 30

Fig5 Load-Deflection Curves for Slab S3-503 at the Centre

Fig6 Load-Deflection Curves for Reinforcement Type-2

layout appears to be more effective compared to type-1 and type-2 without welding However the type-2 layout with provision for sufficient end anchorage of the main bars ending at the free edges is perhaps the most effective steel arrangement for skew slabs The end anchorage may easily be achieved by welding the main bars ending at the free edge to another reinforcing bar or flat bar Thus if reinforcement pattern-2 (ie main reinforcement perpendicular to the support) is selected then sufficient end anchorage should be provided along the free edge lines in order to get the best result

275

8 Conclusion From the present study of skew slabs with pOint loading the following conclus ions may be drawn

(i) Type-1 reinforcement layout is the most common and widely used steel layout in practice even for skew slabs Its preference over the other two types is more because of its ease of fabrication than performance

(ii) Any of the three possible reinforcement layouts (including type-2 without proper anchorage of main steel at free edge lines) performs almost equally well for skew slabs from ultimate strength consideration However slab with type-3 reinforcement fails at slightly higher load and may be considered to have an edge over the other two

(iii) Type-2 reinforcement layout with the main bar tips welded to an extra bar at the free edges is perhaps the most effective and desirable reinforcement layout from both serviceability (load-deflection behavior) and ultimate strength requirement

(iv) Reinforcement layout type-2 should always be used with provision for sufficient end anchorage of the main bars ending at the free edges to get the best performance of skew slabs subject to point loading system An extra bar at the free edges welded to the main bars ensures sufficient anchorage

References [1] Desayi P And Prabhakara A Load Deflection Behaviour of Restrained Reinforced Concrete

Skew Slabs Journal of Structural Div Proceedings of the ASCE May 1981 Vol 107 No ST5 pp 873-888

[2] Johnarry T Elast ic-Plastic Analysis of Concrete Structures Using Finite Elements PhD Thesis University of Strathclyde May 1979

[3] Cope R J and Rao P V Nonlinear Response of Reinforced Concrete Skewed Slab Bridges University of Liverpool 1 Research Report 1981

[4] EI-Hafez LMA Direct Design of Reinforced Concrete Skew Slabs Ph D Thesis University of Glasgow 1986

[5] ASTM A 370 Methods and Definitions for Mechanical Testing of Steel Products American Society of Testing Materials VoI0104 Section-1 Philadelphia 1988 pp 198

[6] Nizamud-doulah S M Nonlinear Analysis of Reinforced Concrete Skew Slabs PhD Thesis Dept of Civil Engineering Bangladesh University of Engineering amp Technology Dhaka June 2000

[7] Nizamud-doulah S M and Kabir A Analysis of Reinforced Concrete Skew Slabs Using Layered Mindlin Plate Element Journal of the Institution of Engineers India Civil Engineering Division Vol 78 November 1997

276

8 Conclusion From the present study of skew slabs with pOint loading the following conclus ions may be drawn

(i) Type-1 reinforcement layout is the most common and widely used steel layout in practice even for skew slabs Its preference over the other two types is more because of its ease of fabrication than performance

(ii) Any of the three possible reinforcement layouts (including type-2 without proper anchorage of main steel at free edge lines) performs almost equally well for skew slabs from ultimate strength consideration However slab with type-3 reinforcement fails at slightly higher load and may be considered to have an edge over the other two

(iii) Type-2 reinforcement layout with the main bar tips welded to an extra bar at the free edges is perhaps the most effective and desirable reinforcement layout from both serviceability (load-deflection behavior) and ultimate strength requirement

(iv) Reinforcement layout type-2 should always be used with provision for sufficient end anchorage of the main bars ending at the free edges to get the best performance of skew slabs subject to point loading system An extra bar at the free edges welded to the main bars ensures sufficient anchorage

References [1] Desayi P And Prabhakara A Load Deflection Behaviour of Restrained Reinforced Concrete

Skew Slabs Journal of Structural Div Proceedings of the ASCE May 1981 Vol 107 No ST5 pp 873-888

[2] Johnarry T Elast ic-Plastic Analysis of Concrete Structures Using Finite Elements PhD Thesis University of Strathclyde May 1979

[3] Cope R J and Rao P V Nonlinear Response of Reinforced Concrete Skewed Slab Bridges University of Liverpool 1 Research Report 1981

[4] EI-Hafez LMA Direct Design of Reinforced Concrete Skew Slabs Ph D Thesis University of Glasgow 1986

[5] ASTM A 370 Methods and Definitions for Mechanical Testing of Steel Products American Society of Testing Materials VoI0104 Section-1 Philadelphia 1988 pp 198

[6] Nizamud-doulah S M Nonlinear Analysis of Reinforced Concrete Skew Slabs PhD Thesis Dept of Civil Engineering Bangladesh University of Engineering amp Technology Dhaka June 2000

[7] Nizamud-doulah S M and Kabir A Analysis of Reinforced Concrete Skew Slabs Using Layered Mindlin Plate Element Journal of the Institution of Engineers India Civil Engineering Division Vol 78 November 1997

276