Abstract
The present work uses yield-line theory to find the strength of uniformly loaded rectangular reinforced concrete slabs with and without rectangular openings. Five positions of openings are considered, i.e. the slab centre, the slab corner, the centre of a short side, the centre of a long side and the opening eccentric to the slab centre. All possible admissible yield line patterns are considered for all given configurations of the slab subjected to uniformly distributed load keeping in view the basic principles of yield line theory. The ratios of the corresponding lengths of the sides of the opening and the slab are different and sizes of opening up to 0.4× the length of the slab sides are considered. Symmetric edge conditions like continuous slab, simply supported, two long sides continuous and two short sides continuous are considered for various sizes of openings in order to plot the design charts for isotropic reinforcement coefficients only. Affine transformation is also performed for slab with openings.
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Abbreviations
-
: -
Continuous edge
-
: -
Simply supported edge
-
: -
Free edge
-
: -
Negative yield line
- A st :
-
Area of steel
- b :
-
Width of the slab (1000 mm)
- CS:
-
A slab supported on all sides continuously (restrained)
- d :
-
Effective depth
- f ck :
-
Characteristic compressive strength of concrete
- f y :
-
Characteristic strength of steel
- I 1 and I 2 :
-
Negative moment coefficients in their corresponding directions
- I 1 m ult :
-
Negative ultimate yield moment per unit length provided by top tension reinforcement bars placed parallel to x-axis
- I 2 m ult :
-
Negative ultimate yield moment per unit length provided by top tension reinforcement bars placed parallel to y-axis
- K 1 x m ult :
-
Positive ultimate yield moment per unit length provided by bottom tension bars placed parallel to X-axis
- K 1 y m ult :
-
Positive ultimate yield moment per unit length provided by bottom tension bars placed parallel to Y-axis
- L x , L y :
-
Slab dimensions in X and Y directions respectively
- m ult :
-
Ultimate yield moment per unit length of the slab
- M u :
-
Moment of resistance of a section
- M ulim :
-
Limiting moment of resistance of a section without compression reinforcement
- r :
-
Aspect ratio of slab defined by L x /L y
- r 1, r 2, r 3, r 4 :
-
Non dimensional parameters of yield line propagation
- SS:
-
A slab simply supported on all sides
- TLC:
-
A slab restrained on two long edges and other two sides simply supported
- TSC:
-
A slab restrained on two short edges and other two sides simply supported
- UDL:
-
Uniformly distributed load
- W ll :
-
Live load/imposed load per unit area
- W dl :
-
Dead load per unit area
- W ult :
-
Ultimate uniformly distributed load per unit area of slab
- x umax :
-
Limiting value of depth of neutral axis
- α, β :
-
Coefficients of opening in the slab
- μ :
-
Coefficient of orthotropy = \(\frac{{\left[ {K_{x}^{\prime } + I_{1} } \right]}}{{\left[ {K_{y}^{\prime } + I_{2} } \right]}}\)
:
:
:
:References
K.W. Johansen, Yield-Line Theory (Cement and Concrete Association, London, 1962), p. 181
K.W. Johansen, Yield-Line Formulae for Slabs (Cement and Concrete Association, London, 1972)
ACI 421.3R-15, Guide to design of reinforced two-way slab systems. American Concrete Institute, p. 11
British Standards Institution, BS 8110–1: The structural use of concrete—part 1, Code of practice for design and construction. BSI (1997)
IS 456:2000, Indian standard plain and reinforced concrete-code of practice, BIS New Delhi, India
R. Park, W.L. Gamble, Reinforced Concrete Slabs (Wiley, New York, 2000)
S. Islam, R. Park, Yield line analysis of two-way reinforced concrete slabs with openings. J. Struct. Eng. 49(6), 269–275 (1971)
A. Zaslavasky, Yield line analysis of rectangular slabs with central opening. Proc. ACI 64, 838–844 (1967)
K. Rambabu, Yield line analysis of orthotropic rectangular two-way slab supported on four sides with openings. Ph.D. Thesis in Struct. Engg., Vol. 2, Andhra University, India (2001)
K. Rambabu, H.B. Goli, Y.D. Shaik, Application of affine theorem to orthotropic rectangular reinforced concrete slab with unequal corner opening. J. Struct. Eng. 36(3), 202–211 (2009). (India, 2013)
S. Venkata, T. Vara Lakshmi, Analysis and design of orthotropic two-way rectangular slab with long side central opening using yield line analysis. Ph.D. Thesis in Struct. Engg., Andhra University, India (2014)
M. Ravindra, K. Rambabu, H.B. Goli, Application of the affine theorem to an orthotropic rectangular reinforced concrete slab continuous over two adjacent sides and simply supported on other two sides having a short side opening. J. Struct. Eng. 41(2), 116–132 (2009). (India, 2014)
M. Ravindra, Yield-line analysis of two-way reinforced rectangular slab with central short side opening, Ph.D. Thesis in Struct. Engg., Andhra University, India (2015)
C.E. Reynolds, J.C. Steedman, Reinforced Concrete Designers Hand Book (Taylor and Francis, London, 2008). (pp. 31–33, 137–150)
Acknowledgment
The authors acknowledge sincere thanks to Department of Civil Engineering, Andhra University College of Engineering, Visakhapatnam, India for their continuous encouragement and valuable suggestions.
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Ravindra, M., Rakesh, V. & Rambabu, K. A Comparative Study of Strength of Two-Way Rectangular Slabs with and without Openings. J. Inst. Eng. India Ser. A 98, 1–14 (2017). https://doi.org/10.1007/s40030-016-0176-9
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DOI: https://doi.org/10.1007/s40030-016-0176-9