Yield Line Analysis of Reinforced Concrete Slabs with Openings by Dip and Strike Angles Method

Abstract

Using the dip and strike angles method of representing the geometry of yield line pattern in terms of the dip and strike angles of the deflected slab segments, the yield line analysis of reinforced concrete slabs had been successfully computerized. In this study, the dip and strike angles method is generalized for applications to slabs with any number of arbitrary-shaped openings subjected to point, line, patch and uniformly distributed loads. As before, the external work done by applied loads and the internal energy dissipation along yield lines are evaluated as functions of the dip and strike angles, but to allow for the presence of openings, the external work done and internal energy dissipation within the openings are discounted. Based on the principle of virtual work, the load factor is evaluated in terms of the dip and strike angles and the yield line pattern is determined by minimizing the load factor with respect to the dip and strike angles. Examples of slabs with openings under various boundary conditions and loading patterns are presented to illustrate the applicability, efficiency and accuracy of the generalized method.

Keywords

opening reinforced concrete slabs yield line analysis

References

Dickens

J.G.

and Jones

L.L.

(1988). “A general computer program for the yield-line solution of edge supported slabs”, Computers and Structures, Vol. 30, No. 3, pp. 465–476.

Hognestad

(1953). “Yield-line theory for the ultimate flexural strength of reinforced concrete slabs”, ACI Journal, Vol. 49, No. 3, pp. 637–656.

Ingerslev

(1923). “The strength of rectangular slabs”, Journal of Institution of Structural Engineers, Vol. 1, No. 1, pp. 3–14.

Islam

and Park

(1971). “Yield-line analysis of two way reinforced concrete slabs with openings”, The Structural Engineer, Vol. 49, No. 6, pp. 269–276.

Jackson

A.M.

and Middleton

C.R.

(2013). “Closely correlating lower and upper bound plastic analysis of real slabs”, The Structural Engineer, Vol. 91, No. 1, pp. 34–40.

Johansen

K.W.

(1962). Brudlinieteorier, Copenhagen, Denmark. (in Danish) (English translation: Yield Line Theory, Cement and Concrete Association, London, UK.)

Jones

L.L.

(1962). “Recent British advances in yield line analysis by the equilibrium method”, Proceedings of the International Symposium on Flexural Mechanics of Reinforced Concrete, Sawyer, Miami, Florida, USA, pp. 295–381.

Jones

L.L.

and Wood

R.H.

(1967). Yield-Line Analysis of Slabs, Thames and Hudson, London, UK.

Johnson

(1994). “Mechanism determination by automated yield-line analysis”, The Structural Engineer, Vol. 72, No. 19, pp. 323–327.

10.

Johnson

(1995). “Yield-line analysis by sequential linear programming”, Solids and Structures, Vol. 32, No. 10, pp. 1395–1404.

11.

Kennedy

and Goodchild

C.H.

(2004). Practical Yield Line Design, The Concrete Centre, Surrey, UK.

12.

Kumar

and Roy

B.N.

(1991). “Limit analysis of reinforced concrete slabs”, Journal of Structural Engineering (Madras), Vol. 17, No. 4, pp. 127–136.

13.

Kumar

and Prakash

(2001). “Yield line analysis of two way reinforced concrete slabs with central opening”, Journal of Structural Engineering (Madras), Vol. 27, No. 4, pp. 251–262.

14.

Kwan

A.K.H.

(2004). “Dip and strike angles method for yield line analysis of reinforced concrete slabs”, Magazine of Concrete Research, Vol. 56, No. 8, pp. 487–498.

15.

Lash

S.D.

and Banerjee

(1967). “Strength of simply supported square plates with square openings”, Transactions of the Engineering Institute of Canada, Vol. 10, No. 5, pp. 3–11.

16.

Middleton

C.R.

(1997). “Concrete bridge assessment: An alternative approach”, The Structural Engineer, Vol. 75, No. 23–24, pp. 403–409.

17.

Middleton

C.R.

(2008). “Generalised collapse analysis of concrete bridges”, Magazine of Concrete Research, Vol. 60, No. 8, pp. 575–585.

18.

Park

and Gamble

W.L.

(2000). Reinforced Concrete Slabs, 2nd Edition, John Wiley & Sons, New York, USA.

19.

Thavalingam

Jennings

McKeown

J.J.

and Sloan

(1998). “A computerised method for rigid-plastic yield-line analysis of slabs”, Computers and Structures, Vol. 68, No. 6, pp. 601–612.

20.

Thavalingam

Jennings

Sloan

and McKeown

J.J.

(1999). “Computer-assisted generation of yield-line patterns for uniformly loaded isotropic slabs using an optimisation strategy”, Engineering Structures, Vol. 21, No. 6, pp. 488–496.

21.

Zaslavsky

(1967). “Yield-line analysis of rectangular slabs with central openings”, ACI Journal, Vol. 64, No. 2, pp. 838–844.