YLiDOn – Yield Line Design Online
A program for the calculation of bending moments in a two-way reinforced concrete slab at the ultimate limit state using the Yield Line Theory
Author: Jakub Holan, Radek Štefan
Inputs
Slab geometry and supports
m
m
Slab load
Legend
fis the value of a uniformly distributed total load (i.e. including dead load) in kN/m2.
αis the ration between the maximal sagging moment in the a direction and the maximal sagging moment in the b direction. This value can be chosen arbitrarily by the designer or calculated using the Equal Deflection Strip Method [2].
γis a safety coefficient which increases the calculated moments by the factor of γ. Minimal recommended value is 1.1 [1]. Value used in the standard is 1.35 [3].
Lais the shorter side of the slab.
Lbis the longer side of the slab.
iiis the ration between the support moment at side i and the maximal sagging moment in the corresponding direction (i.e. mi/mspan);
i = 0 for rotationally free support (i.e. hinge support);
i > 0 for for rotationally resistant support (i.e. continuous (fixed) support, cantilever, etc.).
For more see [1].
αis the ration between the maximal sagging moment in the a direction and the maximal sagging moment in the b direction. This value can be chosen arbitrarily by the designer or calculated using the Equal Deflection Strip Method [2].
γis a safety coefficient which increases the calculated moments by the factor of γ. Minimal recommended value is 1.1 [1]. Value used in the standard is 1.35 [3].
Lais the shorter side of the slab.
Lbis the longer side of the slab.
iiis the ration between the support moment at side i and the maximal sagging moment in the corresponding direction (i.e. mi/mspan);
i = 0 for rotationally free support (i.e. hinge support);
i > 0 for for rotationally resistant support (i.e. continuous (fixed) support, cantilever, etc.).
For more see [1].
Module 1 - Bending moments
Moments in the b-axis direction
Module 2 - Reinforcing bars (Rebar)
mm
MPa
MPa
mm
Instructions
In order to carry out the calculations, the slab geometry and loading must be specified.First, the dimensions of the slab must be specified, where the dimension Lb must be greater than the dimension La. Then, the support conditions must be specified. The supports are assumed to be ideally fixed in the horizontal and vertical direction. However, the resistance to rotation of each support must be specified. The resistance is expressed using the fixity ratio, which is a ration between the hogging moment at the support i and the maximal sagging moment in the corresponding direction (i.e. mi/mspan).
In terms of the slab loading, not only the load but also the moments ratio and safety coefficient must be specified. The moments ratio is the ration between the maximal sagging moment in the a direction and the maximal sagging moment in the b direction. This value can be chosen arbitrarily by the designer or calculated using the Equal Deflection Strip Method [2]. Safety coefficient γ is a coefficient which increases the moments calculated using the Yield Line Theory by the factor of γ. The calculated moments should be increased as the Yield Line Theory is a upper boundary method, which means that bending moments in a real structural membet will be higher or equal to the calculated bending moments. Minimal recommended value of the safety coefficient is 1.1 [4].
Background information
The YiLiDOn program employs a code based on the equations derived by Holan and Štefan [1,2]. For detailed information regarding the program algorithm see [1]. For detailed information regarding the Yield Line Theory and its use for the design of reinforced concrete slabs see [3,4].References
[1] Holan J. and Štefan R. (2020) Bending moments in an orthotropic reinforced concrete slab using Yield Line Theory. Not yet published - contact the authors for more information.[2] Holan J. and Štefan R. (2020) Bending moments in a slab with arbitrarily rotationally-resistant supports using a Deflection Strip Method: A web-based application. Not yet published - contact the authors for more information.
[3] Johansen K. W. (1972) Yield-line formulae for slabs. E. & F. N. Spon, ISBN 978-1138470392.
[4] Kennedy G. and Goodchild C. H. (2004) Practical Yield Line Design. The Concrete Centre, ISBN 1-904818-08-0.
Authors: Jakub Holan, Radek Štefan
jakub.holan@fsv.cvut.cz, radek.stefan@fsv.cvut.cz
This work was supported by the Grant Agency of the Czech Technical University in Prague, project no. SGS20/041/OHK1/1T/11.
jakub.holan@fsv.cvut.cz, radek.stefan@fsv.cvut.cz
This work was supported by the Grant Agency of the Czech Technical University in Prague, project no. SGS20/041/OHK1/1T/11.