DeSMOn – Deflection Strip Method Online
A program for the calculation of bending moments in a two-way reinforced concrete slab at the service limit state using the Deflection Strip Method
Author: Jakub Holan, Radek Štefan
Inputs
m
m
Legend
fis the value of a uniformly distributed total load (i.e. including dead load) in kN/m2.
Lais the vertical side of the slab.
Lbis the horizontal side of the slab.
iiis the ration between the support moment at side i and the maximal sagging mid-span moment in the corresponding direction (i.e. mi/mspan);
i = 0 for rotationally free support (i.e. hinge support);
i > 0 for rotationally resistant support (i.e. continuous (fixed) support, cantilever, etc.),
i = (1/12)/(1/24) = 2 for a member supported by continuous (fixed) supports on both sides,
i = (1/8)/(9/128) = 16/9 for a member supported by a free (hinge) support and a continuous (fixed) support.
For more see [1].
Lais the vertical side of the slab.
Lbis the horizontal side of the slab.
iiis the ration between the support moment at side i and the maximal sagging mid-span moment in the corresponding direction (i.e. mi/mspan);
i = 0 for rotationally free support (i.e. hinge support);
i > 0 for rotationally resistant support (i.e. continuous (fixed) support, cantilever, etc.),
i = (1/12)/(1/24) = 2 for a member supported by continuous (fixed) supports on both sides,
i = (1/8)/(9/128) = 16/9 for a member supported by a free (hinge) support and a continuous (fixed) support.
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 first be specified.In terms of the slab loading, the value of the total uniformly distributed load (including the dead load) in kN/m2 must be specified.
In terms of the slab geometry, both dimensions and support conditions must be specified. All supports are assumed to be ideally fixed in the horizontal and vertical direction. However, the resistance to rotation of each support must be specified by the designer. 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). For example, in a simple beam, the fixity ratio of each support is 0 since 0/(1/8)=0. In a beam with one simple (free) support and one fixed support, the fixity ratio of the fixed support is 16/9 since (1/8)/(9/128)=16/9. In a fixed beam, the fixity ratio of each support is 2 since (1/12)/(1/24)=2.
Background information
The DeSMOn program employs a code based on the equations derived by Holan and Štefan [1]. For detailed information regarding the program algorithm see [1]. For detailed information regarding the Strip method and its use see [2,3].References
[1] 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. Under preparation.[2] Park R. and Gamble W. L. (1999) Reinforced concrete slabs. Ed. 2, John Wiley & Sons, Inc., ISBN 978-0-471-34850-4.
[3] Hillerborg A. (1960) A Plastic Theory for the Design of Reinforced Concrete Slabs. Proceedings, 6th Congress of International Association of Bridge and Structural Engineering, Stockholm.
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.