Fig 1: Winkler's Model |

*k*

_{s}).

*k*

_{s}= q/

*S*------------------- (1)

where;

q is the contact pressure at a point in the footing, and

*S*is the settlement at the same point.

Equation (1) assumes that for granular soils, the value of

*k*

_{s}is independent of the magnitude of pressure, and is the same at all points on the surface of the footing. These two assumptions are however not very accurate for obvious reasons, especially for flexible foundations. There are lots of literature available on the topic of 'coefficient of subgrade reaction', and you are advised to read them up on Google. However, it is accepted that the method gives realistic contact pressures especially when considering very low order of settlement. Coefficient of subgrade reaction is obtained in the field using in-situ plate load test. Plate load tests are usually carried out using (300 x 300) mm plate, and there is usually need to correct the obtained value for the actual width of the foundation (for a quick check of procedure, see page 696 of Murthy, 2012). I will not actually dabble into the accuracy of application of coefficient of subgrade reaction for foundation design in this post, but the reader is advised to consult wide range of literature since opinion on this seems to vary.

[

*Get this publication on Design of Swimming Pools and Underground Water Tanks into your mailbox by clicking HERE or by clicking on the book cover*]In Staad Pro software, the use of Winkler's Model can easily be done by applying 'foundation' support option to the structure in question. Under this option, you can use 'elastic mat' or 'plate mat'. Elastic mat is suitable for beam and plate combination (e.g beam and raft slab in a building) while plate mat is good when you have plate elements only forming the base (e.g base of an underground water tank). For training on how to use Staad Pro efficiently, contact the author on ubani@structville.com

In many parts of Nigeria, beam and raft slab is employed for low-medium rise buildings when the soil has low bearing capacity (usually between 100 kPa and 50kPa) or where providing separate bases will pose so many challenges. For manual analysis of such foundations, the rigid approach is usually used, which yields higher value of internal stresses, while on the other hand, finite element based foundation design softwares can be used, which usually yields lower internal stresses but higher settlement (flexible approach).

In the design of beam and raft slab foundation, it is usually assumed that the column load gets transferred/distributed to the ground beams, and tries to push them down into the soil. This action is resisted by the earth pressure intensity, which is mainly transferred to the ground floor slab. The schematic diagram of this action is shown below.

Fig 2: Load Path of Beam and Raft Foundation |

**Design Example**

As an example, let us consider a two storey building with the foundation layout shown below.

Fig 3: Typical Foundation Layout of Structure |

Ground beam dimensions = 1200 x 250 mm

Thickness of ground floor slab = 150 mm

Dimension of all columns = 230 x 230 mm

First floor slab = 150 mm

First floor beams = 450 x 230 mm

Roof beams = 300 x 230 mm

Additional dead load on floors (finishes and partition allowance) = 2 kN/m

^{2}

Imposed load on building (variable action) = 2 kN/m

^{2}

Load at ultimate limit state = 1.35gk + 1.5qk

Coefficient of subgrade reaction

*k*

_{s}= of 20000 kN/m

^{2}/m (assumed for very soft clay, reference taken from CSC Orion Software)

The 3D view of the frame is shown in Figure 4 below;

Fig 4: 3D Model of the Building |

Fig 5: Column Loads on the Foundation |

When the ground beams and elastic mat foundations are applied on Staad Pro, the results are as follows;

Fig. 6: Typical View of the Structure with Elastic Mat Foundation |

(1) Base Pressure(1) Base Pressure

Fig. 7: Base Pressure |

*(2) Moment in the raft slab (x-direction)*Fig 8: Mx Moment |

[

*Get this publication on Design of Residential Buildings Using Staad, Orion, and Manual Calculations into your mailbox by clicking HERE or by clicking on the book cover*]

*(3) Bending moment in the Y-direction*Fig 9: My Moment |

(4) Twisting Moment(4) Twisting Moment

Fig 10: Mxy Moment |

(5) Bending Moment in the ground beams

Fig 11: Bending Moment Diagram of the Ground Beams |

For simplicity, the maximum design forces have been presented in the table below;

The bending moment on ground beam of grid line (2) is given below;

Fig 12: Bending Moment for Ground Beam Grid line 2 |

Thank you for visiting Structville, and God bless you.

*Citation***Murthy V.N.S (2012)**: Textbook of Soil Mechanics and Foundation Engineering (

*Geotechnical Engineering Series*) 1st Edition. CBS Publishers and Distributors Pvt Ltd, India ISBN: 81-239-162-1

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