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## Thursday, July 18, 2019

Modern codes of practice are increasingly recognising the computational power of structural analysis  softwares. Staad Pro is a renowned structural analysis and design software that is used all over the world, and this post is aimed at investigating the analysis of beam and raft foundation using Staad Pro V8i. Winkler's model has been used as a basis for the analysis. This post will help engineers who use Staad Pro to make decisions on whether raft slab can be confidently analysed on Staad Pro V8i environment, or there will be need to move to Staad Foundation, or any other foundation analysis software.

 Fig 1: Winkler's Model
Winkler's model assumes that soil possesses stiffness which is considered to be the ratio of the contact pressure of the soil, and the vertical deformation associated with it. This relationship is assumed to be linear, and can be given by what is called the coefficient of subgrade reaction (ks).

ks = q/S ------------------- (1)

where;
q is the contact pressure at a point in the footing, and
S is the settlement at the same point.

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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
For the beam and raft layout shown in Fig. 3, the necessary data are as follows;

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
Imposed load on building (variable action) = 2 kN/m2
Load at ultimate limit state = 1.35gk + 1.5qk
Coefficient of subgrade reaction ks =  of 20000 kN/m2/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
After analysis of the superstructure on Staad, the following ultimate column axial loads which are transferred to the foundation are shown below;

 Fig 5: Column Loads on the Foundation
From figure 5 above, I believe you can easily model the foundation in another software, or carry out manual analysis for checks of the procedure adopted here.

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

 Fig. 7: Base Pressure
A little consideration will show that we are obtaining a maximum base pressure of 73 kPa at the edges, which might be higher than the bearing capacity of the soil. The engineer is advised to review this properly. However, along grid lines 2 and 3, we have base pressure of 39 kPa which increases towards the edges. The minimum base pressure occurred at the mid-spans.

(2) Moment in the raft slab (x-direction)

 Fig 8: Mx Moment
The bending moment on the raft slab was discovered to be low when compared with the value that could be gotten using the rigid approach (the maximum moment can be seen to be within 10.9 and 13.4 kNm/m)

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(3) Bending moment in the Y-direction

 Fig 9: My 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
What are your thoughts on the values obtained? At your convenience, you can model the raft slab on the software you normally use, and compare the results obtained. You can present your observations in the comment section for review.

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