Example (6.1): Analysis and design of a raft for a high rise building
Introduction
The presence of the structure on compressible subsoil causes
settlements for the foundation and also for the structure itself. Values of settlements and
settlement differences depend not only on the thickness of the compressible soil layer under the
foundation, the value and distribution of structure loads, the foundation depth and contact pressure
under the foundations but also on the flexural rigidity of the structure.
One of the properties that has a considerable influence on
the development of settlement is the rigidity of the superstructure. The more rigid structure has
more uniform settlement and conversely, structure that is more flexible has greatest
difference in settlement. The entire structure can be defined as the three media: superstructure,
foundation and soil. The analysis of the entire structure as one unit is very important to find
the deformations and internal forces.
However, most of the practical analyses of structures
neglect the interaction among the three media to avoid the three-dimensional analysis and modeling.
The structure is designed on the assumption of non-displaceable supports while the foundation
is designed on the assumption that there is no connection between columns. Such accurate
analysis of the entire structure is extremely complex.
The early studies for consideration the effect of the
superstructure were by *Meyerhof
*(1953) who suggested an approximate method to evaluate the
equivalent stiffness that includes the combined effect of the superstructure and the strip beam
foundation. *Kany *
(1959) gave the flexural rigidity of a multi-storey frame structure by an
empirical formulae. Also, *Kany
*(1977) analyzed the structure with foundation using a direct
method. *Demeneghi *
(1981) used the stiffness method in the structural analysis.
*Panayotounakos/ Spyropoulos/
Prassianakis *(1987) presented an exact matrix solution for the static analysis
of a multi-storey and multi-column rectangular plexus frame on an elastic foundation in the
most general case of response and loading.
At the analysis of foundations with considering the
superstructure stiffness, it is required to distinguish between the analysis for plane structures
(two-dimensional analysis) and that for space structures (three-dimensional analysis). Further, it
is required to distinguish between approximation methods with closed form equations (*Kany
*(1974),
*Meyerhof *
(1953),
*Sommer
*(1972)) and refined methods such as conventional plane or
space frame analysis (*Kany *
(1976)), *
Finite Elements *(*Meyer
*(1977),
*Ellner/ Kany *
(1976), Zilch (1993),
*Kany/ El Gendy *
(2000)) or *
Finite Differences *(*Bowles
*(1974),
*Deninger *
(1964)).
In addition, many analytical methods are reported for
analysis of the entire structure as one unit by using the finite element.
For examples:
*
**Haddadin *(1971)
presented an explicit program for the analysis of the raft on Winkler's foundation including the effects of superstructure rigidity.
*
**Lee/ Browen *(1972)
analyzed a plane frame on a two-dimensional foundation.
*
**Hain/ Lee *(1974)
employed the finite element method to analyze the flexural behavior of a flexible raft foundation taking into account stiffness
effect of a framed superstructure. They proposed the use of substructure techniques with finite
element formulation to model space frame-raft-soil systems. The supporting soil was represented
by either of two types of soil models (Winkler and half-space models).
*
**Poulos *(1975)
formulated the interaction of superstructure and foundation by two sets of equations. The first set links the behavior of the structure
and foundation in terms of the applied structural loads and the unknown foundation reactions. The
second set links the behavior of the foundation and underlying soil in terms of the unknown
foundation reactions.
*
**Mikhaiel *(1978)
considered the effect of shear walls and floors rigidity on the foundation.
*
**Bobe/ Hertwig/ Seiffert *
(1981) considered the plastic behavior of the
soil with the effect of the superstructure.
*
**Lopes/ Gusmao *(1991)
analyzed the symmetrical vertical loading with the effect of the superstructure.
*
**Jessberger/ Yuan/ Thaher/ Ming-bao *
(1992) considered the effect of the
superstructure in case of raft foundation on a group of piles.
*
**Zilch *(1993) proposed
a method for interaction of superstructure and foundation via iteration.
*
**Kany/ El Gendy *(2000)
proposed an iterative procedure to consider the effect of superstructure rigidity on the foundation. In the procedure, the stiffness
of any substructure such as floor slab or foundation, connected by the columns can be represented
by equivalent spring constants due to forces and moments at the connection nodes. Consequently
the stiffness matrices of the slab floors, columns and foundation remain unaffected during the
iteration process.
**
**Description of the problem
This example was carried out to show the influence of
flexure rigidity of the superstructure on the settlements, contact pressures for a raft of high rise
building. It is required to analysis a raft for the building shown in
Figure (6.6) in three simplified sections. The building is a reinforced concrete skeleton
structure consists of a cellar and 13 storeys. The floor height is 3 [m] while the bay width is
3.6 [m]. The number of bays is 18. The total building length is 66 [m] while the total width of the
cellar basement is 17.55 [m]. The raft thickness is 1.2 [m]. In the following study the raft is
analyzed considering subsoil behavior.
Also, a simplification estimation of the superstructure
deformations is carried out. In the analysis, settlements and contact pressures are determined
in which a comparison is carried out in four cases as:
i) For not stiffened raft
ii) For compound system raft-cellar
iii) For compound system raft-cellar-superstructure
iv) For completely rigid raft
The stiffness of the structure system parallel to the long
axis can be determined from the data given in Figures (6.6) and (6.7). |