CE421 REINFORCED CONCRETE

STRUCTURE DESIGN

FOUNDATIONS

FOUNDATIONSThe loads of the building are transferred to the soil through foundations. The sizes

and type of the foundation should be chosen so as,

• to ensure structural safety of the foundation (no damage at the foundation),

• to ensure that there is no settlement (no excess of the bearing capacity of soil),

• to provide economy.

The first step for the design of foundation is correct determination of soil properties

(i.e. by soil survey at the site).

FOUNDATIONSThe stress distribution under the foundation depends on,

• type of loading (loads transferred through the foundation),

• type of soil,

• rigidity of the foundation.

It is important to ensure that the max. stress under the foundation is smaller than the bearing capacity (allowable stress) of the soil (σz,max.≤ σz,allow.).

FOUNDATIONSThe types of foundations,

1. Shallow foundations

a. Wall Footings: a continuous strip along the length of wall having a width larger than the wall thickness.

FOUNDATIONSThe types of foundations,

b. Independent Isolated Column (Single) Footings: isolated rectangular or square slabsunder the column. The length of all sides from the column face to the edge of foundationmay be different (due to presence of the bending moments). They are reinforced alongboth directions and economical solution for relatively small loads.

FOUNDATIONSThe types of foundations,

c. Combined Column Footings: support two or more columns. They are used to provide a uniform stress distribution over the soil. If the geometric center of the footing slab and location of the resultant forces transferred by the columns coincide, this uniform stress distribution can be achieved. They may also be used if the columns are too close to each other.

FOUNDATIONSThe types of foundations,

d. Strap Footings: transfers the loads of two or more columns/shear walls to the groundsafely. The straps may be either one-way or two-way. They are much more effectivecompared to isolated columns, especially when subjected to earthquake loads (i.e. Whenconsiderable bending moments are transferred by the column). Besides, thesefoundations prevent relative settlement, which may be a problem in case of isolatedfootings.

One-way strap footings Two-way strap footings

FOUNDATIONSThe types of foundations,

e. Raft (Mat) Foundations: When the allowable bearing capacity of the soil is low and/orthe loads that are transferred from the building are high, the use of raft foundations maybe necessary. The loads from the columns/shear walls are distributed over a large area ofsoil and relative support settlements are prevented. Also, if the ground water level ishigh, then mat foundation with water proofing may be ideal. The mat foundation may beassumed as an inverted floor system.

L (1/4~1/5)L

MAT FOUNDATIONSThe analysis and design of mat foundations are performed by assuming these systems:

a. Rigid

b. Flexible

Rigid Foundation Assumption: It is assumed that the rigidity of the foundation isvery high compared to the rigidity of soil. The stress distribution under thefoundation will then depend on the magnitude and type of loads transferred by thestructure and weight of the foundation itself.

(Case I) (Case II)

MAT FOUNDATIONSRigid Foundation Assumption:

(Case I)

Case I: If the resultant of vertical loads from the structure passes close to geometric center of the

mat and if the mat plate is thick, then the effect of bending moments may be ignored and stress

distribution may be assumed as uniform.

𝜎𝑧,𝑚𝑎𝑥 = 𝑁𝑑𝐴

Case II: If the eccentricity (distance between the resultant of vertical loads and geometric center

of the mat) may not be ignored, then the stress distribution changes linearly along both axes. Then

the maximum stress may be calculated as:

𝜎𝑧,𝑚𝑎𝑥 = 𝑁𝑑𝐴

+ 𝑀𝑑𝑥 × 𝑦𝑚𝑎𝑥

𝐼𝑥+ 𝑀𝑑𝑦 × 𝑥𝑚𝑎𝑥

𝐼𝑦

Nd: Total vertical loads from the structure

A: Area of the mat foundation

Mdx: Moment along x direction (Nd x eccentricity along y-direction)

Mdy: Moment along y direction (Nd x eccentricity along x-direction)

Ix: Moment of inertia of mat area about x-axis

Iy: Moment of inertia of mat area about y-axis

ymax: max. distance from the geometric center, along y-direction

xmax: max. distance from the geometric center, along x-direction(Case II)

MAT FOUNDATIONSFlexible Foundation Assumption: If the mat foundation is not rigid (low thicknessand no beams), then uniform or linear stress distribution may not be valid.

In this case, finite element approach should be used. In this approach, elasticsprings are defined under the mat foundation, in order to represent the response ofelastic soil (spring coefficient is defined for each different type of soil).

MAT FOUNDATIONSIn finite element analysis, the mat foundation should be meshed into parts whichhave approximately 1 m2 area. The multiplication of spring coefficient (ko; unit:kN/m3) and max. vertical displacement (δz,max., found by analysis) will then givethe max. stress under the foundation (σz,max.= ko× δz,max.).

ko→ unit: kN/m3

δz,max. → unit: m

σz,max.→ unit: kN/m2

Check:

σz,max.≤ σz,allow.