(Clauses 7.4.4.1, 7.4.4.2 and B-4) · NBC 2016 (SP 7:2016) Volume 1

Rigidity of Superstructure and Foundation

C-1 DETERMINATION OF THE RIGIDITY OF THE STRUCTURE

The flexural rigidity EI of the structure of any section may be estimated according to the relation given below (see also Fig. 8)

FIG. 8 DETERMINATION OF RIGIDITY OF STRUCTURE

E I = \frac {E _ {1} I _ {\mathrm{i}} b ^ {2}}{2 H ^ {2}} + \sum E _ {2} I _ {\mathrm{b}} \left[ 1 + \frac {\left(I _ {\mathrm{u}} ^ {\prime} + I _ {1} ^ {\prime}\right) b ^ {2}}{\left(I _ {\mathrm{b}} ^ {\prime} + I _ {\mathrm{u}} ^ {\prime} + I _ {\mathrm{f}} ^ {\prime}\right) l ^ {2}} \right]

where

$E_{1}$ = modulus of elasticity of the infilling material (wall material), in kN/m $^{2}$ ;

$I_{\mathrm{i}} =$ moment of inertia of the infilling, in $\mathrm{m^4}$ ;

b = length or breadth of the structure in the direction of bending, in m;

$H =$ total height of the infilling, in $\mathrm{m}$

$E_{2}$ = modulus of elasticity of the frame material, in kN/m $^{2}$ ;

$I_{\mathrm{b}} =$ moment of inertia of the beam, in $\mathrm{m}^4$

I _ {\mathrm{u}} ^ {\prime} = \frac {I _ {\mathrm{u}}}{h _ {\mathrm{u}}};

I _ {1} ^ {\prime} = \frac {I _ {1}}{h _ {1}};

I _ {\mathrm{b}} ^ {\prime} = \frac {I _ {\mathrm{b}}}{l};

$l =$ spacing of the columns, in $\mathrm{m}$

$h_{u}$ = length of the upper column, in m;

$h_1 =$ length of the lower column, in $\mathrm{m}$

PART 6 STRUCTURAL DESIGN — SECTION 2 SOILS AND FOUNDATIONS

I _ {\mathrm{f}} ^ {\prime} = \frac {I _ {\mathrm{f}}}{l};

$I_{u}$ = moment of inertia of the upper column, in $m^{4}$ ;

$I_{1} =$ moment of inertia of the lower column, in $\mathrm{m^4}$ ; and

$I_{f}$ = moment of inertia of the foundation beam or raft, in m $^{4}$ .

NOTE — The summation is to be done over all the storeys including the foundation beam or raft. In the case of the foundation, $I_{f}^{\prime}$ replaces $I_{b}^{\prime}$ and $I_{l}$ becomes zero, whereas for the topmost beam becomes zero.

C-2 Relative Stiffness Factor, K

C-2.1 Whether a structure behaves as rigid or flexible depends on the relative stiffness of the structure and the foundation soil. This relation is expressed by the relative stiffness factor K given below:

a) For the whole structure, $K = \frac{EI}{E_{\mathrm{s}}b^{3}a}$

C-3 Determination of Critical Column Spacing

Evaluation of the characteristics $\lambda$ is made as follows:

\lambda = \sqrt [ 4 ]{\left(\frac {k B}{4 E _ {\mathrm{c}} I}\right)}