B-4Members subjected to combined axial load and bending

B-4.1 Design Based on Uncracked Section

A member subjected to axial load and bending (due to

eccentricity of load, monolithic construction, lateral forces, etc) shall be considered safe provided the following conditions are satisfied:

a) $\frac{\sigma_{\mathrm{cc}, \mathrm{cal}}}{\sigma_{\mathrm{cc}}}+\frac{\sigma_{\mathrm{chc}, \mathrm{cal}}}{\sigma_{\mathrm{cbc}}} \leq 1$

where

• $f_{\mathrm{cc}, \mathrm{cal}}=$ calculated direct compressive stress in concrete,
• $\begin{aligned} \sigma_{c c} & =\text { permissible axial compressive stress } \\ & \text { in concrete, }\end{aligned}$
• $\sigma_{\mathrm{cbc}, \mathrm{cal}}=$ calculated bending compressive stress in concrete, and
• $\sigma_{c h c}=$ permissible bending compressive stress in concrete.
• b) The resultant tension in concrete is not greater than 35 percent and 25 percent of the resultant compression for biaxial and uniaxial bending respectively, or does not exceed three-fourths, the 7 day modulus of rupture of concrete.

NOTES

$1 \quad \sigma_{\text {max }}=\frac{P}{A_{c}+1.5 m A_{s}}$ for columns with ties where $P, A_{c}$ and

$A_{\mathrm{~s}}$ defined in B-3.1 and $m$ is the modular ratio.

$2 \sigma_{\text {ch,col }}=\frac{M}{Z}$ where $M$ equals the moment and $Z$ equals

modulus of section. In the case of sections subject to moments in two directions, the stress shall be calculated separately and added algebraically.

B-4.2 Design Based on Cracked Section

If the requirements specified in B-4.1 are not satisfied,

the stresses in concrete and steel shall be calculated by the theory of cracked section in which the tensile resistance of concrete is ignored. If the calculated stresses are within the permissible stress specified in Tables 21, 22 and 23 the section may be assumed to be safe.

NOTE — The maximum stress in concrete and steel may be found from tables and charts based on the cracked section theory or directly by determining the no-stress line which should satisfy the following requirements:

• a) The direct load should be equal to the algebraic sum of the forces on concrete and steel,
• b) The moment of the external loads about any reference line should be equal to the algebraic sum of the moment of the forces in concrete (ignoring the tensile force in concrete) and steel about the same line, and
• c) The moment of the external loads about any other reference lines should be equal to the algebraic sum of the moment of the forces in concrete (ignoring the tensile force in concrete) and steel about the same line.

B-4.3 Members Subjected to Combined Direct Load and Flexure

Members subjected to combined direct load and flexure and shall be designed by limit state method as in 39.5 after applying appropriate load factors as given in Table 18.