11.5Combined Stresses

11.5.1 Combined Bending and Shear

Reduction in allowable moment need not be considered under combined bending and shear.

11.5.2 Combined Bending and Axial Force

Members subjected to combined axial compression and bending shall be so proportioned to satisfy the following requirements:

• a) Member stability requirement:

$\begin{aligned} \frac{f_{\mathrm{c}}}{f_{\mathrm{acy}}}+0.6 K_{\mathrm{y}} \frac{C_{\mathrm{my}} f_{\mathrm{bcy}}}{f_{\mathrm{abcy}}}+K_{\mathrm{LT}} \frac{f_{\mathrm{bcz}}}{f_{\mathrm{abcz}}} & \leq 1.0 ; \\ \frac{f_{\mathrm{c}}}{f_{\mathrm{acz}}}+0.6 K_{\mathrm{y}} \frac{C_{\mathrm{my}} f_{\mathrm{bcy}}}{f_{\mathrm{abcy}}}+K_{\mathrm{z}} \frac{C_{\mathrm{mz}} f_{\mathrm{bcz}}}{f_{\mathrm{abcz}}} & \leq 1.0\end{aligned}$ where

$C_{m y}, C_{m z}=$ equivalent uniform momer factor as per Table 18,

• $\begin{aligned} f_{\mathrm{c}} & =\text { applied axial compressive stress } \\ & \text { under service load, }\end{aligned}$

$f_{b c y}, f_{b c z}=$ applied compressive stresses due to bending about the major (y) and minor (z) axis of the member, respectively,

$f_{\mathrm{acy}}, f_{\mathrm{acz}}=$ allowable axial compressive stress as governed by buckling about minor (y) and major (z) axis, respectively,

$f_{\mathrm{abcy}}, f_{\mathrm{abcz}}=$ allowable bending compressive stresses due to bending about minor (y) and major (z) axes of the cross-section (see 11.4),

$\begin{aligned} K_{y} & =1+\left(\lambda_{y}-0.2\right) n_{y} \leq 1+0.8 n_{y} \\ K_{z} & =1+\left(\lambda_{z}-0.2\right) n_{z} \leq 1+0.8 n_{z}\end{aligned}$

$1-\frac{0.1 \lambda_{\mathrm{LT}} n_{\mathrm{y}}}{\left(C_{\mathrm{mLT}}-0.25\right)} \geq 1$

$K_{\mathrm{LT}}=-\frac{0.1 n_{y}}{\left(C_{\mathrm{mLT}}-0.25\right)}$,

where

$n_{y}, n_{z}=$ ratio of actual applied axial stress to the allowable axial stress for buckling about the $y$ and $z$ axis, respectively;

$\mathrm{C}_{\mathrm{MLT}}=$ equivalent uniform moment factor; and

$\begin{aligned} \lambda_{\mathrm{LT}} & =\text { non-dimensional slenderness } \\ & \text { ratio (see } 8.2 .2)\end{aligned}$

• b) Member strength requiremer

At a support he values $f_{\mathrm{abcy}}$ and $f_{\mathrm{abcz}}$ shall be calculated using laterally supported member and shall satisfy:

$\frac{f_{\mathrm{c}}}{0.6 f_{y}}+\frac{f_{\mathrm{bcy}}}{f_{\mathrm{abcy}}}+\frac{f_{\mathrm{bcz}}}{f_{\mathrm{abcz}}} \leq 1.0$

11.5.3 Combined Bending and Axial Tension

Members subjected to both axial tension and bending shall be proportioned so that the following condition is satisfied:

$\frac{f_{\mathrm{t}}}{f_{\mathrm{at}}}+\frac{f_{\mathrm{bty}}}{f_{\mathrm{abty}}}+\frac{f_{\mathrm{btz}}}{f_{\mathrm{abtz}}} \leq 1.0$

where

$f_{\mathrm{abty}}, f_{\mathrm{abtz}}=$ permissible tensile stresses under bending about minor (y) and major (z) axis when bending alone is acting, as given in 11.4.1.

11.5.4 Combined Bearing, Bending and Shear Stresses

Where a bearing stress is combined with tensile or compressive stress, bending and shear stresses under the most unfavourable conditions of loading, the equivalent stress, $f_{\mathrm{e}}$ obtained from the following

formula, shall not exceed $0.9 f_{y}$

$f_{\mathrm{e}}=\sqrt{f_{\mathrm{b}}^{2}+f_{\mathrm{p}}^{2}+f_{\mathrm{b}}^{2} f_{\mathrm{p}}^{2}+3 \tau_{\mathrm{b}}^{2}}$

where

$\tau \quad=$ actual shear stress

• $f_{\mathrm{t}} \quad=$ actual tensile stress

$f_{y} \quad=$ yield stress, and

$f_{\mathrm{p}} \quad=$ actual bearing stress.

The value of permissible bending stresses $f_{\mathrm{bcy}}$ and $f_{\mathrm{bcz}}$ to be used in the above formula shall each be lesser of the values of the maximum allowable stresses $f_{\mathrm{abc}}$ and $f_{\mathrm{abt}}$ in bending about appropriate axis.