G-1Rectangular sections

G-1.1 Sections Without Compression Reinforcement

The moment of resistance of rectangular sections without compression reinforcement should be obtained as follows:

• a) Determine the depth of netutral axis from the following equation:

$\frac{x_{u}}{d}=\frac{0.87 f_{y} A_{st}}{0.36 f_{c k} b . d}$

b) If the value of $x_{\mathrm{v}} / d$ is less than the limiting

• If the value of $\alpha_{y d}$ is less than the limiting value (see Note below 38.1), calculate the moment of resistance by the following expression:

$M_{u}=0.87 f_{y} A_{s t} d\left(1-\frac{A_{s t} f_{y}}{b d f_{c k}}\right)$

• c) If the value of $x_{u} / d$ is equal to the limiting value, the moment of resistance of the section is given by the following expression :

$M_{\mathrm{u} \cdot \mathrm{lim}}=0.36 \frac{x_{\mathrm{u}, \max }}{d}\left(1-0.42 \frac{x_{\mathrm{u}, \max }}{d}\right) b d^{2} f_{\mathrm{ck}}$

• d) If $x_{u} / d$ is greater than the limiting value, the section should be redesigned.

In the above equations,

= depth of neutral axis,

$d=$ effective depth,

$\begin{aligned} f_{y} & =\text { characteristic strength of reinforce- } \\ & \text { ment, }\end{aligned}$

$A_{s}=$ area of tension reinforcement,

= characteristic compressive strength of concrete,

$b \quad=$ width of the compression face,

$M_{\mathrm{u}, \mathrm{lim}}=$ limiting moment of resistance of a section without compression reinforcement, and

$x_{u, \text { lima }}=$ limiting value of $x_{u}$ from 39.1.

G-1.2 Section with Compression Reinforcement

Where the ultimate moment of resistance of section

exceeds the limiting value, $M_{u, \text { lim }}$ compression reinforcement may be obtained from the following equation :

$M_{u}-M_{u, l l m}=f_{n o} A_{n o}\left(d-d^{\prime}\right)$

where

$M_{u}, M_{u}$, lim, $d$ are same as in G-1.1,

$f_{c}=$ design stress in compression reinforce- ment corresponding to a strain of

0.00035 $\left(\frac{x_{\mathrm{u}, \max }}{x_{\mathrm{u}, \max }}-1\right)$

where

$x_{u, \max }=$ the limiting value of $x_{u}$ from 38.1.

= area of compression reinforcement, and

$d^{\prime}$ = depth of compression reinforcement from compression face.

The total area of tension reinforcement shall be obtained from the following equation :

$A_{\mathrm{el}}=A_{\mathrm{el} 1}+A_{\mathrm{el} 2}$

where

$A_{s}=$ area of the total tensile reinforcement,

$\begin{aligned} A_{\mathrm{st} 1} & =\text { area of the tensile reinforcement for a } \\ & \text { singly reinforced section for } M_{\mathrm{u}, \mathrm{lim}^{\prime}} \\ & \text { and }\end{aligned}$

$A_{M 2}=A_{s c} f_{s c} / 0.87 f_{y}$