Annex H(Clause 37.1)

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 898

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Moments of Resistance for Rectangular and T-sections

H-0 The moments of resistance of rectangular and T-sections based on the assumption of 37.1 are given in this annex.

H-1 Rectangular Sections

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

a) Determine the depth of neutral axis from the following equation:

\frac {x _ {\mathrm{u}}}{d} = \frac {0 . 8 7 f _ {\mathrm{y}} A _ {\mathrm{st}}}{0 . 3 6 f _ {\mathrm{ck}} b . d}

b) If the value of $x_{u}/d$ is less than the limiting value (see Note below 37.1), calculate the moment of resistance by the following expression:

M _ {\mathrm{u}} = 0. 8 7 f _ {\mathrm{y}} A _ {\mathrm{st}} d \left[ 1 - \frac {A _ {\mathrm{st}} f _ {\mathrm{y}}}{b d f _ {\mathrm{ck}}} \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}, \lim} = 0. 3 6 \frac {x _ {\mathrm{u} , \max}}{d} \left[ 1 - 0. 4 2 \frac {x _ {\mathrm{u} , \max}}{d} \right] b d ^ {2} f _ {\mathrm{ck}}

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

In the above equations,

x _ {\mathrm{u}} = \text { depth of neutral axis },

d = \text {effective depth},

\left| \begin{array}{c} f _ {\mathrm{y}} = \text {characteristic} \quad \text {strength} \quad \text {of} \\ \text {reinforcement,} \end{array} \right|

A _ {\mathrm{st}} = \text {area of tension reinforcement}

$f_{ck}$ = characteristic compressive strength of concrete,

$b =$ width of the compression face,

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

$x_{\mathrm{u,max}} =$ limiting value of $x_{\mathrm{u}}$ from 37.1.

Where the ultimate moment of resistance of section exceeds the limiting value, $M_{\mathrm{u,lim}}$ compression

reinforcement may be obtained from the following equation:

M _ {\mathrm{u}} - M _ {\mathrm{u,lim}} = f _ {\mathrm{sc}} A _ {\mathrm{sc}} (d - d ^ {\prime})

where

M _ {\mathrm{u}}, M _ {\mathrm{u,lim}}, d \text {are same as in H - 1.1}

\begin{array}{r l} f _ {\mathrm{sc}} = & \text {design stress in compression reinforcement} \\ & \text {corresponding to a strain of} \end{array}

0. 0 0 3 5 \frac {\left(x _ {\mathrm{u,max}} - d ^ {\prime}\right)}{x _ {\mathrm{u,max}}}

x _ {\mathrm{u}, \max} = \text {the limiting value of} x _ {\mathrm{u}} \text {from 37.1.}

A _ {\mathrm{sc}} = \text { area of compression reinforcement, and }

$d' = \text{depth of compression reinforcement from compression face.}$

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

A _ {\mathrm{st}} = A _ {\mathrm{st1}} + A _ {\mathrm{st2}}

where

$A_{\mathrm{st}} =$ area of the total tensile reinforcement,

$A_{st1}$ = area of the tensile reinforcement for a singly reinforced section for $M_{u,lim}$ , and

\mathrm{A} _ {\mathrm{st2}} = A _ {\mathrm{sc}} f _ {\mathrm{sc}} / 0. 8 7 f _ {\mathrm{y}}