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Derive the expression for the ultimate moment of resistance in respect of singly reinforced rectangular beam using Ultimate Load Method as prescribed by IS

written 8.8 years ago by teamques10 ★ 69k

•   modified 4.3 years ago

reinforced concrete structures theory

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written 8.8 years ago by teamques10 ★ 69k

•   modified 8.8 years ago

To find depth of actual N.A

$$C_u=T_u \\ \frac{2}{3}f_ckla=f_yAst \\ a=\frac{f_yAst}{\frac{2}{3}f_ckl} \\ a_{max}=\frac{d}{2}$$

If $a \lt a_{max}→$ under reinforced section

$$M_u=T_u×L_a=f_y×Ast×\Big( d-\frac{a}{2}\Big) \\ and \\ M_u=C_u×L_a=\frac{2}{3}f_ckl×a\Big(d-\frac{a}{2}\Big)$$

If $a \gt a_{max}→$ over reinforced section

It is not permitted.

Restrict $a= a_{max}$

$$M_{umax}=C_uL_a=\frac{2}{3}f_ckba_{max}\Big(d-\frac{a max}{2}\Big) \\ M_{umax}=\frac{2}{3}×f_ckb\frac{d}{2}×\Big(d-\frac{d}{4}\Big) \\ M_{umax}=0.25f_ckbd^2$$

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