written 8.4 years ago by
teamques10
★ 68k
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modified 8.4 years ago
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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 $a= a_{max}$
$$M_{umax}=C_uL_a=\frac{2}{3}f_ckba_{max}\Big(d-\frac{a max}{2}\Big) \\
M_{umax}=\frac{2}{3}×f_ckb\frac{d}{2}×\Big(d-\frac{d}{4}\Big) \\
M_{umax}=0.25f_ckbd^2$$