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According to ACI 9.6.1.2, a minimum area of flexural reinforcement, As,min is equal to the greater of the following relations;

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hostConfluence:2933017122
body--uriencoded--$$ \normalsize A_%7Bs,min%7D = \Bigg[ \frac%7B3 \sqrt%7Bf_c'%7D%7D%7Bf_%7By%7D%7Db_wd \; \; \;, \; \; \; \frac%7B200%7D%7Bf_%7By%7D%7D b_wd \Bigg]_%7Bmax%7D $$

According to ACI 9.6.1.3, if As provided at every section is greater than one-third of As calculated by analysis, As,min need not be satisfied.

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In other words, if ϕλ√fc‘(bwd) < Vu < [ Vc + 8√fc‘(bwd) ], minimum shear reinforcement area ,Av,min, is calculated given below.

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hostConfluence:2933017122
body--uriencoded--$$ \normalsize A_%7Bv,min%7D = \bigg[ 0.75 \sqrt%7Bf_c'%7D \frac%7Bb_w s%7D%7Bf_%7Byt%7D%7D \; \; \;, \; \; \; 50 \frac%7Bb_ws%7D%7Bf_%7Byt%7D%7D \bigg]_%7Bmax%7D $$

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Minimum torsional reinforcement

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Minimum transverse reinforcement (Av + 2At)min / s

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hostConfluence:2933017122
body--uriencoded--$$ \normalsize \frac %7B(A_%7Bv%7D+2A_%7Bt%7D)_%7Bmin%7D%7D%7Bs%7D = \bigg[ 0.75 \sqrt%7Bf_c'%7D \frac%7Bb_w%7D%7Bf_%7Byt%7D%7D \; \; \;, \; \; \; 50 \frac%7Bb_w%7D%7Bf_%7Byt%7D%7D \bigg]_%7Bmax%7D $$

minimum area of longitudinal reinforcement Al,min

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hostConfluence:2933017122
body--uriencoded--$$ \normalsize (A_l)_%7Bmin%7D = \Bigg[ \frac%7B5 \sqrt%7Bf_c'%7DA_%7Bcp%7D %7D%7Bf_y%7D - \Big( \frac%7BA_t%7D%7Bs%7D\Big)p_h \frac%7Bf_%7Byt%7D%7D%7Bf_y%7D \; \; , \; \; \frac%7B5 \sqrt%7Bf_c'%7DA_%7Bcp%7D %7D%7Bf_y%7D - \Big( \frac%7B25b_w%7D%7Bf_%7Byt%7D%7D\Big)p_h \frac%7Bf_%7Byt%7D%7D%7Bf_y%7D \Bigg]_%7Bmin%7D $$

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Reinforcement Limits for Beams of Earthquake Resistant Structures

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