Question

If $\varphi$ = nominal diameter of reinforcing bar, $f_s=$ compressive stress in the bar and $f_{bd}$= design bond sress of concrete, the anchorage length, $L_s$ of straight bar in compression is equal to

• A. $L_a=\frac{\varphi f_s}{f_{bd}}$
• B. $L_a=\frac{\varphi f_s}{2f_{bd}}$
• C. $L_a=\frac{\varphi f_s}{\pi f_{bd}}$
• D. $L_a=\frac{\varphi f_s}{4f_{bd}}$

Answer 1

The correct option is D $L_a=\frac{\varphi f_s}{4f_{bd}}$



Compressive force
$c=f_s\times A_s$
$=f_s\times \frac{\pi }{4}{\varphi }^2$ ...(i)

This force must be transferred from steel to concrete through bond acing over the perimeter of the bar along its length of embedment.
Hence,

$C=f_{bd}\times \pi \varphi L_a$ ....(ii)
From (i) & (ii)

$f_{bd}\times \pi \varphi \times L_a=f_s\times \frac{\pi }{4}{\varphi }^2$

$L_a=\frac{f_s\varphi }{4f_{bd}}$

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Note : It is a standard result please remember this.
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