A RCC member of total width 250 mm and effective depth 450 mm is

SOLUTION

Concept:

Development Length \(\left( {{\ell _d}} \right) = \frac{{0.87\;{f_y}}}{{4\;{\tau _{bd}}}}\)

Also,

\({\ell _d} \le 1.3\frac{{{M_u}}}{{{V_u}}} + {\ell _0}\)             (When there is compression confinement)

Where,

M_u = Ultimate MOR at a section considering stress in all bars as 0.87 f_y

V_u = Factored shear force at the point of zero moment.

ℓ₀ = Anchorage length

Calculation:

M_u = 50 kN – m, V_u = 200 kN, ℓ₀ = 400 mm

\(\therefore {\ell _d} \le 1.3 \times \frac{{50}}{{200}} + \frac{{400}}{{1000}} = 0.725\;m\)

⇒ ℓ_d ≤ 725 mm

At limiting condition,

ℓ_d = 725 mm

Also,

\({\ell _d} \ge \frac{{0.87\;{f_y}\;\phi }}{{4\;{\tau _{bd}}}} \Rightarrow 725 \ge \frac{{0.87 \times 415 \times \phi }}{{4 \times 1.2}}\)

⇒ ϕ ≤ 9.638 mm  

Thus the maximum bar dia that can be provided is 9 mm.

Mistake Point:

The value of bond stress is given for Fe 415 bar and we need not add 60 % in the given value.

Important Point:

In case of simple support or the places where there is no compression confinement, tension R/F should be limited to a diameter, such that

\({\ell _d} \le \frac{{{M_u}}}{{{V_u}}} + {\ell _0}\)