Question

If nominal shear stress τ_v exceeds the design shear strength of concrete τ_c, the nominal shear reinforcement as per IS: 456:2000 shall be provided for shear stress equal to:
1. τ_v
2. τ_c
3. τ_v - τ_c
4. τ_v + τ_c

Answer 1

Correct Answer - Option 3 : τ_v - τ_c

Explanation:

If the calculated shear stress (τv) is

(i) Less than allowable shear stress (τc) but more than 0.5τc, the minimum shear reinforcement in the form of stirrups shall be provided such that

\(\frac{{{A_{sv}}}}{{b{S_v}}} \ge \frac{{0.4}}{{0.87{f_y}}}\)

(ii) if τ_v > τ_c then provided shear reinforcement for (τv - τc) which should mot less than minimum shear reinforcement

III) If \({τ _v} > {τ _{c,max}}\) redesign the section.

 If the nominal shear stress at a section does not exceed the permissible shear stress, then minimum shear reinforcement in the form of vertical stirrups shall be provided such that,

\(\frac{{{{\rm{A}}_{{\rm{sv}}}}}}{{{\rm{b\;}}{{\rm{S}}_{\rm{v}}}}}{\rm{\;}} \ge {\rm{\;}}\frac{{0.4}}{{0.87{\rm{\;}}{{\rm{f}}_{\rm{y}}}}}\)

Where,

Asv = Total cross-sectional area of stirrup legs effective in shear

Sv = Stirrup spacing along the length of the member in mm

b = width of the beam

fy = Characteristics strength of the stirrup reinforcement in MPa ≤ 415 MPa

As per the code, the maximum spacing of stirrups shall not exceed:

i) 0.75 d for vertical stirrups

ii) d for inclined stirrups

iii) 300 mm