An RCC beam of rectangular cross-section has factored shear of 200 {kN} at its critical section. Its width b is 250 {mm} and effective depth {d} is 350 {mm}. Assume design shear strength \tau_{c} of concrete as 0.62 {N}{/} {mm}^{2} and maximum allowable shear stress \tau_{c \max } in concrete as 2.8 {N} {/} {mm}^{2}. If two legged 10 {mm} diameter vertical stirrups of Fe250 grade steel are used, then the required spacing (in {cm}, up to one decimal place) as per unit state method will be

GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 45 of 65

Marks: +1, -0

An RCC beam of rectangular cross-section has factored shear of

200 {kN}

at its critical section. Its width

b

250 {mm}

and effective depth

{d}

350 {mm}

. Assume design shear strength

τ_{c}

of concrete as

0.62 {N}{/} {mm}^{2}

and maximum allowable shear stress

\;\; τ_{c \max }

in concrete as

2.8 {N} {/} {mm}^{2}

. If two legged

10 {mm}

diameter vertical stirrups of Fe250 grade steel are used, then the required spacing (in

{cm}

, up to one decimal place) as per unit state method will be

Solution:

Nominal shear stress

=τ_{v}=\;{V_{u}}/{b d}=\;{200 × 10^{3}}/{250 × 350}

2.286 {N} {/} {mm}^{2}<τ_{c, \max }( {OK})

SF taken by stirrups

=(τ_{v}-τ_{c}) b d

=(2.286-0.62) × 250 × 350=145.75 {kN}

Now,

V_{u s}=\;{0.87 f_{y} A_{s v} d}/{S_{v}}

⇒\;S_{v}=\;{0.87 × 250 × 350 × 2 × {π}/{4} × 10^{2}}/{145.75 × 10^{3}}

\;\; =82 {mm}=8.2 {cm}

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