GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 52 of 65

Marks: +1, -0

The singly reinforced concrete beam section shown in the figure (not drawn to the scale) is made of M25 grade concrete and Fe500 grade reinforcing steel. The total cross-sectional area of the tension steel is

942 {mm}^{2}

As per Limit State design of IS 456-2000, the design moment capacity (in kN.m, round off to two decimal places) of the beam section, is

Your Answer:

Validate

Solution:

{A}_{ {st}}=942 {mm}^{2}, {f}_{ {ck}}=25 {N} {/} {mm}^{2}

For

{Fe} 500 → {x}_{ {U}, \max }=0.46 {d}

=0.46 ×(450)

x_{u, \max }=207 {mm}

Finding actual depth of neutral axis

{C}= {T}

0.36 {fck} . {b} ⋅ {X}_{ {u}}=0.87 {fy} . {Ast}

→ 0.36 × 25 × 300 × x_{u}=0.87 × 500 × 942

{x}_{ {u}}=151.766 {mm}

{X}_{ {u}}< {Xu}_{ {u}, \max } →

The section is under reinforced section

M_{u}=M ⋅ R=0.36 f_{c k} .

x_{u}(d-0.42 x_{u})

=0.36 × 25 × 300 × 151.766 ×(450-0.42 × 151.76)

M_{u}=158.277 {kN}- {m}

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