SSC JE Civil Engineering 30-Oct-2020 Shift 2 Paper

Question : 114 of 200

Marks: +1, -0

A cantilever beam of size 300 mm × 550 mm with 3 bars of 12 mm diameter in tension zone, has a span of 3 m, adopt M20 concrete and Fe500 grade steel. The depth of neutral axis is ______(assume clear cover as 25 mm).

68.27 mm
259.5 mm
415 mm
121.5 mm

Validate

Solution:

Concept:

To find actual depth of NA
C = T

⇒[0.67\f_\ck × 3/7\x_\a + 0.67\f_\ck × 2/3 × 4/7\x_\a]× \b = 0.87 \f_\y. \A_\st

⇒0.36×\f_\ck×\b×\x_\a= 0.87 × \f_\y \ \A_\st

\x_\a={0.87\f_\y\A_\st}/{0.36\b\f_\ck}

Where,

\x_\a =

Depth of neutral axis,

\f_\ck

= Grade of concrete,

\f_\y =

Grade of steel,

\b =

width of the beam,

\A_\st =

Area of steel
Calculation:
Given,
b = 300 mm,

\A_\st = 3 × π/4 × 122 = 339.29 \mm^2

\f_\ck= 20 \N\/\mm^2, \f_y=500 \N\/\mm^2

{\x}_{{\a}}={0.87 {\f}_{{\y}} {\A}_{{\st}}} /{0.36 {\b\f}_{{\ck}}}

{\x}_{{\a}}={0.87 ×500 ×339.29}/{0.36 ×300 ×20}

{\x}_{{\a}}=68.32 {\mm}

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