GATE 2024 CE (CE2) – Question 51
A concrete column section of size 300 mm × 500 mm as shown in the figure is subjected to both axial compression and bending along the major axis. The depth of the neutral axis ($x_u$) is 1.1 times the depth of the column, as shown.
[Figure: a column cross-section of width B = 300 mm and depth D = 500 mm, with bars at the top and bottom, and a strain diagram with a linear variation of strain from $\varepsilon_c$ at the highly compressed face to zero at the neutral axis, which lies at $x_u = 1.1D$ from that face, outside the section.]
The maximum compressive strain ($\varepsilon_c$) at highly compressed extreme fiber in concrete, where there is no tension in the section, is ______________ $\times 10^{-3}$ (rounded off to 2 decimal places).
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Correct answer: 3.26 to 3.30
Explanation
When the neutral axis lies outside the section, IS 456 takes the strain at the level $\frac{3}{7}D$ from the highly compressed face to be 0.002. The strain varies linearly from $\varepsilon_c$ at the compressed face to zero at the neutral axis, a distance $x_u = 1.1D$ from that face. At the distance $\frac{3D}{7}$ the strain is $\varepsilon_c\frac{x_u - 3D/7}{x_u} = 0.002$. So $\varepsilon_c = 0.002 \times \frac{1.1}{1.1 - 0.4286} = 3.277 \times 10^{-3}$.