A square slab base of 2000 mm is provided for a column made of tw
| A square slab base of 2000 mm is provided for a column made of two rolled channel section. The 500 mm × 500 mm column carries an axial compressive load of 500 kN. The line of action of the load passes through the centroid of the column section as well as of the slab base. The permissible bending stress in the slab base is 160 MPa. Required minimum thickness of slab base is (As per working stress method)
A. 25 mm
B. 28 mm
C. 30 mm
D. 32 mm
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Right Answer is: D
SOLUTION
Calculation
Given,
\(\begin{array}{l} Overhang,\;a = b = \frac{{2000 - 500}}{2} = 750\;mm\\ w = \frac{P}{{Actual\;area}} = \frac{{500 \times {{10}^3}}}{{{{\left( {2000} \right)}^2}}} = 0.125\;N/m{m^2} \end{array}\)
∴ The thickness of the base plate
\(\begin{array}{l} t = \sqrt {\frac{{3w}}{{{\sigma _{bs}}}}\left[ {{a^2} - \frac{{{b^2}}}{4}} \right]} \\ = \sqrt {\frac{{3 \times 0.125}}{{160}}\left[ {{{750}^2} - \frac{{{{750}^2}}}{4}} \right]} \end{array}\)
= 31.44 mm
≃ 32 mm