Question

A square steel slab base of area 1 m ${}^2$ is provided for a column made of two rolled channel sections. The 300 mm x 300 mm column carries an axial compressive load of 2000 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 185 MPa. The required minimum thickness of the slab base is ______.

• A. 55 mm
• B. 63 mm
• C. 110 mm
• D. 89 mm

Answer 1

The correct option is A 55 mm

Area of square plate
$=1m^2$
Size of plate = 1 m x 1 m
Load intensity at the base of plate


$w=\frac{Load}{Area}=\frac{2000kN}{1m^2}$

$=2N/m{m}^2$

Permissible bending stress,
${\sigma }_b=185N/m{m}^2$

Projection
a = b
$=\frac{1000-300}{2}$
= 350 mm

Thickness of slab base,
$t=\sqrt{\frac{3w}{{\sigma }_b}(a^2-\frac{b^2}{4})}$

$=\sqrt{\frac{3\times 2}{185}({350}^2-\frac{{350}^2}{4})}$

= 54.59 mm
= 55 mm