Explanation:
Formula to calculate the maximum column load is as follows.
[tex]P_{max} = \sigma \times A[/tex]
= [tex]110 N/mm^{2} \times 11200 mm^{2}[/tex]
= 1232000 N
Over a large area, the column load has to be distributed such that the bearing stress between base plate an concrete slab does not exceed 8 MPa. Hence, we will calculate the minimum plate area as follows.
[tex]A_{min} = \frac{P}{\sigma_{b}}[/tex]
= [tex]\frac{1232000 N}{8 N/mm^{2}}[/tex]
= 154000 [tex]mm^{2}[/tex]
As the plate is of square shape. Hence, the minimum plate dimension "a" must be calculated as follows.
[tex]A_{min} = a \times a[/tex]
[tex]154000 mm^{2} = a^{2}[/tex]
a = 392.42 mm
Thus, we can conclude that minimum required dimension of the given base plate is 392.42 mm.
