The following information is given for proportioning a cantilever footing with reference to Fig. 14.2.

Column Loads: $Q_{1}=1455 kN , Q_{2}=1500 kN$ .

Size of column: 0.5 x 0.5 m.
$L_{c}=6.2 m , q_{s}=384 kN / m ^{2}$
It is required to determine the size of the footings for columns 1 and 2.

Question

The following information is given for proportioning a cantilever footing with reference to Fig. 14.2.

Column Loads: [latex]Q_{1}=1455 kN , Q_{2}=1500 kN[/latex].

Size of column: 0.5 x 0.5 m.

[latex]L_{c}=6.2 m , q_{s}=384 kN / m ^{2}[/latex]

It is required to determine the size of the footings for columns 1 and 2.

Accepted Answer

Assume the width of the footing for column [latex]1=B_{1}=2 m[/latex].

First trial

[latex] ext { Try } e=0.5 m ext {. Now, } L_{R}=6.2-0.5=5.7 m[/latex].

Reactions

[latex]R_{1}=Q_{1} 1+\frac{e}{L_{R}}=14551+\frac{0.5}{5.7}=1583[/latex]

[latex]R_{2}=Q_{2}-\frac{Q_{1} e}{L_{R}}=1500-\frac{1455 imes 0.5}{5.7}=1372 kN[/latex]

Size of footings - First trial

Col. 1. Area of footing [latex]A_{1}=\frac{1583}{384}=4.122 sq . m[/latex]

Col. 2. Area of footing [latex]A_{2}=\frac{1372}{384}=3.57 sq \cdot m[/latex]

Try 1.9 x 1.9m

Second trial

New value of [latex]e=\frac{B_{1}}{2}-\frac{b_{1}}{2}=\frac{2}{2}-\frac{0.5}{2}=0.75 m[/latex]

New [latex]L_{R}=6.20-0.75=5.45 m[/latex]

[latex]R_{1}=14551+\frac{0.75}{5.45}=1655 kN[/latex]

[latex]R_{2}=1500-\frac{1455 imes 0.75}{5.45}=1300 kN[/latex]

[latex]A_{1}=\frac{1655}{384}=4.31 sq \cdot m ext { or } 2.08 imes 2.08 m[/latex]

[latex]A_{2}=\frac{1300}{384}=3.38 sq \cdot m ext { or } 1.84 imes 1.84 m[/latex]

Check [latex]e=\frac{B_{1}}{2}-\frac{b_{1}}{2}=1.04-0.25=0.79 \approx 0.75 m[/latex]

Use 2.08 x 2.08 m for Col. 1 and 1.90 x 1.90 m for Col. 2.

Note: Rectangular footings may be used for both the columns.

Question 14.3: The following information is given for proportioning a canti...