Footings: Worked Examples

A wall carries a service structural load of $250\text{ kN/m}$. The geotechnical report gives a gross allowable pressure of $200\text{ kPa}$. The footing base is $1.50\text{ m}$ below grade, the trial footing thickness is $0.30\text{ m}$, soil unit weight is $18\text{ kN/m}^3$, and concrete unit weight is $24\text{ kN/m}^3$. Size the strip footing per metre length.

A column reaction consists of service dead load $D=800\text{ kN}$ and live load $L=600\text{ kN}$. A compatible net allowable bearing pressure of $200\text{ kPa}$ is supplied. Determine the theoretical square footing side, then compute the factored structural reaction per unit area for $P_u=1.2D+1.6L$ using a selected $2.65\text{ m}$ square footing.

A column has compatible service actions $P_s=1600\text{ kN}$ and $M_s=240\text{ kN}\cdot\text{m}$, producing pressure variation along footing length $L$. The allowable service pressure is $220\text{ kPa}$. Compare trial footings $2.40\text{ m}\times3.40\text{ m}$ and $2.60\text{ m}\times3.60\text{ m}$.

A $2.0\text{ m}\times3.0\text{ m}$ footing carries $P=600\text{ kN}$ and $M=150\text{ kN}\cdot\text{m}$ about the axis that produces pressure variation along $L=3.0\text{ m}$.

The same $2.0\text{ m}\times3.0\text{ m}$ footing carries $P=600\text{ kN}$ but now $M=420\text{ kN}\cdot\text{m}$. Determine the no-tension contact length and maximum compressive pressure.

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A $2.60\text{ m}\times3.00\text{ m}$ footing supports a $0.45\text{ m}\times0.50\text{ m}$ interior column. The factored soil reaction is uniform at $q_u=230\text{ kPa}$. Use $h=550\text{ mm}$, $75\text{ mm}$ bottom cover, and $20\text{ mm}$ bars. The lowest layer runs in the $X$ direction and the orthogonal layer is one bar diameter above it. Let $f'_c=28\text{ MPa}$, $\lambda=1.0$, and $\phi=0.75$.

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Use the same $2.60\text{ m}\times3.00\text{ m}$ footing and $0.45\text{ m}\times0.50\text{ m}$ column from the preceding example. Take $q_u=230\text{ kPa}$, $d=(465+445)/2=455\text{ mm}$, $f'_c=28\text{ MPa}$, $\lambda=1$, $\phi=0.75$, and $\alpha_s=40$.

For the same footing, use $q_u=230\text{ kPa}$, $h=550\text{ mm}$, $d_x=465\text{ mm}$, $d_y=445\text{ mm}$, $f'_c=28\text{ MPa}$, and $f_y=420\text{ MPa}$. Determine required steel and check a trial of $20\text{ mm}$ bars at a maximum nominal spacing of $180\text{ mm}$.

A $400\text{ mm}\times400\text{ mm}$ reinforced-concrete column delivers $P_u=3500\text{ kN}$ in compression to a footing with $f'_c=28\text{ MPa}$. The supporting-area geometry permits the maximum bearing enhancement factor of $2.0$. Check the illustrated bearing strength and the minimum reinforcement crossing the interface.

An exterior column carries $P_s=900\text{ kN}$ on a $2.40\text{ m}\times3.00\text{ m}$ trial footing. Along the $3.00\text{ m}$ length, the column line is only $0.50\text{ m}$ from the property-line edge. Determine the service contact state and maximum no-tension pressure. The allowable service pressure is $250\text{ kPa}$.

Two service column loads act near a property line: $P_1=1000\text{ kN}$ at $x_1=0.60\text{ m}$ and $P_2=1500\text{ kN}$ at $x_2=4.60\text{ m}$. A $6.00\text{ m}$ long rectangular combined footing begins at the property line. Determine whether its centroid aligns with the load resultant, and find the uniform service pressure for a selected width $B=2.10\text{ m}$.

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An exterior column load $P_1=900\text{ kN}$ acts at $x=0.35\text{ m}$ and an interior column load $P_2=1400\text{ kN}$ acts at $x=4.40\text{ m}$. The exterior pad soil reaction acts at its center $x=0.90\text{ m}$ and the interior pad reaction acts at $x=4.40\text{ m}$. Assume the strap itself is not counted as soil-bearing area. Solve the pad reactions from global vertical equilibrium.

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A $2.40\text{ m}$ square footing supports a $450\text{ mm}$ square interior column with factored load $P_u=2200\text{ kN}$. Use uniform factored soil reaction, $f'_c=28\text{ MPa}$, $75\text{ mm}$ cover, $25\text{ mm}$ bars, $\lambda=1$, and $\phi=0.75$. Compare trial thicknesses $h=450\text{ mm}$ and $h=600\text{ mm}$ using the average directional effective depth for the punching perimeter.