Footings: Worked Examples

Problem: A wall carries service dead plus live load $P=250\text{ kN/m}$. A gross allowable bearing pressure of $200\text{ kPa}$ is given. The footing base is $1.5\text{ m}$ below grade, trial 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 a strip footing per metre length.

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

Problem: For the same $2.0\text{ m}\times3.0\text{ m}$ footing and $P=600\text{ kN}$, let $M=420\text{ kN}\cdot\text{m}$ act about the same axis.

Problem: A $2.0\text{ m}\times2.0\text{ m}$ footing supports a $400\text{ mm}\times400\text{ mm}$ column. Use $d=350\text{ mm}$, factored upward design pressure $q_u=250\text{ kPa}$, $f'_c=28\text{ MPa}$, $\lambda=1.0$, and $\phi=0.75$.

Problem: Use the same footing, column, depth, pressure, and concrete strength as the preceding example. For this square interior-column illustration, check the $0.33\lambda\sqrt{f'_c}b_od$ limit.

Problem: For the same $2.0\text{ m}$ square footing, take $q_u=250\text{ kPa}$, column width $0.40\text{ m}$, trial $h=450\text{ mm}$, $d=350\text{ mm}$, $f'_c=28\text{ MPa}$, and $f_y=420\text{ MPa}$.

Problem: A $3.0\text{ m}\times3.0\text{ m}$ footing supports a $400\text{ mm}$ square column. Bottom bars are $20\text{ mm}$ diameter with $75\text{ mm}$ edge cover. Suppose the corrected Topic 05 tension-development calculation for the actual cover, spacing, and material factors gives $l_d=462\text{ mm}$.

Problem: A $25\text{ mm}$ column dowel in normal-weight concrete has $f_y=420\text{ MPa}$ and $f'_c=28\text{ MPa}$. Only $375\text{ mm}$ of straight compression-development length is available in the footing. Determine whether adding a standard 90-degree hook cures the deficiency.