Column Analysis and Design Examples

A short tied column is $400\text{ mm}\times400\text{ mm}$ with eight 25 mm bars ($A_{\mathrm{st}}=3927\text{ mm}^2$), $f'_c=28\text{ MPa}$, and $f_y=420\text{ MPa}$. Determine the maximum factored axial design strength.

A $400\text{ mm}\times400\text{ mm}$ tied column has two 25 mm bars at $d'=65\text{ mm}$ and two at $d=335\text{ mm}$, so $A'_s=A_s=982\text{ mm}^2$. Use $f'_c=28\text{ MPa}$, $f_y=420\text{ MPa}$, $E_s=200{,}000\text{ MPa}$, and $\beta_1=0.85$. Find the balanced nominal resultants.

Use the section and materials from Example 2 for $P_u=1000\text{ kN}$ and $M_u=180\text{ kN-m}$. Check section strength without interpolating between interaction-diagram landmarks.

For the section in Example 2, find the strain-compatible point at zero nominal axial force.

A braced, nonsway $400\text{ mm}\times400\text{ mm}$ column is pin-ended for the axis considered, so $k=1.0$. Let $L_u=4.0\text{ m}$, $f'_c=28\text{ MPa}$, $P_u=3000\text{ kN}$, $M_1/M_2=+0.50$ for single curvature, and $M_2=120\text{ kN-m}$. Use $EI=0.4E_cI_g/(1+\beta_{dns})$ with $\beta_{dns}=0.20$.

At the specified eccentricities, a column has $P_o=4000\text{ kN}$, $P_{nx}=1500\text{ kN}$, and $P_{ny}=1200\text{ kN}$. Estimate the nominal biaxial axial capacity within the range where the reciprocal approximation is applicable.

A circular column has overall diameter $400\text{ mm}$ and $40\text{ mm}$ clear cover to the outside of the spiral, so the core diameter measured outside-to-outside is $320\text{ mm}$. Use $f'_c=28\text{ MPa}$ and $f_{yt}=420\text{ MPa}$.

Two otherwise comparable short columns each have $P_o=4000\text{ kN}$. Compare their maximum factored axial strengths, assuming the first is tied and the second fully qualifies for spiral-member provisions.

A $450\text{ mm}\times600\text{ mm}$ tied column uses 25 mm longitudinal bars and 12 mm ties. Determine the maximum ordinary non-seismic tie spacing from the three spacing limits taught in this topic.

A tied-column strain-compatible state has $f_y=420\text{ MPa}$, $E_s=200{,}000\text{ MPa}$, and net extreme tensile strain $\epsilon_t=0.0040$. Determine the applicable $\phi$.

A rectangular corner column has significant $M_x$ and $M_y$. A preliminary reciprocal-load calculation produces an estimated biaxial strength below $0.10P_o$, and the actual reinforcement is strongly asymmetric. Select the appropriate analysis path.