> ## Documentation Index > Fetch the complete documentation index at: https://calcs.com/docs/llms.txt > Use this file to discover all available pages before exploring further. # Steel Column Validation Examples > Steel Column Validation Examples This article shows validation and design examples for steel columns per the *AISC Specification*, 2016. Note that values will vary slightly (+/- 1%) due to round-off errors. ## Example 1 - W-Shape Column with Pinned Ends (LRFD) Reference: *AISC Companion to the Steel Construction Manual Version 15.1,* 2019, **Example E.1A** In this example, we find the compression capacity of a standard W-shape column. The example looks at both 50 ksi and 65 ksi steel. ### Inputs | Parameter | Values (Grade 50 / Grade 65) | | -------------------- | ---------------------------- | | Axial Loads | D = 140 kips, L = 420 kips | | Length $L$ | 30' | | Yield Strength $F_y$ | 50 ksi / 65 ksi | | Section Size | W14x132 / W14x120 | ### Outputs | Value | Example (Gr. 50 / Gr. 65) | Calcs.com (Gr. 50 / Gr.65) | | ------------------ | ------------------------- | -------------------------- | | Factored Load | 840 kip | 840 kip | | Available Strength | 893 kip / 856 kip | 893 kip / 856 kip | ## Example 2 - WT-Shape Column with Slender Elements (ASD) Reference: *AISC Companion to the Steel Construction Manual Version 15.1,* 2019, **Example E.8** ### Inputs | Parameter | Values | | -------------------- | ----------------------- | | Axial Loads | D = 6 kips, L = 18 kips | | Length $L$ | 20' | | Yield Strength $F_y$ | 50 ksi | | Section Size | WT7x15 | ### Outputs | Value | Example | Calcs.com | | ------------------------------------------ | -------- | --------- | | Applied Load | 24 kip | 24 kip | | Elastic Flexural Buckling Stress (X-Axis) | 21.3 ksi | 21.3 ksi | | Elastic Flexural Buckling Stress (Y-Axis) | 11.0 ksi | 11.0 ksi | | Elastic Flexural-Torsional Buckling Stress | 10.5 ksi | 10.5 ksi | | Critical Buckling Stress | 9.21 ksi | 9.21 ksi | | Effective Area | 4.42 in2 | 4.42 in2 | | Available Compressive Strength | 24.4 kip | 24.4 kip | ## Example 3 - HSS Column with Slender Elements (ASD) Reference: *AISC Companion to the Steel Construction Manual Version 15.1,* 2019, **Example E.10** ### Inputs | Parameter | Values | | -------------------- | ----------------- | | Length $L$ | 24' | | Yield Strength $F_y$ | 50 ksi | | Section Size | HSS 12 x 8 x 3/16 | ### Outputs | Value | Example | Calcs.com | | ------------------------------ | -------- | ---------- | | Critical Buckling Stress | 29.1 ksi | 29.1 ksi | | Effective Area | 5.77 in2 | 5.7 in2 \* | | Available Compressive Strength | 101 kip | 99.4 kip | \*We conservatively use the nominal HSS wall thickness when calculating the reduction in area, which the design example does not do. This also affects the available compressive strength. ## Example 4 - HSS Column with Slender Elements (ASD) Reference: *AISC Companion to the Steel Construction Manual Version 15.1,* 2019, **Example H.4** ### Inputs | Parameter | Values | | ---------------------- | --------------------------------------- | | Axial Loads | D = 5 kip, L = 15 kip | | Lateral Loads (X-Axis) | wD = 0.612 kip/ft, wL = 1.837 kip/ft | | Lateral Loads (Y-Axis) | wD = 0.08163 kip/ft, wL = 0.2449 kip/ft | | Length $L$ | 14' | | Yield Strength $F_y$ | 50 ksi | | Section Size | W10x33 | ### Outputs | Value | Example | Calcs.com | | ------------------------------------ | ------------ | ------------ | | Factored Axial Load | 20 kip | 20 kip | | Unamplified Moment (X-Axis) | 60 kip\*ft | 60 kip\*ft | | Unamplified Moment (Y-Axis) | 8 kip\*ft | 8 kip\*ft | | Available Axial Strength | 168 kip | 168 kip | | Amplified Moment (X-Axis) | 61.2 kip\*ft | 61.1 kip\*ft | | Amplified Moment (Y-Axis) | 8.72 kip\*ft | 8.76 kip\*ft | | Available Flexural Strength (X-Axis) | 91.0 kip\*ft | 90.7 kip\*ft | | Available Flexural Strength (Y-Axis) | 34.9 kip\*ft | 34.9 kip\*ft | | Interaction Check | 0.982 | 0.984 | | | | | ## Example 5 - Concentric Axial Loading (LRFD/ASD) Reference: [A Beginner's Guide to Structural Engineering 15th Edition](https://www.bgstructuralengineering.com/BGSCM15/BGSCM007/BGSCM0070802.htm), **Example 7.2** In this example, we find the compression capacity of a circular HSS column. Self-weight is not considered in this example. ### Inputs | Parameter | Values | | -------------------- | ---------------------------- | | 2nd Floor Loads | D = 12.2 kips, L = 2.88 kips | | 3nd Floor Loads | D = 12.5 kips, L = 2.88 kips | | Roof | D = 4.59 kips, L = 3.6 kips | | Length $L$ | 10.67 ft | | Yield Strength $F_y$ | 42 ksi | | Section Size | HSS5.563X0.134
| ### Outputs | Value | Example (LRFD / ASD) | Calcs.com ( LRFD / ASD) | | ----------------------------------------------------------------------- | -------------------- | ----------------------- | | Factored Axial Load $P_u$ (LRFD) or $P_a$ (ASD) | 46.7 kip / 36.3 kip | 46.7 kip / 36.3 kip | | Factored Available Strength $\phi_{P_n}$ (LRFD) or $P_n/\Omega$ (ASD)\* | 61 kip / 40.6 kip | 61 kip / 40.6 kip | | Effective Area | 2.12 in2 | 2.12 in2 | | Critical Flexural Buckling Stress $F_{crx}$/$F_{cry}$ \*\* | 31.97 ksi | 32.0 ksi | \*Note: the example includes the resistance/safety factor in the loads to find the nominal capacity required. In Calcs.com, we apply resistance factors to the member capacity - this is what you see here. \*\* Note: the HSS5.563X0.134 section is circular and will have the same strength and slenderness ratio in the X-axis and Y-Axis ## Example 6 - Combined Axial & Flexure Interaction (LRFD) Reference: [A Beginner's Guide to Structural Engineering 15th Edition](https://www.bgstructuralengineering.com/BGSCM15/BGSCM009/BGSCM0090601.htm)*,* **Example 9.1** In this example, we solve for the interaction value, axial and flexural strength of a W40X199 steel column. Self-Weight and Lateral Torsional Buckling are not considered in this example. Reduced companion live load conditions are applied in this situation. The wind load was been adjusted by a factor of 1.6 to accommodate for differences in the load combinations between ASCE 7-05 and ASCE 7-10. ### Inputs | Parameter | Values | | --------------------------- | --------------------------------------- | | Axial Loads | D = 300 kip, L = 200 kip, Wdn = 640 kip | | Lateral Loads | Wdn = 240 kip at 13.5 ft | | Length $L$ | 27 ft | | Yield Strength $F_y$ | 50 ksi | | Weak Axis Support Locations | 9 ft, 18 ft | | Section Size | HSS5.563X0.134 | ### Outputs | Value | Example | Calcs.com | | ------------------------------------------ | -------- | --------- | | Factored Axial Load $P_u$ | 1100 kip | 1100 kip | | Factored Compression Strength $\phi_{P_n}$ | 2223 kip | 2220 kip | | Factored Flexural Strength $\phi_{M_n}$ | 3259 kip | 3260 kip | | Compression - Bending Interaction | 0.949 | 0.949 |