USA Based Calculations
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.
*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.
*Note: the example includes the resistance/safety factor in the loads to find the nominal capacity required. In ClearCalcs, 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 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 | 30’ |
| Yield Strength | 50 ksi / 65 ksi |
| Section Size | W14x132 / W14x120 |
Outputs
| Value | Example (Gr. 50 / Gr. 65) | ClearCalcs (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.8Inputs
| Parameter | Values |
|---|---|
| Axial Loads | D = 6 kips, L = 18 kips |
| Length | 20’ |
| Yield Strength | 50 ksi |
| Section Size | WT7x15 |
Outputs
| Value | Example | ClearCalcs |
|---|---|---|
| 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.10Inputs
| Parameter | Values |
|---|---|
| Length | 24’ |
| Yield Strength | 50 ksi |
| Section Size | HSS 12 x 8 x 3/16 |
Outputs
| Value | Example | ClearCalcs |
|---|---|---|
| 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 |
Example 4 - HSS Column with Slender Elements (ASD)
Reference: AISC Companion to the Steel Construction Manual Version 15.1, 2019, Example H.4Inputs
| 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 | 14’ |
| Yield Strength | 50 ksi |
| Section Size | W10x33 |
Outputs
| Value | Example | ClearCalcs |
|---|---|---|
| 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, 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 | 10.67 ft |
| Yield Strength | 42 ksi |
| Section Size | HSS5.563X0.134 |
Outputs
| Value | Example (LRFD / ASD) | ClearCalcs ( LRFD / ASD) |
|---|---|---|
| Factored Axial Load (LRFD) or (ASD) | 46.7 kip / 36.3 kip | 46.7 kip / 36.3 kip |
| Factored Available Strength (LRFD) or (ASD)* | 61 kip / 40.6 kip | 61 kip / 40.6 kip |
| Effective Area | 2.12 in2 | 2.12 in2 |
| Critical Flexural Buckling Stress / ** | 31.97 ksi | 32.0 ksi |
Example 6 - Combined Axial & Flexure Interaction (LRFD)
Reference: A Beginner’s Guide to Structural Engineering 15th Edition, 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 | 27 ft |
| Yield Strength | 50 ksi |
| Weak Axis Support Locations | 9 ft, 18 ft |
| Section Size | HSS5.563X0.134 |
Outputs
| Value | Example | ClearCalcs |
|---|---|---|
| Factored Axial Load | 1100 kip | 1100 kip |
| Factored Compression Strength | 2223 kip | 2220 kip |
| Factored Flexural Strength | 3259 kip | 3260 kip |
| Compression - Bending Interaction | 0.949 | 0.949 |