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 | 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.8
Inputs
| 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.10
Inputs
| 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 |
*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 | 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 |
*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 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 |