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 L L 30' Yield Strength F y F_y Fy​ 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 L L L 20' Yield Strength F y F_y Fy​ 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 L L L 24' Yield Strength F y F_y Fy​ 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 L L L 14' Yield Strength F y F_y Fy​ 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 L L L 10.67 ft Yield Strength F y F_y Fy​ 42 ksi Section Size HSS5.563X0.134

Outputs

Value Example (LRFD / ASD) ClearCalcs ( LRFD / ASD) Factored Axial Load P u P_u Pu​ (LRFD) or P a P_a Pa​ (ASD) 46.7 kip / 36.3 kip 46.7 kip / 36.3 kip Factored Available Strength ϕ P n \phi P_n ϕPn​ (LRFD) or P n / Ω P_n/\Omega Pn​/Ω (ASD)* 61 kip / 40.6 kip 61 kip / 40.6 kip Effective Area 2.12 in2 2.12 in2 Critical Flexural Buckling Stress F c r x F_{crx} Fcrx​/ F c r y F_{cry} Fcry​ ** 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 L L L 27 ft Yield Strength F y F_y Fy​ 50 ksi Weak Axis Support Locations 9 ft, 18 ft Section Size HSS5.563X0.134

Outputs

Value Example ClearCalcs Factored Axial Load P u P_u Pu​ 1100 kip 1100 kip Factored Compression Strength ϕ P n \phi P_n ϕPn​ 2223 kip 2220 kip Factored Flexural Strength ϕ M n \phi M_n ϕMn​ 3259 kip 3260 kip Compression - Bending Interaction 0.949 0.949