Columns

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)	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 $L$	20'
Yield Strength $F_y$	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 $L$	24'
Yield Strength $F_y$	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 $L$	14'
Yield Strength $F_y$	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 $L$	10.67 ft
Yield Strength $F_y$	42 ksi
Section Size	HSS5.563X0.134

Outputs

Value	Example (LRFD / ASD)	ClearCalcs ( 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 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 $L$	27 ft
Yield Strength $F_y$	50 ksi
Weak Axis Support Locations	9 ft, 18 ft
Section Size	HSS5.563X0.134

Outputs

Value	Example	ClearCalcs
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