Columns

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

Axial LoadsD = 140 kips, L = 420 kips
Length $L$30'
Yield Strength $F_y$50 ksi / 65 ksi
Section SizeW14x132 / W14x120

Outputs

ValueExample (Gr. 50 / Gr. 65)ClearCalcs (Gr. 50 / Gr.65)
Available Strength893 kip / 856 kip893 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

ParameterValues
Axial LoadsD = 6 kips, L = 18 kips
Length $L$20'
Yield Strength $F_y$50 ksi
Section SizeWT7x15

Outputs

ValueExampleClearCalcs
Elastic Flexural Buckling Stress (X-Axis)21.3 ksi21.3 ksi
Elastic Flexural Buckling Stress (Y-Axis)11.0 ksi11.0 ksi
Elastic Flexural-Torsional Buckling Stress10.5 ksi10.5 ksi
Critical Buckling Stress9.21 ksi9.21 ksi
Effective Area4.42 in24.42 in2
Available Compressive Strength24.4 kip24.4 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

ParameterValues
Length $L$24'
Yield Strength $F_y$50 ksi
Section SizeHSS 12 x 8 x 3/16

Outputs

ValueExampleClearCalcs
Critical Buckling Stress29.1 ksi29.1 ksi
Effective Area5.77 in25.7 in2 *
Available Compressive Strength101 kip99.4 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

ParameterValues
Axial LoadsD = 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 SizeW10x33

Outputs

ValueExampleClearCalcs
Unamplified Moment (X-Axis)60 kip*ft60 kip*ft
Unamplified Moment (Y-Axis)8 kip*ft8 kip*ft
Available Axial Strength168 kip168 kip
Amplified Moment (X-Axis)61.2 kip*ft61.1 kip*ft
Amplified Moment (Y-Axis)8.72 kip*ft8.76 kip*ft
Available Flexural Strength (X-Axis)91.0 kip*ft90.7 kip*ft
Available Flexural Strength (Y-Axis)34.9 kip*ft34.9 kip*ft
Interaction Check0.9820.984

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

ParameterValues
2nd Floor LoadsD = 12.2 kips, L = 2.88 kips
3nd Floor LoadsD = 12.5 kips, L = 2.88 kips
RoofD = 4.59 kips, L = 3.6 kips
Length $L$10.67 ft
Yield Strength $F_y$42 ksi
Section SizeHSS5.563X0.134

Outputs

ValueExample (LRFD / ASD)ClearCalcs ( LRFD / ASD)
Factored Axial Load $P_u$ (LRFD) or $P_a$ (ASD)46.7 kip / 36.3 kip46.7 kip / 36.3 kip
Factored Available Strength $\phi P_n$ (LRFD) or $P_n/\Omega$ (ASD)*61 kip / 40.6 kip61 kip / 40.6 kip
Effective Area2.12 in22.12 in2
Critical Flexural Buckling Stress $F_{crx}$/$F_{cry}$ **31.97 ksi32.0 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

ParameterValues
Axial LoadsD = 300 kip, L = 200 kip, Wdn = 640 kip
Lateral LoadsWdn = 240 kip at 13.5 ft
Length $L$27 ft
Yield Strength $F_y$50 ksi
Weak Axis Support Locations9 ft, 18 ft
Section SizeHSS5.563X0.134

Outputs

ValueExampleClearCalcs
Factored Axial Load $P_u$1100 kip1100 kip
Factored Compression Strength $\phi P_n$2223 kip2220 kip
Factored Flexural Strength $\phi M_n$3259 kip3260 kip
Compression - Bending Interaction0.9490.949

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