Worked Compression-Member Examples

Example 1: Euler Buckling as an Ideal Reference

A pinned-pinned column has E=29,000 ksiE=29,000\text{ ksi}, Iy=93.4 in4I_y=93.4\text{ in}^4, and L=15 ft=180 inL=15\text{ ft}=180\text{ in}. Determine the ideal elastic weak-axis buckling load.

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Example 2: AISC Flexural Column Curve for a Nonslender W-Shape

An A992 W14x90 has Fy=50 ksiF_y=50\text{ ksi}, Ag=26.5 in2A_g=26.5\text{ in}^2, rx=6.14 inr_x=6.14\text{ in}, ry=3.70 inr_y=3.70\text{ in}, and KL=180 inKL=180\text{ in} about both axes. Assume the section elements are nonslender and flexural buckling governs.

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Example 3: Directional Bracing Can Change the Governing Axis

A W12x50 has rx=5.18 inr_x=5.18\text{ in} and ry=1.96 inr_y=1.96\text{ in}. The x-axis unbraced length is 24 ft while a valid mid-height brace reduces the y-axis unbraced length to 12 ft. For this idealized example use Kx=Ky=1.0K_x=K_y=1.0.

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Example 4: Very Slender Flexural Buckling

A W8x24 has Ag=7.08 in2A_g=7.08\text{ in}^2, ry=1.61 inr_y=1.61\text{ in}, Fy=50 ksiF_y=50\text{ ksi}, and KL=300 inKL=300\text{ in}.

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Example 5: Slender Cross-Section Elements Require the Adopted Edition's Procedure

A built-up box column has one or more plate elements that exceed the compression width-to-thickness limit.

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Example 6: Single Angle — Flexural-Torsional Buckling Warning

A single angle is proposed as an 8 ft compression brace.

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Example 7: Stability-Method Consistency

A frame analysis uses Direct Analysis assumptions, but the member calculation later substitutes an arbitrary alignment-chart KK value greater than 1 because the frame is unbraced.

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Key Takeaways
  • Euler buckling is an ideal reference, not the final available strength.
  • Directional restraint can change which flexural axis governs.
  • The AISC column curve uses elastic buckling stress together with the specified column-strength equations.
  • A preferred KL/rKL/r recommendation is not a binary strength cutoff.
  • Slender cross-section elements must use the procedure from the adopted AISC edition; do not mix legacy QQ notation with later provisions without an explicit basis.
  • Single angles and other unsymmetric members can require flexural-torsional treatment.