Local Buckling of Flexural Members per ADM 2020 in RFEM 6

• F.3.1 Weighted Average Method

This is the most common method used in the ADM examples and also the default option in RFEM 6. The weighted average method combines strengths determined separately for each element using equation F.3-1 of ADM 2020 [1].

• F.3.2 Direct Strength Method

In this method, the local buckling strength of the cross-section as a whole is determined by analysis which directly includes the interaction of the elements. This method is the most accurate and comprehensive of the three methods.

• F.3.3 Limiting Element Method

This method limits the flexural strength of the member based on the lowest local buckling strength of all elements. This method is often less accurate and more conservative since it does not account for the interaction between elements.

All three methods used in section F.3 to determine the local buckling strengths reference Section B.5.4 and B.5.5. These sections include determining the strength of elements in uniform compression and elements in flexural compression. The local buckling strength further depends on whether the element is supported on one or both edges in addition to the width to thickness ratio, b/t.

Comparison of RFEM Results Using the Three Different Methods

The local buckling strength of an aluminum beam in Example 3 of ADM is compared to the RFEM results using the three different methods previously described.

AW 5 x 3.70 section and 6061-T6 (B221) material is used for the 16 ft long beam. The beam has continuous lateral support and vertical support spacing at 4.0 ft on center. It is supporting a uniform dead load of 4.50 k/ft (Image 2).

The section properties are shown in Image 3.

The flange and web local buckling stresses are needed to determine the nominal flexural strength of the member.

Flange Local Buckling Stress

The flange (a flat element supported on one edge) is in uniform compression. Its local buckling stress is determined according to section B.5.4.1.

The slenderness ratio, b/t is equal to [(3.5 in -0.19 in - 2*0.30 in)/2] / 0.32 in = 4.234

The slenderness factor, λ₁ = 6.7 can be found using the equation listed in section B.5.4.1 or directly taken from Table 2-19 of Part VI.

Since b/t = 4.234 is less than λ₁ = 6.7, the yielding limit state controls. Therefore, the uniform compressive stress, F_c = F_cy = 35.0 ksi (Table A.4.1 & Table A.4.3).

Web Local Buckling Stress

The web (a flat element supported on two edges) is in flexural compression. Its local buckling stress is determined according to section B.5.5.1.

The slenderness ratio, b/t is equal to [(5.0 in -2*0.32 in -2*0.3 in)] / 0.19 in = 19.789

The slenderness factor, λ₁ = 33.1 can be found using the equation listed in section B.5.5.1 or directly taken from Table 2-19 of Part VI.

Since b/t = 19.789 is less than λ₁ = 33.1, the yielding limit state controls. Therefore, the flexural compressive stress, F_b = 1.5*F_cy = 1.5*35.0 ksi = 52.5 ksi (Table A.4.1 & Table A.4.3).

The Design Check Details in RFEM 6 provides the equations and references used in each method. The result output of each method can be verified easily.

• Nominal Flexural Strength, M_nlb per F.3.1 Weighted Average Method

• Nominal Flexural Strength, M_nlb per F.3.2 Direct Strength Method

• Nominal Flexural Strength, M_nlb per F.3.3 Limiting Element Method

This is the method used in Example 3 [1]. The negligible difference in the utilization ratio is from the Beam Formula used to determine the maximum required bending moment.

Conclusion

In this example, the design check ratios of from the Weighted Average Method and Direct Strength Method are almost identical (0.657 and 0.662). And as expected, the Limiting Element Method is the most conservative and has the highest design check ratio (0.749).

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Model | ADM Flexure Example