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Extruded 2024-T4 tee LS 236 of NACA TN 3784 Table 9: Gerard's T-type crippling formula against the test

Tool	Crippling Strength
Source	Gerard, G. (1957). Handbook of Structural Stability Part IV: Failure of Plates and Composite Elements. NACA Technical Note 3784, National Advisory Committee for Aeronautics, Washington, DC. Table 9 (Crockett's extruded angle and T-section tests), eq. (A6) and Table 13; Gerard, G. (1957). Handbook of Structural Stability Part V. NACA Technical Note 3785, eqs. (2) to (5), Table 4 and figure 6 (g = flanges + cuts).
Level	Professional

Problem

An extruded aluminum-alloy tee (stem 1.00 in, flange 1.50 in wide, thickness 0.065 in; σ_cy = 43 ksi, E = 10,500 ksi) is loaded in compression as a short column. Find the crippling stress by Gerard's generalized method for T-type elements and by the element method, the crippling load, and the margin of safety against an ultimate load of 4,000 lb.

Inputs to Enter

Shape: tee; web (stem) width 1.00 in, flange outstand 0.75 in (total flange 1.50 in), thickness 0.065 in; extruded
E = 10.5 Msi, F_cy = 43 ksi, cladding factor 1.0; applied ultimate load 4,000 lb

Open the Crippling Strength tool (loaded with this example)

Answers

A = 0.1625 in², A/t² = 38.5 (table 38.5); g = 3 flanges + 0 cuts (TN 3785 fig. 6); abscissa A/(g t²) √(F_cy/E) = 0.820 (table 0.82)
Gerard T-type: F_cs/F_cy = 0.670 (1/0.820)^0.40 = 0.725 → F_cs = 31.2 ksi (test 31.0 ksi, ratio 0.721, +0.6 %); below the 3/4 cutoff
Element method (Needham's form, C = 0.316 for one edge free): stem 27.3 ksi, outstands 33.9 ksi, area-weighted 31.3 ksi
P_cc = F_cs A = 5,067 lb; M.S. = 5,067 / 4,000 − 1 = +0.27 (ultimate)

Notes

The tool's default inputs are this specimen; press Submit. Needham's angle-element method does not apply to a T junction and is reported as not applicable. Every printed value is checked in test_crippling.php (252 checks) together with the Table 9 angles LS 208 to 210, the Table 10 two-corner sections (β = 4.0), the Table 12 multicorner sections (β_c = 1.30), the TN 3785 Table 4 identities and the numpy script References/Crippling/crippling_check.py.