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Shear-resistant 2024-T3 web, 10 in deep with single angle stiffeners at 6 in: buckling stress by NACA TN 2661 equation (32) and the stiffener inertia by four published criteria

Tool	Shear-Resistant Web
Source	Kuhn, P., Peterson, J. P., and Levin, L. R. (1952). A Summary of Diagonal Tension. Part I: Methods of Analysis. NACA Technical Note 2661, Section 4.2 equation (32) and Figure 12; Moore, R. L. (1942). An Investigation of the Effectiveness of Stiffeners on Shear-Resistant Plate-Girder Webs. NACA Technical Note 862, conclusion 5; Stein, M., and Fralich, R. W. (1949). Critical Shear Stress of Infinitely Long, Simply Supported Plate with Transverse Stiffeners. NACA Technical Note 1851, Table I; Bruhn, E. F. (1973). Analysis and Design of Flight Vehicle Structures. Jacobs Publishing, Carmel, IN, equation C10.8 and Figure C10.9.
Level	Professional

Problem

A 2024-T3 shear web 10 in deep between flange centroids (clear depth 9 in) and 0.063 in thick is stiffened by single 0.75 × 0.75 × 0.063 in angles at 6 in (clear spacing 5.25 in) between double 1 × 1 × 0.125 in flange angles, and carries an ultimate shear of 6,000 lb (a limit shear of 4,000 lb with the ultimate factor 1.5). Is the web shear-resistant at limit load, what is its margin against the shear strength at ultimate, do the stiffeners have the inertia required to act as nodal lines by Bruhn's, Moore's and Stein and Fralich's criteria, and what do the web-to-flange rivets (5/32 in at 0.75 in pitch) carry?

Inputs to Enter

h 10 in, h_c 9 in, t 0.063 in, d 6 in, d_c 5.25 in; single stiffeners A_u 0.0905 in², I_u 0.0102 in⁴ about the web median plane, ρ_u 0.233 in, t_u 0.063 in, e_u 0.242 in, h_u 9 in; double flange angles A_f 0.47 in², t_f 0.125 in
2024-T3: E 10,500 ksi, ν 0.33, F_cy 39 ksi, F_tu 64 ksi, F_su 39 ksi, Ramberg-Osgood n 20, density 0.100 lb/in³; V 6,000 lb entered as Ultimate (radio), FS 1.5, so V_L = 4,000 lb
Web-to-flange rivets D_f 5/32 in, pitch 0.75 in, one row, shear allowable 596 lb, web bearing allowable 125 ksi; stiffener rivet pitch 1.0 in

Open the Shear-Resistant Web tool (loaded with this example)

Answers

τ_L = 4,000/(10 × 0.063) = 6.349 ksi, τ_U = 9.524 ksi; h_c/d_c = 1.714 → k_ss = 6.18 (Figure 12(a)); t_u/t = 1.0 → R_h = 0.70 (lower curve), t_f/t = 1.98 → R_d = 1.49 (upper curve); τ_cr,e = 6.18 × 10,500 × (0.063/5.25)² × [0.70 + ½(1.49 − 0.70)(5.25/9)³] = 7.279 ksi, elastic (√3 τ = 12.6 ksi below the proportional limit)
TN 3781 bounds for the same panel: 9.35 ksi simply supported (k_s 6.70), 15.19 ksi clamped (k_s 10.89); shear-resistant margin at limit M.S. = 7.279/6.349 − 1 = +0.15; at ultimate τ_U/τ_cr = 1.308, k = tanh(0.5 log 1.308) = 0.058; web shear strength M.S. = 39/9.524 − 1 = +3.10
Stiffener inertia required: Bruhn C10.8 2.29 (6/0.063)(4,000 × 10/(33 × 10.5 × 10⁶))^(4/3) = 0.001226 in⁴; Bruhn Figure C10.9 0.002054 in⁴ (I/(d t³) = 1.37); Moore λ = 14/(6/9)³ = 47.25 → 0.006646 in⁴; Stein-Fralich E I/(D d) = 27.6 (Table I cut-offs 6.59 / 76.2 / 672 at h_c/d = 1 / 2 / 5) → 0.003872 in⁴; Bleich fit 0.005814 in⁴; the 0.0102 in⁴ angle gives M.S. +0.53 against Moore's, the largest
Stiffener compression at ultimate from the diagonal tension 0.916 ksi against the Johnson column allowable 33.6 ksi (L_e 8.97 in, L_e/ρ 38.5); rivet shear flow max(V/h = 600, V Q/I = 516) × (1 + 0.414 × 0.058) = 614.5 lb/in → 460.9 lb per rivet, M.S. +0.29 shear, bearing 46.8 ksi M.S. +1.67; weight 2.047 lb/ft

Notes

The tool's default inputs are this web; press Submit. The case is the tool's own default checked against the report formulas and an independent numpy recomputation (References/Shear-Resistant-Web/checks/shearweb_check.py, 52 values to 2e-6) in test_shear_resistant_web.php (215 checks), which also reproduces the TN 2661 example buckling stresses (0.416 and 16.55 ksi), the TN 1851 Table I values and the TN 3781 Figure 22 readings; it is not a worked example printed in a book. Moore's formula is the most demanding criterion for every ordinary proportion; the brief's 0.040 in web at the same load is not shear-resistant (τ/τ_cr ≈ 2.2).