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NACA Report 1255 numerical example: wrinkling strength of a 2024-T3 Z-stiffened compression panel
| Tool | Stiffened Panel Compression |
| Source | Semonian, J. W., and Peterson, J. P. (1956). An Analysis of the Stability and Ultimate Compressive Strength of Short Sheet-Stringer Panels With Special Reference to the Influence of the Riveted Connection Between Sheet and Stringer. NACA Report 1255, National Advisory Committee for Aeronautics, Washington, DC. Appendix, Numerical Example (Figures 8 and 9, equations 3, 6-9, 11 and 12). |
| Level | Professional |
Problem
A short 2024-T3 Z-stiffened compression panel has t_w = 0.064 in, t_s = 0.102 in, b_w/t_w = 40, b_s/t_s = 30, b_A/t_w = 8, b_F/b_w = 0.40 and a rivet offset b_o/t_w = 5; it is assembled with 3/32-inch brazier-head 2117-T3 rivets at a 1-inch pitch; E = 10,600 ksi, ν = 0.32, F_cy = 43.6 ksi, and the stringer alone cripples at 27.5 ksi (tests). Find the effective rivet offset, the wrinkling stress of the plate with the plasticity correction, the average panel stress at failure, and check the rivet pitch and the rivet strength against the report's criteria.
Inputs to Enter
- Stringer: Z, formed 2024-T3-type; b_w 2.56 in, b_A 0.512 in, b_F 1.024 in, t_w 0.064 in; F_cc override 27.5 ksi
- Sheet: t_s 0.102 in, stringer pitch b_s 3.06 in; rivets p 1.0 in, d 0.09375 in, offset b_o 0.32 in, brazier head, rivet tensile strength 268 lb
- Material: E 10.6 Msi, F_cy 43.6 ksi, ν 0.32, Ramberg-Osgood n 9; frame spacing 19.6 in, c = 1; running load 4,500 lb/in entered as Ultimate (radio; 3,000 lb/in limit × FS 1.5)
Answers
- β = 1.33, p/d = 10.7, A_z = 0.262 in², b_s t_s = 0.312 in² (book 1.33 / 10.7 / 0.262 / 0.312)
- f/t_w = 6.94 from the digitized Figure 8 (book reading 6.98); k_M = 3.66 (book 3.64); σ_M/η = 39.5 ksi (book 39.2); σ_M = 34.3 ksi (book 34.1)
- Panel average stress at wrinkling failure (34.3 × 0.312 + 27.5 × 0.262)/0.574 = 31.2 ksi (book 31.1 ksi); monolithic crippling by TN 3785 eq. (25) 32.1 ksi (book, Figure 10: 31.6)
- Allowable rivet pitch p_a = 0.9 b_s √(2/k_M) = 2.04 in ≥ 1.00 in; required rivet strength R_R = 0.243 kips (book 0.239) ≤ 0.268 kips available
- Johnson-Euler column of the stringer plus effective sheet at L′/ρ = 20: F_c = 26.8 ksi, allowable running load 5,024 lb/in (governs); M.S. = 5,024/4,500 − 1 = +0.12
Notes
The tool's default inputs are this panel; press Submit. With the report's own chart reading f/t_w = 6.98 the chain gives k_M 3.63, σ_M/η 39.2, σ_M 34.1 (n = 9), 31.1 ksi, p_a 2.04 in and R_R 0.239 kips, every printed digit; the digitized chart differs by 0.6 % in f/t_w. Checked in test_stiffened_panel.php (140 checks) with the numpy script References/Stiffened-Panel/checks/panel_check.py, which also predicts the report's Table I 7075-T6 panel tests 6 % conservative on average.