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Quasi-isotropic carbon/epoxy laminate with a 0.25 in hole and one fastener row: Whitney-Nuismer open-hole strength and Hart-Smith bearing-bypass margins

Tool	Composite Hole and Joint Strength
Source	Whitney, J. M. (1983). "Notch Strength of Composites." In Noor, A. K., Shuart, M. J., Starnes, J. H., Jr., and Williams, J. G. (eds.), Failure Analysis and Mechanisms of Failure of Fibrous Composite Structures, NASA Conference Publication 2278, Langley Research Center, Hampton, VA, pp. 241–263 (pp. 247, 248: criteria and width correction). Hart-Smith, L. J. (1976). Bolted Joints in Graphite-Epoxy Composites. NASA Contractor Report 144899, Douglas Aircraft Company, Long Beach, CA (eqs 1, 2, 8, 16, 17, 27, 28, 32, 33).
Level	Professional

Problem

A [45/0/−45/90]2s laminate of 0.005 in carbon/epoxy plies (16 plies, 0.080 in) carries 1,200 lb/in ultimate. Find its open-hole tension strength with a 0.25 in hole in a 1.5 in wide panel by the point-stress and average-stress criteria, and check one fastener of a joint row (0.25 in fastener, pitch 1.5 in, end distance 0.75 in) that reacts 720 lb in bearing while 1,080 lb bypasses it, in bearing, net tension, shear-out and bearing-bypass interaction.

Inputs to Enter

Lamina (AS4/3501-6 example values of the Classical Laminate Theory tool): E_1 21.3 Msi, E_2 1.49 Msi, G_12 1.02 Msi, ν_12 0.27, ply 0.005 in; allowable strains 10,000 / 8,000 / 5,000 / 15,000 / 12,000 με; stacking code [45/0/-45/90]2s
Unnotched strengths left blank (first-ply failure of the stacking code); hole D 0.25 in, panel width W 1.5 in, d_0 0.04 in, a_0 0.15 in, criterion average stress, remote load N_x 1,200 lb/in
Joint: fastener 0.25 in, pitch 1.5 in, end distance 0.75 in, protruding head, F_br 100 ksi, shear-out allowable 20 ksi, C 0.27, minimum e/d 3 and w/d 4; one row with P_br 720 lb, P_by 1,080 lb
Load level Ultimate (FS 1.5 not applied)

Open the Composite Hole and Joint Strength tool (loaded with this example)

Answers

Laminate theory: E_x = E_y = 8.434 Msi, G_xy = 3.272 Msi, ν_xy = 0.2887, t = 0.080 in; first-ply failure in tension at 5,000 με in the 90° plies, 42.17 ksi (compression 67.47 ksi)
K_T = 1 + √(2(√(E_x/E_y) − ν_xy) + E_x/G_xy) = 3.000 (quasi-isotropic); width correction Y = (2 + (1 − D/W)³)/(3(1 − D/W)) = 1.031
Point stress: ξ = 0.125/0.165 = 0.7576, σ_N/σ_0 = 0.5615; average stress: ξ = 0.125/0.275 = 0.4545, σ_N/σ_0 = 0.6231 (1/K_T = 0.333 for a large hole)
Open-hole strength (average stress) 26.28 ksi infinite plate, 25.48 ksi gross in the panel, 30.57 ksi net; applied 15.00 ksi: M.S. = +0.70 (ULT)
Fastener hole: Θ = 0.5, k_te = 6.464 loaded and 2.579 open; k_tc = 1 + 0.27 (6.464 − 1) = 2.475, k_t = 1.426, k_b = 0.4951
Single fastener: bearing 2,000 lb, net tension 1,704 lb, shear-out 2,000 lb; joint efficiency 33.7 %
σ_br = 36.00 ksi, σ_by = 10.80 ksi net, net-section peak 0.4951 · 36.00 + 1.426 · 10.80 = 33.23 ksi; load factor to the envelope 1.269 (net tension)
M.S.: bearing +1.78, net tension +0.27, shear-out +1.78, bearing-bypass +0.27 (all ULT)

Notes

The tool's default inputs are this case; press Submit. The case is illustrative, not a printed example: the lamina values are the example values of the site's laminate tool, the bearing and shear-out allowables are round numbers, d_0, a_0 and C are the values the sources report for comparable laminates (Whitney: d_0 0.0358 to 0.0437 in, a_0 0.143 to 0.163 in; Hart-Smith: C = 0.27 for quasi-isotropic T300/5208). The unnotched strength is the first-ply-failure stress, which is conservative. Checked by test_composite_hole_joint_strength.php (466 checks) against the printed equations and values of the two NASA documents and an independent numpy / scipy implementation.