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Fastened Joint Stiffness Calculator

Calculates effective shear and tension fastener stiffness for a single or double lap joint.

• Translational stiffness by eight published methods: Huth, Tate & Rosenfeld, Swift, Vought, Boeing, Delft, Grumman and Hart-Smith (NASA CR-3710)

• Rotational stiffness components taken from user input for finite element modeling

• All six degrees of freedom for input in finite element model

• Input multiple joint configurations at once

• Supports bolted metallic, riveted metallic, and bolted graphite/epoxy joints

Methods: Huth-Schwarmann (default), Tate & Rosenfeld, Swift, Vought, Boeing, Delft (McCarthy), Grumman, Hart-Smith (NASA CR-3710)

Huth Type: bm = bolted metallic (a=2/3, b=3.0), rm = riveted metallic (a=2/5, b=2.2), bg = bolted graphite/epoxy (a=2/3, b=4.2)
Hart-Smith Type: ph = protruding head, torqued (β = 0.15), cs = countersunk (β = 0.5), pin = shear pin (β = 1.0); used by the Hart-Smith method only
DS = double shear (checked: t₁ is the centre plate, t₂ each of the two outer straps, as in the figure)

Joint Properties Input

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Unit System: SI / USCS

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Equation Display:Value OnlySymbolicResultFullHide All

Rotational Stiffnesses (for FEA input)

Torsional - K_mx:

GN-m MN-m kN-m hN-m daN-m N-m dN-m cN-m mN-m μN-m nN-m pN-m lb-in lb-ft kip-in kip-ft

Bending Y - K_my:

GN-m MN-m kN-m hN-m daN-m N-m dN-m cN-m mN-m μN-m nN-m pN-m lb-in lb-ft kip-in kip-ft

Bending Z - K_mz:

GN-m MN-m kN-m hN-m daN-m N-m dN-m cN-m mN-m μN-m nN-m pN-m lb-in lb-ft kip-in kip-ft

Analysis Method

Huth-Schwarmann (ASTM)ℹ️Huth (1984 LBF report FB-172; 1986 ASTM STP 927) fastener flexibility, C = ((t₁+t₂)/(2d))^a · (b/n) · [1/(t₁·E₁) + 1/(n·t₂·E₂) + 1/(2·t₁·E_f) + 1/(2·n·t₂·E_f)], n = 1 single shear, 2 double shear (t₁ centre plate, t₂ each strap). Coefficients by Huth Type: bolted metallic a = 2/3, b = 3.0; riveted metallic a = 2/5, b = 2.2; bolted graphite/epoxy a = 2/3, b = 4.2. Equation form from the 1984 report.
Swift (Douglas)ℹ️Swift (Douglas Aircraft, 1971) empirical fastener flexibility, C = 5.0/(d·E_f) + 0.8·(1/(t₁·E₁) + 1/(t₂·E₂)), developed for the DC-10 fail-safe analysis; coefficients for aluminium fasteners. Single shear only.
Tate & Rosenfeld (NACA TN 1051)ℹ️Bolt constant of Tate and Rosenfeld (NACA TN 1051, 1946): bolt shear, bolt bending, bolt bearing and plate bearing. A double-shear row (DS checked) uses the report's eq. (A14) for a symmetrical butt joint, t₁ the centre plate and t₂ each strap; a single-shear row uses the two-member lap form of the same model. Double shear: K = 2/C (C is per shear plane).
Voughtℹ️Empirical relation of the Swift form, C = A/(d·E_f) + 0.8·(e₁/(d·E₁) + e₂/(d·E₂)), with a thickness correction e on the member terms (e = 1.0 for t/d ≤ 0.65, 1.29·t/d for t/d ≥ 0.90, linear between) and A = 5.0 in single shear or 2.2 in double shear. Attributed to Vought; the original source has not been found, so use with care.
Boeingℹ️Boeing fastener flexibility equation, C = sum over the two members of 2^{(t/d)^0.85}/t · (1/E_plate + 3/(8·E_f)), from unpublished Boeing Co. reports, as tabulated in Huth (1986, ASTM STP 927) and quoted by de Rijck (2005, eq. 3-71). Single shear only. Not the Nelson, Bunin and Hart-Smith (Douglas) equation.
Delft Universityℹ️Fastener flexibility of the Swift form, C = 1.5/(d·E_f) + 1/(t₁·E₁) + 1/(t₂·E₂), i.e. coefficients 1.5 on the fastener term and 1.0 on the member terms. Attributed to McCarthy et al. (2005), analytical model for load distribution in highly loaded single-shear composite bolted joints. Single shear only.
Grummanℹ️Grumman empirical fastener flexibility, C = (t₁ + t₂)²/(E_f·d³) + 3.7·(1/(t₁·E₁) + 1/(t₂·E₂)), as tabulated by de Rijck (2005, eq. 3-72) and ICAS 2018 (eq. 3). Single shear only.
Hart-Smith (NASA CR-3710)ℹ️Nelson, Bunin and Hart-Smith (Douglas Aircraft, NASA CR-3710, 1983). Single shear: the Tate and Rosenfeld bolt constant without the bending term, bearing terms multiplied by (1 + 3β), where β is the fraction of the bolt bending moment reacted by non-uniform bearing and is set by the Hart-Smith Type column. Double shear: NACA TN 1051 eq. (A14), K = 2/C. Member moduli E₁, E₂ stand in for the laminate value sqrt(E_L·E_T).

Joint Configurations

	Fast. Diam. d hm dam m dm cm mm μm nm pm fm am zm mil in ft yd sm nmi	Fast. Mod. Ef YPa ZPa EPa PPa TPa GPa MPa kPa hPa daPa Pa dPa PSI KSI MSI GSI inH2O psf ksf	Thickness t1 hm dam m dm cm mm μm nm pm fm am zm mil in ft yd sm nmi	Thickness t2 hm dam m dm cm mm μm nm pm fm am zm mil in ft yd sm nmi	Modulus E1 YPa ZPa EPa PPa TPa GPa MPa kPa hPa daPa Pa dPa PSI KSI MSI GSI inH2O psf ksf	Modulus E2 YPa ZPa EPa PPa TPa GPa MPa kPa hPa daPa Pa dPa PSI KSI MSI GSI inH2O psf ksf	DS	Huth Type	Hart-Smith Type
1	hm dam m dm cm mm μm nm pm fm am zm mil in ft yd sm nmi	YPa ZPa EPa PPa TPa GPa MPa kPa hPa daPa Pa dPa PSI KSI MSI GSI inH2O psf ksf	hm dam m dm cm mm μm nm pm fm am zm mil in ft yd sm nmi	hm dam m dm cm mm μm nm pm fm am zm mil in ft yd sm nmi	YPa ZPa EPa PPa TPa GPa MPa kPa hPa daPa Pa dPa PSI KSI MSI GSI inH2O psf ksf	YPa ZPa EPa PPa TPa GPa MPa kPa hPa daPa Pa dPa PSI KSI MSI GSI inH2O psf ksf		bm | bolted metallic rm | riveted metallic bg | bolted graphite/epoxy	ph | protruding head, torqued (β = 0.15) cs | countersunk (β = 0.5) pin | shear pin (β = 1.0)

References

Huth, H. (1986). "Influence of Fastener Flexibility on the Prediction of Load Transfer and Fatigue Life for Multiple-Row Joints." In Fatigue in Mechanically Fastened Composite and Metallic Joints, ASTM STP 927, American Society for Testing and Materials, Philadelphia, pp. 221–250.

Huth, H. (1984). Zum Einfluß der Nietnachgiebigkeit mehrreihiger Nietverbindungen auf die Lastübertragungs- und Lebensdauervorhersage. Bericht FB-172, Fraunhofer-Institut für Betriebsfestigkeit (LBF), Darmstadt.

de Rijck, J. J. M. (2005). Stress Analysis of Fatigue Cracks in Mechanically Fastened Joints: An Analytical and Experimental Investigation. PhD thesis, Delft University of Technology, Delft.

de Sá Martins, R., dos Santos, M. T., and Sales Palma, E. (2018). "Fastening Analysis Using Low Fidelity Finite Element Models." Paper 0659, 31st Congress of the International Council of the Aeronautical Sciences (ICAS), Belo Horizonte.

Tate, M. B., and Rosenfeld, S. J. (1946). Preliminary Investigation of the Loads Carried by Individual Bolts in Bolted Joints. NACA Technical Note 1051, National Advisory Committee for Aeronautics, Washington, D.C.

Rosenfeld, S. J. (1947). Analytical and Experimental Investigation of Bolted Joints. NACA Technical Note 1458, National Advisory Committee for Aeronautics, Washington, D.C.

Yeh, H.-Y., Lee, J. J., and Yang, D. Y. T. (2004). "Study of Multirow Highly Loaded Bolt Joints in Composite Wing Structure." Journal of Aircraft, Vol. 41, No. 2, pp. 380–385.

Swift, T. (1971). "Development of the Fail-Safe Design Features of the DC-10." In Damage Tolerance in Aircraft Structures, ASTM STP 486, American Society for Testing and Materials, Philadelphia, pp. 164–214.

Vlieger, H., and Broek, D. (1974). "Built-up Sheet Structures, Wings." In Fracture Mechanics of Aircraft Structures, AGARDograph 176, Section V.C.1, Advisory Group for Aerospace Research and Development, NATO, Neuilly-sur-Seine, pp. 195–225.

Nelson, W. D., Bunin, B. L., and Hart-Smith, L. J. (1983). Critical Joints in Large Composite Aircraft Structure. NASA Contractor Report 3710, Douglas Aircraft Company, Long Beach, CA.

McCarthy, C. T., McCarthy, M. A., and Lawlor, V. P. (2005). "An Analytical Model for the Prediction of Load Distribution in Highly Loaded, Single-Shear Composite Bolted Joints." Composite Structures, Vol. 71, No. 2, pp. 157–171.

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