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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

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

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

Analysis Method

Huth-Schwarmann (ASTM)ℹ️Huth (1984 LBF report FB-172; 1986 ASTM STP 927) fastener flexibility, C = ((t_1+t_2)/(2d))^a · (b/n) · [1/(t_1·E_1) + 1/(n·t_2·E_2) + 1/(2·t_1·E_f) + 1/(2·n·t_2·E_f)], n = 1 single shear, 2 double shear (t_1 centre plate, t_2 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/(t_1·E_1) + 1/(t_2·E_2)), 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, t_1 the centre plate and t_2 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·(e_1/(d·E_1) + e_2/(d·E_2)), 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/(t_1·E_1) + 1/(t_2·E_2), 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 = (t_1 + t_2)²/(E_f·d³) + 3.7·(1/(t_1·E_1) + 1/(t_2·E_2)), 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 E_1, E_2 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	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	Modulus E2 YPa ZPa EPa PPa TPa GPa MPa kPa hPa daPa Pa dPa PSI KSI MSI GSI	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	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	YPa ZPa EPa PPa TPa GPa MPa kPa hPa daPa Pa dPa PSI KSI MSI GSI		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. Used for: the Huth-Schwarmann method (coefficients a, b by joint type; its printed equation has n in place of 2 in the third term and is not used, see the 1984 report) and the Boeing equation as tabulated there.

Huth, H. (1984). Zum Einfluß der Nietnachgiebigkeit mehrreihiger Nietverbindungen auf die Lastübertragungs- und Lebensdauervorhersage. Bericht Nr. FB-172, Fraunhofer-Institut für Betriebsfestigkeit (LBF), Darmstadt. Used for: the Huth-Schwarmann method (original derivation; the equation as used, with 1/(2t₁E_f) in the third term, is taken from this report).

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. Section 3.5.1, eqs. (3-71)–(3-75): the Boeing equation (cited there to unpublished reports of the Boeing Co., Renton, WA), Grumman, Huth, Swift and Tate & Rosenfeld relations. Used for: the Boeing equation, the Grumman equation (cited there to Kroes, R. A., Description of the Computer Program SLAPJO, Fokker report SF-63, 1992), and as a check on the Swift and Tate & Rosenfeld single-shear forms.

de Sá Martins, R., dos Santos, M. T., & 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. Page 2 lists the Swift, Grumman, Huth, Tate & Rosenfeld and Morris relations. Used for: the Grumman equation (second listing).

Tate, M. B., & Rosenfeld, S. J. (1946). Preliminary Investigation of the Loads Carried by Individual Bolts in Bolted Joints. NACA TN-1051. National Advisory Committee for Aeronautics, Washington, DC. Bolt constant (shear, bending, bolt bearing, plate bearing), eq. (A14), derived for double-shear butt joints; eq. (A8) defines it per shear plane (δ = CR/2), so the fastener stiffness in double shear is 2/C. Used for: the Tate & Rosenfeld method (eq. (A14) as printed for a double-shear row; the single-shear lap form of the same model otherwise) and the double-shear case of the Hart-Smith method.

Rosenfeld, S. J. (1947). Analytical and Experimental Investigation of Bolted Joints. NACA TN-1458. National Advisory Committee for Aeronautics, Washington, DC. Background to TN-1051.

Yeh, H.-Y., Lee, J. J., & 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. DOI: 10.2514/1.9332. Comparison of fastener flexibility methods in multirow composite joints; cited for context, not as the source of any equation here.

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. Used for: the Swift (Douglas) method.

Vlieger, H., & Broek, D. (1974). Built-up Sheet Structures, Wings. In Fracture Mechanics of Aircraft Structures, AGARDograph 176, section V.C.1, pp. 195–225. Advisory Group for Aerospace Research and Development, NATO. Quotes the Swift relation as its eq. (6), p. 203; not a source for the Vought variant.

Vought method: original source not located. The equation is a variant of the Swift form with a thickness correction e on the member terms and a coefficient of 5.0 (single shear) or 2.2 (double shear); see the tooltip and the results page.

Nelson, W. D., Bunin, B. L., & Hart-Smith, L. J. (1983). Critical Joints in Large Composite Aircraft Structure. NASA CR-3710, Douglas Aircraft Company, August 1983. Used for: the Hart-Smith method (single shear with the (1 + 3β) bolt-rotation factor, p. 10; double shear by the TN-1051 bolt constant with laminate moduli, p. 9). Distinct from the Boeing equation.

McCarthy, C. T., McCarthy, M. A., & 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, Issue 2, pp. 157–171. Used for: the Delft method.

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