VDI 2230-1 Single-bolt Joint Calculation v1.0 · 2026-10-24

VDI 2230 Blatt 1:2015 — Systematic single bolt joint calculation, with optional eccentric clamping/loading

VDI 2230 Part 1 single-bolt joint

The calculator designs or checks one high-strength bolted joint with the calculation steps R0 to R13 (VDI 2230 Part 1:2015, §4.2 R0–R13).

  • Joint types: through-bolt joint (TBJ) and tapped thread joint (TTJ) (VDI 2230 Part 1:2015, §2).
  • Working loads: axial load F_A, transverse load F_Q, torque M_Y about the bolt axis and internal pressure (VDI 2230 Part 1:2015, §2, F_A; §5.4.1, Eq. (108)(109)).
  • Optional eccentric clamping and loading, tensile load, cases I to III (VDI 2230 Part 1:2015, §5.3.2, Table 4).
  • Design mode picks a size from Table A7 (VDI 2230 Part 1:2015, §4.2 R0, Annex A, Table A7); verification mode checks the size you give. R1 to R13 run in both modes.
  • Checks: assembly stress R7, static strength R8, fatigue R9, surface pressure R10, length of engagement R11 (TTJ only), slip and shear R12; tightening torque R13 (VDI 2230 Part 1:2015, §4.2 R7–R13).

Not implemented: an external bending moment M_B (VDI 2230 Part 1:2015, §5.3.1.3, Eq. (96)–(98); §5.3.2, Eq. (102)–(107)) and an eccentric joint of clamped parts of different materials (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (68)–(70)).

Data sources:

  • VDI 2230 Part 1:2015
  • DIN EN ISO 898-1:2013-05, 7, Table 3 (R_{p0,2} and R_m of the strength classes)
  • DIN ISO 724:2024 (thread sizes); DIN EN ISO 898-1:2013-05, Table 4 (stress area)

Load introduction and eccentricity: reading the figures, filling in the inputs

Eccentric loading uses a and s_{sym}; a_k and l_A only serve to find n

  • a and s_{sym} both appear in the relationship for the additional bolt load of an eccentrically clamped joint (VDI 2230 Part 1:2015, §3.2.2, Eq. (15)).
  • The height h, the distance a_k and the length l_A are determined from the geometry of the joint and are used to read n from Table 2 (VDI 2230 Part 1:2015, §5.2.2.2 d)–e), Figure 17, Figure 23).
  • For eccentric loading, set "Eccentric clamping / loading" to "Yes" in card "11. Eccentric clamping and loading (optional)" and enter a; for eccentric clamping, also enter s_{sym} and the cross-section inputs of that card. These inputs enter steps R3b-e and R3d (\Phi^*_{en}) and the opening check R3e.
  • "Joint type for load introduction (optional)", a_k and l_A only give a suggested value of n from Table 2 in step R3c; the calculation uses the value entered in "Load Introduction Factor (n)".
  • Example B4 writes a-s_{sym}-d_W/2 as l_A, with a_k=0 (VDI 2230 Part 1:2015, Annex B, Example B4, R3); Example B5 writes the same expression as a_k, with l_A=0 (VDI 2230 Part 1:2015, Annex B, Example B5, R3).

① What is the step on the right (the connecting solid), and what is l_A for?

  • a_k is the distance between the edge of the preloading area and the load introduction point at the basic solid (VDI 2230 Part 1:2015, §2, a_k).
  • l_A is the length between the basic solid and the load introduction point K in the connecting solid (VDI 2230 Part 1:2015, §2, l_A).
  • K is the load introduction point; K_G is the load introduction point at the basic solid (VDI 2230 Part 1:2015, §2, K, K_G).
  • Every joint can be divided into a basic solid and a connecting solid with regard to load introduction; the basic solid contains the region that affects the elasticity of the plates (at most up to G) and so also the compression cone; working loads can be passed into the basic solid via the connecting solid; K_G is approximately located half way up the connecting solid (VDI 2230 Part 1:2015, §5.2.2.2 b), Figure 21).
  • In the six figures of the help for "Joint type for load introduction" and in the parameter figure of the help for a_k and l_A, the small circle on the connecting solid is the load introduction point K in the connecting solid; K_G at the basic solid is not drawn (VDI 2230 Part 1:2015, §2, K, K_G, l_A; §5.2.2.2 b), Figure 21).
  • Example B1 takes the basic solid as ending with the piston rod, so the piston region next to it, under pressure in service, is the connecting solid; because the load is concentric, l_A=0; it takes a_k=(D_{St}-d_W)/2=3.89 mm and SV 4 (VDI 2230 Part 1:2015, Annex B, Example B1, R3), with D_{St}=25 mm (VDI 2230 Part 1:2015, Annex B, Example B1, B1.1, Figure B1).
  • For concentric loading l_A=0 (VDI 2230 Part 1:2015, §5.2.2.2 d)).
  • n is read directly from Table 2 or found by linear interpolation (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2).
  • In Table 2, for the same SV row and the same a_k/h column, as l_A/h rises from 0.00 to ≥ 0.30, n does not increase; for example, SV 1 at a_k/h=0.00: 0.70, 0.52, 0.34, 0.16 (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2).
  • In the full method of Annex C, for a joint with a connecting solid of length l_A, n is found from n_G of the basic solid and the effect of the connecting solid; this effect depends mainly on the position of the connecting solid relative to the deformation cone and on the length l_A (VDI 2230 Part 1:2015, Annex C, C4).
  • If the height of the connecting solid is small compared with the height h of the basic solid, n=n_G+n_M\cdot(l_A/h), with enough accuracy up to a height ratio h_K/h\approx1/3 (VDI 2230 Part 1:2015, Annex C, C4, Eq. (C10)).
  • The effect of a connecting solid that introduces a force into the evenly clamped region of two plates (load introduction point K_{Gc}) can be neglected; Figure C3 marks K_{Gc} with n_{Mc}=0 (VDI 2230 Part 1:2015, Annex C, C4, Figure C3).
  • Connecting solids arranged in the region of the spreading substitutional compression solid generally reduce n; a negative calculated n indicates opening of the joint as a result of the moment effect of the working load, and then the preconditions for these relationships no longer exist (VDI 2230 Part 1:2015, Annex C, C4).
  • The calculator does not implement the full method of Annex C (VDI 2230 Part 1:2015, Annex C, C4).
  • Explanation, not the standard text: a force acting at a distance equals the same force plus a moment, and the moment rotates the side.

② Eccentric loading uses a, measured to the axis 0–0

  • s_{sym} is the distance of the bolt axis S from the axis 0 of the imaginary laterally symmetrical clamp solid; a is the distance of the substitutional line of action A of the axial working load F_A from that axis (VDI 2230 Part 1:2015, §3.2.2, Figure 4).
  • a is always positive; s_{sym} is positive when the line of action A and the bolt axis S lie on the same side of the axis 0, and negative when they lie on opposite sides (VDI 2230 Part 1:2015, §3.2.2, Figure 4).
  • This axis is the axis 0–0 of the laterally symmetrical deformation body in the basic solid (VDI 2230 Part 1:2015, §5.1.2.3); in Figure 4 it is marked "0" and the bolt axis "S" (VDI 2230 Part 1:2015, §3.2.2, Figure 4).
  • Eccentric clamping means that the bolt axis does not coincide with the axis of the laterally symmetrical clamp solid; s_{sym} is the distance between the two axes, so they coincide when s_{sym}=0 (concentric clamping) (VDI 2230 Part 1:2015, §2, s_{sym}; §3.2.2).
  • The distance a is in the end a lever arm; the substitutional line of action of F_A follows from the position of the zero point of the bending moment characteristic in the system that is closest to the bolt (VDI 2230 Part 1:2015, §5.2.1).
  • Example B4 takes SV 1; the connecting solid begins directly next to the head bearing area, so a_k=0; the lever arm of the substitutional load F_A is l_A=a-s_{sym}-d_W/2=2.95 mm; with l_A/h=0.066, linear interpolation gives n=0.58 (VDI 2230 Part 1:2015, Annex B, Example B4, R3).
  • With the Example B4 values a=9.6 mm (VDI 2230 Part 1:2015, Annex B, Example B4, B4.1), s_{sym}=0.5 mm (VDI 2230 Part 1:2015, Annex B, Example B4, R2) and d_W=12.3 mm (VDI 2230 Part 1:2015, Annex B, Example B4, Figure B6), l_A=9.6-0.5-12.3/2=2.95 mm (VDI 2230 Part 1:2015, Annex B, Example B4, R3).
  • a is measured from the axis 0–0, l_A from the basic solid (VDI 2230 Part 1:2015, §2, a, l_A).

③ How is n found, and why is it needed?

  • n is defined as the ratio of the influence number \delta_{VA} to the resilience of the plates \delta_P: n=\delta_{VA}/\delta_P=(f_{VK1}+f_{VK2})/(f_{V1}+f_{V2}); \delta_{VA} is the displacement of the bolt head under F_A=1 N, f_{V1} and f_{V2} are the displacements of the two bolt bearing areas, and f_{VK1} and f_{VK2} are the displacements of the points K where the working load acts (VDI 2230 Part 1:2015, §5.2.2.1, Eq. (76)).
  • n is a decisive factor in finding the additional bolt loads and their size; besides the height of load introduction, mainly the distance of the load introduction point from the preloading area and the thickness of the joint affect n (VDI 2230 Part 1:2015, §5.2.2).
  • For concentric clamping and loading, \Phi_n=n\cdot\Phi_K (VDI 2230 Part 1:2015, §5.3.1, Eq. (83)), and with M_B=0, F_{SA}=\Phi_n\cdot F_A (VDI 2230 Part 1:2015, §5.3.1, Eq. (84)); with all other quantities unchanged, a smaller n gives a smaller F_{SA} (VDI 2230 Part 1:2015, §5.3.1, Eq. (83), (84)).
  • Explanation, not the standard text: only the part of the clamped parts held between the two load introduction points is relieved by the working load.
  • The previous definition of n as the ratio of the length l of the relieved sections of the clamped parts to the clamping length l_K only remains valid for a clamped sleeve (D_A\le d_W); in this special case each cross section stays flat under preload (VDI 2230 Part 1:2015, §5.2.2.1). In general, n is defined by the ratio of displacements (VDI 2230 Part 1:2015, §5.2.2.1, Eq. (76)).
  • The simplified method has five steps: a) separate the single-bolt joint from the whole joint; b) divide the joint into basic solid and connecting solid; c) fix the joint type; d) determine the parameters; e) read n from Table 2 directly or by linear interpolation (VDI 2230 Part 1:2015, §5.2.2.2 a)–e), Table 2).
  • The simplified method assumes that the parameters for the spatial extent are estimated on the safe side with k_{ar}\cdot k_{dh}\cdot k_{dw}=0.8, that the clamped plates have the same Young's modulus, and that the joint does not open, is prismatic and has the working loads of the two plates nearly on one line (VDI 2230 Part 1:2015, §5.2.2.2).
  • When the clamped layers have different E_P, the calculator gives no suggested value of n.
  • For a tapped thread joint (TTJ), only the height of the top plate is taken as h, and with a recessed thread h starts at the beginning of the thread; the height of an extension sleeve under the bolt head or nut is not taken into h as long as no external forces act on it (VDI 2230 Part 1:2015, §5.2.2.2 c)–d)).
  • The suggested value in step R3c always takes h=l_K; for a tapped thread joint (TTJ) this differs from the choice of h in §5.2.2.2 c) (VDI 2230 Part 1:2015, §5.2.2.2 c)).
  • With very small n the joint may tend to open, and the preconditions of the simplified method are then no longer met (VDI 2230 Part 1:2015, §5.2.2.2 e)).

④ How do SV 1 to SV 6 differ; what are the hatched band and the dashed lines?

  • A joint is assigned to one of the joint types in Figure 22 by the position of its load introduction points (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22).
  • The band of horizontal lines marks the interface region evenly clamped and appropriate from the design point of view, and the interface must lie in it (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22); Figure 23 marks the same region for a through-bolt joint (VDI 2230 Part 1:2015, §5.2.2.2 d), Figure 23).
  • The figures of SV 1 to SV 5 do not draw an interface line and only require the interface to lie in the band; in SV 6 the band is only a narrow strip at the interface (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22).
  • The dashed lines are a cone of 30° to the bolt axis starting from the bolt bearing area, which finds the band approximately; in each drawing of Figure 22 the four dashed lines start at the edge of the bearing area and end at the side of the basic solid (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22).
  • The deformation cone used for \delta_P is a different cone, whose angle \varphi is calculated with Eq. (42) or (43) (VDI 2230 Part 1:2015, §5.1.2.1, Eq. (42), (43)).
  • In the first cell of Table 2 (l_A/h=0.00, a_k/h=0.00), n for SV 1 to SV 6 is 0.70, 0.57, 0.44, 0.42, 0.30, 0.15 (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2).
  • A tapped thread joint (TTJ) uses the types SV 1, SV 2 and SV 4, and the bottom plate is the tapped thread side (VDI 2230 Part 1:2015, §5.2.2.2 c)).
  • Explanation, not the standard text: position of the connecting solids that carry the upper and lower load introduction points in each type:
    • SV 1: upper connecting solid at the top face, lower at the bottom face;
    • SV 2: upper connecting solid some way below the top face, lower at the bottom face;
    • SV 3: upper connecting solid some way below the top face, lower the same way above the bottom face (mirror image);
    • SV 4: lower edge of the upper connecting solid at half the plate height, lower connecting solid at the bottom face;
    • SV 5: lower edge of the upper connecting solid at half the plate height, lower connecting solid some way above the bottom face;
    • SV 6: the two connecting solids directly above and below the interface.
  • Explanation, not the standard text: in the three types used for a tapped thread joint (SV 1, SV 2, SV 4), the load introduction point of the bottom plate is at its lowest end.

Engineering data

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