VDI 2230-1 single-bolt joints: Verification

The table lists the example value and the MechCalc value for each example. “Agrees” means MechCalc matches the example value within tolerance; “Method difference (see note N)” means the two use different methods or conventions, with the reasons numbered after the table. “[Source N]” points to Source N in the list below the table; it is not repeated when the previous result of the same example has the same source.

Notes:

• Note 1 (Steel flange bolt, static load check): The textbook uses a head length of $0.4d$ (Eq. 10.26); the calculator uses $0.5d$ for a hexagon head (VDI 2230:2015, Eq. 30), so $\delta_S$ is 1.33 % larger.
• Note 2 (Steel flange bolt, static load check): Different clamped-part models: the textbook uses the 1986 substitute cylinder ($\delta_P = 5.6\times10^{-7}$), the calculator uses the 2015 deformation cone ($7.08\times10^{-7}$); $\Phi$, $F_Z$ and $F_{Mmax}$ follow. The example value of $\Phi$ is converted from the book’s $F_{SA} = 1508$ N and $F_A = 20\,000$ N: $\Phi_n = 1508/20\,000 = 0.0754$ (the printed $\Phi = 0.1077$ is not multiplied by $n$).
• Note 3 (Steel flange bolt, static load check): The textbook prints $S_F = 1.257$ (p. 305, Eq. 10.75), which contradicts its own Eqs. (10.74)–(10.75): with $F_{Smax} = F_{Mmax} + F_{SA} = 30\,498$ N they give 0.9935 (the printed value comes out with the pre-selection $F_{Smax} = 20\,140$ N of Eq. 10.68; the book does not say so, this is an inference). By the textbook’s own formulas $S_F < S_{F,min} = 1.1$, so its pass verdict does not hold; the calculator gives 1.13 from VDI 2230:2015, step R8 (a different basis), and still passes.
• Note 4 (Connecting-rod necked-down bolt, dynamic load check): The textbook prints $\delta_S = 70.5\times10^{-7}$ mm/N (p. 306, Eq. 10.25), but its terms cover only 60 mm of shank while $l_K = 70$ mm, so the resilience of 10 mm is missing. Taken as thread (an assumption in this example’s input), the missing segment adds $9.11\times10^{-7}$ mm/N, about 12.9 % of the textbook’s chain; the head length $0.4d$ versus the calculator’s $0.5d$ adds another 0.9 % (method difference), and the calculator gets $8.02\times10^{-6}$ mm/N for the full $l_K$. The gap carries over to $\Phi$ and $F_Z$; with the full $l_K$ both the static check and the fatigue check still pass.
• Note 5 (Connecting-rod necked-down bolt, dynamic load check): Different clamped-part models (1986 substitute cylinder versus the 2015 cone-and-sleeve model) plus the printed $\delta_S$ missing 10 mm of the bolt; $\Phi$, $F_Z$ and $F_{Mmax}$ follow. The example value of $\Phi$ is converted from the book’s $F_{SA} = 900$ N and $F_A = 15\,000$ N: $\Phi_n = 900/15\,000 = 0.06$ (the printed $\Phi = 0.12$ is not multiplied by $n$).
• Note 6 (Connecting-rod necked-down bolt, dynamic load check): The textbook uses the minor-diameter area $A_3$; the calculator uses the stress area $A_S$ as in VDI 2230:2015, and $\Phi_n$ differs (0.0552 versus 0.06).
• Note 7 (Connecting-rod necked-down bolt, dynamic load check): The textbook prints $\sigma_A = 0.85\,(150/d + 45) = 61.67$ N/mm² (p. 306), but the same formula (Eq. 10.60, $d$ = nominal diameter) gives 51.0 N/mm² for $d = 10$ mm, and the chart value in Figure 10.28 is 60 N/mm² (p. 285); the printed value is 20.9 % too high. The calculator gives 51.0 from the same formula in VDI 2230:2015, step R9/5-1; with the corrected value the safety margin against fatigue failure is still above $S_{D,min} = 1.5$, so the pass verdict stands.
• Note 8 (Connecting-rod necked-down bolt, dynamic load check): The textbook prints $S_D = 7.2$ (p. 306, Eq. 10.76), consistent with its printed $\sigma_A = 61.67$, which is too high (see the note on $\sigma_{AS}$); with $\sigma_A = 51.0$ from its own formula it is 5.93, with the chart value 60 it is 6.98. The calculator’s 7.14 is close to the printed value only because two differences cancel (the high $\sigma_A$ and the different area used for $\sigma_a$); every variant is above $S_{D,min} = 1.5$, so the pass verdict stands.
• Note 9 (Connecting-rod necked-down bolt, dynamic load check): The textbook prints $S_F = 1.55$ (p. 306, Eq. 10.75) using $F_{Smax} = 15\,700$ N from the pre-selection Eq. (10.68), although p. 286 says the pre-selection equations are for sizing only, not for the strength check; with $F_{Smax} = F_{Mmax} + F_{SA} = 23\,612$ N from the check Eq. (10.74), the same Eq. (10.75) gives 1.274, so the printed value is 21.7 % too high. The verdict $S_F > S_{F,min} = 1.1$ still holds; the calculator gives 1.20 from VDI 2230:2015, step R8 (a different basis).
• Note 10 (Connecting-rod bolt, eccentric clamping and loading): The $\delta_S$ and $l_{ers}$ differences come from the head term ($0.5d$ for a special head in the calculator, $0.4d$ in the book); the $\delta_P$, $\Phi$, $F_Z$ and $F_{M\min}$ differences come from the clamped-part model (1986 equivalent cross-section (Ersatzquerschnitt) in the book, 2015 deformation cone with sleeve in the calculator); the $F_{MTab}$ and $p_{M\max}$ differences come from the shank diameter of the necked-down bolt (5.8 mm vs 5.82 mm); the $\sigma_{AS}$ difference comes from two different empirical formulas for the endurance limit.
• Note 11 (Connecting-rod bolt, eccentric clamping and loading): The book estimates the preload of angle-controlled tightening with $\nu = 1.06$ and finds that $F_{M\min}$ is reached; VDI 2230:2015 uses $F_{M0,2\min}$ at $\nu = 1$ as the lower bound, and with it the calculator finds the check not met (conservative).
• Note 12 (Connecting-rod bolt, eccentric clamping and loading): The book estimates the preload of angle-controlled tightening with $\nu = 1.06$ and finds it enough to prevent one-sided opening; in VDI 2230:2015 the opening criterion is equivalent to Eq. (164), so $F_V$ is taken as $F_{V1\min}$ at $\nu = 1$, and with it the calculator finds that the joint opens (conservative).

Sources:

• Source 1: VDI 2230 Part 1:2015-11, Annex B, Example B1 (R0–R13)
• Source 2: VDI 2230 Part 1:2015-11, Annex B, Example B2 (R0–R13)
• Source 3: VDI 2230 Part 1:2015-11, Annex B, Example B3, Table B1 (R0–R13)
• Source 4: VDI 2230 Part 1:2015-11, Annex B, Example B4 (R0–R13)
• Source 5: Niemann et al., Maschinenelemente 1, 5th ed., Springer Vieweg 2019, §10.11 Example 10.1 (pp. 304–305)
• Source 6: Niemann et al., Maschinenelemente 1, 5th ed., Springer Vieweg 2019, §10.11 Example 10.1 (p. 305)
• Source 7: VDI 2230 Part 1:2015-11, steps R3–R8 and R13 (independent hand calculation, inputs from the textbook example)
• Source 8: Niemann et al., Maschinenelemente 1, 5th ed., Springer Vieweg 2019, §10.11 Example 10.2 (pp. 305–306)
• Source 9: VDI 2230 Part 1:2015-11, steps R3–R9 and R13 (independent hand calculation, inputs from the textbook example)
• Source 10: Kloos/Thomala, Schraubenverbindungen, 5th ed., Springer 2007, §4.5 connecting-rod bolted joint (pp. 118–133)