VDI 2230-1 Single-Bolt Joint Calculator: User Manual

The MechCalc VDI 2230-1 single-bolt joint 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).

Scope

What it can calculate

• Standard: VDI 2230 Part 1:2015 (November 2015 edition).
• Joint types: the through-bolt joint (TBJ, German DSV) and the tapped thread joint (TTJ, German ESV) (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, §5.4.1, Eq. (108)(109)). Optional eccentric clamping and eccentric loading, for a tensile working load only (cases I to III of Table 4) (VDI 2230 Part 1:2015, §5.3.2, Table 4).
• Calculation modes: design mode preselects the nominal diameter from the load (R0, Table A7) (VDI 2230 Part 1:2015, §4.2 R0, Table A7); verification mode checks the size you give. Both modes run R1 to R13.
• Bolt forms: solid or hollow; coarse thread M4 to M39 (VDI 2230 Part 1:2015, §1) or fine thread; hexagon head, socket head cap or special head. In verification mode, five product standards (ISO 4014, 4017, 4762, 8765, 8676) can fill in the geometry (DIN EN ISO 4014:2022-10; ISO 4017:2022; DIN EN ISO 4762:2004-06; DIN EN ISO 8765:2022-10; DIN EN ISO 8676:2022-10).
• Six checks: assembly stress (R7), static strength (R8), fatigue (R9), surface pressure (R10), length of engagement (R11, TTJ only) and slip and shear (R12). The tightening torque is given as well (R13) (VDI 2230 Part 1:2015, §4.2 R7–R13).

What it cannot calculate

None of the items below is implemented in this calculator; this does not mean that the standard leaves them out.

• An external bending moment $M_B$: the standard gives equations for it (VDI 2230 Part 1:2015, §5.3.1.3, Eq. (96)–(98); §5.3.2, Eq. (102)–(107)); the calculator has no input for $M_B$.
• A compressive working load: the standard lists the compressive cases IV to VI in Table 4 (VDI 2230 Part 1:2015, §5.3.2, Table 4); the calculator accepts only a non-negative $F_A$.
• Eccentric joints with clamped parts of different materials: the standard gives the eccentric resilience equations for different moduli (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (68)–(70); §5.1.2.3, Eq. (72); §5.5.3, Eq. (189)); with eccentric clamping or loading, the calculation is refused if the layers have different moduli.
• Approximating the resilience of the clamped parts of a tapped thread joint (TTJ) as a through-bolt joint (TBJ) with eccentric clamping: the standard treats a TTJ with $D_A$ up to about $1.4\,d_W$ and a clearly wider base body as a TBJ (VDI 2230 Part 1:2015, §5.1.2); with eccentric clamping, “Calculate the clamped parts as a TBJ” set to Yes is refused, and Automatic calculates the TTJ without the simplification.
• Partially opening joints: the standard gives an approximate method in Annex D (VDI 2230 Part 1:2015, Annex D).
• Preload loss by relaxation (creep) (VDI 2230 Part 1:2015, §5.4.2.2): the calculator does not include it.
• The contact resilience of a pack of thin plates: the resilience equations of the standard do not include it (VDI 2230 Part 1:2015, §5.1.2).
• Fatigue and shear check of a hollow bolt: not implemented in this calculator (fatigue: VDI 2230 Part 1:2015, §5.5.3, Eq. (170)(171); shear: VDI 2230 Part 1:2015, §5.5.6.3, Eq. (219)).
• The load distribution in a multi-bolt joint: see VDI 2230 Part 2:2014; the button under $F_A$ takes $F_A$ and $F_Q$ of the selected bolt from the multi-bolt calculator (VDI 2230-2 multi-bolt calculator ).
• Design mode gives coarse thread sizes only; the standard-bolt picker covers only the five product standards above, not washers, nut products or stainless steel classes.

The input cards

Card	Title	When it appears
1	Control	Always; the standard-bolt picker, the fine pitch and the bore of a hollow bolt only in verification mode; the available length of engagement only for TTJ; the head product grade only for a hex head; the special head height only for a special head; the bearing diameter from product data only for a special head or in verification mode; the unthreaded shank length is hidden when bolt segments are entered
2	Clamped parts geometry	Always; the through-hole diameter only in verification mode; the choice to calculate the clamped parts as a TBJ only for TTJ; the nut-side inputs only for TBJ, and the nut bearing-face outer diameter also only in verification mode
3	Loads & load introduction	Always; the minimum axial load only with the fatigue check on
4	Material & strength	Always; the modulus of the tapped part only for a tapped thread joint (TTJ)
5	Friction	Always; $q_M$ and the friction radius only with $M_Y>0$; the loading type for slipping and the required safety margin against slipping only with $F_Q>0$ or $M_Y>0$
6	Tightening	Always; the work-hardening factor and the upper limit of the coefficient of friction in the thread only for yield-point control and angle control, and the utilisation is hidden for these two methods; the head friction is hidden for hydraulic frictionless and torsion-free tightening; with the embedding amount entered directly the embedding $f_Z$ is shown, and with Table 5 the surface roughness, the load direction and the number of inner interfaces
7	Thermal (optional)	Always; the inputs appear with “Include Thermal Effects”
8	Fatigue (optional)	Always; the inputs appear with “Fatigue Check”
9	Shear & bolt bearing pressure	Only with $F_Q>0$
10	Length of engagement check (TTJ, optional)	Only for TTJ; the four thread limit dimensions only in verification mode
11	Eccentric clamping and loading (optional)	Always; the inputs appear with the switch; the interface width only when the interface moment of gyration is empty; the thinner clamped plate only for TBJ, the counterbore depth $t_S$ only for TTJ

Inputs

The inputs are in 11 cards whose titles are the same as in the calculator; each input lists its meaning, where to get the value, its effect on the results and the standard reference.

Calculation Mode

R0 roughly determines the bolt nominal diameter $d$ from Table A7 (VDI 2230 Part 1:2015, §4.2, R0; Annex A, Table A7).

Where to get the value

• Design mode: R0 selects the nominal diameter from Table A7, and R1 to R13 run on the selected size (VDI 2230 Part 1:2015, §4.2, R0; Annex A, Table A7).
• Verification mode: R0 is skipped, and R1 to R13 run on the size you enter.
• In design mode the through-hole diameter $d_h$ is not an input; it is taken for the selected size from the medium (mittel) series of DIN EN 20273:1992-02.
• Only in verification mode: standard bolt, fine pitch, bore of a hollow bolt, through-hole diameter, and the thread limits of card 10.

Standard reference: VDI 2230 Part 1:2015, §4.2, R0; Annex A, Table A7; DIN EN 20273:1992-02

Joint Type

• Through-bolt joint (TBJ, Durchsteckschraubverbindung, DSV); tapped thread joint (TTJ, Einschraubverbindung, ESV) (VDI 2230 Part 1:2015, §2, Abbreviations).
• Substitutional length of the nut or the engaged thread: $l_M=0.4\,d$ for a TBJ, $l_M=0.33\,d$ for a TTJ (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (26), (27)).
• In a TTJ the flow of the working load runs markedly through the engaged thread, unlike in a TBJ; therefore the resilience of the clamped parts gets the supplement $\delta_{PZu}=(w-1)\,\delta_M$, with $w=1$ (TBJ) and $w=2$ (TTJ) (VDI 2230 Part 1:2015, §5.3.1, Eq. (80), (81); §5.1.2, Eq. (39)).

Where to get the value

• The default is TBJ.
• With TTJ the calculator shows: the Young’s modulus $E_{BI}$ of the part with the internal thread, the available length of engagement, “Calculate the clamped parts as a TBJ”, and card 10.

Standard reference: VDI 2230 Part 1:2015, §2, Abbreviations; §5.1.1.1, Eq. (26), (27); §5.1.2, Eq. (39); §5.3.1, Eq. (80), (81)

Standard bolt (optional)

With a product standard, a size and a nominal length selected, the calculator fills in the bolt data from the standard (verification mode only).

Where to get the value

• Standards offered: DIN EN ISO 4014:2022-10 (hexagon head bolt, partly threaded, coarse thread), ISO 4017:2022 (hexagon head screw, fully threaded, coarse thread), DIN EN ISO 4762:2004-06 (hexagon socket head cap screw, coarse thread), DIN EN ISO 8765:2022-10 (hexagon head bolt, partly threaded, fine thread), DIN EN ISO 8676:2022-10 (hexagon head screw, fully threaded, fine thread).
• The default is “None”: all bolt data are entered by hand.
• Filled in as read-only: bolt size, pitch and head type. To change them, change the size in this card.
• Also filled in: head product grade, bearing diameter $d_W$ and the shank length $l_1$ inside the clamping length. For a partly threaded bolt $l_1=\max(\min(l-b-h_S,\,l_K),\,0)$, with $b$ the thread length of the standard and $h_S$ the washer thickness under the head; for a fully threaded bolt $l_1=0$.
• The strength class list is limited to the classes the standard allows for this size (DIN EN ISO 4014:2022-10, 5, Table 7; ISO 4017:2022, Table 5; DIN EN ISO 4762:2004-06, Table 2; DIN EN ISO 8765:2022-10 and DIN EN ISO 8676:2022-10, Table 6).
• If the through-hole $d_h$ is not larger than $d$, it is replaced by the value of the medium series of DIN EN 20273:1992-02, with a note; a $d_h$ that you changed yourself is kept.
• Product grade and $l_1$ can be changed by hand. The changed value is used, and a “Use ISO value” link appears next to the field. $d_W$ is changed in the field “Bearing diameter from product data”.
• Changing the standard or the size resets the hand-entered values, with a note.
• In design mode this field is ignored.
• Washers (ISO 7089, ISO 7090), nut products and stainless steel classes (ISO 3506-1) are not implemented in this calculator.

Standard reference: DIN EN ISO 4014:2022-10; ISO 4017:2022; DIN EN ISO 4762:2004-06; DIN EN ISO 8765:2022-10; DIN EN ISO 8676:2022-10; DIN EN 20273:1992-02

Size (d or d×P)

The bolt diameter $d$ is the outside diameter of the thread (nominal diameter) (VDI 2230 Part 1:2015, §2, $d$). The designation of a coarse thread has the form M12 × 80 (DIN EN ISO 4014:2022-10, 7 Designation) and that of a fine thread the form M12 × 1,5 × 80 (DIN EN ISO 8765:2022-10, 7 Designation).

Where to get the value

• The list shows only the sizes of the selected standard, within M4 to M39; non-preferred sizes are marked “non-preferred”.
• If the standard is changed and the current size is not in the new standard, the size with the same nominal diameter, or else the closest one, is selected.
• Changing the size resets the hand-entered values, with a note.

Standard reference: VDI 2230 Part 1:2015, §2, $d$; DIN EN ISO 4014:2022-10, 7 Designation; DIN EN ISO 8765:2022-10, 7 Designation; ISO 4017:2022; DIN EN ISO 4762:2004-06; DIN EN ISO 8676:2022-10

Nominal length (l) [mm]

The length $l$ of the bolt is the nominal length given in the designation of the product standard, for example $l=80$ mm in M12 × 80 (DIN EN ISO 4014:2022-10, 7 Designation; DIN EN ISO 8765:2022-10, 7 Designation).

Where to get the value

• It must be greater than the clamping length $l_K$; otherwise the calculation is refused.
• While it is empty, the note “Enter the nominal length” is shown under the field.
• A length outside the standard lengths of the selected size, or not in the length series, is calculated as entered, with the note that it must be agreed with the supplier.
• For ISO 4014, the smallest standard length is 55 mm for M14 and 120 mm for M33 (DIN EN ISO 4014:2022-10, Table 3, Table 5; Figure 1, footnote d).
• For ISO 4014, the standard gives no thread length $b$ for M16, M18 and M20 with $l>200$ mm, nor for M36 and M39 with $l\le125$ mm; the calculation is refused for these inputs (DIN EN ISO 4014:2022-10, Table 4, Table 5).
• For a through-bolt joint (TBJ) a note is given if the nut does not fit on the free end: $l-l_K-h_S\ge m+2P$ is not fulfilled, with $m$ the nut height.
• For a tapped thread joint (TTJ) a note is given if the available total length of engagement, reduced by $2P$, is smaller than the required $m_{eff,min}$ (VDI 2230 Part 1:2015, Annex B, Example B1, R11, Eq. (208)). The available total length of engagement is $l-l_K-h_S$ for a fully threaded bolt and for the thread-to-head zone of ISO 4762, and $\min(l-l_K-h_S,\,b)$ for a partly threaded bolt, with $b$ the thread length of the standard.
• Both notes do not change the result.

Standard reference: DIN EN ISO 4014:2022-10, 7 Designation; DIN EN ISO 8765:2022-10, 7 Designation; ISO 4017:2022; DIN EN ISO 4762:2004-06; DIN EN ISO 8676:2022-10; VDI 2230 Part 1:2015, Annex B, Example B1, R11, Eq. (208)

Bolt size (d)

The bolt diameter $d$ is the outside diameter of the thread (nominal diameter) (VDI 2230 Part 1:2015, §2, $d$). For the coarse sizes M4 to M39, $P$, $d_2$ and $d_3$ are taken from DIN ISO 724:2024-09, 5 Basic dimensions, Table 1, and $A_S$ from DIN EN ISO 898-1:2013-05, Table 4.

Where to get the value

• Verification mode: R1 to R13 run on this size.
• Design mode: this size is only the starting size of the schematic; after R0 the schematic uses the recommended size, and the size is not used in the calculation.
• The list offers coarse threads only. For a fine thread enter the pitch in “Fine pitch”, or select ISO 8765 or ISO 8676 under “Standard bolt”.
• With a standard bolt selected, this field is set by the standard bolt and is read-only.

Standard reference: VDI 2230 Part 1:2015, §2, $d$; DIN ISO 724:2024-09, 5 Basic dimensions, Table 1; DIN EN ISO 898-1:2013-05, Table 4

Fine pitch (P, optional) [mm]

$P$ is the pitch of the thread (VDI 2230 Part 1:2015, §2, $P$). In the designation of a fine thread bolt it follows the thread size, as in M12 × 1,5 × 80 (DIN EN ISO 8765:2022-10, 7 Designation).

Where to get the value

• Leave it empty for a coarse thread. Shown in verification mode only.
• A pitch $P$ larger than the coarse pitch of the diameter is refused; a pitch equal to it is treated as a coarse thread.
• $d_2$, $d_3$ and $D_1$ are calculated with the equations of DIN ISO 724:2024-09, 5 Basic dimensions, and $A_S$ with Eq. (2) of DIN EN ISO 898-1:2013-05.
• With the fatigue check on, R9 notes that the lower endurance limit of a fine thread is to be taken into account with the fatigue knockdown factor; no reduction is applied automatically.
• With a standard bolt selected, this field is set by the standard bolt.

Effect on the results

• ↓ Decrease: The endurance limit of fine threads decreases with increasing strength and fineness of the thread; for strength class 12.9 it may be up to 30 % lower than for a standard thread (VDI 2230 Part 1:2015, §5.5.3).

Standard reference: VDI 2230 Part 1:2015, §2, $P$; §5.5.3; DIN EN ISO 8765:2022-10, 7 Designation; DIN ISO 724:2024-09, 5 Basic dimensions; DIN EN ISO 898-1:2013-05, Eq. (2)

Head Type

• Substitutional extension length of the head: $l_{SK}=0.5\,d$ for hexagon head bolts and $l_{SK}=0.4\,d$ for cap screws with hexagon socket (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (30), (31)).
• For other head shapes there are no reliable findings; the values above can be used as an approximation (VDI 2230 Part 1:2015, §5.1.1.1).

Where to get the value

• Options: hexagon head (ISO 4014), socket cap head (ISO 4762), special head (verification mode only).
• For hexagon and socket heads the bearing diameter $d_W$ is the minimum value $d_{w,min}$ of DIN EN ISO 4014:2022-10, Table 1 to Table 5, Table A.1, Table A.2 or DIN EN ISO 4762:2004-06, Table 1.
• For M4 and M5, $d_{w,min}$ is 6.20 mm and 7.20 mm for product grade A, and 6.06 mm and 7.06 mm for product grade B (DIN EN ISO 4014:2022-10, Table 1, Table 2, Table A.1, Table A.2).
• Special head: $d_W$ is the value you enter in “Bearing diameter from product data” (required), and $l_{SK}=0.5\,d$.
• With a standard bolt selected, this field is set by the standard bolt.

Standard reference: VDI 2230 Part 1:2015, §5.1.1.1, Eq. (30), (31); DIN EN ISO 4014:2022-10, Table 1 to Table 5, Table A.1, Table A.2; DIN EN ISO 4762:2004-06, Table 1

Head product grade

DIN EN ISO 4014 gives $d_{w,min}$ for product grade A and product grade B. Grade A applies to $d\le$ M24 and $l\le10\,d$ or $\le150$ mm (the smaller value); grade B applies to sizes above M24, or $l>10\,d$ or $>150$ mm (DIN EN ISO 4014:2022-10, 5, Table 7, Product grade, footnote d).

Where to get the value

• Shown for hexagon heads only.
• “Auto” takes grade A up to M24 and grade B above M24; it also takes grade B when the clamping length $l_K\ge\min(10\,d,\,150\ \mathrm{mm})$.
• If grade A is selected although $l_K\ge\min(10\,d,\,150\ \mathrm{mm})$, the grade A value is used, with a warning.
• Grade A for a size above M24 is refused in verification mode.
• With a standard bolt selected, the grade is filled in from the nominal length $l$ and the standard; it can be changed by hand.

Standard reference: DIN EN ISO 4014:2022-10, 5, Table 7, Product grade, footnote d

Bearing diameter from product data (d_W) [mm]

Outside diameter of the plane head bearing surface of the bolt (at the inlet of the transition radius of the head); in general the outside diameter of the bearing surface (VDI 2230 Part 1:2015, §2, $d_W$).

Where to get the value

• Required for a special head. Optional for hexagon and socket heads: a value entered here replaces the table value; while the field is empty, the placeholder shows the table value in use and its source.
• In design mode a hexagon or socket head always uses the table value, and this field has no effect.
• For a socket head of size M18, M22, M27, M33 or M39, which DIN EN ISO 4762:2004-06, Table 1 does not list, the field is required in verification mode; without it no calculation is made. In design mode R0 selects the next ISO 4762 size instead, and for M39 the calculation is refused.
• For every head type, a value entered here must be larger than $d_h$, and larger than $D_{Ki}$ if $D_{Ki}$ is given; otherwise the calculation is refused.
• With ISO 4017 selected as standard bolt, $d_W$ is the minimum value $d_w$ of ISO 4017:2022 itself.

Standard reference: VDI 2230 Part 1:2015, §2, $d_W$; DIN EN ISO 4014:2022-10, Table 1 to Table 5, Table A.1, Table A.2; DIN EN ISO 4762:2004-06, Table 1; ISO 4017:2022

Special head height (k, for the sketch only) [mm]

Height of the bolt head (VDI 2230 Part 1:2015, §2, $k$).

Where to get the value

• Optional; shown only for a special head.
• It is used only to draw the head in the schematic and does not enter $\delta_{SK}$ or any other calculation.
• If it is empty, the schematic uses a schematic height of $0.6\,d$ and says so.

Standard reference: VDI 2230 Part 1:2015, §2, $k$

Bore of a hollow bolt (d_b) [mm]

Bore diameter of a hollow bolt (VDI 2230 Part 1:2015, Annex B, Example B3, Table B1). 0 means a solid bolt.

Where to get the value

• Verification mode only.
• It must be smaller than the minor diameter $d_3$, the diameter $d_0$ of the relevant cross-section and the diameter $d_i$ of every segment; otherwise the calculation is refused.
• With a bore, all bolt cross-sections are annular. The permissible assembly preload $F_{Mzul}$ and the polar moment of resistance $W_P$ follow the derivation of Example B3 (VDI 2230 Part 1:2015, Annex B, Example B3, R7, R8).
• Fatigue (R9) and bolt shear (R12b) are not checked for a hollow bolt, and R11 gives only an estimate to be confirmed by a test (VDI 2230 Part 1:2015, Annex B, Example B3, R11). The result page lists the checks that were not made, and the overall verdict leaves them out.

Standard reference: VDI 2230 Part 1:2015, Annex B, Example B3, Table B1, R7, R8, R11

Clamped layers (h_i, E_P,i)

• Layer thickness $h_i$: the lengths of the partial deformation bodies add up to the clamping length, $\sum l_i=l_K$ (VDI 2230 Part 1:2015, §5.1.2.1, Notes 3).
• $E_P$: Young’s modulus of the clamped parts (VDI 2230 Part 1:2015, §2, $E_P$). For clamped parts with different moduli the deformation body is divided into partial deformation bodies of equal modulus, $\delta_P=\sum\delta_{Pi}^V+\sum\delta_{Pi}^H$ (VDI 2230 Part 1:2015, §5.1.2.1, Notes 3, Eq. (52), (53)).
• $p_G$: limiting surface pressure; the surface pressure under head and nut must not exceed it, $p_{Mmax}\le p_G$ and $p_{Bmax}\le p_G$ (VDI 2230 Part 1:2015, §5.5.4, Eq. (190), (191)). Reference values are given in Table A9 (VDI 2230 Part 1:2015, §5.5.4).
• $R_{p0,2P}$: 0.2 % proof stress of the clamped part, used for the permissible transverse force limited by bolt bearing pressure (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (222), (223)).
• The contact resilience is not taken into account; for a relatively large number of thin sheets that are not completely flat, $\delta_P$ increases and, if needed, is to be determined experimentally (VDI 2230 Part 1:2015, §5.1.2).

Where to get the value

• The layers are listed from the bolt head down, one to three layers. Each row has the thickness and a material button (Table A9 or the material library); the arrow at the end of the row shows $E_P$, $p_G$ and $R_{p0,2P}$ of the layer. With thermal effects on, it also shows the mean expansion coefficient $\bar\alpha_P$ and the modulus $E_{P,T}$ at working temperature (VDI 2230 Part 1:2015, §5.4.2.3, Eq. (117), (118)).
• The default is two layers of 15 mm, material S355 JO from Table A9.
• The layer under the head, and for a through-bolt joint (TBJ) the last layer under the nut, give the $p_G$ of that side. If such a layer has no $p_G$ entered, the calculator looks up the material name of the layer in Table A9; if it is not found there either, the surface pressure check of that side is skipped and the result says so; no default value is used.
• The simplified table method for the load introduction factor $n$ requires the same Young’s modulus for all clamped plates (VDI 2230 Part 1:2015, §5.2.2.2); if the layers have different moduli, the table suggestion is not available, and then $n$ is given directly.

Standard reference: VDI 2230 Part 1:2015, §5.1.2; §5.1.2.1, Notes 3, Eq. (52), (53); §5.2.2.2; §5.4.2.3, Eq. (117), (118); §5.5.4, Eq. (190), (191); §5.5.6.3, Eq. (222), (223); Annex A, Table A9

Equivalent OD at the interface (D_A) [mm]

Substitutional outside diameter of the basic solid at the interface; if the interface area differs from the circular form, an average diameter is to be used (VDI 2230 Part 1:2015, §2, $D_A$). For non-cylindrical components, $D_A$ is generally twice the mean edge distance at the interface (VDI 2230 Part 1:2015, §5.1.2).

Where to get the value

• When a single-bolt joint is released from a multi-bolt joint, the hole distance (spacing $t$) is not to be used as the substitutional outside diameter; use the full spread of the deformation body up to the neighbouring hole (VDI 2230 Part 1:2015, §5.1.2).
• The default is 40 mm.

Effect on the results

• ↑ Increase: For $d_W\lt D_A\lt D_{A,Gr}$ the deformation body consists of cone and sleeve; for $D_A\ge D_{A,Gr}=d_W+w\,l_K\tan\varphi$ it consists of the cone(s) only (VDI 2230 Part 1:2015, §5.1.2, Eq. (39); §5.1.2.1).

Standard reference: VDI 2230 Part 1:2015, §2, $D_A$; §5.1.2, Eq. (39); §5.1.2.1

Equivalent OD of the base body (D_A’, optional) [mm]

Substitutional outside diameter of the basic solid, twice the mean distance from the edge of the plate above the interface; the whole material region around the bolt is to be considered. In general $D_A'\ge D_A$ (VDI 2230 Part 1:2015, §5.1.2.1, after Eq. (45)).

Where to get the value

• If it is empty, $D_A'\approx D_A$ is used.
• It must not be smaller than $D_A$; otherwise the calculation is refused.
• For a tapped thread joint (TTJ) it is also used, together with $D_A$ and $d_W$, to decide whether the clamped parts are calculated as a through-bolt joint (TBJ).

Effect on the results

• ↑ Increase: The diameter ratio $y=D_A'/d_W$ increases, and with it the cone angle $\varphi$ (VDI 2230 Part 1:2015, §5.1.2.1, Eq. (42), (43), (45)).

Standard reference: VDI 2230 Part 1:2015, §5.1.2.1, Eq. (42), (43), (45)

Calculate the clamped parts as a TBJ

A tapped thread joint (TTJ) whose interface area is only slightly larger than the head bearing surface ($D_A$ up to about $1.4\,d_W$) and whose basic solid ($D_A'$) is mostly clearly larger is to be treated as a through-bolt joint (TBJ), taking the shape of the deformation body into account (VDI 2230 Part 1:2015, §5.1.2).

Where to get the value

• Shown for a TTJ only. The default is “Automatic”.
• Automatic: the clamped parts are calculated as a TBJ if $D_A'$ is given, $d_W\lt D_A\le1.4\,d_W$ and $D_A'>D_A$; without $D_A'$ nothing is switched, and the step text says so.
• Yes: the clamped parts are calculated as a TBJ on your judgement; $D_A'>D_A$ is required, otherwise the calculation is refused. Example B1 does the same (VDI 2230 Part 1:2015, Annex B, Example B1, R3).
• No: nothing is switched.
• Only the resilience of the clamped parts $\delta_P$ changes ($w=1$, the TBJ cone angle of Eq. (43), the mean bearing diameter $d_{Wm}=(d_W+D_A)/2$, and $D_A'$ as the outside diameter of the virtual interface); the bolt resilience $\delta_S$ and $\delta_{PZu}$ stay on the TTJ model (VDI 2230 Part 1:2015, §5.1.2.1, Eq. (39), (43); Annex B, Example B1, R3).
• With eccentric clamping, “Automatic” does not switch, and “Yes” is refused.

Standard reference: VDI 2230 Part 1:2015, §5.1.2; §5.1.2.1, Eq. (39), (43); Annex B, Example B1, R3

Through-hole Diameter (d_h) [mm]

Hole diameter of the clamped parts (VDI 2230 Part 1:2015, §2, $d_h$).

Where to get the value

• Verification mode: you enter it; it must be larger than the bolt diameter $d$, otherwise the calculation is refused. The default is 9 mm.
• Design mode: it is not an input; it is taken for the selected size from the medium (mittel) series of DIN EN 20273:1992-02.
• With a standard bolt selected, a $d_h$ not larger than $d$ is replaced by the value of the medium series of DIN EN 20273:1992-02, with a note; a value you changed yourself is kept.

Effect on the results

• ↑ Increase: $D_{Ki}=\max(D_a,d_{ha},d_h,d_a)$ can increase, and the minimum bearing area $A_{p\,min}=\frac{\pi}{4}(d_{Wa}^2-D_{Ki}^2)$ decreases (VDI 2230 Part 1:2015, §5.4.3.1, Eq. (129); §5.5.4, Eq. (193)).

Standard reference: VDI 2230 Part 1:2015, §2, $d_h$; §5.4.3.1, Eq. (129); §5.5.4, Eq. (193); DIN EN 20273:1992-02

Unthreaded shank length in the clamp (l_1) [mm]

Length of the unthreaded shank within the clamping length $l_K$. The length of the free loaded thread is then $l_{Gew}=l_K-l_1$ (VDI 2230 Part 1:2015, §5.1.1.1, Figure 6). The standard lists only the lengths $l_i$ of individual cylindrical elements (VDI 2230 Part 1:2015, §2, $l_i$); $l_1$ is the name this calculator gives to the shank element.

Where to get the value

• The default is 0: the clamping length is fully threaded.
• With a standard bolt selected, $l_1$ is filled in from the standard and can be changed by hand; a “Use ISO value” link appears next to the changed value.
• With bolt segments entered, the table is used and this field is hidden.

Effect on the results

• ↑ Increase: A longer shank and a shorter free thread: the shank resilience is $\delta_1=l_1/(E_S A_N)$ and the free thread resilience is $\delta_{Gew}=l_{Gew}/(E_S A_{d3})$, with $A_{d3}$ the cross-section at the minor diameter (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (18), (19), (28)).

Standard reference: VDI 2230 Part 1:2015, §2, $l_i$; §5.1.1.1, Figure 6, Eq. (18), (19), (28)

Available length of engagement (m_eff,vorh, optional) [mm]

The length of engagement is $m_{ges}=m_{eff}+m_{Zu}$. The supplement $m_{Zu}=2\,P$ covers the part of the length of engagement without thread contact (countersink, chamfer) and the thread turns that do not carry fully (tip) (VDI 2230 Part 1:2015, §5.5.5, Eq. (208)). In Example B1: $m_{eff,vorh}=m_{ges,vorh}-2\,P$ (VDI 2230 Part 1:2015, Annex B, Example B1, R11).

Where to get the value

• Shown for a tapped thread joint (TTJ) only.
• If it is given, R11 compares it with the required $m_{eff,min}$ and includes the result in the overall verdict.
• If it is empty, R11 still reports the required $m_{eff,min}$, but records the check as “not performed”, and it is not counted in the overall verdict.
• Without the thread limits of card 10 the required $m_{eff,min}$ is the estimate $1.0\,d$, which does not depend on the shear strength of the tapped part. With $R_{mM}$ (steel) or $\tau_{BM}$ (other materials) alone, the calculator also reports $R_S$ and the critical thread, and the estimate $1.0\,d$ remains.
• With the thread limits of card 10 in addition, $m_{eff,min}$ is calculated with Eq. (210) for a critical internal thread or Eq. (213) for a critical bolt thread (VDI 2230 Part 1:2015, §5.5.5.1, Eq. (210); §5.5.5.2, Eq. (213)).
• Figure 36 gives guide values of the required effective length of engagement, related to the nominal diameter, for a critical internal thread as a function of the shear strength of the nut material, for the strength grades 8.8, 10.9 and 12.9 (VDI 2230 Part 1:2015, §5.5.5.1, Figure 36).

Effect on the results

• ↓ Decrease: With a length of engagement below the critical one, an overload strips the threads instead of breaking the bolt (VDI 2230 Part 1:2015, §5.5.5). R11 then fails and the overall verdict fails.

Standard reference: VDI 2230 Part 1:2015, §5.5.5, Eq. (207)–(210), (213); §5.5.5.1, Figure 36; Annex B, Example B1, R11

Bolt segments (l_i, A_i)

The bolt is divided into cylindrical elements of length $l_i$ and cross-section $A_i$, with the elastic resilience $\delta_i=l_i/(E_S A_i)$ each (VDI 2230 Part 1:2015, §5.1.1.1, Figure 6, Eq. (18)). The resilience of the bolt is the sum $\delta_S=\delta_{SK}+\delta_1+\delta_2+\dots+\delta_{Gew}+\delta_{GM}$ (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (19)).

Where to get the value

• Each row has a length and a segment type: shank, thread or custom $d$; a custom segment also needs its diameter $d$. Up to 6 segments.
• The cross-section is $A_N=\frac{\pi}{4}d^2$ for a shank segment, $A_{d3}=\frac{\pi}{4}d_3^2$ for a thread segment and $A_i=\frac{\pi}{4}d_i^2$ for a custom segment (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (23), (25)).
• The segment lengths must add up to the clamping length $l_K$; otherwise the calculation is refused, and the lengths are not scaled or padded.
• With segments entered, the table is used and “Unthreaded shank length in the clamp” is hidden. With an empty table the calculation uses the two parts defined by $l_1$.
• The head, the engaged thread core and the nut region ($\delta_{SK}$, $\delta_G$, $\delta_M$) are not part of this table (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (19), (20)).
• If the shank diameter $d_i$ is smaller than $d_S=(d_2+d_3)/2$, the weakest cross-section lies in the shank and $d_0=d_{i\,min}$ is used for the comparative stress (VDI 2230 Part 1:2015, §5.5.1).
• A necked-down bolt ($d_0\le d_3$) goes through the same R0 to R13 steps, with $d_0=d_{i,min}$ (VDI 2230 Part 1:2015, §5.5.1).

Standard reference: VDI 2230 Part 1:2015, §5.1.1.1, Figure 6, Eq. (17)–(20), (23), (25); §5.5.1

Head-side bearing-face inner diameter (D_Ki, optional) [mm]

Inside diameter of the plane head bearing surface. For flat circular ring bearing areas, $D_{Ki}=\max(D_a,d_{ha},d_h,d_a)$, with the chamfer diameter $D_a$ of the nut, the chamfer diameter $d_{ha}$ at the clamped components, the hole diameter $d_h$ and the inside diameter $d_a$ of the plane head bearing area (VDI 2230 Part 1:2015, §5.4.3.1, Eq. (129)).

Where to get the value

• If it is empty, $D_{Ki}=d_h$ is used and the result is marked; the bearing area then ignores the chamfers.
• Special head: the value is used as entered and is not compared with $d_h$; it must be larger than 0 and smaller than $d_W$.
• Example B3 takes $d_{ha,max}=28$ mm as the inside diameter of the bearing area (VDI 2230 Part 1:2015, Annex B, Example B3, R10) and $d_h=29$ mm (VDI 2230 Part 1:2015, Annex B, Example B3, Table B1).

Effect on the results

• ↑ Increase: The minimum bearing area $A_{p\,min}$ decreases and the friction diameter $D_{Km}=(d_W+D_{Ki})/2$ increases (VDI 2230 Part 1:2015, §5.5.4, Eq. (193); §5.4.3.1, Eq. (128)).

Standard reference: VDI 2230 Part 1:2015, §2, $D_{Ki}$; §5.4.3.1, Eq. (128), (129); §5.5.4, Eq. (193)

Washer thickness under the head (h_S, optional) [mm]

Washer thickness (VDI 2230 Part 1:2015, §2, $h_S$). For the surface pressure between a standard washer and the clamped parts, the outside diameter $d_{Wa}=d_W+1.6\,h_S$ is used (VDI 2230 Part 1:2015, §5.5.4, Eq. (194)).

Where to get the value

• Optional. If it is empty, there is no washer and $d_{Wa}=d_W$.
• It enters only the bearing area of the surface pressure check R10 and is not part of the clamping length $l_K$.
• With a standard bolt selected, the washer is taken to lie under the head and is deducted from the shank length $l_1$.

Effect on the results

• ↑ Increase: $d_{Wa}$ increases, and with it the minimum bearing area $A_{p\,min}$ (VDI 2230 Part 1:2015, §5.5.4, Eq. (193), (194)).

Standard reference: VDI 2230 Part 1:2015, §2, $h_S$; §5.5.4, Eq. (193), (194)

Counterbore depth for the head (t, optional) [mm]

Depth $t$ of the counterbore according to DIN 974 in which the bolt head sits; the clamping length is $l_K=L-t$, in Example B1 with $L=55$ mm and $t=13$ mm $l_K=42$ mm (VDI 2230 Part 1:2015, Annex B, Example B1, R0, Figure B1). In Example B1, $L$ is the height of the piston from its top face to the interface between piston and piston rod and includes the counterbore depth $t$; it is not the overall piston height $L_g=60$ mm (VDI 2230 Part 1:2015, Annex B, Example B1, B1.1, Figure B1).

Where to get the value

• It only changes the schematic and does not change any result.
• The layers hold only the thicknesses below the bottom of the counterbore; the calculator takes their sum as $l_K$.
• It is not the counterbore depth $t_S$ of the tapped hole under “Eccentric clamping and loading”, which is used only for $G''$ (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (57)), and not the bolt spacing $t$ of a multi-bolted joint (VDI 2230 Part 1:2015, §2, $t$).

Standard reference: VDI 2230 Part 1:2015, Annex B, Example B1, B1.1, R0, Figure B1; §2, $t$; §5.1.2.2, Eq. (57)

Nut standard (nut side)

The surface pressure is limited at the bearing areas of the bolt head and of the nut on the clamped parts (VDI 2230 Part 1:2015, §5.5.4). The nut standard gives the outside diameter $d_{WMu}$ of the nut bearing area (VDI 2230 Part 1:2015, Annex B, Example B4, R10).

Where to get the value

• Shown for a through-bolt joint (TBJ) only. The default is “Automatic”.
• Automatic: coarse thread takes ISO 4032, fine thread takes ISO 8673 (same nominal diameter and pitch); ISO 4033 can be selected.
• $d_{WMu}$ is the minimum bearing diameter $d_{w,min}$ of the selected size in the standard table. If the size is not in the table and $d_{WMu}$ is empty, the calculation is refused.

Standard reference: VDI 2230 Part 1:2015, §5.5.4; Annex B, Example B4, R10; DIN EN ISO 4032:2023-12; EN ISO 4033:2023; EN ISO 8673:2023

Nut bearing-face outer diameter (d_WMu, optional) [mm]

Outside diameter of the bearing area on the nut side; Example B4 uses $d_{WMu}=11.6$ mm for a nut to DIN EN ISO 4032 (VDI 2230 Part 1:2015, Annex B, Example B4, R10).

Where to get the value

• Shown for a through-bolt joint (TBJ) in verification mode. If it is empty, the value $d_{w,min}$ of the nut standard table is used and the result shows its source.
• A value you enter replaces the table value. It must be larger than $D_{Ki,Mu}$, otherwise the calculation is refused.
• The table value of ISO 4032 for M8 is 11.63 mm; Example B4 prints 11.6 mm (VDI 2230 Part 1:2015, Annex B, Example B4, R10).
• In design mode the field is not read; the size selected in R0 is looked up in the nut standard table.

Effect on the results

• ↑ Increase: The minimum bearing area $A_{pMu,min}=\frac{\pi}{4}(d_{Wa,Mu}^2-D_{Ki,Mu}^2)$ increases and the surface pressure on the nut side decreases (VDI 2230 Part 1:2015, §5.5.4, Eq. (193)).

Standard reference: VDI 2230 Part 1:2015, §5.5.4, Eq. (193); Annex B, Example B4, R10

Nut-side bearing-face inner diameter (D_Ki,Mu, optional) [mm]

For the nut side, $D_{Ki}=\max(D_a,D_{ha},d_h)$, with the inside diameter $D_a$ of the plane nut bearing area (chamfer diameter), the inside diameter $D_{ha}$ of the plane bearing area of the clamped parts on the nut side and the hole diameter $d_h$ (VDI 2230 Part 1:2015, §5.4.3.1, Eq. (129); §2, $D_a$, $D_{ha}$).

Where to get the value

• Shown for a through-bolt joint (TBJ). It must not be smaller than $d_h$ and must be smaller than $d_{WMu}$, otherwise the calculation is refused.
• If it is empty, the larger of $d_{a,max}$ of the nut standard table and $d_h$ is used and the result is marked: the bearing area is not reduced for the chamfer of the clamped part, so $S_P$ is optimistic. Without a table entry for the size, $d_h$ is used.
• Example B4 takes $d_h=9$ mm on the nut side (VDI 2230 Part 1:2015, Annex B, Example B4, R10).

Effect on the results

• ↑ Increase: The minimum bearing area $A_{pMu,min}$ on the nut side decreases (VDI 2230 Part 1:2015, §5.5.4, Eq. (193)).

Standard reference: VDI 2230 Part 1:2015, §2, $D_a$, $D_{ha}$; §5.4.3.1, Eq. (129); §5.5.4, Eq. (193); Annex B, Example B4, R10

Washer thickness under the nut (h_S,Mu, optional) [mm]

Thickness of the standard washer under the nut (VDI 2230 Part 1:2015, §2, $h_S$). For the surface pressure between it and the clamped parts, the outside diameter is $d_{Wa}=d_W+1.6\,h_S$ (VDI 2230 Part 1:2015, §5.5.4, Eq. (194)); the calculator applies it to the nut side with $d_{WMu}$ in place of $d_W$.

Where to get the value

• Shown for a through-bolt joint (TBJ). Optional. If it is empty, there is no washer under the nut and $d_{Wa,Mu}=d_{WMu}$.
• It enters only the bearing area of the surface pressure check R10 and is not part of the clamping length $l_K$.

Effect on the results

• ↑ Increase: $d_{Wa,Mu}$ increases, and with it the minimum bearing area $A_{pMu,min}$ (VDI 2230 Part 1:2015, §5.5.4, Eq. (193), (194)).

Standard reference: VDI 2230 Part 1:2015, §2, $h_S$; §5.5.4, Eq. (193), (194)

Tapped part is steel (R_S by Eq.(199))

• The strength ratio $R_S = \tau_{BM}\,A_{SGM}/(\tau_{BS}\,A_{SGS})$ decides whether the bolt thread strips the internal thread or the other way round (VDI 2230 Part 1:2015, §5.5.5, Eq. (195)).
• For steel with the same shear strength ratio $\tau_B/R_m$, $R_S$ follows from the tensile strengths (VDI 2230 Part 1:2015, §5.5.5, Eq. (196), (199)).
• $R_S \lt 1$ means that the internal thread is critical; $R_S \geq 1$ means that the bolt thread is critical (VDI 2230 Part 1:2015, §5.5.5.1; §5.5.5.2).

Where to get the value

• Yes (default): the calculator takes $R_S$ from Eq. (199) and needs $R_{mM}$; No: it takes $R_S$ from Eq. (195) and needs $\tau_{BM}$, with $\tau_{BS}$ from Table 7 for the strength class (VDI 2230 Part 1:2015, §5.5.5, Eq. (195), (199); §5.5.6.3, Table 7).
• Choosing a Table A9 material for the tapped part sets this switch: non-alloy structural steel, fine-grained structural steel, low-alloy tempering steel and austenitic CrNi steel give Yes; the other groups give No.

Standard reference: VDI 2230 Part 1:2015, §5.5.5, Eq. (195), (196), (199); §5.5.5.1; §5.5.5.2; §5.5.6.3, Table 7

Nut/internal-thread tensile strength (R_mM) [N/mm²]

$R_{mM}$ is the tensile strength of the nut (VDI 2230 Part 1:2015, §2, $R_{mM}$).

Where to get the value

• $\tau_{BM}$ can be obtained from Table 6 for a nut material with known tensile strength $R_{mM}$ or Brinell hardness HB, taking Table A9 into consideration (VDI 2230 Part 1:2015, §5.5.5.1, Table 6).
• The calculator takes $R_{mM}$ as the tensile strength of the material of the component with the internal thread.
• For steel, entering $R_{mM}$ makes the calculator find the critical thread from Eq. (199).
• If the tapped part is not steel, entering $R_{mM}$ without $\tau_{BM}$ is rejected.
• The material picker fills $R_{mM}$ from the minimum tensile strength of the chosen Table A9 row.

Effect on the results

• ↓ Decrease: $R_{mM}$ is in the numerator of Eq. (199), so $R_S$ becomes smaller (VDI 2230 Part 1:2015, §5.5.5, Eq. (199)).

Standard reference: VDI 2230 Part 1:2015, §2, $R_{mM}$; §5.5.5, Eq. (199); §5.5.5.1, Table 6

Nut/internal-thread shear strength (τ_BM,min) [N/mm²]

$\tau_{BM}$ is the shearing strength of the nut (VDI 2230 Part 1:2015, §2, $\tau_{BM}$). For a tapped thread joint (TTJ) it is the shear strength of the material of the component with the internal thread (VDI 2230 Part 1:2015, §5.5.5, before Eq. (195)). Eq. (210) uses its minimum value $\tau_{BM,min}$ (VDI 2230 Part 1:2015, §5.5.5.1, Eq. (210)).

Where to get the value

• $\tau_{BM}$ can be obtained from Table 6 for a nut material with known $R_{mM}$ or HB, taking Table A9 into consideration (VDI 2230 Part 1:2015, §5.5.5.1, Table 6).
• The calculator reads only the value entered and does not convert between Table 6 and Table A9.
• If the tapped part is not steel, the label shows “required”. The calculator rejects the input if $R_{mM}$ or any thread limit is given without $\tau_{BM,min}$; if none of them is given, it uses the estimate $1.0\,d$ for $m_{eff,min}$.
• For steel it is required only if the internal thread is critical ($R_S \lt 1$) and the tolerance limits are given.
• For a row of Table A9 chosen for the tapped part, the material picker fills the field with $\tau_{B,min}$ of the row, or empties it if the row has no such value (VDI 2230 Part 1:2015, Annex A, Table A9).

Effect on the results

• ↓ Decrease: $\tau_{BM,min}$ is in the denominator of Eq. (210), so $m_{ges,min}$ becomes larger; in Eq. (195) $R_S$ becomes smaller (VDI 2230 Part 1:2015, §5.5.5, Eq. (195); §5.5.5.1, Eq. (210)).

Standard reference: VDI 2230 Part 1:2015, §2, $\tau_{BM}$; §5.5.5, Eq. (195); §5.5.5.1, Eq. (210), Table 6

Equivalent diameter around the internal thread (s) [mm]

$s$ is the equivalent diameter of the material area around the internal thread. For $1.4 \leq s/d \leq 1.9$ the correction factor is $C_1 = 3.8\,s/d - (s/d)^2 - 2.61$; for $s/d > 1.9$, as is usual with tapped thread joints (TTJs), $C_1 = 1$ (VDI 2230 Part 1:2015, §5.5.5.1, Eq. (201)).

Where to get the value

• The field is used only when the R11 calculation chain runs, that is when $R_{mM}$ (steel) or $\tau_{BM}$ (other materials) is given; otherwise $s$ is not checked.
• When the chain runs and the field is empty, the calculator takes $C_1 = 1$ and says so in the step text.
• When the chain runs and $s/d \lt 1.4$, the calculator refuses the calculation.

Effect on the results

• ↑ Increase: $C_1$ becomes larger up to 1, the stripping force $F_{mGM} = \tau_{BM}\,A_{SGM}\,C_1\,C_3$ becomes larger and $m_{ges,min}$ becomes smaller (VDI 2230 Part 1:2015, §5.5.5.1, Eq. (200), (201), (209)).

Standard reference: VDI 2230 Part 1:2015, §5.5.5.1, Eq. (200), (201), (209)

Bolt major diameter, lower limit (d_min) [mm]

The case most unfavourable for the load-bearing capacity of the thread is the outside diameter $d$ of the bolt thread at its lower tolerance limit $d_{min}$ and the pitch diameter $D_2$ of the nut thread at its upper tolerance limit (VDI 2230 Part 1:2015, §5.5.5.1, before Eq. (210)).

Where to get the value

• Eq. (210) for the internal thread and Eq. (213) for the bolt thread both use $d_{min}$ (VDI 2230 Part 1:2015, §5.5.5.1, Eq. (210); §5.5.5.2, Eq. (213)).
• The field is shown in verification mode only, and the calculator requires $d_{min} \leq d$.
• If only some of the limits that the critical branch needs are given, the input is rejected.

Effect on the results

• ↓ Decrease: $m_{ges,min}$ becomes larger in Eq. (210) and in Eq. (213) (VDI 2230 Part 1:2015, §5.5.5.1, Eq. (210); §5.5.5.2, Eq. (213)).

Standard reference: VDI 2230 Part 1:2015, §5.5.5.1, Eq. (210); §5.5.5.2, Eq. (213)

Bolt pitch diameter, lower limit (d_2min) [mm]

$d_{2min}$ is the pitch diameter of the bolt thread at its lower tolerance limit, used in the bracket $[P/2 + (d_{2min} - D_{1max})\tan 30°]$ for the case of a critical bolt thread (VDI 2230 Part 1:2015, §5.5.5.2, Eq. (213)).

Where to get the value

• The field is shown in verification mode only, and the calculator requires $d_{2min} \leq d_2$.

Effect on the results

• ↓ Decrease: The bracket in the denominator of Eq. (213) becomes smaller, so $m_{ges,min}$ becomes larger (VDI 2230 Part 1:2015, §5.5.5.2, Eq. (213)).

Standard reference: VDI 2230 Part 1:2015, §5.5.5.2, Eq. (213)

Internal minor diameter, upper limit (D_1max) [mm]

$D_{1max}$ is the minor diameter of the internal thread at its upper tolerance limit, used in the bracket $[P/2 + (d_{2min} - D_{1max})\tan 30°]$ for the case of a critical bolt thread (VDI 2230 Part 1:2015, §5.5.5.2, Eq. (213)).

Where to get the value

• The field is shown in verification mode only, and the calculator requires $D_{1max} \geq D_1$.

Effect on the results

• ↑ Increase: The bracket in the denominator of Eq. (213) becomes smaller, so $m_{ges,min}$ becomes larger (VDI 2230 Part 1:2015, §5.5.5.2, Eq. (213)).

Standard reference: VDI 2230 Part 1:2015, §5.5.5.2, Eq. (213)

Internal pitch diameter, upper limit (D_2max) [mm]

$D_{2max}$ is the pitch diameter of the nut thread at its upper tolerance limit, used in the bracket $[P/2 + (d_{min} - D_{2max})\tan 30°]$ for the case of a critical internal thread (VDI 2230 Part 1:2015, §5.5.5.1, Eq. (210)).

Where to get the value

• The field is shown in verification mode only, and the calculator requires $D_{2max} \geq D_2$.

Effect on the results

• ↑ Increase: The bracket in the denominator of Eq. (210) becomes smaller, so $m_{ges,min}$ becomes larger (VDI 2230 Part 1:2015, §5.5.5.1, Eq. (210)).

Standard reference: VDI 2230 Part 1:2015, §5.5.5.1, Eq. (210)

Axial Load (F_A) [N]

A component of a working load $F_B$ in any direction, directed in the bolt axis and related proportionally to one bolt (VDI 2230 Part 1:2015, §2, symbols). The calculator takes $F_A$ as a tensile load, $F_A\ge 0$, and uses it as $F_{A,max}$.

Where to get the value

• The button below the field takes $F_A$ and $F_Q$ of the selected bolt from the multi-bolt calculator (VDI 2230-2).
• With the fatigue check on, the lower value of the load is entered in $F_{A,min}$.

Effect on the results

• ↑ Increase: $F_{SA}=\Phi F_A$ and $F_{PA}=(1-\Phi)F_A$ increase (VDI 2230 Part 1:2015, §4.2, R3, (R3/1), (R3/2)); $F_{Mmin}$ contains the term $(1-\Phi_{en}^{*})F_{A\max}$ (VDI 2230 Part 1:2015, §4.2, R5, (R5/1)).

Standard reference: VDI 2230 Part 1:2015, §2; §4.2, R3, (R3/1), (R3/2); R5, (R5/1)

Transverse Load (F_Q) [N]

A working load directed perpendicular to the bolt axis, or its component for a working load $F_B$ in any direction (VDI 2230 Part 1:2015, §2, symbols). The calculator uses it as $F_{Q,max}$; with $F_Q>0$ the card “Shear & bolt bearing pressure” appears.

Where to get the value

Impact stresses caused by alternating loading directions must be prevented by suitable measures (slide-proof joint, close-fitting bolt, pins or similar) (VDI 2230 Part 1:2015, §5.5.6.4). The default is 0.

Effect on the results

• ↑ Increase: $F_{KQ}$ increases (VDI 2230 Part 1:2015, §5.4.1, Eq. (108)); $F_{Qres}$ increases (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (217)), which must stay within $F_{Qzul\mu}$ (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (215)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.1, Eq. (108); §5.5.6.3, Eq. (215)–(217); §5.5.6.4

Load Introduction Factor (n)

Load introduction factor: describes the effect of the introduction point of $F_A$ on the displacement of the bolt head, generally and for concentric clamping (VDI 2230 Part 1:2015, §2, symbols). It is defined as $n=\delta_{VA}/\delta_P$, the ratio of the influence coefficient $\delta_{VA}$ to the plate resilience (VDI 2230 Part 1:2015, §5.2.2.1, Eq. (76)). The calculation always uses the $n$ entered here, with $0\lt n\le 1$.

Where to get the value

• For beam-like joints (Table 1) a load introduction factor of 0.4 can be assumed (VDI 2230 Part 1:2015, §5.2.2.2 e)).
• $n$ can be determined directly or by linear interpolation from Table 2 (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2). The joined plates must have the same Young’s modulus, and the proposed values are on the safe side for the additional bolt loads because $k_{ar}\cdot k_{dh}\cdot k_{dw}=0.8$ is assumed (VDI 2230 Part 1:2015, §5.2.2.2).
• With a very small $n$ the joint may tend to open, and the preconditions of the simplified determination no longer exist (VDI 2230 Part 1:2015, §5.2.2.2 e)).
• Annex B, Example B1, R3: $n=0.35$ from Table 2 (VDI 2230 Part 1:2015, Annex B, Example B1, R3).
• The default is 0.5. The optional helper “Joint type for load introduction”, $a_k$ and $l_A$ shows the Table 2 suggestion in step R3c; the suggestion is not used in the calculation.

Effect on the results

• ↑ Increase: $\Phi_n=n\,(\delta_P+\delta_{PZu})/(\delta_S+\delta_P)$ increases in proportion (VDI 2230 Part 1:2015, §4.2, R3, (R3/3)), and so does $F_{SA}=\Phi F_A$ (VDI 2230 Part 1:2015, §4.2, R3, (R3/1)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.2.2.1, Eq. (76); §5.2.2.2 e), Table 2; §4.2, R3, (R3/1), (R3/3); Annex B, Example B1, R3

Joint type for load introduction (optional)

• Joint type according to the type of load introduction, SV 1 to SV 6; each joint is assigned to one type by the position of the load introduction points (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22).
• It is an optional helper for the suggestion of $n$ in Table 2; the calculation uses the $n$ entered.
• Working loads can be passed into the basic solid via the connecting solid; the load introduction point $K_G$ is approximately located half way up the connecting solid (VDI 2230 Part 1:2015, §5.2.2.2 b), Figure 21).
• In the figure, the small circle is the load introduction point $K$ in the connecting solid; the load introduction point $K_G$ at the basic solid is at the same height on the side of the basic solid and is not drawn (VDI 2230 Part 1:2015, §2, $K$, $K_G$, $l_A$; §5.2.2.2 b), Figure 21).
• $F_A$ is the axial load, a component, directed in the bolt axis and proportionally related to the bolt, of a working load $F_B$ in any direction (VDI 2230 Part 1:2015, §2, $F_A$).
• In the figure, the label “1” marks the interface region evenly clamped and appropriate from the design point of view (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22).

Where to get the value

• The interface must lie in the marked region of Figure 22, which can be found approximately by a cone of 30° to the bolt axis starting from the bolt bearing area (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22).
• For a tapped thread joint the types SV 1, SV 2 and SV 4 are used, and only the height of the top plate is taken as $h$ (VDI 2230 Part 1:2015, §5.2.2.2 c)).
• The suggestion appears in step R3c when this field, $a_k$ and $l_A$ are given and $l_K>0$; it is switched off when the clamped layers have different $E_P$. Left empty, $n$ is entered directly.
• The figure is schematic and not to scale; as in Figure 22, the six types are drawn as through-bolt joints, and the connecting solids and $F_A$ only on the right side (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22).
• The six drawings differ in the position of the connecting solids and their load introduction points along the bolt axis (VDI 2230 Part 1:2015, §5.2.2.2 c), Figure 22).
• The lateral position of the load introduction enters Table 2 through $a_k/h$ and $l_A/h$ (VDI 2230 Part 1:2015, §5.2.2.2 d)–e), Figure 23, Table 2).
• Annex B takes SV 4 and $l_A=0$ for the concentric Example B1, where the force acts in the region of the interface (VDI 2230 Part 1:2015, Annex B, Example B1, R3); SV 1 and $l_A=2.95$ mm for the eccentric Example B4 (VDI 2230 Part 1:2015, Annex B, Example B4, R3); SV 2 and $l_A=0$ for the eccentric Example B5 (VDI 2230 Part 1:2015, Annex B, Example B5, R3).
• Eccentric clamping and loading are entered with the inputs “Eccentric clamping / loading”, $s_{sym}$ and $a$; this field does not enter the eccentric calculation.

Effect on the results

• ↑ SV 1 → SV 6: $n$ in Table 2 decreases, for example from 0.70 (SV 1) to 0.15 (SV 6) at $a_k/h=0$ and $l_A/h=0$ (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2).

Standard reference: VDI 2230 Part 1:2015, §2, $F_A$, $K$, $K_G$, $l_A$; §5.2.2.2 b), Figure 21; §5.2.2.2 c), Figure 22; §5.2.2.2 d), Figure 23; §5.2.2.2 e), Table 2; Annex B, Examples B1, B4, B5, R3

Distance bearing face → load point (a_k, optional) [mm]

Distance between the edge of the preloading area and the force introduction point at the basic solid (VDI 2230 Part 1:2015, §2, symbols; §5.2.2.1, Figure 17; §5.2.2.2 d), Figure 23). It is an optional helper for the suggestion of $n$ in Table 2.

Where to get the value

• Table 2 is entered with the ratio $a_k/h$ in the columns 0.00, 0.10, 0.30 and ≥ 0.50 (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2); the calculator takes $h=l_K$ and interpolates between the table values.
• Annex B, Example B1, R3: $a_k=3.89$ mm and $a_k/h=0.093$ (VDI 2230 Part 1:2015, Annex B, Example B1, R3).

Effect on the results

• ↑ Increase: $n$ in Table 2 decreases, for example from 0.70 to 0.13 for SV 1 when $a_k/h$ rises from 0 to ≥ 0.50 at $l_A/h=0$ (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2).

Standard reference: VDI 2230 Part 1:2015, §2; §5.2.2.1, Figure 17; §5.2.2.2 d), Figure 23; §5.2.2.2 e), Table 2; Annex B, Example B1, R3

Length basic solid → load point (l_A, optional) [mm]

Length between the basic solid and the load introduction point $K$ in the connecting solid (VDI 2230 Part 1:2015, §2, symbols; §5.2.2.2 d), Figure 23). It is an optional helper for the suggestion of $n$ in Table 2.

Where to get the value

• For concentric loading $l_A=0$ (VDI 2230 Part 1:2015, §5.2.2.2 d)).
• Table 2 is entered with the ratio $l_A/h$ in the column groups 0.00, 0.10, 0.20 and ≥ 0.30 (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2); the calculator takes $h=l_K$.

Effect on the results

• ↑ Increase: $n$ in Table 2 decreases, for example from 0.70 to 0.16 for SV 1 when $l_A/h$ rises from 0 to ≥ 0.30 at $a_k/h=0$ (VDI 2230 Part 1:2015, §5.2.2.2 e), Table 2).

Standard reference: VDI 2230 Part 1:2015, §2; §5.2.2.2 d), Figure 23; §5.2.2.2 e), Table 2

Torque about the bolt axis (M_Y) [N·mm]

Torque about the bolt axis (VDI 2230 Part 1:2015, §2, symbols). The calculator uses it as $M_{Y,max}$; with $M_Y>0$ the fields $q_M$ and $r_a$ appear, and $r_a$ is required.

Where to get the value

Annex B, Example B3, R2: $M_Y=110$ N·m, that is 110 000 N·mm (VDI 2230 Part 1:2015, Annex B, Example B3, R2). The default is 0.

Effect on the results

• ↑ Increase: The second term of $F_{KQ}$ increases (VDI 2230 Part 1:2015, §5.4.1, Eq. (108)); $F_{Qres}$ increases (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (217)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.1, Eq. (108); §5.5.6.3, Eq. (217); Annex B, Example B3, R2

Internal Pressure (p_i) [N/mm²]

Internal pressure to be sealed (VDI 2230 Part 1:2015, §2, symbols). The calculator uses it as $p_{i,max}$.

Where to get the value

With $p_i=0$ the sealing clamp load $F_{KP}$ is 0. The default is 0.

Effect on the results

• ↑ Increase: $F_{KP}=A_D\,p_{i,max}$ increases (VDI 2230 Part 1:2015, §5.4.1, Eq. (109)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.1, Eq. (109)

Sealing area (A_D, for F_KP=A_D·p_i) [mm²]

Sealing area: at most the interface area less the through-hole for the bolt (VDI 2230 Part 1:2015, §2, symbols). In this field it enters only $F_{KP}=A_D\,p_{i,max}$ (VDI 2230 Part 1:2015, §5.4.1, Eq. (109)); the contact area for the opening check is the separate input “Opening-check contact area” in card 11.

Where to get the value

With $A_D=0$ the sealing clamp load $F_{KP}$ is 0. The default is 0.

Effect on the results

• ↑ Increase: $F_{KP}=A_D\,p_{i,max}$ increases (VDI 2230 Part 1:2015, §5.4.1, Eq. (109)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.1, Eq. (109)

Required residual clamp load (F_KR,req) [N]

An input of this calculator, not a term of the standard: a minimum clamp load given directly for a sealing or functional requirement. The standard defines $F_{Kerf}$ as the clamp load required for sealing functions, friction grip and prevention of one-sided opening at the interface (VDI 2230 Part 1:2015, §2, symbols); the calculator takes $F_{Kerf}=\max(F_{KQ};\,F_{KP};\,F_{KR,req})$, and with eccentric clamping or loading $F_{Kerf}=\max\big(F_{KQ};\,\max(F_{KP},F_{KR,req})+F_{KA}\big)$ (VDI 2230 Part 1:2015, §4.2, R2, (R2/4); §5.4.1, Eq. (111)).

Where to get the value

The default is 0; $F_{Kerf}$ then follows from $F_{KQ}$ and $F_{KP}$ only.

Effect on the results

• ↑ Increase: When it governs, $F_{Kerf}$ increases, and so does $F_{Mmin}=F_{Kerf}+(1-\Phi_{en}^{*})F_{A\max}+F_Z+\Delta F'_{Vth}$ (VDI 2230 Part 1:2015, §4.2, R5, (R5/1)).

Standard reference: VDI 2230 Part 1:2015, §2; §4.2, R2, (R2/4); §5.4.1, Eq. (111); §4.2, R5, (R5/1)

Strength Class

Strength class of the bolt according to DIN EN ISO 898-1; $R_{p0,2}$ and $R_m$ of the bolt are the minimum values according to DIN EN ISO 898-1 (VDI 2230 Part 1:2015, §2, symbols). Picking a class fills in $R_{p0,2}$ and $R_m$ below; both stay editable.

Where to get the value

• Filled values $R_{p0,2}$ / $R_m$ in N/mm² (DIN EN ISO 898-1:2013-05, 7, Table 3): 4.6: 240 / 400; 4.8: 340 / 420; 5.6: 300 / 500; 6.8: 480 / 600; 8.8: 640 / 800 (660 / 830 above M16 in verification mode); 10.9: 940 / 1040; 12.9: 1100 / 1220.
• For 4.6 and 5.6 the filled value is the lower yield strength $R_{eL}$, for 4.8 and 6.8 it is $R_{pf,min}$ (DIN EN ISO 898-1:2013-05, 7, Table 3).
• The class 4.8 appears in the list only when ISO 4014 or ISO 4017 is selected as standard bolt (DIN EN ISO 4014:2022-10, 5, Table 7; ISO 4017:2022, Table 5). The class 9.8 is not in the list.
• In design mode, class 8.8 is always filled with 640 / 800.
• With a standard bolt picked in card 1, the list shows only the classes that standard allows for the size; a class that is not allowed is replaced by 8.8 with a message.
• Table 7 lists the shear strength ratio $\tau_B/R_m$ for the classes 4.6, 5.6, 8.8, 10.9 and 12.9 (VDI 2230 Part 1:2015, §5.5.6.3, Table 7). For the other classes (4.8, 6.8, and a class 9.8 passed to the calculator directly) the calculator gives no bolt shear safety $S_A$ with $F_Q>0$. In a tapped thread joint (TTJ) it refuses the calculation for these classes if the tapped part is not steel and $R_S$ is calculated with Eq. (195), or if the bolt thread is critical and the thread limits of card 10 are given for Eq. (213).

Standard reference: DIN EN ISO 898-1:2013-05, 7, Table 3; VDI 2230 Part 1:2015, §2; §5.5.6.3, Table 7

⚡ Yield Strength (R_p0,2) [N/mm²]

0.2 % proof stress of the bolt according to DIN EN ISO 898-1 (VDI 2230 Part 1:2015, §2, symbols); the calculation uses the minimum value $R_{p0,2min}$ (VDI 2230 Part 1:2015, §5.5.1, Eq. (145)).

Where to get the value

It is filled from the strength class and stays editable. For class 8.8 the calculation steps flag a value above 640 N/mm² for sizes up to M16, and a value below 660 N/mm² above M16 (DIN EN ISO 898-1:2013-05, 7, Table 3).

Effect on the results

• ↑ Increase: $\sigma_{Mzul}$ and $F_{Mzul}=\sigma_{Mzul}A_0\nu$ increase (VDI 2230 Part 1:2015, §5.5.1, Eq. (143), (144)); $S_F=R_{p0,2min}/\sigma_{red,B}$ increases (VDI 2230 Part 1:2015, §4.2, R8, (R8/5-2)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.5.1, Eq. (143)–(145); §4.2, R8, (R8/5-2); DIN EN ISO 898-1:2013-05, 7, Table 3

⚡ Tensile Strength (R_m) [N/mm²]

Tensile strength of the bolt; minimum value according to DIN EN ISO 898-1 (VDI 2230 Part 1:2015, §2, symbols).

Where to get the value

It is filled from the strength class and stays editable. The calculator uses $R_{mS}=R_m$ in Eq. (199).

Effect on the results

• ↑ Increase: $F_{QzulS}=A_\tau R_m(\tau_B/R_m)/S_A$ increases (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (220)); the strength ratio $R_S$ of a tapped thread joint decreases with $R_{mS}$ in the denominator (VDI 2230 Part 1:2015, §5.5.5, Eq. (199)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.5.5, Eq. (199); §5.5.6.3, Eq. (220)

Elastic Modulus (E_S) [N/mm²]

Young’s modulus of the bolt material (VDI 2230 Part 1:2015, §2, symbols).

Where to get the value

The default is 210 000 N/mm². The button “Pick bolt material” fills $E_S$, the thermal expansion coefficient and the modulus at working temperature from the material library.

Effect on the results

• ↑ Increase: $\delta_i=l_i/(E_S A_i)$ decreases (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (18)), so $\delta_S$ decreases and $\Phi_n$ increases (VDI 2230 Part 1:2015, §4.2, R3, (R3/3)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.1.1.1, Eq. (18), (19); §4.2, R3, (R3/3)

Tapped-body modulus (E_BI, optional) [N/mm²]

Young’s modulus of the component with internal thread (VDI 2230 Part 1:2015, §2, symbols); for a tapped thread joint $E_M=E_{BI}$ is used in $\delta_M=l_M/(E_M A_N)$ with $l_M=0.33\,d$ (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (24), (27)). The field is shown only for a tapped thread joint.

Where to get the value

• Reference values of the properties of the materials of bolted components are given in Table A9 (VDI 2230 Part 1:2015, Annex A, Table A9); the button “Pick material” fills the field from the material library.
• Left empty, the modulus of the clamped parts is used, and the calculation steps note that this is optimistic if the tapped body is softer.

Effect on the results

• ↓ Decrease: $\delta_M$ increases, so $\delta_{GM}=\delta_G+\delta_M$ and $\delta_S$ increase (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (19), (20), (24)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.1.1.1, Eq. (19), (20), (24), (27); Annex A, Table A9

Friction class (Table A5)

Class of the coefficient of friction, with guide values for $\mu_G$ and $\mu_K$ for different materials, surfaces and lubrication states: A 0.04 to 0.10; B 0.08 to 0.16; C 0.14 to 0.24; D 0.20 to 0.35; E ≥ 0.30 (VDI 2230 Part 1:2015, Annex A, Table A5). If $\mu_G$ and $\mu_K$ are not known, Table A5 can be consulted (VDI 2230 Part 1:2015, §4.2, R7).

Where to get the value

• The aim is a coefficient of friction in class B, for the highest possible preload with low scatter; this does not automatically mean using the smallest values, and the scatter present need not correspond to the class spread. Table A5 applies for room temperature (VDI 2230 Part 1:2015, Annex A, Table A5).
• Picking a class once fills $\mu_{G,min}$ and $\mu_{K,min}$ with the lower limit of the class range, and $\mu_{G,max}$ with the upper limit for classes A to D when that field is shown; class E has no upper limit, so $\mu_{G,max}$ is not filled. The values stay editable and are not changed again by the class.
• The calculation steps show the selected class and its range, mark inputs outside the range as a reminder only, and add a note when the thermal option is on.

Effect on the results

• ↑ Class A → E: The guide range of $\mu_G$ and $\mu_K$ rises from 0.04 to 0.10 (A) to ≥ 0.30 (E) (VDI 2230 Part 1:2015, Annex A, Table A5).

Standard reference: VDI 2230 Part 1:2015, §4.2, R7; §5.5.1; Annex A, Table A5

Thread Friction (μ_G,min)

Coefficient of friction in the thread, minimum value (VDI 2230 Part 1:2015, §2, symbols). For $F_{Mzul}$ the smallest value $\mu_{G,min}$ of the coefficient of friction in the thread for the existing conditions is to be used (VDI 2230 Part 1:2015, §5.5.1).

Where to get the value

If the coefficients of friction are not known, guide values may be taken from Table A5 (VDI 2230 Part 1:2015, §5.5.1; Annex A, Table A5); the friction class above fills them. The default is 0.10.

Effect on the results

• ↑ Increase: $\sigma_{Mzul}$ and $F_{Mzul}$ decrease because $1.155\,\mu_{G,min}$ is in the denominator (VDI 2230 Part 1:2015, §5.5.1, Eq. (143), (144)); the thread torque $M_G=F_M(0.16\,P+0.58\,d_2\,\mu_G)$ increases (VDI 2230 Part 1:2015, §5.4.3.1, Eq. (125)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.5.1, Eq. (143), (144); §5.4.3.1, Eq. (125); Annex A, Table A5

Head Friction (μ_K,min)

Coefficient of friction in the head bearing area, minimum value (VDI 2230 Part 1:2015, §2, symbols). When the tightening torque is calculated, the minimum coefficients of friction are always to be used (VDI 2230 Part 1:2015, §5.4.3.1).

Where to get the value

If the coefficients of friction are not known, guide values may be taken from Table A5 (VDI 2230 Part 1:2015, §5.5.1; Annex A, Table A5); the friction class above fills them. The default is 0.10.

Effect on the results

• ↑ Increase: The head torque $M_K=F_M\,(D_{Km}/2)\,\mu_K$ and the tightening torque $M_A$ increase (VDI 2230 Part 1:2015, §5.4.3.1, Eq. (126), (127)); $F_{Mzul}$ does not contain $\mu_K$ (VDI 2230 Part 1:2015, §5.5.1, Eq. (143)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.3.1, Eq. (126), (127); §5.5.1; Annex A, Table A5

Interface Friction (μ_T,min)

Coefficient of friction at the interface, minimum value (VDI 2230 Part 1:2015, §2, symbols); in $F_{KQ}$ it is the coefficient of static friction in the interface (VDI 2230 Part 1:2015, §5.4.1, Eq. (108)).

Where to get the value

• Table A6 gives approximate ranges of the coefficient of static friction by material pairing, for example steel – steel/cast steel (general) dry 0.1 to 0.3 and lubricated 0.07 to 0.12 (VDI 2230 Part 1:2015, Annex A, Table A6).
• Coefficients of static friction of 0.1 ≤ $\mu_T$ ≤ 1.0 can normally occur between engineering surfaces (VDI 2230 Part 1:2015, §5.5.6.3).
• In a specific case the minimum coefficient of friction need not correspond to the lower limit of the range, and experimental investigations may be necessary (VDI 2230 Part 1:2015, Annex A, Table A6, note).
• With dynamic stress it is advisable to use the coefficient of slip friction in Eq. (108) (VDI 2230 Part 1:2015, §5.4.1); for slip-resistant joints the coefficient of static friction is to be used (VDI 2230 Part 1:2015, §5.5.6.4).
• The default is 0.12.

Effect on the results

• ↓ Decrease: $F_{KQ}$ increases (VDI 2230 Part 1:2015, §5.4.1, Eq. (108)) and $F_{Qzul\mu}=\mu_{T,min}F_{KRmin}/S_G$ decreases (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (216)). It has an effect only when $F_Q>0$ or $M_Y>0$.

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.1, Eq. (108); §5.5.6.3, Eq. (216); §5.5.6.4; Annex A, Table A6

Number of force-transmitting inner interfaces (q_F)

Number of force-transmitting ($F_Q$) inner interfaces which are involved in possible slipping or shearing of the bolt (VDI 2230 Part 1:2015, §2, symbols). It is obtained when the joint is imagined as if it were loaded to failure; each inner interface involved in the slipping of the clamped components or the shearing of the bolt is taken into account, and interfaces at which no relative movement can occur are not relevant (VDI 2230 Part 1:2015, §5.5.6.1).

Where to get the value

A whole number of at least 1; the default is 1.

Effect on the results

• ↑ Increase: $F_{KQ}$ decreases (VDI 2230 Part 1:2015, §5.4.1, Eq. (108)) and $F_{Qres}=F_{Qmax}/q_F+\dots$ decreases (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (217)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.1, Eq. (108); §5.5.6.1; §5.5.6.3, Eq. (217)

Number of torque-transmitting inner interfaces (q_M)

Number of torque-transmitting ($M_Y$) inner interfaces which are involved in possible slipping (VDI 2230 Part 1:2015, §2, symbols). It is obtained in the same way as $q_F$ (VDI 2230 Part 1:2015, §5.5.6.1). The field is shown when $M_Y>0$.

Where to get the value

A whole number of at least 1; the default is 1.

Effect on the results

• ↑ Increase: The second term of $F_{KQ}$ decreases (VDI 2230 Part 1:2015, §5.4.1, Eq. (108)) and $F_{Qres}$ decreases (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (217)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.1, Eq. (108); §5.5.6.1; §5.5.6.3, Eq. (217)

Friction radius for M_Y (r_a, required if M_Y>0) [mm]

Friction radius at the clamped parts when $M_Y$ is acting (VDI 2230 Part 1:2015, §2, symbols); it is derived from the dimensions of the clamped components (VDI 2230 Part 1:2015, §5.4.1, Eq. (108)). The field is shown and required when $M_Y>0$; there is no default, and with $r_a$ empty the calculation stops with an input error.

Where to get the value

Annex B, Example B3, R2: $r_a=(D_A+D_{h,a,max})/4=(48+30)/4=19.5$ mm (VDI 2230 Part 1:2015, Annex B, Example B3, R2).

Effect on the results

• ↑ Increase: The second term of $F_{KQ}$ decreases (VDI 2230 Part 1:2015, §5.4.1, Eq. (108)) and $F_{Qres}$ decreases (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (217)).

Standard reference: VDI 2230 Part 1:2015, §2; §5.4.1, Eq. (108); §5.5.6.3, Eq. (217); Annex B, Example B3, R2

Loading type for slipping (S_G)

• Chooses the normal value of the required safety margin against slipping when “Required safety margin against slipping” is left empty (VDI 2230 Part 1:2015, §4.2, R12/4).
• Static loading: 1.2. Alternating loading by $F_Q$ and/or $M_Y$: 1.8 (VDI 2230 Part 1:2015, §4.2, R12/4).
• VDI 2230 sets the limit at 1.0 ($S_G>1.0$) and leaves the required safety margin to the user (VDI 2230 Part 1:2015, §4.2, R12/4).

Where to get the value

• Shown when $F_Q>0$ or $M_Y>0$.
• Has no effect when you enter a value in “Required safety margin against slipping”.
• The result shows the value used and where it comes from.

Effect on the results

• ↑ Alternating loading: With the required value left empty, the value used rises from 1.2 to 1.8, so $S_G$ must be higher to pass (VDI 2230 Part 1:2015, §4.2, R12/4).

Standard reference: VDI 2230 Part 1:2015, §4.2, R12 (R12/4)

Required safety margin against slipping (S_G, optional)

• The safety margin against slipping $S_G$ must be greater than 1.0 and not lower than this required value (VDI 2230 Part 1:2015, §4.2, R12/4).
• VDI 2230 sets the limit at 1.0 and leaves the required safety margin to the user (VDI 2230 Part 1:2015, §4.2, R12/4).
• Normal values in the standard: 1.2 for static loading, 1.8 for alternating loading by $F_Q$ and/or $M_Y$ (VDI 2230 Part 1:2015, §4.2, R12/4).

Where to get the value

• Leave it empty to use the value for the chosen loading type; the placeholder shows it.

• Shown when $F_Q>0$ or $M_Y>0$.

• Not below 1.0.

• The calculator accepts only $S_G \ge 1$.

Effect on the results

• ↑ Increase: A higher $S_G$ is needed to pass the slip check (VDI 2230 Part 1:2015, §4.2, R12/4).

Standard reference: VDI 2230 Part 1:2015, §4.2, R12 (R12/4)

Tightening Method

• In yield-controlled tightening the bolt is tightened until the yield point or proof stress is approximately reached, $\sigma_{red} \approx R_{p0,2}$ (VDI 2230 Part 1:2015, §5.4.3.4).
• In hydraulic frictionless and torsion-free tightening the preload is applied to the bolted joint solely by tensile loading, so no thread moments $M_G$ nor head and nut frictional moments $M_K$ occur (VDI 2230 Part 1:2015, §5.4.4).
• A necessary condition for this method is that the end of the thread extends beyond the nut (VDI 2230 Part 1:2015, §5.4.4).

Where to get the value

• Selecting a method overwrites the tightening factor $\alpha_A$ with 1.6 for torque-controlled tightening, with 1.0 for angle-controlled and yield-point controlled tightening, and with 1.4 for hydraulic frictionless and torsion-free tightening; $\alpha_A$ can be edited afterwards.
• Angle-controlled and yield-point controlled tightening show $k_V$ and $\mu_{G,max}$ and are calculated as tightening beyond the elastic limit (VDI 2230 Part 1:2015, §5.5.2.3; §5.5.2.4).
• For hydraulic frictionless and torsion-free tightening the calculator takes $F_{Mzul} = \nu\,R_{p0,2min}\,A_0$ (VDI 2230 Part 1:2015, §5.5.1, Eq. (146)), sets $M_G = 0$ and $\tau = 0$ in the working stress check, and gives no tightening torque $M_A$.
• With this method the calculator hides $\mu_{K,min}$, $k_V$ and $\mu_{G,max}$ and does not support design mode: Table A7 step C lists only torque, angle and yield-point controlled tightening (VDI 2230 Part 1:2015, Annex A, Table A7).
• Table A8 does not give the multipartite nut method (mechanical elongation by multipartite nuts) as a case of Eq. (146); the calculator offers no option for it (VDI 2230 Part 1:2015, Annex A, Table A8).

Standard reference: VDI 2230 Part 1:2015, §5.4.3.4; §5.4.4; §5.5.1, Eq. (146); §5.5.2.3; §5.5.2.4; Annex A, Tables A7, A8

Tightening Factor (α_A)

The tightening factor takes into account the scatter of the achievable assembly preload between $F_{Mmin}$ and $F_{Mmax}$, $\alpha_A = F_{Mmax}/F_{Mmin}$ (VDI 2230 Part 1:2015, §5.4.3.1, Eq. (130)).

Where to get the value

• $\alpha_A$ is determined from Table A8 according to the tightening and setting method and, where applicable, the coefficient of friction class (Table A5) (VDI 2230 Part 1:2015, §4.2, R1).
• For torque-controlled tightening Table A8 gives 1.6 to 2.0 for friction class B and 1.7 to 2.5 for class A when the coefficient of friction is estimated, and 1.4 to 1.6 when the setpoint torques are determined on the original joint (VDI 2230 Part 1:2015, Annex A, Table A8).
• For yield-controlled and angle-controlled tightening $\alpha_A = 1$ is substituted (VDI 2230 Part 1:2015, §4.2, R1; Annex A, Table A8); if another value is entered, the calculator uses the entered value and shows a note.
• For hydraulic frictionless and torsion-free tightening Table A8 gives 1.1 to 1.4 (VDI 2230 Part 1:2015, Annex A, Table A8); selecting the method fills in the upper limit 1.4.
• Table A8 notes for that method: recovery losses occur which are not taken into account in the tightening factor; application from M20 upwards (VDI 2230 Part 1:2015, Annex A, Table A8).
• The default is 1.6.

Effect on the results

• ↑ Increase: For a constant maximum assembly preload stress $\sigma_{Mmax}$ the required bolt size follows $d_{01}/d_{02} \approx \sqrt{\alpha_{A1}/\alpha_{A2}}$ (VDI 2230 Part 1:2015, §5.4.3.1, Eq. (133)). $F_{KRmin}$ contains $F_{Mzul}/\alpha_A$, so it becomes smaller (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (218)).

Standard reference: VDI 2230 Part 1:2015, §4.2, R1; §5.4.3.1, Eq. (130), (133); Annex A, Table A8

Utilisation (ν)

The utilization factor $\nu$ ($\leq 1$) expresses the permissible utilization of the minimum yield point $R_{p0,2min}$ by the comparative stress in the assembly state, $\nu = \sigma_{red,Mzul}/R_{p0,2min}$ (VDI 2230 Part 1:2015, §5.5.1, Eq. (145)).

Where to get the value

• For torque-controlled tightening often only a proportional utilization (normally 90 %) is permitted, so that the yield point is not exceeded in service (VDI 2230 Part 1:2015, §5.5.1).
• When tightening within the elastic range, $\nu = 0.9$ is to be aimed at (VDI 2230 Part 1:2015, §5.5.1, before Eq. (147)).
• Table A1 to Table A4 are made for $\nu = 0.9$ (VDI 2230 Part 1:2015, §5.5.1; Annex A, Tables A1 to A4).
• The default is 0.9.
• Not shown, and not read, for yield-point or angle-controlled tightening: $F_{Mzul}$ is then $F_{MTab}/0.9$ (VDI 2230 Part 1:2015, §5.5.1; Annex B, Example B4, R7).

Effect on the results

• ↑ Increase: The permissible assembly preload $F_{Mzul} = \sigma_{Mzul}\,A_0\,\nu$ becomes larger (VDI 2230 Part 1:2015, §5.5.1, Eq. (144)).

Standard reference: VDI 2230 Part 1:2015, §5.5.1, Eq. (144), (145), (147); Annex A, Tables A1 to A4

Embedding amount

The embedding comes from three sources: plastic flattening of surface roughness in the bearing areas, in the loaded flanks of the mating threads and in other interfaces; Table 5 gives one guide value for each of the three by $R_z$ class and load direction (VDI 2230 Part 1:2015, §5.4.2.1, Table 5).

Where to get the value

• With “Enter $f_Z$ directly” the calculator uses the entered $f_Z$ and does not read the three Table 5 inputs.
• With “From Table 5 (add up)” the calculator does not read the entered $f_Z$ and shows the inputs “Surface roughness ($R_z$)”, “Load direction (Table 5)” and “Number of inner interfaces”.
• With “From Table 5 (add up)” the calculator adds the thread value, the bearing-area value times the number of bearing areas and the inner-interface value times the number of inner interfaces, converted from μm to mm.
• For $R_z \geq 160$ μm Table 5 has no value, so $f_Z$ can only be entered with “Enter $f_Z$ directly” (VDI 2230 Part 1:2015, §5.4.2.1, Table 5).
• The number of bearing areas follows the joint type: 2 for a through-bolt joint (head and nut), 1 for a tapped thread joint (head only); Table 5 names the column “per head or nut bearing area” (VDI 2230 Part 1:2015, §5.4.2.1, Table 5; Annex B, Examples B1 to B5).
• Annex B counts one inner interface in Examples B1, B2, B4 and B5 and two in Example B3 (VDI 2230 Part 1:2015, Annex B, Examples B1 to B5, R4).
• Table 5 applies to bolts, nuts and compact clamped parts made of steel, without coatings (VDI 2230 Part 1:2015, §5.4.2.1, Table 5).
• If the surface roughness is not flattened during the tightening operation (hydraulic or thermal preloading), the amounts of embedding after assembly may be markedly greater than the guide values (VDI 2230 Part 1:2015, §5.4.2.1).
• The default is “Enter $f_Z$ directly”.

Standard reference: VDI 2230 Part 1:2015, §5.4.2.1, Table 5; Annex B, Examples B1 to B5

Embedding (f_Z) [mm]

Plastic flattening of surface roughness at the bearing areas, the loaded flanks of the mating threads and other interfaces is designated as embedding; $f_Z$ is the plastic deformation as a result of embedding (VDI 2230 Part 1:2015, §2, $f_Z$; §5.4.2.1). The assembly preload is reduced by $F_Z$ through the deformations $f_Z$ occurring after assembly (VDI 2230 Part 1:2015, §5.4.2.1).

Where to get the value

• If no values determined experimentally are available, Table 5 gives guide values in µm in the thread, per head or nut bearing area and per inner interface, by average roughness height $R_z$ and by tension/compression or shear loading (VDI 2230 Part 1:2015, §5.4.2.1, Table 5).
• The guide values are not appropriate if the limiting surface pressures of Table A9 are exceeded (VDI 2230 Part 1:2015, §5.4.2.1; Annex A, Table A9).
• The guide values come from massive cylindrical joints; for clamped sheet-metal stacks $F_Z$ should be determined experimentally and not by Eq. (113) (VDI 2230 Part 1:2015, §5.4.2.1).
• Amounts of embedding in aluminium are greater than in steel (VDI 2230 Part 1:2015, §5.4.2.1).
• Amounts of embedding which already occur during assembly do not lead to a loss of preload (VDI 2230 Part 1:2015, §5.4.2.1).
• The default is 0.009 mm.

Effect on the results

• ↑ Increase: $F_Z = f_Z/(\delta_S + \delta_P)$ becomes larger (VDI 2230 Part 1:2015, §5.4.2.1, Eq. (113)).

Standard reference: VDI 2230 Part 1:2015, §2, $f_Z$; §5.4.2.1, Eq. (113), Table 5

Surface roughness (R_z)

Table 5 gives the guide values for embedding by the roughness height $R_z$ in three classes: $R_z < 10$ μm, $10 \leq R_z < 40$ μm and $40 \leq R_z < 160$ μm (VDI 2230 Part 1:2015, §5.4.2.1, Table 5).

Where to get the value

• The field is shown and required when the embedding amount is taken from Table 5; there is no default.
• Table 5 has no value for $R_z \geq 160$ μm; the calculator offers no option for it and does not extrapolate (VDI 2230 Part 1:2015, §5.4.2.1, Table 5).
• Annex B takes the class for $R_z = 16$ μm as “$10 \leq R_z < 40$ μm” (VDI 2230 Part 1:2015, Annex B, Example B1, R4).

Standard reference: VDI 2230 Part 1:2015, §5.4.2.1, Table 5; Annex B, Example B1, R4

Load direction (Table 5)

Table 5 gives separate guide values for tension/compression and for shear loading (VDI 2230 Part 1:2015, §5.4.2.1, Table 5).

Where to get the value

• The field is shown and required when the embedding amount is taken from Table 5; there is no default.
• Annex B takes shear for Examples B2 and B3, and tension for Examples B1, B4 and B5; in Example B4 the transverse load is disregarded because of the centering collar (VDI 2230 Part 1:2015, Annex B, Examples B1 to B5, R4).
• The calculator does not change the choice from $F_Q$ or $M_Y$; for tension/compression with $F_Q > 0$ or $M_Y > 0$ the R4 step shows a note.

Standard reference: VDI 2230 Part 1:2015, §5.4.2.1, Table 5; Annex B, Examples B1 to B5, R4

Number of inner interfaces

Table 5 gives the embedding “per inner interface” (VDI 2230 Part 1:2015, §5.4.2.1, Table 5); the other interfaces are named in the introduction of §5.4.2.1 (VDI 2230 Part 1:2015, §5.4.2.1).

Where to get the value

• The field is shown and required when the embedding amount is taken from Table 5; it is an integer of 0 or more and has no default.
• The calculator does not derive it from the number of clamped layers, because a layer is a calculation segment of $\delta_P$ and not a part: Example B3 is entered with three layers, while the standard counts two inner interfaces (VDI 2230 Part 1:2015, Annex B, Example B3, R4).
• The calculator’s examples count each contact face between two adjacent solid parts as one (a washer is a part) and, for a tapped thread joint, the face between the last clamped part and the tapped body; head or nut bearing areas and the thread contact are not counted again.

Standard reference: VDI 2230 Part 1:2015, §5.4.2.1, Table 5; Annex B, Example B3, R4

Hardening coefficient (k_V)

For assembly in which the yield point is exceeded, the hardening coefficient is $k_V = 1.1 \dots 1.2$ and multiplies $R_{p0,2min}$ in the preload after the first loading and unloading (VDI 2230 Part 1:2015, §5.5.2.3, Eq. (161), (163)).

Where to get the value

• The default is 1.1.
• The field is shown for yield-point control and angle control only.
• Values from 1.0 to 1.2 are accepted.

Effect on the results

• ↑ Increase: $R_{p0,2min}\,k_V$ in Eq. (161) and (163) becomes larger, so the preload $F_{V1}$ after yielding becomes larger (VDI 2230 Part 1:2015, §5.5.2.3, Eq. (161), (163)).

Standard reference: VDI 2230 Part 1:2015, §5.5.2.3, Eq. (161), (163)

Max thread friction (μ_G,max, optional)

If the yield point is exceeded, $F_{V1}$ and $F_{M0,2min}$ are to be calculated with the maximum coefficient of friction in the thread $\mu_{G,max}$ (VDI 2230 Part 1:2015, §5.5.2.4, after Eq. (166)).

Where to get the value

• Table A5 gives the range of $\mu_G$ and $\mu_K$ for each coefficient of friction class (VDI 2230 Part 1:2015, Annex A, Table A5).
• The field is shown for yield-point control and angle control only.
• The calculator also uses it with torque control when the working load takes the bolt to its yield point, that is when the comparative stress reaches $R_{p0,2min}$ (R8b). The field is hidden then, and a value left in it is still used.
• Choosing class A to D in the friction card fills it with the upper limit of the class; class E has no upper limit and does not fill it.
• Left empty, the calculation uses $\mu_{G,min}$ and the step text says so.

Effect on the results

• ↑ Increase: The thread torque $M_G$ in Eq. (163) becomes larger, so the preload $F_{V1}$ becomes smaller (VDI 2230 Part 1:2015, §5.5.2.3, Eq. (163); §5.4.3.1, Eq. (125)).

Standard reference: VDI 2230 Part 1:2015, §5.5.2.4, Eq. (164), (166); Annex A, Table A5

Include Thermal Effects

• Significant preload changes may occur due to temperature-dependent changes in the Young’s moduli and different coefficients of thermal expansion of the bolt and the clamped parts (VDI 2230 Part 1:2015, §5.4.2.3).
• The working states with the lowest and the highest steady-state temperatures and unsteady temperature fields are to be considered (VDI 2230 Part 1:2015, §5.4.2.3).

Where to get the value

• If the Young’s moduli change only slightly, the approximate preload change of Eq. (118) can be used; otherwise Eq. (117) applies (VDI 2230 Part 1:2015, §5.4.2.3, Eq. (117), (118)).
• No general equation exists for the preload loss by relaxation; a marked relaxation occurs from about 160 °C in aluminium alloys and from about 240 °C in structural and tempering steels (VDI 2230 Part 1:2015, §5.4.2.2).
• The calculator does not calculate relaxation; if 20 °C plus the larger of $\Delta T_S$ and $\Delta T_P$ reaches 160 °C, a note is shown.
• The calculator takes $\Delta F'_{Vth}$ from Eq. (118) for the minimum assembly preload, the maximum bolt load, the surface pressure and the residual clamp load $F_{KR1min}$ of R8b. For the opening limit (R3e) and the residual clamp load of R12 it adds the modulus softening term of Eq. (117) (VDI 2230 Part 1:2015, §5.4.2.3, Eq. (117), (118)).
• The default is No; Yes shows $\Delta T_S$, $\Delta T_P$, $\alpha_S$, $\alpha_P$ and $E_{S,T}$.

Standard reference: VDI 2230 Part 1:2015, §5.4.2.2; §5.4.2.3, Eq. (117), (118)

Bolt Temp. Difference (Δ T_S) [K]

$\Delta T_S$ is the temperature difference of the bolt (VDI 2230 Part 1:2015, §2, $\Delta T_S$). The linear deformation of a part of length $l$ is $f_T = \alpha_T\,l\,\Delta T$ (VDI 2230 Part 1:2015, §5.4.2.3, Eq. (114)).

Where to get the value

• The default is 0 K.

Effect on the results

• ↑ Increase: If the bolt is heated to a greater extent than its surroundings, the preload decreases in accordance with the difference in the linear deformation (VDI 2230 Part 1:2015, §5.4.2.3).

Standard reference: VDI 2230 Part 1:2015, §2, $\Delta T_S$; §5.4.2.3, Eq. (114), (118)

Component Temp. Difference (Δ T_P) [K]

$\Delta T_P$ is the temperature difference of the plates (clamped parts) (VDI 2230 Part 1:2015, §2, $\Delta T_P$).

Where to get the value

• The default is 0 K.

Effect on the results

• ↑ Increase: If the bolt is elongated to a smaller degree than the clamped parts, the preload increases (VDI 2230 Part 1:2015, §5.4.2.3). If $\Delta F'_{Vth} \lt 0$ and loading may occur before the working temperature is reached, $\Delta F'_{Vth} = 0$ is substituted in $F_{Mmin}$ (VDI 2230 Part 1:2015, §5.4.5, Eq. (136)).

Standard reference: VDI 2230 Part 1:2015, §2, $\Delta T_P$; §5.4.2.3, Eq. (118); §5.4.5, Eq. (136)

Bolt Thermal Expansion Coeff. [1/K]

$\alpha_S$ is the coefficient of linear thermal expansion of the bolt (VDI 2230 Part 1:2015, §2, $\alpha_S$).

Where to get the value

• Table A9 gives guide values of the coefficient of thermal expansion; Table A10 gives it for high-temperature materials from 20 °C to the temperature $T$ (VDI 2230 Part 1:2015, Annex A, Tables A9 and A10).
• The button “Pick bolt material” fills the field. The Table A9 tab gives the value listed in Table A9. The material library tab gives the mean value from 20 °C to the temperature $T = 20 + \Delta T_S$ in °C (20 °C with thermal effects off).
• The default is 0.000011 1/K.

Effect on the results

• ↑ Increase: If the coefficient of expansion of the bolt is greater than that of the clamped parts at the same temperature change, the preload decreases (VDI 2230 Part 1:2015, §5.4.2.3).

Standard reference: VDI 2230 Part 1:2015, §2, $\alpha_S$; §5.4.2.3; Annex A, Tables A9, A10

Clamped-part expansion coeff., used where a layer has none [1/K]

$\alpha_P$ is the coefficient of linear thermal expansion of the plate (clamped part) (VDI 2230 Part 1:2015, §2, $\alpha_P$).

Where to get the value

• The calculator uses this value for every layer whose own coefficient in the layer table is empty.
• The material picker of a layer fills the coefficient of that layer in the layer table, not this field: from the Table A9 tab the value listed in Table A9, from the material library tab the mean value from 20 °C to the temperature $T = 20 + \Delta T_P$ in °C.
• The default is 0.000011 1/K.

Effect on the results

• ↑ Increase: If the bolt is elongated to a smaller degree than the clamped parts, the preload increases (VDI 2230 Part 1:2015, §5.4.2.3).

Standard reference: VDI 2230 Part 1:2015, §2, $\alpha_P$; §5.4.2.3; Annex A, Tables A9, A10

Bolt modulus at working temperature (E_S,T, optional) [N/mm²]

$E_{S,T}$ is the Young’s modulus of the bolt material at a temperature different from room temperature (VDI 2230 Part 1:2015, §2, $E_{ST}$; §5.4.2.3, Eq. (117), (118)).

Where to get the value

• Table A10 gives the Young’s modulus $E_T$ at 200 °C to 700 °C for high-temperature materials (VDI 2230 Part 1:2015, Annex A, Table A10).
• Left empty, the calculator takes the room-temperature value $E_S$. If no layer has a modulus at working temperature either, the step text says that $E_T = E_{RT}$ was assumed.

Effect on the results

• ↓ Decrease: The Young’s moduli of the usual materials decrease with increasing temperature, and the preload decreases with increasing temperature even for the same thermal expansion of bolt and clamped parts (VDI 2230 Part 1:2015, §5.4.2.3).

Standard reference: VDI 2230 Part 1:2015, §2, $E_{ST}$; §5.4.2.3, Eq. (117), (118); Annex A, Table A10

Fatigue Check

The alternating stress is $\sigma_a = (F_{SAo} - F_{SAu})/(2A_S)$ (VDI 2230 Part 1:2015, §5.5.3, Eq. (168)), and the check requires $\sigma_a \leq \sigma_{AS}$ (VDI 2230 Part 1:2015, §4.2, R9, (R9/3)).

Where to get the value

• The guide values of the endurance limit apply to high-strength bolts to DIN EN ISO 898-1 with standard 6g/6H threads, within $0.3 \leq F_{Sm}/F_{0,2min} \lt 1$ (VDI 2230 Part 1:2015, §5.5.3, Eq. (170)).
• The safety margin against fatigue failure is $S_D = \sigma_{AS}/\sigma_a$; the safety margin is to be established by the user, and $S_D \geq 1.2$ is recommended (VDI 2230 Part 1:2015, §4.2, R9, (R9/4)).
• The calculator checks $S_D \geq 1.0$ and $S_D \geq$ the value in “Required safety margin against fatigue failure” (default 1.2).
• The default is Yes; Yes shows the thread process, $N_Z$ and the knockdown factor, and $F_{A,min}$ in the loads card.
• For a hollow bolt the fatigue check is not made, and the step text says so.

Standard reference: VDI 2230 Part 1:2015, §4.2, R9; §5.5.3, Eq. (168), (170)

Min. Axial Load (F_A,min) [N]

Lower value of the axial load $F_A$ in the load cycle. It is an input of this calculator, not a symbol of the standard, which uses the lower limit $F_{SAu}$ of the additional axial bolt load in $\sigma_a=(F_{SAo}-F_{SAu})/(2A_S)$ (VDI 2230 Part 1:2015, §5.5.3, Eq. (168)). The calculator takes $F_{SAo}=\Phi_n F_A$ and $F_{SAu}=\Phi_n F_{A,min}$.

Where to get the value

• The field is shown when the fatigue check is on; the default is 0.
• The calculation stops with an input error if $F_{A,min}$ is larger than $F_A$.

Effect on the results

• ↑ Increase: $\sigma_a$ decreases (VDI 2230 Part 1:2015, §5.5.3, Eq. (168)) and the safety $S_D=\sigma_{AS}/\sigma_a$ increases (VDI 2230 Part 1:2015, §4.2, R9, (R9/4)).

Standard reference: VDI 2230 Part 1:2015, §5.5.3, Eq. (168); §4.2, R9, (R9/1), (R9/4)

Thread Process

• SV: the bolt thread is rolled before heat treatment (schlussvergütet); $\sigma_{ASV} = 0.85(150/d + 45)$ with $\sigma$ in N/mm² and $d$ in mm (VDI 2230 Part 1:2015, §5.5.3, Eq. (170)).
• SG: the bolt thread is rolled after heat treatment (schlussgewalzt); within $0.3 \leq F_{Sm}/F_{0,2min} \lt 1$ it has a higher fatigue strength than SV, which depends on the mean stress because of the induced residual compressive stresses, $\sigma_{ASG} = (2 - F_{Sm}/F_{0,2min})\,\sigma_{ASV}$ (VDI 2230 Part 1:2015, §5.5.3, Eq. (171)).

Where to get the value

• The default is SV.

Effect on the results

• ↑ SG: $\sigma_{ASG}$ is higher than $\sigma_{ASV}$ within $0.3 \leq F_{Sm}/F_{0,2min} \lt 1$, and it depends on the steady stresses through $F_{Sm} = (F_{SAo} + F_{SAu})/2 + F_{Mzul}$ (VDI 2230 Part 1:2015, §5.5.3, Eq. (171), (172)).

Standard reference: VDI 2230 Part 1:2015, §5.5.3, Eq. (170), (171), (172)

Design cycles (N_Z, optional)

$N_Z$ is the number of alternating cycles during loading within the fatigue strength range (VDI 2230 Part 1:2015, §2, $N_Z$). If only a few thousand cycles ($N_Z > 10^4$) with stress amplitudes above the endurance limit occur in service, the joint can be designed for finite life (VDI 2230 Part 1:2015, §5.5.3, Eq. (173), (174)).

Where to get the value

• The endurance limits apply for more than $N_D = 2\cdot10^6$ cycles (VDI 2230 Part 1:2015, §5.5.3).
• If the calculation gives a smaller value for SG than for SV, $\sigma_{AZSG} = \sigma_{AZSV}$ applies (VDI 2230 Part 1:2015, §5.5.3).
• Left empty, the joint is designed for the endurance limit.
• The finite-life values are used only when $N_Z > 10^4$ and $\sigma_a > \sigma_{AS}$. For any other positive whole number the calculator accepts the input and designs for the endurance limit, without a message.

Effect on the results

• ↓ Decrease: $\sigma_{AZSV} = \sigma_{ASV}(N_D/N_Z)^{1/3}$ and $\sigma_{AZSG} = \sigma_{ASG}(N_D/N_Z)^{1/6}$ become larger (VDI 2230 Part 1:2015, §5.5.3, Eq. (173), (174)).

Standard reference: VDI 2230 Part 1:2015, §2, $N_Z$; §5.5.3, Eq. (173), (174)

Fatigue knockdown factor

• The endurance limit of fine threads decreases with increasing strength and fineness; for strength grade 12.9 it may be up to 30 % lower than for standard threads (VDI 2230 Part 1:2015, §5.5.3).
• For hot-galvanized bolts the endurance strength is about 20 % lower than calculated with Eq. (170) and (171) (VDI 2230 Part 1:2015, §5.5.3).
• For high-strength friction-grip fasteners (HV sets) a value about 10 % lower can be expected (VDI 2230 Part 1:2015, §5.5.3).
• For hot-galvanized HV sets the reduction is about 30 % (10 % geometry, 20 % hot-dip galvanizing) (VDI 2230 Part 1:2015, §5.5.3).

Where to get the value

• For bolts rolled before heat treatment (SV) and tightened beyond the elastic limit, no reduction of the thread endurance limit need be expected (VDI 2230 Part 1:2015, §5.5.3).
• Fatigue strength values for austenitic steels and non-ferrous metals are in the literature [42 to 47] (VDI 2230 Part 1:2015, §5.5.3).
• The field is a factor on $\sigma_{AS}$; the default 1.0 means no reduction, and values above 0 up to 1 are accepted.
• For a fine thread the R9 step shows a note to set this factor; the calculator does not reduce $\sigma_{AS}$ by itself.

Effect on the results

• ↓ Decrease: $\sigma_{AS}$ becomes smaller, so $S_D = \sigma_{AS}/\sigma_{a}$ becomes smaller (VDI 2230 Part 1:2015, §4.2, R9, (R9/4)).

Standard reference: VDI 2230 Part 1:2015, §5.5.3, Eq. (170), (171)

Required safety margin against fatigue failure (S_D)

• The safety margin against fatigue failure $S_D$ must not be lower than 1.0 and not lower than this required value (VDI 2230 Part 1:2015, §4.2, R9/4).
• VDI 2230 sets the limit at 1.0 and leaves the required safety margin to the user (VDI 2230 Part 1:2015, §4.2, R9/4).
• [4] recommends $S_D\ge1.2$, as quoted in VDI 2230 (VDI 2230 Part 1:2015, §4.2, R9/4).

Where to get the value

• The default is 1.2.

• Shown when the fatigue check is on.

• Not below 1.0.

• The calculator accepts only $S_D \ge 1$.

Effect on the results

• ↑ Increase: A higher $S_D$ is needed to pass the fatigue check (VDI 2230 Part 1:2015, §4.2, R9/4).

Standard reference: VDI 2230 Part 1:2015, §4.2, R9 (R9/4)

Shear cross-section diameter (d_τ, optional) [mm]

Depending on the position of the interface, the relevant shearing cross section is $A_\tau = d_\tau^2\pi/4$ with $d_\tau = d_S$, or $d_\tau = d_i$ (cross section of the shank), or $d_\tau = d_P$ (cross section of the body-fit shank) (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (219)).

Where to get the value

• For bolts of stainless steel to DIN EN ISO 3506-1, the stress cross section of the thread $A_\tau = A_S$ is always decisive, irrespective of the interface position (VDI 2230 Part 1:2015, §5.5.6.3).
• Left empty, the calculator takes $d_\tau = d_0$, the diameter of the relevant cross section of the bolt; $d_0=d_S$, or $d_0=d_{i\,min}$ if a bolt segment is thinner than $d_S$ (VDI 2230 Part 1:2015, §5.5.1).
• For a hollow bolt the shear check is not made.

Effect on the results

• ↑ Increase: $A_\tau$ becomes larger, so $F_{QzulS} = A_\tau\tau_B/S_A$ becomes larger; $F_{QzulL} = h\,d_\tau R_{p0,2P}/S_L$ becomes larger as well (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (219), (220), (222)).

Standard reference: VDI 2230 Part 1:2015, §5.5.6.3, Eq. (219), (220), (222)

Edge distance along F_Q (e_0, optional) [mm]

$e_0$ is the distance of the bolt axis from the edge of the clamped part in the direction of the transverse load (VDI 2230 Part 1:2015, §2, $e_0$).

Where to get the value

• Left empty, the edge distance check is skipped and the halving rule is not applied.
• The edge distance is used only when the transverse load $F_Q$ is greater than 0.
• For $e_0 \geq 3\,d_h$ the check passes with the full $F_{QzulL}$.
• For $1.5\,d_h \leq e_0 \lt 3\,d_h$ the calculator halves $F_{QzulL}$, and the check passes with a note.
• For $e_0 \lt 1.5\,d_h$ the check step is marked as not passed, and the halved $F_{QzulL}$ is still shown. The result of this step does not enter the overall verdict.

Effect on the results

• ↓ Decrease: The minimum distance up to the edges in the direction of the transverse load is $e_{0min} = 3\,d_h$; if the distance is only $e_0 = 1.5\,d_h$, only half the bolt bearing pressure $F_{QzulL}/2$ may be assumed (VDI 2230 Part 1:2015, §5.5.6.3).

Standard reference: VDI 2230 Part 1:2015, §2, $e_0$; §5.5.6.3

Target safety against bolt bearing pressure (S_L)

$S_L$ is the safety margin against bolt bearing pressure (VDI 2230 Part 1:2015, §2, $S_L$). The permissible bolt bearing pressure is $F_{QzulL} = h\,d_\tau R_{p0,2P}/S_L$ (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (222)).

Where to get the value

• The default is 1.1.
• The field is shown only when the transverse load $F_Q$ is greater than 0.
• Any value greater than 0 is accepted.

Effect on the results

• ↑ Increase: $S_L$ is in the denominator, so $F_{QzulL}$ becomes smaller (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (222), (223)).

Standard reference: VDI 2230 Part 1:2015, §2, $S_L$; §5.5.6.3, Eq. (222), (223)

Use Eq. (223) for the permissible bolt bearing pressure

• If plastic deformation of the clamped parts is to be largely avoided, $F_{QzulL} = h\,d_\tau R_{p0,2P}/S_L$ must apply (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (222)).
• On account of the multi-axial compressive stress state at the hole wall, markedly higher loads may be transmitted in highly preloaded joints when the distances $e_0$ to $e_3$ are maintained, $F_{QzulL} = 2.5\,h\,d_\tau R_{p0,2P}/S_L$ (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (223)).

Where to get the value

• In general the proof stress of the bolt is higher than that of the plates; otherwise the proof stress of the bolt $R_{p0,2min}$ is to be substituted (VDI 2230 Part 1:2015, §5.5.6.3).
• The default is No, which uses Eq. (222); Yes uses Eq. (223).

Effect on the results

• ↑ Yes: $F_{QzulL}$ is 2.5 times the value of Eq. (222) (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (222), (223)).

Standard reference: VDI 2230 Part 1:2015, §5.5.6.3, Eq. (222), (223)

Single shear plane

The interfaces involved in the slipping of the clamped components or the shearing of the bolt are determined by imagining the joint loaded to failure (VDI 2230 Part 1:2015, §5.5.6.1). If a single-shear joint is executed with only one bolt, only half the bolt bearing pressure $F_{QzulL}/2$ may be assumed (VDI 2230 Part 1:2015, §5.5.6.3).

Where to get the value

• The default is Yes, which halves $F_{QzulL}$; No (double shear or more) uses the full value.
• The calculator handles one bolt, so the input only decides whether the halving rule for a single-shear joint with one bolt applies.

Effect on the results

• ↓ Yes: $F_{QzulL}$ is halved to $F_{QzulL}/2$ (VDI 2230 Part 1:2015, §5.5.6.3).

Standard reference: VDI 2230 Part 1:2015, §5.5.6.1; §5.5.6.3

Eccentric clamping / loading

• Eccentric clamping: the bolt axis does not coincide with the axis of the laterally symmetrical clamp solid (VDI 2230 Part 1:2015, §3.2.2, Figure 4).
• Eccentric loading: the line of action of the load $F_A$ does not lie in the bolt axis, at a distance $a$ from the axis 0–0 (VDI 2230 Part 1:2015, §5.1.2.3; §5.2.1).

Where to get the value

• Default: No. With “No”, the other inputs of this card are ignored.
• With “Yes” and $s_{sym}=a=0$, the calculator uses the concentric formulas and adds a note step (VDI 2230 Part 1:2015, §5.3.1.2, Eq. (90)).
• The calculator uses cases I to III of Table 4 (tensile working load) (VDI 2230 Part 1:2015, §5.3.2, Table 4).
• Not implemented in this calculator, although the standard gives them: an external bending moment $M_B$ (VDI 2230 Part 1:2015, §5.3.1.3, Eq. (98); §5.3.2, Eq. (102), (103)), and clamped parts with different Young’s moduli (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (68)–(70); §5.1.2.3, Eq. (72)). The calculator rejects the input if the layers do not all have the same $E_P$.
• With a tapped thread joint (TTJ), the calculator rejects “Calculate the clamped parts as a TBJ” set to “Yes”.

Standard reference: VDI 2230 Part 1:2015, §3.2.2, Figure 4; §5.1.2.2; §5.1.2.3; §5.2.1; §5.3.1.2; §5.3.2, Table 4

Clamping eccentricity (s_sym) [mm]

• Distance of the bolt axis S from the axis 0–0 of the imaginary laterally symmetrical clamp solid (VDI 2230 Part 1:2015, §3.2.2, Figure 4; §2, $s_{sym}$).
• Positive if the line of action of the working load and the bolt axis lie on the same side of 0–0, negative if they lie on opposite sides (VDI 2230 Part 1:2015, §3.2.2; §5.3.2, Table 4).
• For a rectilinearly defined basic solid: $s_{sym}=c_T/2-e\le G/2-e$, with $e$ the smallest distance of the bolt from the edge of the interface (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (66)).

Where to get the value

• Default 0.
• The calculator requires $|s_{sym}|\lt c_T$.
• The calculator uses $s_{sym}$ and $a$ to select the case of Table 4 (VDI 2230 Part 1:2015, §5.3.2, Table 4).
• For a case III joint ($s_{sym}\lt 0$), the calculator shows a note at the top of the results.
• For a non-rectilinear edge, the calculator takes $s_{sym}$ as entered and does not calculate it with Eq. (66).

Effect on the results

• ↑ Increase of $|s_{sym}|$: the resilience $\delta_P^{*}$ of the eccentrically clamped parts becomes larger than for concentric clamping, $\delta_P^{*}=\delta_P+s_{sym}^2\,l_K/(E_P\,I_{Bers})$ (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (67))
• ↓ Negative value (opposite side to $a$): the additional bolt load $F_{SA}$ may become larger than calculated, in particular for $a\gg|s_{sym}|$ (VDI 2230 Part 1:2015, §5.1.2.3)

Standard reference: VDI 2230 Part 1:2015, §2, $s_{sym}$; §3.2.2, Figure 4; §5.1.2.2, Eq. (66), (67); §5.1.2.3; §5.3.2, Table 4

Loading eccentricity (a) [mm]

• Distance of the substitutional line of action of the axial working load $F_A$ from the axis 0–0 of the imaginary laterally symmetrical clamp solid (VDI 2230 Part 1:2015, §2, $a$; §5.2.1).
• The distance $a$ is always positive (VDI 2230 Part 1:2015, §5.1.2.3; §5.3.2, Table 4).
• The substitutional line of action of $F_A$ follows from the zero point of the bending moment characteristic closest to the bolt (VDI 2230 Part 1:2015, §5.2.1).

Where to get the value

• Default 0; the calculator does not accept a negative value.
• For eccentric clamping with $a=0$ (concentric loading), the calculator uses $\Phi_n^{*}$ from Eq. (89) (VDI 2230 Part 1:2015, §5.3.1.1, Eq. (89)).

Effect on the results

• ↑ Increase: even a relatively small eccentricity of the load introduction may have a considerable effect on the deformation behaviour of the clamped parts (VDI 2230 Part 1:2015, §5.1.2.3)

Standard reference: VDI 2230 Part 1:2015, §2, $a$; §5.1.2.3, Eq. (71); §5.2.1; §5.3.1.1, Eq. (89); §5.3.2, Table 4

Opening-side edge distance (e) [mm]

• Distance of the bolt axis from the edge of the interface on the side at risk of opening (VDI 2230 Part 1:2015, §2, $e$).
• Approximately constant interface pressure can be expected on the bending tension side of the basic solid if $e\le G/2$ (instead of $G$: $G'$, $G''$, $G'_{max}$); this condition takes priority over $c_T\le G$ (VDI 2230 Part 1:2015, §5.1.2.2).

Where to get the value

• Required when eccentric clamping/loading is on; the calculator requires $0\lt e\lt c_T$.
• The calculator checks $e\le G/2$ with the lower limit of $G'$ for a tapped thread joint (TTJ); if it is not met, the calculator shows a note at the top of the results and still calculates.
• If $e$ differs from $|u-s_{sym}|$, the calculator shows a warning and does not reject the input.

Effect on the results

• ↑ Increase beyond $G/2$: exceeding the limiting dimensions entails a relatively large calculation error (VDI 2230 Part 1:2015, §4.2, R0)

Standard reference: VDI 2230 Part 1:2015, §2, $e$; §4.2, R0, Eq. (R0/1), (R0/2); §5.1.2.2, Eq. (54)–(57)

Opening-point distance (u) [mm]

• Edge distance of the opening point $U$ from the axis 0–0 of the imaginary laterally symmetrical clamp solid (VDI 2230 Part 1:2015, §2, $u$).
• Point $U$ always lies at the outermost location of the side of the interface at risk of opening (VDI 2230 Part 1:2015, §5.3.2, Table 4).
• Sign: positive in cases I and III, negative in case II (VDI 2230 Part 1:2015, §5.3.2, Table 4).

Where to get the value

• If left empty, the calculator sets $u=e+s_{sym}$ for cases I and III, and $u=s_{sym}-e$ for case II.
• A given or preset $u$ must have the sign of its case and satisfy $0\lt |u|\le c_T$; otherwise the calculator rejects the input.

Standard reference: VDI 2230 Part 1:2015, §2, $u$; §5.3.2, Table 4, Figure 25

Interface dimension (c_T) [mm]

• Measurement of the interface area perpendicular to the width $b$ (VDI 2230 Part 1:2015, §2, $c_T$).
• It is the size of the interface in the plane of bolt axis and line of action of the axial working load (VDI 2230 Part 1:2015, §4.2, R0).
• If the sealing area $A_D$ is smaller than the interface area for design reasons, $c_T$ is reduced accordingly (VDI 2230 Part 1:2015, §5.1.2.2, after Eq. (65)).

Where to get the value

• Required when eccentric clamping/loading is on.
• The calculator requires $0\lt |u|\le c_T$, $|s_{sym}|\lt c_T$ and $e\lt c_T$.
• If $c_T>G$, the calculator shows a secondary note at the top of the results and still calculates.

Effect on the results

• ↑ Increase beyond $G$: the basic requirement is $c_T\le G$; if the dimensions of the interface exceed $G$ or $G'$, the relationships at the opening limit are no longer valid (VDI 2230 Part 1:2015, §5.1.2.2; §5.3.2)

Standard reference: VDI 2230 Part 1:2015, §2, $c_T$; §4.2, R0; §5.1.2.2, Eq. (61), (65), (66); §5.3.2

Deformation sleeve width (b) [mm]

Width $b$ in the moment of gyration of the deformation sleeve, $I_{Bers}^{H}=b\cdot c_T^3/12$, with $b\le D_{A,Gr}$ (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (61)).

Where to get the value

• Required if the deformation body has a sleeve part ($l_H>0$ in R3b); if left empty then, the calculator rejects the input.
• The calculator rejects $b>D_{A,Gr}$.

Standard reference: VDI 2230 Part 1:2015, §5.1.2.2, Eq. (61)

Opening-check contact area (A_D) [mm²]

• The sealing area $A_D$ is at most the interface area less the through-hole for the bolt (VDI 2230 Part 1:2015, §2, $A_D$; §5.3.2).
• The compressive stresses resulting from the preload are assumed to be distributed constantly over the contact or sealing area $A_D$ (VDI 2230 Part 1:2015, §5.3.2, Eq. (99)).

Where to get the value

• Required when eccentric clamping/loading is on.
• It is a separate input from “Sealing area” on the “Loads” card; the calculator does not copy a value from one to the other.

Standard reference: VDI 2230 Part 1:2015, §2, $A_D$; §5.3.2, Eq. (99)

Interface moment of gyration (I_BT) [mm⁴]

• Moment of gyration of the interface area, required for $F_{Kerf}$ (VDI 2230 Part 1:2015, §2, $I_{BT}$; §5.1.2.2, Eq. (65)).
• Area proportions that are asymmetrical to the transverse axis passing through the axis 0–0 are to be taken into account (Steiner proportion) (VDI 2230 Part 1:2015, §5.1.2.2, after Eq. (65)).

Where to get the value

• If given, the calculator uses the value as entered.
• If left empty, the calculator uses $I_{BT}=b_T\,c_T^3/12$ with the input $b_T$ (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (65)).
• If both $I_{BT}$ and $b_T$ are empty, the calculator rejects the input.

Standard reference: VDI 2230 Part 1:2015, §2, $I_{BT}$; §5.1.2.2, Eq. (65); §5.3.2, Eq. (104)–(107)

Interface width, rectangular aid (b_T) [mm]

Width of the interface area, $b_T=\min[G\,|\,G'\,|\,G'';\,t]\le b$, with $t$ the bolt spacing in a multi-bolted joint (VDI 2230 Part 1:2015, §2, $b_T$, $t$; §5.1.2.2, Eq. (65)).

Where to get the value

• Shown and used only if $I_{BT}$ is left empty, for $I_{BT}=b_T\,c_T^3/12$ (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (65)).
• The calculator does not select $b_T$ from $G$, $G'$, $G''$ and $t$; it takes the entered value.
• If $b$ is entered, the calculator requires $b_T\le b$.

Standard reference: VDI 2230 Part 1:2015, §2, $b_T$, $t$; §5.1.2.2, Eq. (65)

Thinner clamped plate (h_min) [mm]

• For two clamped plates, the thickness of the thinner plate (VDI 2230 Part 1:2015, §2, $h_{min}$).
• Limiting value for a through-bolt joint (TBJ): $G=d_W+h_{min}$ (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (54)).

Where to get the value

• Shown only for a TBJ.
• If left empty, the calculator uses the thinnest of the entered layer thicknesses.
• If there is only one clamped layer, it is required and the calculator rejects the input if it is empty.

Effect on the results

• ↓ Decrease: $G=d_W+h_{min}$ becomes smaller; exceeding the limiting dimensions entails a relatively large calculation error (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (54); §4.2, R0)

Standard reference: VDI 2230 Part 1:2015, §2, $h_{min}$; §4.2, R0, Eq. (R0/1); §5.1.2.2, Eq. (54)

Counterbore depth (t_S) [mm]

• Counterbore depth (VDI 2230 Part 1:2015, §2, $t_S$).
• Corrected limiting value for a tapped thread joint (TTJ) with a counterbore: $G''\approx(1{,}5\dots2)\,d_W+1{,}2\,t_S$ (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (57)).

Where to get the value

• Shown only for a TTJ.
• If left empty or 0, the calculator uses $G'\approx(1{,}5\dots2)\,d_W$ (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (55)).

Effect on the results

• ↑ Increase: $G''$ becomes larger; a counterbore in the tapped thread component increases $G'$ and evens out the pressure distribution at the interface (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (57))

Standard reference: VDI 2230 Part 1:2015, §2, $t_S$; §5.1.2.2, Eq. (55), (57), Figure 12

Calculation steps

The Steps tab lists the formulas, the numbers put in, the results, the verdicts and the clauses of the standard, step by step by R number.

Step	What it does	Related results
R0, R0p, R0b, R0c, R0d	R0: design mode selects the size from Table A7, verification mode keeps the size you give (VDI 2230 Part 1:2015, §4.2 R0, Table A7). R0p: geometry filled in from the selected product standard. R0b: through-hole diameter $d_h$; design mode takes it from the medium series of DIN EN 20273 (DIN EN 20273:1992-02, 2 Maße, Table). R0c: fine-thread geometry. R0d: validity and case of the eccentric model (VDI 2230 Part 1:2015, §4.2 R0, R0/1, R0/2; §5.1.2.2, Eq. (54)–(57))	Recommended size, bolt geometry, standard bolt group
R1	Tightening factor $\alpha_A$; 1.0 for yield-point control and angle control (VDI 2230 Part 1:2015, §4.2 R1, Table A8)
R2	Required minimum clamp load $F_{Kerf}$: friction against slip $F_{KQ}$, sealing $F_{KP}$, anti-opening $F_{KA}$ (eccentric) and the residual clamp load given directly (VDI 2230 Part 1:2015, §4.2 R2; §5.4.1, Eq. (108)–(111))	Required minimum clamp load
R3	Resilience and load factor: R3a bolt resilience $\delta_S$, with segments and hollow bolts (VDI 2230 Part 1:2015, §5.1.1.1, Eq. (18)–(31); Annex B, Example B3, R3); R3b clamped-part resilience $\delta_P$, with cone, sleeve and layers (VDI 2230 Part 1:2015, §5.1.2, Eq. (39); §5.1.2.1, Eq. (40)–(50), (52)(53)); R3c load introduction factor $n$ (VDI 2230 Part 1:2015, §5.2.2.2); R3d load factor $\Phi$, $\Phi^*_{en}$ for eccentric (VDI 2230 Part 1:2015, §5.3.1, Eq. (82); §5.3.1.2, Eq. (90)–(95)); R3e opening limit (VDI 2230 Part 1:2015, §5.3.1.1, Eq. (87); §5.3.2, Eq. (104))	Resilience and load factor, eccentric group, opening limit
R4	Preload loss due to embedding $F_Z$, and the preload change by temperature $\Delta F'_{Vth}$ (VDI 2230 Part 1:2015, §4.2 R4; §5.4.2.1, Eq. (113); §5.4.2.3, Eq. (118))	Preload loss due to embedding, thermal preload change
R5, R6	Minimum assembly preload $F_{Mmin}$ and maximum assembly preload $F_{Mmax}=\alpha_A\,F_{Mmin}$ (VDI 2230 Part 1:2015, §4.2 R5, R6)	Assembly preloads
R7	Permissible assembly preload $F_{Mzul}$ and the assembly stress check $F_{Mmax}\le F_{Mzul}$, with the upper bound $F_{Mzul}\le 1.4\,F_{MTab}$ (VDI 2230 Part 1:2015, §4.2 R7; §5.5.1, Eq. (143)(144)(147))	Permissible assembly preload, table assembly preload
R8, R8b	Working stress $\sigma_{red,B}$ and safety margin against exceeding the yield point $S_F$; the post-yield chain when the bolt is tightened past yield (VDI 2230 Part 1:2015, §4.2 R8; §5.5.2.1; §5.5.2.2–§5.5.2.4)	Maximum bolt load, comparative working stress, preload after yielding
R9	Fatigue: stress amplitude $\sigma_a$, endurance limit $\sigma_{AS}$, safety margin against fatigue failure $S_D$ (VDI 2230 Part 1:2015, §4.2 R9; §5.5.3, Eq. (168)–(171))	Alternating stress, endurance limit
R10	Surface pressure: assembly state $S_P$ and working state $S_{pB}$ (VDI 2230 Part 1:2015, §4.2 R10; §5.5.4, Eq. (190)(191))	Pressures of both states, minimum bearing area
R11	Length of engagement: the strength ratio $R_S$ decides the critical side, then the required length of engagement follows; tapped thread joint (TTJ) only (VDI 2230 Part 1:2015, §4.2 R11; §5.5.5, Eq. (195)–(199); §5.5.5.1, Eq. (200)–(210); §5.5.5.2, Eq. (211)–(213))	Minimum length of engagement and its source, critical side, correction factors
R12	R12: safety margin against slipping $S_G$. R12b: bolt shear $S_A$. R12c: interaction of axial and transverse load. R12d: bolt bearing pressure $S_L$. R12e: edge distance of the hole (VDI 2230 Part 1:2015, §4.2 R12; §5.5.6.3, Eq. (219)–(223))	Transverse load group
R13	Tightening torque $M_A$, and the torque table by friction class (VDI 2230 Part 1:2015, §4.2 R13; §5.4.3.1, Eq. (127); Annex A, Table A5)	Tightening torque, tightening torque table

Engineering section: spring model and force distribution , bolt resilience δS , clamped-part resilience δP and the cone model , preload design R1–R6 , the six strength checks R7–R13 and eccentric load and bending .

Reading the results

Where to look first

1. Overall verdict: it shows “passed” only if all checks that were made have passed; checks that were not made are not counted, and they are not counted as passed.
2. Banner of unchecked items: it lists only the two kinds of unchecked items given by the backend: fatigue of a hollow bolt (with the fatigue check on) and shear of a hollow bolt (with a transverse load); the overall verdict has already left these items out. When no available length of engagement is entered, the length of engagement criterion is not in the banner; step R11 only states that it was not checked, and it is not counted in the overall verdict. When there is no limiting surface pressure $p_G$ under the head or the nut, the surface pressure check of that side is likewise stated as not checked only in step R10.
3. Eccentric warnings (with eccentric clamping): when $e>G/2$ or the interface dimension $c_T>G$, a warning is shown at the top of the results. $G$ is $d_W+h_{min}$ for a through-bolt joint (TBJ) and, for a tapped thread joint (TTJ), the lower limit $1.5\,d_W$ of $G'$; with a counterbore, $G''$ is used (VDI 2230 Part 1:2015, §4.2 R0, R0/1, R0/2; §5.1.2.2, Eq. (54)–(57)). Beyond the limit dimension the calculation error is larger (VDI 2230 Part 1:2015, §4.2 R0). The same warning is given when the load line and the bolt lie on opposite sides of the axis 0–0 (case III). Then the lever ratio with $a\gg|s_{sym}|$ is unfavourable, and $F_{SA}$ may be larger than calculated (VDI 2230 Part 1:2015, §5.1.2.3).
4. Safety matrix: one cell for each check that was made, with the value and the criterion value; the colour shows whether the criterion is met.

Safety margins and criteria

Quantity	Meaning	Requirement
$S_F$	Static strength: yield strength against the comparative working stress	$\ge 1.0$ (VDI 2230 Part 1:2015, §4.2 R8, R8/5-2)
$S_D$	Fatigue: endurance limit against the stress amplitude	$\ge 1.0$ and $\ge$ the required value (VDI 2230 Part 1:2015, §4.2 R9, R9/4)
$S_P$, $S_{pB}$	Surface pressure: limiting surface pressure against the pressure in the assembly state and in the working state	$\ge 1.0$ (VDI 2230 Part 1:2015, §4.2 R10, R10/4)
$S_G$	Slip: residual clamp load against the clamp load needed against slip	$>1.0$ and $\ge$ the required value (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (216); §4.2 R12, R12/4)
$S_A$	Bolt shear (only with $F_Q>0$)	$\ge 1.1$ (VDI 2230 Part 1:2015, §4.2 R12, R12/7)
$S_L$	Bolt bearing pressure (only with $F_Q>0$)	$\ge S_{L,req}$, taken from the input “Target safety against bolt bearing pressure” (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (222)(223))

The criterion for $S_D$ reads $S_D\ge 1.0$ and $S_D\ge$ the required value; the safety margin is set by the user, and [4] recommends $S_D\ge 1.2$, as quoted in VDI 2230 (VDI 2230 Part 1:2015, §4.2 R9, R9/4). The criterion for $S_G$ reads $S_G>1.0$ and $S_G\ge$ the required value; the safety margin is set by the user, and the usual values are $S_G\ge 1.2$ for static loading and $S_G\ge 1.8$ for alternating $F_Q$ and/or $M_Y$ (VDI 2230 Part 1:2015, §4.2 R12, R12/4). The required value of $S_D$ is the input “Required safety margin against fatigue failure” (default 1.2). The required value of $S_G$ is the input “Required safety margin against slipping”; when it is empty, the calculator takes 1.2 or 1.8 according to the input “Loading type for slipping”. The results show the required value used and where it comes from.

Below the matrix, criteria that give only a conclusion and no value are listed separately: the upper bound of the permissible assembly preload $F_{Mzul}\le 1.4\,F_{MTab}$ (VDI 2230 Part 1:2015, §5.5.1, Eq. (147)), the axial load below the opening limit (VDI 2230 Part 1:2015, §5.3.1.1, Eq. (87); §5.3.2, Eq. (104)), the interaction of axial and transverse load (VDI 2230 Part 1:2015, §5.5.6.3, Eq. (221)), the residual clamp load after yielding (VDI 2230 Part 1:2015, §5.5.2.4, Eq. (164)) and the length of engagement (VDI 2230 Part 1:2015, §5.5.5). A row without a value is not shown.

Figures and tables

• Joint diagram (Results tab, below the bolt specification card): it draws the forces and deformations of the bolt and the clamped parts under preload and working load (VDI 2230 Part 1:2015, §3.2, Figure 2; §4.2, Figure 5).
  • Three triangles: ① assembly, with its top at $F_{Mzul}$; ② lowest after scatter, with its top at $F_{Mzul}/\alpha_A$; ③ working state, with its top at $F_V$; the range of the working load $F_A$ is drawn on ③.
  • Threshold lines: $F_{Mzul}$, $F_{Mmax}$, $F_{Mzul}/\alpha_A$, $F_{Mmin}$, $F_V$, $F_{Smax}$, $F_{KRmin}$, $F_{Kerf}$.
  • When the mouse is over an element, a tooltip shows its name, value and reference; the reference is the same as in that step of the Steps tab. A value that is drawn from the results and is not a calculator output is marked as such in the tooltip.
  • Clicking an element that has a step opens that step in the Steps tab; on a touch screen, the second tap opens it.
  • Clicking a legend item turns that group of elements on or off.
  • The enlarge button opens the chart in a dialog and lays it out again for the dialog size.
  • When the chart is narrower than 600 px, the threshold lines only carry numbers at their right ends; names and values are listed in the caption below the chart, and caption items that have a step can be clicked.
  • With an eccentric joint, a note below the chart says that the forces use $\Phi^*_{en}$ and that bending of the bolt and the clamped parts is not shown.
• Schematic tab: the deformation cone and the deformation sleeve change live with the inputs (VDI 2230 Part 1:2015, §5.1.2, Figure 8, Figure 9); with the eccentric switch on, a sketch of the eccentric geometry is drawn below (VDI 2230 Part 1:2015, §5.3.2, Figure 25). With a counterbore depth for the head entered, the cone figure draws the bolt head in the counterbore; this input is used only for the figure. When the clamped parts of a TTJ are calculated as a TBJ, the cone figure also draws the virtual interface with a leader label; the outside diameter of the virtual interface is $D_A'$ (VDI 2230 Part 1:2015, Annex B, Example B1, R3).
• Result groups: bolt geometry, resilience and load factor, eccentric clamping, clamp load and preload, bolt stress and fatigue, surface pressure and length of engagement, transverse load, tightening torque; a row for a quantity that the backend does not give is not shown. With a product standard selected, a “Standard bolt” group comes before these groups. For a TBJ, the surface pressure is shown in two blocks, “Surface pressure — head side” and “Surface pressure — nut side”, and the critical side is marked “critical side”; for a TTJ there is one block, “Surface pressure (R10)”. For a TTJ, one more line states whether the clamped parts are calculated as a TBJ, and why.
• Torque table: one column for the lower limit of each friction class A to E and one for the given inputs, with the table assembly preload and the tightening torque; it is for reference only and does not enter the verdict (VDI 2230 Part 1:2015, §5.4.3.1; Annex A, Table A1–A5).
• Steps tab and report: the Steps tab lists each formula with its numbers; “Download Report (PDF)” collects the inputs, the key results and the joint diagram.

Limits and cautions

• Model of the clamped parts: the cone model does not take contact resilience into account (VDI 2230 Part 1:2015, §5.1.2); for a pack of thin plates $\delta_P$ is larger and, if needed, is determined by tests (VDI 2230 Part 1:2015, §5.1.2); for such joints the preload loss due to embedding $F_Z$ is to be determined experimentally, not by an equation (VDI 2230 Part 1:2015, §5.4.2.1, Eq. (113)).
• $D_A$: for a non-cylindrical component, $D_A$ is twice the mean edge distance at the interface; when a single bolt is taken from a multi-bolt joint, the hole spacing $t$ must not be used as $D_A$, and the deformation body extends at most to the edge of the neighbouring hole (VDI 2230 Part 1:2015, §5.1.2).
• Shear stress in R8: when transverse load and torque are carried by friction in the interface, the corresponding shear stress in the bolt can be neglected (VDI 2230 Part 1:2015, §5.5.2.1, Eq. (152)(153)); when the joint slips, shear and bolt bearing pressure must be checked (VDI 2230 Part 1:2015, §4.2 R12; §5.5.6.3, Eq. (219)–(223)).
• Endurance limit equations: they apply to high-strength bolts to DIN EN ISO 898-1:2013-05 with standard thread 6g/6H, valid for $0.3\le F_{Sm}/F_{0.2,min}\lt 1$ (VDI 2230 Part 1:2015, §5.5.3, Eq. (170)(171)); the endurance limit given applies to cycle numbers of more than $N_D=2\times10^6$ (VDI 2230 Part 1:2015, §5.5.3). The endurance limit of a fine thread decreases with increasing strength class and thread fineness, and for class 12.9 it may be up to 30 % lower than for a standard thread (VDI 2230 Part 1:2015, §5.5.3).
• Temperature: the thermal preload change uses the simplified equation $\Delta F'_{Vth}$, which assumes that the moduli change very little with temperature (VDI 2230 Part 1:2015, §5.4.2.3, Eq. (118)). Relaxation is not calculated; it becomes marked from about 160 °C for aluminium alloys and about 240 °C for structural and quenched-and-tempered steels (VDI 2230 Part 1:2015, §5.4.2.2); when the estimated working temperature (20 °C plus the larger of the temperature differences between bolt and parts) is not below 160 °C, the Steps tab gives a relaxation note (VDI 2230 Part 1:2015, §5.4.2.2).
• Eccentric: only the tensile cases I to III (VDI 2230 Part 1:2015, §5.3.2, Table 4); all layers must have the same modulus (VDI 2230 Part 1:2015, §5.1.2.2, Eq. (68)–(70); §5.1.2.3, Eq. (72)); an external bending moment $M_B$ is not covered (VDI 2230 Part 1:2015, §5.3.1.3, Eq. (96)–(98)).
• Hollow bolt: the permissible assembly preload uses an equation derived by analogy in Annex B, Example B3, which is not a main-text equation (VDI 2230 Part 1:2015, Annex B, Example B3, R7); the length of engagement is only an estimate and can be confirmed only by a test (VDI 2230 Part 1:2015, Annex B, Example B3, R11).
• Strength classes not listed in Table 7 (for example 6.8; 4.8 can be selected with ISO 4014 or ISO 4017; 9.8 is not in the list and can only be passed in directly): Table 7 has no shear strength ratio for these classes (VDI 2230 Part 1:2015, §5.5.6.3, Table 7), so with a transverse load the calculator does not give $S_A$. For a tapped thread joint (TTJ), when the tapped part is not steel, or when the bolt thread is critical and the thread limit dimensions are given (calculation by Eq. (213)), R11 needs this shear strength ratio; if it cannot be found, the calculation is refused with a note to select a class that is in the table (VDI 2230 Part 1:2015, §5.5.5, Eq. (195); §5.5.5.2, Eq. (213)).

Examples

The “Verification examples” list has 8 verification examples, numbered as in the verification manual (see below; 001–005 are from VDI 2230 Part 1:2015, Annex B; 006 and 007 from Niemann/Winter/Höhn/Stahl, Maschinenelemente 1, 5th ed., 2019, Section 10.11; 008 from Kloos/Thomala, Schraubenverbindungen, 5th ed., 2007, Section 4.5); after loading one, click “Run Calculation”. After you pick an example, the list keeps showing it; after you change an input, click reset, import a file, or your last inputs are restored automatically, the list goes back to “Pick a verification example…”.

• VM-VDI2230-BOLT-001: Annex B, Example B1 (load it in the calculator )
• VM-VDI2230-BOLT-002: Annex B, Example B2 (load it in the calculator )
• VM-VDI2230-BOLT-003: Annex B, Example B3 (load it in the calculator )
• VM-VDI2230-BOLT-004: Annex B, Example B4 (load it in the calculator )
• VM-VDI2230-BOLT-005: VDI 2230 Annex B, Example B5 (under verification) (load it in the calculator )
• VM-VDI2230-BOLT-006: Steel flange bolt, static load check (load it in the calculator )
• VM-VDI2230-BOLT-007: Connecting-rod necked-down bolt, dynamic load check (load it in the calculator )
• VM-VDI2230-BOLT-008: Connecting-rod bolt, eccentric clamping and loading (load it in the calculator )
• Full worked examples: through-bolt joint (TBJ) and tapped thread joint (TTJ)

All examples are in the Verification section for this calculator .

Frequently asked questions

The design mode result has not passed. What does the standard do? R0 only preselects the nominal diameter from Table A7 (VDI 2230 Part 1:2015, §4.2 R0, Table A7), and the selected size still has to pass the checks R1 to R13. If the criterion $F_{Mzul}\ge F_{Mmax}$ of R7 is not met, the standard selects a larger bolt nominal diameter and repeats the calculation from R2; if a larger nominal diameter is not possible, other measures are taken, such as a higher strength grade, another assembly method, a reduction in the friction or in the external loading (VDI 2230 Part 1:2015, §4.2 R7, R7/3). When design mode has not passed, a note below the overall verdict says that you can switch to verification mode and run again with the next size up, or raise the strength class.

The surface pressure under the head is not checked. Why? The safety margin against surface pressure $S_P=p_G/p_{M,max}$ needs the limiting surface pressure $p_G$ (VDI 2230 Part 1:2015, §4.2 R10, R10/4; §5.5.4, Eq. (190)). If the clamped layer under the head has no $p_G$, the surface pressure check of that side is not made, step R10 states that this side was not checked, and it is not counted in the overall verdict; the calculator uses no default value. $p_G$ can be brought in by selecting a Table A9 material in the layer table (VDI 2230 Part 1:2015, Annex A, Table A9), or entered in the material values of that layer.

For eccentric loading, do I enter $a$, or $a_k$ and $l_A$? $a$ 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 $a$. The joint type for load introduction , $a_k$ and $l_A$ only give a suggested value of $n$ from Table 2 in step R3c; the calculation uses the value entered in the load introduction factor . The section “Load introduction and eccentricity: reading the figures, filling in the inputs” in the Info tab of the calculator lists the definitions of these quantities and how to read the figures.

🧮 Online calculator: VDI 2230-1 single-bolt joint calculator — Design or check one high-strength bolted joint with R0 to R13.