Bolt Torque and Preload Calculator

Torque and clamp force

Use a single-start 60° thread with basic geometry derived here: $H=\sqrt{3}P/2$, $d_2=d-3H/4$, $d_3=d-17H/12$, and $A_s=\pi[(d_2+d_3)/2]^2/4$. No standard table is reproduced.

Force balance on a helical inclined plane gives $h=P/(\pi d_2)$ and the exact thread torque factor

NASA RP-1228, printed p.17 (attached p.21), gives this separate-friction model. Use $D_b=(D_o+d_h)/2$ as an effective bearing-diameter approximation and $a_B=\mu_B D_b/2$. Then $T=F(a_G+a_B)$, with explicit N·mm ↔ N·m conversion. The familiar VDI-style small-angle expression is $T\approx F[P/(2\pi)+\mu_Gd_2/(2\cos30^\circ)+\mu_BD_b/2]$. This tool retains the exact helix term. ISO 16047:2005 with Amendment 1:2012 provides the friction-test framework, not assumed friction values.

Assembly stress and uncertainty

Only thread torque $T_G=Fa_G$ is transmitted down the bolt; the bearing torque is excluded from shank torsion. Evaluate $\sigma_z=F/A_s$, $\tau=16T_G/(\pi d_3^3)$ and $\sigma_{VM}=\sqrt{\sigma_z^2+3\tau^2}$. Utilisation is $\sigma_{VM}/R_y$. Minimum strengths follow ISO 898-1:2013 as published by BBS; property class 8.8 changes minimum yield strength above 16 mm. The full thread torque at the basic root is a conservative assembly model, not a reproduction of every VDI stress convention.

Friction bounds are $\mu(1\pm r)$ and torque bounds $T(1\pm\epsilon)$. Preload is largest at both friction minima and maximum torque. Combined stress is checked at all four independent friction corners at maximum torque. At fixed bearing friction, stress squared is proportional to $(A+B a_G^2)/(a_G+a_B)^2$; its only internal stationary point is a minimum. Thus its maximum lies on the friction bounds. The torque ceiling includes the selected yield utilisation and tool variation.

Tapped-hole screen

NASA RP-1228, printed p.21 (attached p.25), estimates internal-thread pullout as $F_{strip}=\pi d_2L_e s_m/3$. Its one-third factor allows for imperfect thread engagement; it is not the user's design factor. Require $F_{strip}/F_{high}\ge n_s$. The strength-only length follows by rearrangement, and the reported required engagement is $L_{need}=\max[3P,\,3n_sF_{high}/(\pi d_2s_m)]$. Thus even at low torque it meets the model's minimum of three fully formed pitches. The stripping torque ceiling follows from the same strength criterion. NASA/TM-2017-219475, printed p.216 (attached p.222), supplies an independent M12 reference value. Its description of the one-third term as a safety factor differs from RP-1228; this tool follows RP-1228 and applies a separate design factor.

The displayed torque ceiling is the smaller of the combined-stress and tapped-hole settings over the stated bounds. The torque split is ideal advance $FP/(2\pi)$, thread friction $T_G-FP/(2\pi)$, and bearing friction $Fa_B$. Their sum must equal total torque.

• Full-loadability carbon/alloy steel bolts, classes 8.8, 10.9 or 12.9, at room temperature. No reduced shank, hollow bolt or weak head.
• ISO metric single-start 60° basic geometry, 3–39 mm nominal diameter. Actual thread tolerances are not resolved.
• Flat annular rotating bearing face; the arithmetic-mean effective friction diameter approximates its pressure distribution. The schematic shows a rotating screw head; rotating-nut tightening uses the same local model.
• Quasi-static elastic tightening with constant friction. No prevailing torque, locking patch, thread forming, seating torque or torsional relaxation.
• Friction and torque variation are bounded inputs, not fitted distributions. No correlation is assumed; all independent combinations are allowed.
• Fully formed engagement in a solid tapped body with a stronger external fastener. A minimum of three pitches is required. Nut proof loads, external bolt threads and radial expansion are not assessed.
• The default tapped-material shear strength of 180 MPa is a user-replaceable illustration, not a catalogued material property. Use shear yield/allowable strength for an elastic check; using ultimate shear strength changes the screen to an ultimate basis. The additional factor must reflect the strength basis.
• Basic geometry and the stress combination are derived here; no VDI or ISO tables or drawings are copied.

Assembly screening only. The torque/friction treatment follows the separate-interface VDI 2230 approach (Part 1, 2015-11), with exact helix equilibrium and a conservative full-root-torsion stress check. This is not a complete VDI 2230 verification or a certified tightening specification. ISO 16047:2005/Amd 1:2012 and ISO 898-1:2013 are the named supporting editions; check against the standard in force and the product specification.

Exceeding 100% combined yield utilisation invalidates the elastic load prediction. A result below the selected stress or stripping limit does not establish joint suitability. The stripping estimate is an empirical internal tapped-thread screen, not VDI 2230's detailed thread failure calculation; it excludes bolt-thread shear, tolerances, thin nuts, inserts, first-thread load concentration and nut/body expansion. Engagement above two diameters triggers a warning because proportional capacity gains become unreliable.

No service force, stiffness, fatigue, relaxation, joint opening, transverse slip, temperature, corrosion or bearing-strength assessment is included. Bearing pressure is an estimate only. Friction-sweep curves show elastic extrapolations above the limits. The calculated torque ceiling applies only to the selected assembly criteria and stated bounds.

The Wurth M12 check allows about 2% for catalogue rounding and the explicit bearing geometry; its published 90% yield maximum is not used to validate this tool's more conservative root-torsion ceiling. NASA's tabulated pullout reference uses ultimate material shear strength; it checks transfer of that equation, not an allowable for service.

Installation work belongs to a qualified person using the approved assembly procedure.