Type a line (stud M36 effective length 400 mm preload 500 kN E 205 GPa elongation) or fill in the fields: the line and the fields stay in step. The modulus in the examples is only an example value.
Enter the stud, as an ISO metric or unified inch thread, a stress area or a reduced shank diameter, with its effective length, the elastic modulus of its steel and either the preload or the measured elongation, and the calculator gives the other one: the elongation from the preload, dL = F x L / (E x A), or the preload from the elongation, F = dL x E x A / L. It shows the area used, the stress in the stud as a figure, the working with your numbers and a sketch of the stud, and gives a line you can copy or add to a request. With both the preload and the elongation entered, it works out each from the other so they can be compared.
The stretch or the hydraulic tensioner pressure in the engine maker’s instructions comes first: the calculator gives no tightening values for any engine or bolt, no grades and no allowable stresses. The effective length is taken as typed: references count different parts of the nut and the thread engagement into it, so use the length as the instructions or the measuring procedure define it. There is no preset elastic modulus: references give different values for steel, so enter the value for the stud material.
For an ISO metric thread As = pi/4 x (d - 0.9382 P)^2. M36 with its coarse pitch of 4 mm: 36 - 0.9382 x 4 = 32.247 mm, As = 0.7854 x 32.247^2 = 816.7 mm2. For a unified inch thread At = pi/4 x (d - 0.9743 / n)^2: 3/4-10 UNC gives 0.3345 in2. A reduced shank uses its own area, pi/4 x ds^2: a 28 mm shank gives 615.8 mm2.
dL = F x L / (E x A). 500 kN on an M36 stud with an effective length of 400 mm and E = 205 GPa (205 000 N/mm2): dL = 500 000 x 400 / (205 000 x 816.7) = 1.195 mm. The stress in the thread is 500 000 / 816.7 = 612 MPa, given as a figure only.
F = dL x E x A / L, the same relation solved for the force. 0.42 mm measured on an M30 stud (As = 560.6 mm2) over 300 mm with E = 205 GPa: F = 0.42 x 205 000 x 560.6 / 300 = 160.9 kN. Entered with a preload as well, the calculator gives both and the difference between them.
| Quantity | Relation | Note |
|---|---|---|
| Elongation from preload | dL = F x L / (E x A) | F the preload, L the effective length as typed, E the elastic modulus, A the area |
| Preload from elongation | F = dL x E x A / L | the same relation solved for the force |
| Stud stiffness | k = E x A / L | F = k x dL |
| Stress area, ISO metric | As = pi/4 x (d - 0.9382 P)^2 | d the nominal diameter, P the pitch, mm |
| Stress area, unified inch | At = pi/4 x (d - 0.9743 / n)^2 | d in inches, n threads per inch |
| Reduced shank | A = pi/4 x ds^2 | ds the shank diameter |
| Stress in the stud | F / A | MPa (N/mm2); a figure only, no verdict |
| Units | 1 in = 25.4 mm; 1 lbf = 4.4482216 N; 1 tf = 9.80665 kN | 1 psi = 0.0068948 MPa; 1 GPa = 1000 MPa |
The coarse pitches the calculator takes from its table: M3 0.5, M4 0.7, M5 0.8, M6 1, M8 1.25, M10 1.5, M12 1.75, M14 and M16 2, M20 and M22 2.5, M24 and M27 3, M30 3.5, M36 4, M42 4.5, M48 5, M56 5.5, M64 6 mm; for other sizes and for fine threads type the pitch (M39 x 4, M24 x 2). The UNC threads per inch from 1/4 to 4 in are in the table too; for UNF and other inch series type the thread count (1-12 UNF).
The elongation dL = F L / (E A) and the stress F / A are Hooke’s law for a stud in tension, as two independent engineering references on bolt stretching and preload give them, each with a worked example in inch units (a 7/8-9 UNC stud under 10 000 lbf over 5 in stretches 0.0036 in; a 3/4-10 UNC bolt under 30 101 lbf over 3 in stretches 0.00900 in, both with E = 30 x 10^6 psi), which the calculator reproduces. The stress areas pi/4 x (d - 0.9382 P)^2 for ISO metric threads and pi/4 x (d - 0.9743 / n)^2 for unified inch threads are each given the same way by two independent engineering references, and the metric values agree with a published table of stress areas (M24 353, M24 x 2 384, M30 561, M36 817 mm2). The coarse metric pitches and the UNC threads per inch are taken only for the sizes where two thread tables agree. Neither elongation reference adds part of the nut to the length, so the length is taken as typed. For E, the worked examples use 30 x 10^6 psi (206.8 GPa) and modulus tables give 200 GPa for a structural steel, so the calculator has no preset value.
With dL = F x L / (E x A): the preload F, the effective length L, the elastic modulus E of the stud material and the area A that carries the load. An M36 stud has a stress area of 816.7 mm2 (coarse pitch 4 mm). With 500 kN over an effective length of 400 mm and E = 205 GPa, that is 205 000 N/mm2: dL = 500 000 x 400 / (205 000 x 816.7) = 1.195 mm. The relation holds while the stud stays elastic.
With the same relation solved for the force: F = dL x E x A / L. 0.42 mm measured on an M30 stud, stress area 560.6 mm2, over an effective length of 300 mm with E = 205 GPa gives F = 0.42 x 205 000 x 560.6 / 300 = 160 888 N, about 160.9 kN. Enter both a preload and an elongation and the calculator gives the elongation expected at that preload, the preload the measured elongation stands for, and the difference between them.
For a thread, its tensile stress area: pi/4 x (d - 0.9382 P)^2 for ISO metric threads, with the coarse pitch from the table or the pitch typed, and pi/4 x (d - 0.9743 / n)^2 for unified inch threads, with n threads per inch. An area typed in mm2, cm2 or in2 is used as it is. For a stud with a reduced shank the shank area pi/4 x ds^2 is used; with a thread entered as well, the stress in the thread is also shown.
The length as the engine maker’s instructions or the measuring procedure define it. References count different parts of the nut and of the thread engagement into the effective length, so the calculator adds nothing: the length is taken as typed, and the stretch scales with it, 10 % more length giving 10 % more stretch at the same preload.
Because references give different values: the inch worked examples use 30 x 10^6 psi (206.8 GPa), while modulus tables give 200 GPa for a structural steel. Between 200 and 206.8 GPa the result changes by about 3.4 %. Take E from the material data of the stud; the examples on this page use 205 GPa only as an example value.
A thread: M36, M24 x 2, M24 with a fine pitch typed, or 1 1/2-6 UNC, 1.5 in UNC, 1-12 UNF; or a stress area in mm2, cm2 or in2; or a reduced shank diameter. Lengths and elongations in mm, cm, m, in or ft, elongations also in micrometres (um) or mils; forces in kN, N, MN, lbf, kip, tonne-force (t, tf) or kgf; the modulus in GPa, MPa (N/mm2), psi, ksi or Mpsi. No tightening values: the stretch or the tensioner pressure in the engine maker’s instructions comes first.
The calculator relates the stretch of a stud to its preload. When studs, nuts or parts for the hydraulic tensioner are needed, send the line from the calculator with the engine details and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
