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Stress at Threaded Tube Connection Design Calculator

Threaded Connections Design and Calculations
Strength of Materials

Stress at Threaded Connections Between Two Tubes Design and Calculator

The following rules are stated for the case of threaded connections between two tube subjected to axial force, P. For the bolt-and-nut assembly, the same rules apply, by substituting D_i = O.

Preview calculator: Design Stress at Threaded Connections Between Two Tubes Calculator

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Eq. 1 Tensile stress in outer tube at root section of thread

${\displaystyle f_t=\frac{P}{\frac{\mathrm{\Pi <!--\; ?\; -->}}{4}[D_o^2-<!--\; -\; -->(D_n+f{)}^2]}}$

Eq. 2 Tensile stress in outer tube at relief groove

${\displaystyle f_t=\frac{P}{\frac{\mathrm{\Pi <!--\; ?\; -->}}{4}[D_o^2-<!--\; -\; -->D_{Ro}^2]}}$

Eq. 3 Tensile stress in inner tube at root section of thread

${\displaystyle f_t=\frac{P}{\frac{\mathrm{\Pi <!--\; ?\; -->}}{4}[(D_N-<!--\; -\; -->e{)}^2-<!--\; -\; -->D_1^2]}}$

Eq. 4 Tensile stress in inner tube at relief groove

${\displaystyle f_t=\frac{P}{\frac{\mathrm{\Pi <!--\; ?\; -->}}{4}[D_{R\mathrm{i}}^2-<!--\; -\; -->D_{\mathrm{i}}^2]}}$

Eq. 5 Shear stress across threads, along a cylindrical surface having a diameter equal to the minimum pitch diameter.

${\displaystyle f_s=\frac{PF}{\frac{\mathrm{\Pi <!--\; ?\; -->}}{2}(D_N-<!--\; -\; -->c)L}}$

Eq. 5a

${\displaystyle f_s\approx <!--\; ˜\; -->\frac{4P}{\mathrm{\Pi <!--\; ?\; -->}DL}}$

Eq. 5b

${\displaystyle f=\frac{U_{tooth}}{L_{tooth}}}$

Eq. 5c Unloaded tooth

U_tooth = Δ_o - Δ_I

Figure 1 - Tube to Tube threaded Connection

Eq. 6 Bearing stress on the surface of contact between inner and outer threads.

${\displaystyle f_{br}=\frac{P}{\frac{nL\mathrm{\Pi <!--\; ?\; -->}}{4}[(D_n-<!--\; -\; -->a-<!--\; -\; -->{\mathrm{\Delta <!--\; ?\; -->}}_{\mathrm{I}}{)}^2-<!--\; -\; -->(D_N-<!--\; -\; -->b-<!--\; -\; -->{\mathrm{\Delta <!--\; ?\; -->}}_O{)}^2]}}$

Eq. 7 Hoop compression stress in inner tube

${\displaystyle f_c=\frac{P}{\sqrt{3}\mathrm{\Pi <!--\; ?\; -->}L(D_N-<!--\; -\; -->c-<!--\; -\; -->D_I)}}$

Eq. 7a The corresponding elastic decrease in diameter of the inner tube is

${\displaystyle {\mathrm{\Delta <!--\; \Delta \; -->}}_I=\frac{f_c}{E}(D_N-<!--\; -\; -->c)}$

Eq. 8 Hoop tension stress in outer tube

${\displaystyle f_t=\frac{P}{\sqrt{3}\mathrm{\Pi <!--\; \Pi \; -->}L(D_o-<!--\; -\; -->D_N+d)}}$

Eq. 8a

${\displaystyle {\mathrm{\Delta <!--\; \Delta \; -->}}_o=\frac{f_t}{E}(D_N-<!--\; -\; -->d)}$

Where

P =axial tensile force
D_N = Nominal diameter
D_o = Outer tube thread root diameter
D_ro = Outer tube major diameter
D_i = Inside tube inside diameter
D_ri = Inside tube root diameter
L = Length of engagement
Δ_I = elastic decrease in diameter of inner tube
Δ_O = elastic increase in diameter of outer tube
a = Truncation of external thread root
b = Total single thread contact width
p = pitch
c = Difference between maximum major and pitch diameter of internal thread
d = Height if internal thread and depth of thread engagement
e = Double height of external thread
f = Addendum of external thread
f_t = Tensile stress
U_tooth = Unloaded tooth height
L_tooth = Loaded tooth height
L = Length of engaged thread

Reference:

• Bell Helicopter Structural Design Manual, 1977

Unloaded Tooth Height

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