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Pipe Straight Pipe or Large Bends Stress Calculator and Equations

Pipe Bending Straight Pipe or Large Bends Stress Calculator and Equations per. ASME B31.9

The nominal bending stress in a straight pipe or large radius bends due to weight or other external load calculator.

Pipe Bending Stress due to Weight or other External Loads is:

Eq. 1
SB = M / Z

The nominal bending stress in fittings and components due to weight or other external loads is:

Eq. 2
SB = MR / Z

Resultant intensified moment across the fitting or component. The resultant moment shall be calculated as:

Eq. 3
MR = [ ( 0.75 ii Mi )2 + ( 0.75 io Mo )2 + Mt 2 ]1/2

Eq. 4
Z = 1 / I

Eq. 5 (area moment of inertia pipe)
I = π ( D4 - d4 ) / 64

Eq. 6 (section modulus pipe)
Z = π ( D4 - d4 ) / ( 32 D )

Where

M = the bending moment across the pipe cross section, lb-in, (N-m)
Z = The pipe section modulus, in3 (m3)
ii = in-plane stress intensification factor
io = out-of-plane stress intensification factor
Mi = in-plane bending moment, lb-in. (N-m)
Mo =out-of-plane bending moment, lb-in. (N-m)
Mt = torsional moment, lb-in (N-m)
D = outer diameter, in (m)
d = inner diameter, in (m)

Figure 1, Pipe Data

If a section of pipe can operate either warmer or colder than the installed temperature, both conditions to T2 may need to be examined.

Table 1, Stress Intensification Factor, i per. ASME B31.8

 Description Out of Plane io In-Plane ii Sketch Welding elbow or pipe bend 0.75 / h2/3 0.90 / h2/3 Welding tee per ASME B16.9 with ro ≥ d / 8 Tc ≥ 1.5 T - 3/4 io + 1/4 Reinforced fabricated tee with pad or saddle - 3/4 io + 1/4 Unreinforced fabricated tee - 3/4 io + 1/4 Extruded outlet ro ≥ d / 8 Tc < 1.5 - 3/4 io + 1/4

Source:

ASME B31.9, Gas Transmission and Distribution Systems

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