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Pipe Straight Pipe or Large Bends Stress Calculator and Equations

Hydraulic & Pneumatics
Fluids Flow Design and Engineering

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.

Preview: Pipe Bending Straight Pipe or Large Bends Stress Calculator

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

Eq. 1
S_B = M / Z

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

Eq. 2
S_B = M_R / Z

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

Eq. 3
M_R = [ ( 0.75 i_i M_i )² + ( 0.75 i_o M_o )² + M_t 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)
i_i = in-plane stress intensification factor
i_o = out-of-plane stress intensification factor
M_i = in-plane bending moment, lb-in. (N-m)
M_o =out-of-plane bending moment, lb-in. (N-m)
M_t = 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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