Design and Analysis of Piping and Support

Abstract

Piping systems are used to transport liquids, gases, slurries, or fine solid particles in process industries. The use of pipe was very common even in the prehistoric era, particularly bamboo pipes used for irrigation purposes.

Appendix 1: Piping Qualification as per ASME B31.1

Example 11.6

A typical piping is shown in Fig. 11.17, and the design and operation conditions are given below:

$$ \begin{array}{*{20}l} {\text{Pipe size}} \hfill & { = 2{\prime \prime }\,{\text{Sch }}40} \hfill \\ {{\text{Outer diameter }}\left( {D_{\text{o}} } \right)} \hfill & { = 60.3\,{\text{mm and wall thickness}}\left( t \right) = 3.91\,{\text{mm}}} \hfill \\ {\text{Section modulus}} \hfill & { = 9.1757 \times 10^{ - 6} \,{\text{m}}^{3} } \hfill \\ {\text{Mass per unit length}} \hfill & { = 5.44\,{\text{kg}}/{\text{m}}} \hfill \\ {{\text{Radius of elbow }}\left( R \right)} \hfill & { = 76.2\,{\text{mm}}} \hfill \\ {\text{Material}} \hfill & {{\text{SS}}304{\text{L}}\left( {{\text{ASME Class 2}},{\text{SA}} - 312,{\text{seamless}}\,\&\, {\text{welded pipe}}} \right)} \hfill \\ \end{array} $$

Fig. 11.17

FE model of a typical piping

(Tables 11.16 and 11.17)

Table 11.16 Material properties

Table 11.17 Forces and moment at critical section of pipe

Solution

Elbow parameter (h) = tR/(r_m)²

r_m = mean pipe radius = (D_o−t)/2 = (60.3−3.91)/2 = 28.195 mm

h = 0.375

Stress intensification factor (i) = 0.9/h^2/3 = 1.73

Qualification Check for sustained load:

$$ SL = \frac{{PD_{\text{o}} }}{{4t_{\text{n}} }} + 0.75i\frac{{M_{\text{A}} }}{Z} \le 1.0S_{\text{h}} $$

$$ \begin{aligned} & \frac{{1.18 \times 10^{5} \times 0.0603}}{4 \times 0.00391} + 0.75 \times 1.73 \times \frac{6}{{9.1757 \times 10^{ - 6} }} \\ & = 454948.85 + 848436.63 \\ & = 1303385.48\,{\text{N}}/{\text{m}}^{2} = 1.30\,{\text{MPa}}\,\left( {S_{\text{L}} } \right) \\ \end{aligned} $$

Actual stress is much lower than the allowable stress (S_h = 115 × 10⁶ N/m²); hence, piping is safe under sustained loads.

Qualification Check for Thermal Load:

$$ S_{\text{E }} = i\frac{{M_{\text{C}} }}{Z} \le [S_{\text{A}} + f\left( {S_{\text{h}} - S_{\text{L}} } \right)] $$

$$ \begin{aligned} {\text{Allowable}}\,{\text{stress}}\,{\text{for}}\,{\text{thermal}}\,{\text{loads}}\,(S_{{{\text{A}})}} & = f\,\left( {1.25S_{\text{C}} + 0.25\,S_{\text{h}} } \right) \\ & = 1 \times \left( {1.25 \times 115 + 0.25 \times 115} \right) \\ & = 172.5\,{\text{MPa}} \\ \end{aligned} $$

S_A + f(S_h−S_L) = 172.5 + 1 × (115−1.30) = 286.2 MPa

Stresses in piping due to thermal expansion

$$ \begin{aligned} i\frac{{M_{\text{C}} }}{Z} & = 1.73 \times \frac{{\left\{ {\left( { - 114} \right)^{2} + \left( {18} \right)^{2} + \left( { - 190} \right)^{2} } \right\}^{{\frac{1}{2}}} }}{{9.1757 \times 10^{ - 6} }} \\ & = 1.73 \times \frac{222.31}{{9.1757 \times 10^{ - 6} }} = 41.91 \times 10^{6} \,{\text{N}}/{\text{m}}^{2} \\ \end{aligned} $$

Actual stress is lower than the allowable stress; hence, piping is safe under thermal loads.