A 12-in. NPS Schedule 160 branch and run pipe are attached to one another. The design pressure is 2200 psi. The allowable stress at ambient temperature is Sc = 17.5 ksi and at design temperature is Sh = 12.0 ksi. In addition to the internal pressure, the branch is subjected to externally applied

Question

A 12-in. NPS Schedule 160 branch and run pipe are attached to one another. The design pressure is 2200 psi. The allowable stress at ambient temperature is [latex]S_c[/latex] = 17.5 ksi and at design temperature is [latex]S_h[/latex] = 12.0 ksi. In addition to the internal pressure, the branch is subjected to externally applied forces and moments from thermal expansion of connecting piping. These moments and force are [latex]M_i[/latex] = 600,000 in.-lb; [latex]M_{o}[/latex] = 900,000 in.-lb; [latex]M_{t}[/latex] = 750,000 in.-lb; and [latex]F_{ ext {axial }}[/latex] = 90,000 lb. The nozzle is designed for 20,000 cycles. Using the design procedure of the ASME-ANSI B31.1 Code, what is the total applied stress and what is the allowable stress?

Accepted Answer

1 . Properties of 12 -in. NPS Schedule 160 are [latex]D_{o}[/latex] = 12.75 in.; inside area = 80.5 in.² ; metal area = 47.14 in.² ; Z = 122.6 in.³ ; [latex]t_{m}[/latex] = 1.312 in.

2 . Data at juncture from Table 11.6:

Table 11.6 Summary of Membrane Stresses at Various Locations
	[latex]\sigma_{\phi}[/latex]				[latex]\sigma_{x}[/latex]
	[latex]A_{U}[/latex]	[latex]A_{L}[/latex]	[latex]B_{U}[/latex]	[latex]B_{L}[/latex]	[latex]A_{U}[/latex]	[latex]A_{L}[/latex]	[latex]B_{U}[/latex]	[latex]B_{L}[/latex]
Due to P	-2,110	-2,110	-2,110	-2,110	-1,920	-1,920	-1,920	-1,920
Due to [latex]M_{L}[/latex]	-3,900	-3,900	+3,900	+3,900	-1,140	-1,140	+1,140	+1,140
Total	-6,010	-6,010	+1,790	+1,790	-3,060	-3,060	-780	-780

[latex]\begin{aligned}&h=\frac{T_{h}}{R_{m}}=\frac{1.312}{5.719}=0.229 \&i_{o}=\frac{0.9}{h^{2 / 3}}=2.40 \&i_{i}=0.75 i_{o}+\frac{1}{4}=0.75(2.40)+0.25=2.05\end{aligned}[/latex]

3 . Determine torsional stress:

[latex]S_{t}=\frac{M_{t}}{2 Z}=\frac{750,000}{2(122.6)}=3060 ext{ psi}[/latex]

4 . Determine the bending stress :

[latex]S_{b}=\frac{\sqrt{(2.05 imes 600,000)^{2}+(2.40 imes 900,000)^{2}}}{122.6}=20,270 ext{ psi}[/latex]

5 . Determine the stress range :

[latex]S_{E}=\sqrt{S_{b}^{2}+4S_{t}^{2}}=\sqrt{(20,270)^{2}+4(3060)^{2}}=21,170 ext{ psi}[/latex]

6 . Determine sustained longitudinal stress:

[latex]S_L = (2200)\frac{80.5}{47.14}=3760 ext{ psi}[/latex]

7 . Determine allowable stress range [latex]S_A[/latex] :

f = 0.8 for 20,000 cycles

[latex]S_A[/latex] = 0.8[1.25 (17,500 + 12,000) - 3760] = 26,490 psi

[latex]S_{E}

Question 11.17: A 12-in. NPS Schedule 160 branch and run pipe are attached t...

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