A rectangular cross-sectional header is made from two C-sections and butt welded along the center of the short-sides. The weld joints are spot examined with the backing strip left in place (from Table UW-12 of the ASME Code, VIII-1, E = 0.8 ). The design pressure is 115 psi at room temperature, and

Question

A rectangular cross-sectional header is made from two C-sections and butt welded along the center of the short-sides. The weld joints are spot examined with the backing strip left in place (from Table UW-12 of the ASME Code, VIII-1, E = 0.8 ). The design pressure is 115 psi at room temperature, and the material is SA-515 Grade 70 with an allowable stress of 17,500 psi. The long side is 13.5 by 1 in. thick and the short-side is 6 by 0.625 in. thick, One long-side contains a row of 1.5 in. diameter holes on 3.75-in. centers. Is the design acceptable?

Accepted Answer

1 . Calculate the ligament efficiency of the long-side with the tube holes:

[latex]e_{m}=e_{b}=\frac{3.75-1.5}{3.75}=0.60[/latex]

2 . Calculate the moments of inertia of both the long-side and the short-side:

[latex]I_{1}=\frac{t_{1}^{3}}{12}=\frac{(0.625)^{3}}{12}=0.0203[/latex] [latex]I_{2}=\frac{t_{2}^{3}}{12}=\frac{(1)^{3}}{12}=0.0833[/latex]

3 . Calculate the bending moment at the corner [latex]M_{Q}[/latex] using Eq. 17.18:

[latex]M_{Q}=\frac{P}{12}\left(\frac{h^{3} / I_{2}+H^{3} / I_{1}}{h / I_{2}+H / I_{1}}\right)[/latex] (17.18)

[latex]M_{Q}=\frac{115}{12}\left[\frac{(13.5)^{3} / 0.0833+(6)^{3} / 0.0203}{13.5 / 0.0833+6 / 0.0203}\right]=841.35[/latex]

4 . Calculate the bending moment at the midpoint of the long-side [latex]M_{M}[/latex] using Eq. 17.19:

[latex]M_{M}=M_{Q}-\frac{P h^{2}}{8}[/latex] (17.19)

[latex]M_{M}=M_{Q}-\frac{P h^{2}}{8}=841.35-\frac{(115)(13.5)^{2}}{8}=-1778.50[/latex]

5 . Calculate the bending moment at the midpoint of the short-side [latex]M_{N}[/latex] using Eq. (17.20):

[latex]M_{N}=M_{Q}-\frac{P H^{2}}{8}[/latex] (17.20)

[latex]M_{N}=M_{Q}-\frac{P H^{2}}{8}=841.35-\frac{(115)(6)^{2}}{8}=323.85[/latex]

6 . Calculate the bending stress at the corner of the long-side with the holes (E=1.0) :

[latex]\left(S_{b}\right)_{Q M}=\frac{M_{Q} c_{2}}{I_{2} E}=\frac{(841.35)(0.5)}{(0.0833)(1.0)}=5050[/latex] psi

7 . Calculate the bending stress at the midpoint of the long-side with the holes (E = [latex]e_{b}[/latex] = 0.60) :

[latex]\left(S_{b}\right)_{M}=\frac{M_{M} c_{2}}{I_{2} E}=\frac{(1778.50)(0.5)}{(0.0833)(0.6)}=17,790[/latex] psi

8 . Calculate the bending stress at the corner of the short-side (E = 1.0) :

[latex]\left(S_{b}\right)_{Q N}=\frac{M_{Q} c_{1}}{I_{1} E}=\frac{(841.35)(0.3125)}{(0.0203)(1.0)}=12,950[/latex] psi

9 . Calculate the bending stress at the midpoint of the short-side (E = 0.80) :

[latex]\left(S_{b}\right)_{N}=\frac{M_{N} c_{1}}{I_{1} E}=\frac{(323.85)(0.3125)}{(0.0203)(0.80)}=6230[/latex] psi

10 . Calculate the membrane stress on the long-side (E = [latex]e_{m}[/latex] =0.60) :

[latex]\left(S_{m}\right)_{M}=\frac{P H}{2 t_{2} E}=\frac{(115)(6)}{2(1)(0.6)}=580[/latex] psi

11 . Calculate the membrane stress on the short-side (E = 0.80) :

[latex]\left(S_{m}\right)_{N}=\frac{P h}{2 t_{1} E}=\frac{(115)(13.5)}{2(0.625)(0.8)}=1550[/latex] psi

12 . Total stress at corner of long-side:

[latex]\left(S_{t}\right)_{QM}=\left(S_{m}\right)_{M}+\left(S_{b}\right)_{Q M}=580+5050=5630[/latex] psi

13 . Total stress at midpoint of long-side:

[latex]\left(S_{t}\right)_{M}=\left(S_{m}\right)_{M}+\left(S_{b}\right)_{M}=580+17,790=18,370[/latex] psi

14 . Total stress at corner of short-side:

[latex]\left(S_{t}\right)_{QN}=\left(S_{m}\right)_{N}+\left(S_{b}\right)_{Q N}=1550+12,950=14,500[/latex] psi

15 . Total stress at midpoint of short-side:

[latex]\left(S_{t}\right)_{N}=\left(S_{m}\right)_{N}+\left(S_{b}\right)_{N}=1550+6230=7780[/latex] psi

The allowable stress for membrane stress is 17,500 psi and for the combined membrane plus bending stresses is 1.5 S = 1.5(17,500) = 26,250 psi. All calculated stresses are less than the allowable stresses and are acceptable.

Question 17.8: A rectangular cross-sectional header is made from two C-sect...

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