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## Q. 10.10

What is the minimum required thickness of a ring flange with the same design data as given in Example 10.9? The inside diameter has been increased to fit over the outside of the shell to where B = 12.75 in. The bolt loadings and bolt size are the same as in Example 10.9. A sample calculation sheet is shown in Figure 10.16. ## Verified Solution

1 . Calculate total flange moment for design condition.

$H_{D}=\frac{\pi}{4} B^{2} p=\frac{\pi}{4}(12.75)^{2}(2500)=319,200$

$H_{G}=H_{p}=250,600$

$H_{T}=H-H_{D}=444,300-319,200=125,100$

Lever Arms

$h_{D}=0.5(C-B)=0.5(22.5-12.75)=4.875 \text { in.}$

$h_{G}=0.5(C-G)=0.5(22.5-15.043)=3.729 \text { in. }$

$h_{T}=0.5\left(h_{D}+h_{G}\right)=0.5(4.875+3.729)=4.302 \text { in. }$

Flange Moments

$M_{D}=H_{D} \times h_{D}=(319,200)(4.875)=1,556,000$

$M_{G}=H_{G} \times h_{G}=(250,600)(3.729)=934,500$

$M_{T}=H_{T} \times h_{T}=(125,100)(4.302)=538,200$

$M_{d c}=M_{D}+M_{G}+M_{T}=3,029,000$

2 . Bolt-up moment is the same as in Example 10.9, $M_{B U}=2,613,000$.

3 . Shape constants are K = A / B = 26.5 / 12.75 = 2.078

From Fig. 2-7.1 of the ASME Code, VIII-1, Y = 2.812.

4 . Required thickness is based on design condition as

$t=\frac{M_{d c} Y}{S_{f} B}=\frac{(3,029,000)(2.812)}{(19,200)(12.75)}=5.898 \text { in. }$