Design the base ring shown in Fig. 12.7a. Stress in the bolts is 17,500 psi; height of gussets 12 in. , and concrete-bearing stress is 100 psi. Allowable stress for base ring is 20,000 psi and yield stress is 36,000 psi.

Question

Accepted Answer

Required base ring thickness due to concrete-bearing stress is obtained from Eq. 12.12 as

[latex]t=\sqrt{\frac{3 f_{c} l^{2}}{\sigma}}[/latex] (12.12)

where t = required base ring thickness on the compressive side of the neutral axis

[latex]f_{c}[/latex] = actual stress in concrete

l = cantilever length of base ring as defined in Fig. 12.5

σ = allowable bending stress of base ring

[latex]\begin{aligned}t &=\sqrt{\frac{3 imes 100 imes 6^{2}}{20,000}} \&=0.73 \ in .\end{aligned}[/latex]

From Table 12.2, the net area of [latex]1 \frac{1}{2}[/latex]-in. bolts is 1.405 in.²

Table 12.2 Bolt Dimensions and Clearances Bolting Data
Bolt Size	Threads		Nut Dimensions		Bolt Spacing B	Radial Distance R	Edge Distance E	Wrench Diameter a
Bolt Size	No. of Threads	Root Area (in.²)	Across Flats	Across Corners	Bolt Spacing B	Radial Distance R	Edge Distance E	Wrench Diameter a
[latex]\frac{1}{2}[/latex]	13	0.126	[latex]\frac{7}{8}[/latex]	0.969	[latex]1 \frac{1}{4}[/latex]	[latex]\frac{13}{16}[/latex]	[latex]\frac{5}{8}[/latex]	[latex]1 \frac{1}{2}[/latex]
[latex]\frac{5}{8}[/latex]	11	0.202	[latex]1 \frac{1}{16}[/latex]	1.175	[latex]1 \frac{1}{2}[/latex]	[latex]\frac{15}{16}[/latex]	[latex]\frac{3}{4}[/latex]	[latex]1 \frac{3}{4}[/latex]
[latex]\frac{3}{4}[/latex]	10	0.302	[latex]1 \frac{1}{4}[/latex]	1.383	[latex]1 \frac{3}{4}[/latex]	[latex]1 \frac{1}{8}[/latex]	[latex]\frac{13}{16}[/latex]	[latex]2 \frac{1}{16}[/latex]
[latex]\frac{7}{8}[/latex]	9	0.419	[latex]1 \frac{7}{16}[/latex]	1.589	[latex]2 \frac{1}{16}[/latex]	[latex]1 \frac{1}{4}[/latex]	[latex]\frac{15}{16}[/latex]	[latex]2 \frac{3}{8}[/latex]
1	8	0.551	[latex]1 \frac{5}{8}[/latex]	1.796	[latex]2 \frac{1}{4}[/latex]	[latex]1 \frac{3}{8}[/latex]	[latex]1 \frac{1}{16}[/latex]	[latex]2 \frac{5}{8}[/latex]
[latex]1 \frac{1}{8}[/latex]	8	0.728	[latex]1 \frac{13}{16}[/latex]	2.002	[latex]2 \frac{1}{2}[/latex]	[latex]1 \frac{1}{2}[/latex]	[latex]1 \frac{1}{8}[/latex]	[latex]2 \frac{7}{8}[/latex]
[latex]1 \frac{1}{4}[/latex]	8	0.929	2	2.209	[latex]2 \frac{13}{16}[/latex]	[latex]1 \frac{3}{4}[/latex]	[latex]1 \frac{1}{4}[/latex]	[latex]3 \frac{1}{4}[/latex]
[latex]1 \frac{3}{8}[/latex]	8	1.155	[latex]2 \frac{3}{16}[/latex]	2.416	[latex]3 \frac{1}{16}[/latex]	[latex]1 \frac{7}{8}[/latex]	[latex]1 \frac{3}{8}[/latex]	[latex]3 \frac{1}{2}[/latex]
[latex]1 \frac{1}{2}[/latex]	8	1.405	[latex]2 \frac{3}{8}[/latex]	2.622	[latex]3 \frac{1}{4}[/latex]	2	[latex]1 \frac{1}{2}[/latex]	[latex]3 \frac{3}{4}[/latex]
[latex]1 \frac{5}{8}[/latex]	8	1.608	[latex]2 \frac{9}{16}[/latex]	2.828	[latex]3 \frac{1}{2}[/latex]	[latex]2 \frac{1}{8}[/latex]	[latex]1 \frac{5}{8}[/latex]	4
[latex]1 \frac{3}{4}[/latex]	8	1.980	[latex]2 \frac{3}{4}[/latex]	3.035	[latex]3 \frac{3}{4}[/latex]	[latex]2 \frac{1}{4}[/latex]	[latex]1 \frac{3}{4}[/latex]	[latex]4 \frac{1}{4}[/latex]
[latex]1 \frac{7}{8}[/latex]	8	2.304	[latex]2 \frac{15}{16}[/latex]	3.242	4	[latex]2 \frac{3}{8}[/latex]	[latex]1 \frac{7}{8}[/latex]	[latex]4 \frac{1}{2}[/latex]
2	8	2.652	[latex]3 \frac{1}{8}[/latex]	3.449	[latex]4 \frac{1}{4}[/latex]	[latex]2 \frac{1}{2}[/latex]	2	[latex]4 \frac{3}{4}[/latex]
[latex]2 \frac{1}{4}[/latex]	8	3.423	[latex]3 \frac{1}{2}[/latex]	3.862	[latex]4 \frac{3}{4}[/latex]	[latex]2 \frac{3}{4}[/latex]	[latex]2 \frac{1}{4}[/latex]	[latex]5 \frac{1}{4}[/latex]
[latex]2 \frac{1}{2}[/latex]	8	4.292	[latex]3 \frac{7}{8}[/latex]	4.275	[latex]5 \frac{1}{4}[/latex]	[latex]3 \frac{1}{16}[/latex]	[latex]2 \frac{3}{8}[/latex]	[latex]5 \frac{7}{8}[/latex]
[latex]2 \frac{3}{4}[/latex]	8	5.259	[latex]4 \frac{1}{4}[/latex]	4.688	[latex]5 \frac{3}{4}[/latex]	[latex]3 \frac{3}{8}[/latex]	[latex]2 \frac{5}{8}[/latex]	[latex]6 \frac{1}{2}[/latex]
3	8	6.324	[latex]4 \frac{5}{8}[/latex]	5.102	[latex]6 \frac{1}{4}[/latex]	[latex]3 \frac{5}{8}[/latex]	[latex]2 \frac{7}{8}[/latex]	7
[latex]3 \frac{1}{4}[/latex]	8	7.487	5	5.515	[latex]6 \frac{3}{4}[/latex]	[latex]3 \frac{7}{8}[/latex]	3	[latex]7 \frac{1}{2}[/latex]
[latex]3 \frac{1}{2}[/latex]	8	8.749	[latex]5 \frac{3}{8}[/latex]	5.928	[latex]7 \frac{1}{8}[/latex]	[latex]4 \frac{1}{8}[/latex]	[latex]3 \frac{1}{4}[/latex]	8
[latex]3 \frac{3}{4}[/latex]	8	10.108	[latex]5 \frac{3}{4}[/latex]	6.341	[latex]7 \frac{5}{8}[/latex]	[latex]4 \frac{3}{8}[/latex]	[latex]3 \frac{1}{2}[/latex]	[latex]8 \frac{1}{2}[/latex]
4	8	11.566	[latex]6 \frac{1}{8}[/latex]	6.755	[latex]8 \frac{1}{8}[/latex]	[latex]4 \frac{5}{8}[/latex]	[latex]3 \frac{5}{8}[/latex]	9

[latex]\begin{aligned} ext { force } F ext { in bolts } &=17,500 imes 1.405 \&=24,600 \ lb\end{aligned}[/latex]

From this table, clearance for wrench diameter is 3.75 in. Allowing for gusset fillet welds, the distance between gussets is as shown in Fig. 12.7b. From Eq. 12.13,

[latex]t=\sqrt{\frac{3.91 F}{S_{y}[2 b / a+a / 2 l-d(2 / a+1 / 2 l)]}}[/latex] (12.13)

where t = required base ring thickness on the tensile side of the neutral axis

F = bolt load

[latex]S_{y}[/latex] = yield stress of base ring

[latex]\begin{aligned}t &=\sqrt{\frac{3.91 imes 24,600}{36,000\left[(2 imes 6) / 5+5 /(2 imes 3)-1.625\left(\frac{2}{5}+1 /(2 imes 3) ight) ight]}} \&=1.07 in.\end{aligned}[/latex]

The designer at this point has a choice to make. One can either use a base ring thickness of 1.07 in., which is controlled by bolt load, or use a base ring thickness of 0.73 in. with anchor chairs, as shown in Fig. 12.7.

The stress in the shell is obtained from Eq. 12.14 as

[latex]\sigma=\frac{1.5 F b}{\pi t^{2} h}[/latex] (12.14)

where σ = allowable stress in shell

t = thickness of shell

F = bolt load

[latex]\begin{aligned}\sigma &=\frac{1.5 imes 24,600 imes 6}{\pi imes 0.75^{2} imes 12} \&=10,400 \ psi\end{aligned}[/latex]

This stress is combined with the axial stress and the total must be less than three times the allowable stress.

Question 12.3: Design the base ring shown in Fig. 12.7a. Stress in the bolt...

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