A set of three bolts is to be used to provide a clamping force of 12 000 lb between two components of a machine. The load is shared equally among the three bolts. Specify suitable bolts, including the grade of the material, if each is to be stressed to 75% of its proof strength. Then compute

Question

A set of three bolts is to be used to provide a clamping force of 12 000 lb between two components of a machine. The load is shared equally among the three bolts. Specify suitable bolts, including the grade of the material, if each is to be stressed to 75% of its proof strength. Then compute the required tightening torque.

Accepted Answer

The load on each screw is to be 4000 lb. Let’s specify a bolt made from SAE Grade 5 steel, having a proof strength of 85 000 psi. Then the allowable stress is
[latex]\sigma_a = 0.75(85 000[/latex] psi[latex]) = 63 750[/latex] psi
The required tensile stress area for the bolt is then

[latex]A_t=\frac{ ext{load}}{\sigma_a}=\frac{4000lb}{63750lb/in^2}=0.0627in^2[/latex]

From Table 19–4(B), we find that the 3/8–16 UNC thread has the required tensile stress area. The required tightening torque will be
[latex]T = KDP[/latex] = 0.15(0.375 in)(4000 lb) = 225 lb . in

TABLE 19–4 American Standard Screw Threads
B. American Standard thread dimensions, fractional sizes
Basic major diameter, D (in)	Coarse threads: UNC		Fine threads: UNF
Basic major diameter, D (in)	Size—Threads per inch, n	Tensile stress area (in[latex]{}^2[/latex])	Size—Threads per inch, n	Tensile stress area (in[latex]{}^2[/latex])
0.2500	[latex]1/4-20[/latex]	0.0318	[latex]1/4-28[/latex]	0.0364
0.3125	[latex]5/16-18[/latex]	0.0524	[latex]5/16-24[/latex]	0.058
0.3750	[latex]3/8-16[/latex]	0.0775	[latex]3/8-24[/latex]	0.0878
0.4375	[latex]7/16-14[/latex]	0.1063	[latex]7/16-20[/latex]	0.1187
0.5000	[latex]1/2-13[/latex]	0.1419	[latex]1/2-20[/latex]	0.1599
0.5625	[latex]9/16-12[/latex]	0.182	[latex]9/16-18[/latex]	0.203
0.6250	[latex]5/8-11[/latex]	0.226	[latex]5/8-18[/latex]	0.256
0.7500	[latex]3/4-10[/latex]	0.334	[latex]3/4-16[/latex]	0.373
0.8750	[latex]7/8-9[/latex]	0.462	[latex]7/8-14[/latex]	0.509
1.000	[latex]1-8[/latex]	0.606	[latex]1-12[/latex]	0.663
1.125	[latex]1\frac{1}{8}-7[/latex]	0.763	[latex]1\frac{1}{8}-12[/latex]	0.856
1.125	[latex]1\frac{1}{4}-7[/latex]	0.969	[latex]1\frac{1}{4}-12[/latex]	1.073
1.375	[latex]1\frac{3}{8}-6[/latex]	1.155	[latex]1\frac{3}{8}-12[/latex]	1.315
1.500	[latex]1\frac{1}{2}-6[/latex]	1.405	[latex]1\frac{1}{2}-12[/latex]	1.581
1.750	[latex]1\frac{3}{4}-5[/latex]	1.90
2.000	[latex]2-4\frac{1}{2}[/latex]	2.50

Question 19.1: A set of three bolts is to be used to provide a clamping for...

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