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Machine Design # Force Calculations for Bolted Joints

Bolted joints are often tightened to 75% to 80% of bolt proof load. This amount of tightening, a rule of thumb, is suitable for many joints, but in some cases, external tensile loads can reduce bolt clamping force to zero. Thus, for some joints, values other than 75% or 80% are needed.

The amount of external tensile force that reduces clamping to zero is given, within the elastic limits of the blot and clamped parts, by:

(Fe/FPR)0 = (Fb/FPR)0

= ((1+r)/r)(Fi/FPR)

where r = Kp/Kb

and Fe is the external load on the joint (lb), FPR is the bolt proof load (lb), Fb is bolt load (lb), Fi is bolt preload (lb), Kp is the spring constant for the clamped members (lb/in), Kb is the spring constant for the bolt (lb/in), and the subscript 0 identifies a value at zero clamping load.

The maximum force that can be applied to a specific joint without the parts separating can be calculated with this equation. For common values of r, the force can determined from the accompanying graph, which is based on the equation. The bolt preload that produces a given non-zero clamping force can be determined from the above graph in combination with the equation:

Fe/FPR = (1-b)(Fe/FPR)0

Where b = |Fp/Fi|

And the corresponding bolt load can be computed from:

Fb/FPR = (Fe/FPR)0Fi/FPR)(b/r)

For example: For a bolted joint where r is 10 and Fi/FPR is 0.75, the graph gives:

(Fe/FPR)0 = (Fb/FPR)0

For a clamping force equal to 25% of the  preload (b=0.25),

(Fe/FPR)=(1-0.25)(0.825)

=0.619

And (Fb/FPR)=0.825-(0.75)(0.5)/10

=0.806

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