machinedesign_bolt1

Apr. 20, 2010

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How External Loads Affect Bolted JointsForces that overcome preload can cause bolted assemblies to leak, rattle, and fail.

Kenneth Korane | Machine Design

Authored by:

Moo-Zung Lee

West Hills, Calif.

Edited by Kenneth J. Korane

[email protected]

Key points:

External loads that exceed the preload can cause joints to leak and assemblies to rattle.

Controlling separation load is critical for precision preloading on mechanisms such as

bearings.

Resources:

Structural Properties of Bolted Joints, Machine Design, Feb. 18, 2010, p. 44.

Detailed free-body diagrams of bolted joints can be found in Juvinall and Marshcek,

Fundamentals of Machine Component Design, John Wiley & Sons, 1991

Understanding the structural behavior of bolted joints is paramount for good designs, and

one key factor is how joints react to external loads.

In sorting out these reactions, remember that preloaded bolted joints are integral mechanical

components consisting of a bolt and clamped members. Its structural properties markedly differ

from those of the bolt itself.

Bolt and member forces

As the accompanying loading-process diagrams depict, a bolt reacts with tension when

the nut is tightened to clamp joint members. The bolt stretches and clamped members

compress from their free states by b and c, respectively. Bolt tension and clamped-

member compression equal the initial clamping (preload) force, Fi, in absolute terms.

Sign convention shows positive force for tension and negative for compression:

Fb = kbb = Fi, and

Fc = kcc = -Fi.

Applying an external force, Fe, to the preloaded joint elongates the bolt by x, and forces in the

bolt and clamped members readjust. As long as external force is not enough to completely relieve

the preload, the following relations hold:

Fb(x) = Fi + kbx,

Fc(x) = Fi + kcx, and

Fb(x) + Fc(x) = Fe(x).

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Page 1 of 4How External Loads Affect Bolted Joints | Archive content from Machine Design

2013-04-29http://machinedesign.com/archive/how-external-loads-affect-bolted-joints

Substituting x = Fe/(kb + kc) links forces of the bolt and clamped member directly to the

external force and eliminates the need to know the displacement. If we define the bolt

load-sharing ratio as:

= kb/(kb + kc), then

Fb(x) = Fi + Fe and

Fb(x) = Fi + (1 )Fe.

The Fb(x) equation indicates combined bolt tension is the sum of the initial tension from

preload and a portion of the external load. The bolt load-sharing ratio is the fraction of

external load on the bolt, with 0 <

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ke = Fe/x = kb + kc.

After joint separation, Fc = 0, the bolt bears the entire external load, and joint stiffness

equals bolt stiffness, ke = kb.

The external-force paradox

Because an external pull increases bolt tension and decreases member compression at the

same time, shouldnt the magnitude of the external force equal the difference of the two?

If so, then joint stiffness should be the difference between the stiffnesses of the bolt and

members.

The diagrams that show external force as the sum of changes in bolt and member force treat

external loading as if it were a two-step process. An external load is assumed to stretch the bolt

first and then relieve compression on the members.

Suppose an external force, Fe, of unknown magnitude stretches a preloaded bolted joint at

the seating plane of the nut by x from preloaded conditions. It needs an external force, F1

= kbx, just to elongate the bolt beyond its preloaded condition. Because clamped members

must also relax by x from their initially compressed state, the clamping force must be

reduced by F2 = kcx. Because clamping force comes from the nut, an external force F2 is

required to compel the nut to relent (without rotating). F2 is in addition to the bolt

stretching force F1. Therefore, the total external force is: Fe = F1 + F2.

The two forces take parallel routes. Force F1 follows the path from the nut through the

thread engagement and bolt rod and to the bolt head on the other end. Force F2 travels

from the seating surface of the nut through the clamped members, then reaches the bolt

head. F1 increases bolt tension, F2, reduces member compression.

The root of the paradox is due to the deviation from the sign convention of forces. An

external pull increases bolt tension and decreases member compression at the same time.

Member compression is a negative force. Decreasing a negative force in absolute

magnitude requires a positive force.

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