Threaded Joints

Threaded joints are detachable connections made with bolts, screws, studs, nuts, and threaded holes. Their behavior is governed not only by bolt strength but also by preload, joint stiffness, friction, and the load path through the clamped parts.

Thread geometry and force

For a power-law estimate of tensile stress in a bolt, use the tensile stress area \(A_s\):

$$\sigma=\frac{F_b}{A_s}.$$

Preload is commonly introduced by tightening torque:

$$T\approx K F_V d,$$

where \(K\) represents thread and bearing-surface friction. Because friction varies, torque control gives appreciable preload scatter.

Joint stiffness

The bolt and clamped members act as elastic springs. Under an external separating force \(F_A\), the bolt load increase is

$$\Delta F_b=\Phi F_A,\qquad \Phi=\frac{c_b}{c_b+c_m},$$

while clamping force decreases by \((1-\Phi)F_A\). Separation must be prevented unless the joint is specifically designed for it.

Checks

• bolt tension and combined tension–torsion during tightening;
• fatigue at the first engaged threads and under-head transition;
• bearing, shear, and tear-out of connected parts;
• slip resistance when transverse force is carried by friction;
• thread stripping, embedment, relaxation, and self-loosening.

For a friction-grip joint, a preliminary slip condition is \(F_t\le \mu m F_V/n_s\), where \(m\) is the number of friction interfaces.

Thread forms and fastener classes

ISO metric threads are defined by nominal diameter, pitch, and tolerance class. Coarse threads are generally more tolerant of damage and assembly variation; fine threads provide a larger tensile area and finer axial adjustment but are more sensitive to contamination and stripping. Property classes define minimum strength characteristics and must be matched with compatible nuts.

Tightening and preload control

The tightening torque is divided mainly between thread friction and friction under the nut or bolt head; only a small fraction produces useful bolt tension. More reliable methods include turn-of-nut control, direct tension indicators, hydraulic tensioning, ultrasonic measurement, and torque-plus-angle procedures. Lubrication changes the torque coefficient and must be specified.

Separation and slip

Before separation, an external tensile load is shared according to bolt and member stiffness. After separation, the bolt may receive nearly the entire additional load and fatigue damage rises sharply. Under transverse load, a preloaded friction joint should remain below its slip resistance. If slip is permitted, bolt shear, hole bearing, and joint movement must be checked.

Thread stripping

Internal and external threads are checked over the effective engagement length. The weaker material, thread geometry, radial expansion of the nut, and unequal load carried by the first threads affect stripping resistance. Excess engagement length does not produce proportional strength because load distribution is nonuniform.

Fatigue and self-loosening

Critical locations are the first engaged thread, thread run-out, and under-head fillet. Rolled threads, smooth transitions, adequate preload, and reduced eccentricity improve endurance. Transverse cyclic slip can cause rotational loosening; locking devices should supplement, not replace, proper preload and joint stiffness.

Calculation sequence

1. Determine external axial, transverse, and eccentric actions.
2. Select fastener class, size, and joint layout.
3. Choose preload and tightening method.
4. Check assembly stress, service bolt force, separation, and slip.
5. Check fatigue, thread stripping, bearing, connected parts, and relaxation.
6. Specify lubrication, locking, tightening order, and inspection.