Screws, Fasteners, and the Design of Nonpermanent Joints
Thread geometry and the mechanics of power screws, then the complete analysis of bolted joints: fastener and member stiffness, the joint stiffness constant, preload, torque-tension relations, static and fatigue safety factors for tension joints, and bolted/riveted joints loaded in shear including eccentric loading.
8–1Thread Standards and Definitions
Learning objectives
- Read thread designations and distinguish pitch, lead, major, pitch, minor, and tensile-stress diameters.
- Model power-screw raising, lowering, friction, self-locking, and efficiency with a consistent torque convention.
- Calculate bolt and clamped-member stiffness and interpret external-load sharing before separation.
- Select preload and evaluate proof, separation, fatigue, and shear-joint failure modes.
- Document grade, lubrication, tightening method, standards edition, tolerances, and inspection requirements.
Geometry comes from a standard
Pitch \(p\) is axial spacing between adjacent threads; lead \(l\) is advance per revolution, so \(l=p\) for a single-start thread and \(l=mp\) for \(m\) starts. Major diameter \(d\), pitch diameter \(d_p\), and root diameter \(d_r\) serve different geometric and stress roles. The tabulated tensile-stress area \(A_t\), not the major-diameter area, represents tensile capacity of a standard threaded fastener.
Always record thread system, nominal size, pitch or threads per length, tolerance class, handedness when nonstandard, profile, and governing standard edition. Do not reconstruct production dimensions from a classroom approximation when certified tables are required.
Physical meaning
Unwrapping one turn of a helix produces an inclined plane with \(\tan\lambda=l/(\pi d_m)\). Power-screw torque is therefore a force-equilibrium problem on an inclined plane, while a preloaded bolt behaves as a tension spring coupled to compressed member springs.
Problem-solving strategy
- Recognize power transmission, preloaded tension, direct shear, slip-critical, or eccentric-joint behavior before selecting equations.
- Draw separate free bodies for the screw or bolt, nut, washers, and clamped members; define positive axial load and tightening torque.
- Obtain geometry, areas, proof and fatigue strengths, friction, and tightening scatter from traceable standards or supplied data.
- Calculate nominal load sharing while clamped, then check proof, separation, fatigue, bearing, net section, threads, and slip as applicable.
- Iterate size, grade, grip, preload, lubrication, and tightening process; verify assembly access and inspection capability.
8–2The Mechanics of Power Screws
Raising, lowering, and self-locking
For a square thread with positive torque defined in the commanded direction, thread friction opposes impending motion. A positive lowering torque means an applied torque is needed to lower: the idealized screw is self-locking. A negative result indicates back-driving tendency, but vibration and uncertain lubrication still require a brake or lock for safety-critical holding.
These relations assume steady Coulomb friction, rigid geometry, uniform collar contact represented by \(d_c\), and quasi-static motion. Acme threads require a thread-angle correction. Also check combined axial and torsional stress, buckling, bearing pressure, thread stripping, wear, thermal effects, and duty cycle.
Recognition strategy
A rotating helical interface plus an explicit collar identifies a power-screw equilibrium problem with two torque contributions, not a bolt torque–preload approximation.
Given information
- Positive torque drives the commanded raising or lowering motion; load acts downward.
- All friction coefficients are supplied test/design inputs and are assumed constant for this calculation.
Model and interpretation
Use a rigid, quasi-static square thread and uniform effective collar radius. Ignore acceleration, bearing rolling elements, lubricant heating, thread deformation, and start-up friction scatter.
Verification
Units: Each torque is force times metre; \(Fl\) and \(2\pi T\) are both joules per revolution, so their efficiency ratio is dimensionless.
Signs and direction: The positive thread lowering torque means the operator must apply torque to descend in this convention. Collar friction also opposes lowering, so it adds in magnitude rather than subtracting.
Plausibility: Raising torque exceeds lowering torque, both are positive, and efficiency is below unity. The large collar share \(18.24/45.28\approx40\%\) explains the modest efficiency.
Engineering interpretation
Collar friction dominates enough that a thrust bearing could materially reduce drive torque. Self-locking is not a certified holding device; wear, contamination, vibration, buckling, and thread/contact stresses still require checks.
8–3Threaded Fasteners
Bolt, screw, and stud load paths
A bolt is normally used with a nut, a cap screw engages a tapped member, and a stud has threads at both ends. Fatigue-critical locations include the first engaged thread, thread runout, and under-head fillet. Ensure adequate thread engagement, edge distance, wrench access, washer bearing area, corrosion compatibility, and replaceability.
8–4Joints — Fastener Stiffness
The bolt as series springs
Within the grip, threaded and unthreaded lengths stretch under the same axial force. Their compliances add. A longer elastic grip generally lowers bolt stiffness and the fraction of external cyclic load entering the bolt, but packaging and joint movement impose limits.
8–5Joints — Member Stiffness
Compressed members are not a solid cylinder
Compression spreads outward beneath the head, nut, or washer. Pressure-cone or finite-element models estimate member compliance; layered materials combine in series. Geometry near edges, holes, gaskets, composites, and thin flanges may invalidate a simple cone model, so test or validated simulation may be necessary.
Here \(F_m\) denotes remaining compressive clamping magnitude. The linear sharing equations cease to apply after \(F_m=0\), because separated members no longer provide the same spring path.
Recognition strategy
The joint remains intended to be clamped and both bolt and member stiffnesses are available, so use the two-spring load-sharing model before checking proof and separation margins.
Given information
- Positive \(P\) opens the joint; positive \(F_i\) is initial bolt tension and member compression.
- The member stiffness and proof strength are supplied, traceable inputs rather than inferred catalog values.
Model and interpretation
Assume concentric axial loading, linear elastic springs, rigid load introduction, no embedding loss, and no separation. Verify the last assumption from remaining clamp force.
Verification
Units: \(EA/L\) gives \(\mathrm{N/mm}\); multiplying \(\mathrm{mm^2}\) by \(\mathrm{N/mm^2}\) gives proof load in newtons, and both factors are dimensionless ratios.
Signs and direction: External opening load increases bolt tension by \(CP=4.41\ \mathrm{kN}\) while reducing compression by \((1-C)P=13.59\ \mathrm{kN}\); their sum recovers \(P\).
Plausibility: Because \(k_m\) is about three times \(k_b\), \(C\) should be below \(0.5\). Positive remaining compression independently confirms that the no-separation model is applicable at the stated load.
Engineering interpretation
The members carry most of the external-load change, demonstrating why preload can protect a bolt from cycling. Real preload scatter, relaxation, eccentricity, washer embedding, and proof data for the purchased lot must be addressed.
8–6Bolt Strength
Proof strength is not applied stress
Proof strength \(S_p\), yield strength \(S_y\), and ultimate strength \(S_{ut}\) describe standardized fastener capacity under specified tests; bolt stress arises from preload and external loading. Grade markings alone do not establish authenticity, coating effects, hydrogen-embrittlement control, temperature capability, or fatigue performance.
The preload fraction \(\alpha\) is a project input tied to reuse, tightening accuracy, lubrication, relaxation, and required clamp force. It must not be treated as universally safe.
8–7Tension Joints — The External Load
Clamp first, separation second
While clamped, external tension is divided by stiffness. At separation, contact stiffness changes abruptly and the bolt approaches carrying the full incremental load. Eccentric load also bends the flange and bolt, requiring a model beyond concentric axial sharing.
8–8Relating Bolt Torque to Bolt Tension
Torque is an indirect preload control
The screening relation \(T=KF_id\) bundles thread and bearing friction into nut factor \(K\). Most input torque is dissipated by friction, so modest friction variation creates large preload scatter. Never assume a generic \(K\) for coated or lubricated fasteners; qualify it by supplier data or representative testing.
For critical joints, consider calibrated torque, torque-angle, turn-of-nut, tension-indicating washers, ultrasonic elongation, or direct-tension methods, with documented tool calibration and tightening sequence.
8–9Statically Loaded Tension Joint with Preload
Independent static checks
Proof factor checks maximum bolt tension; overload factor asks how much the stated external load can increase before proof; separation factor checks remaining clamp. Passing one does not imply passing the others.
8–10Gasketed Joints
Sealing changes the objective
A gasket requires adequate and reasonably uniform seating stress without crushing, extrusion, or excessive relaxation. Its nonlinear, time-dependent stiffness means the simple metal-member cone model may be unsuitable. Use gasket supplier curves and the applicable pressure-boundary code for seating, operating, flange rotation, bolt pattern, and leakage checks.
8–11Fatigue Loading of Tension Joints
Preload reduces bolt stress amplitude
For external load cycling from \(P_{\min}\) to \(P_{\max}\) while clamped, bolt-force amplitude is \(C(P_{\max}-P_{\min})/2\). Mean bolt force includes preload. Evaluate local fatigue at the first engaged thread with suitable fatigue data and concentration treatment, then separately check maximum proof load and minimum clamp.
Recognition strategy
A repeated opening load on a preloaded joint requires three separate decisions: Goodman fatigue, minimum clamp against separation, and maximum bolt load against proof.
Given information
- Positive external load opens the joint; load varies from zero to the stated maximum.
- Areas, stiffness constants, and strengths are explicitly supplied candidate or certified data and must be confirmed for procurement.
Model and interpretation
Assume concentric linear-elastic load sharing while clamp remains positive, no preload loss, and a Goodman representation of the supplied threaded-assembly fatigue limit.
Verification
Units: Kilonewtons divided by square millimetres are converted consistently to \(\mathrm{N/mm^2}=\mathrm{MPa}\); force and stress safety factors are dimensionless.
Signs and direction: Opening load increases bolt tension and relieves member compression. At zero external load, bolt stress returns to the positive preload stress rather than reversing into compression.
Plausibility: Both candidates have small cyclic bolt increments because \(C<0.5\). M16's larger area and slightly lower \(C\) reduce amplitude, while its \(450\ \mathrm{MPa}\) preload stress remains the same fraction of proof.
Engineering interpretation
The M16 passes the supplied deterministic criteria with little fatigue margin. Preload scatter, relaxation, thread-root fatigue data, eccentricity, corrosion, tightening process capability, and service load spectra require validation before release.
8–12Bolted and Riveted Joints Loaded in Shear
Bearing-type and slip-resistant behavior
In a bearing-type joint after slip, check fastener shear, plate bearing, tear-out, and net-section tension using actual load distribution. In a slip-resistant joint, preload and qualified faying-surface slip resistance carry service shear; do not mix that model with post-slip bearing equations. Eccentric loads add moment and nonuniform fastener forces.
Chapter recap
- Use standardized thread geometry and tensile-stress area, with lead distinguished from pitch.
- For power screws, include thread and collar friction, interpret torque sign, and check stresses, wear, and holding safety.
- For preloaded joints, derive stiffness sharing and separately verify proof, separation, fatigue, and member failure.
- Treat tightening friction and preload scatter as design uncertainties controlled by process and inspection.
Before moving on: You should be able to draw the joint load path, select the correct equation family, calculate and audit load sharing, and identify the standard, supplier, test, and code data still needed for a professional decision.