Fasteners, Power Screws and Permanent Joints

Introduction

Fastened joints connect machine members so that forces, moments, heat, vibration, and environmental loads can be transmitted safely. The designer must decide not only whether a joint is strong enough, but also whether it can be manufactured, assembled, inspected, serviced, and kept secure throughout its intended life.

This chapter treats two broad families of joints. Temporary joints, such as bolted and screwed joints, can be dismantled without destroying the connected parts. Permanent joints, such as welded, riveted, brazed, and adhesively bonded joints, are normally not intended for nondestructive disassembly. Their design is governed by load transfer, stress concentration, fatigue, stiffness, temperature, corrosion, and manufacturing process.

A sound design begins with a load path. External forces must be transferred through the joint with acceptable deformation and without separation, slip, yielding, fatigue cracking, leakage, or loss of preload.

Learning objectives

After completing this chapter, the reader should be able to:

1. Explain the behavior of preloaded bolted joints under tensile, shear, and eccentric loading.
2. Select threaded fasteners, locking arrangements, and tightening methods.
3. Analyze and design power screws for torque, self-locking, efficiency, and strength.
4. Design eccentric bolted and welded joints using direct and moment-induced loads.
5. Compare welded, riveted, brazed, and adhesive joints for strength, fatigue, manufacturing, and serviceability.
6. Identify relevant standards, inspection requirements, safety factors, and failure modes.

1. Threaded fasteners and joint terminology

A bolt normally has an externally threaded shank and is tightened with a nut; a screw may engage an internal thread in one of the connected members. Important terms include pitch, lead, major diameter, minor diameter, pitch diameter, thread angle, grip length, preload, proof load, and prevailing torque. For a single-start thread, lead equals pitch. For a multiple-start thread, lead is the axial advance per revolution and is greater than pitch.

Fasteners are selected by diameter, thread form, material, strength class, corrosion resistance, head form, and applicable standard. Metric property classes such as 8.8 and 10.9 identify minimum strength levels, but the designer must use the actual standard and supplier data for detailed design. The nominal tensile-stress area, A_t, rather than the gross shank area, is generally used when checking threaded tensile capacity.

The tensile stress area is commonly approximated for a metric thread by

where d is nominal major diameter and p is pitch, both in the same length units. This approximation applies to standard metric V-threads and should be replaced by the area specified in the relevant standard when precision is required.

The tensile stress in a fastener is

where F_b is the bolt axial force and A_t is tensile-stress area. The nominal direct shear stress is

where V is shear force and A_s is the area resisting shear. In a threaded section, the effective shear area depends on whether the shear plane passes through the threads; this must be checked rather than assumed.

2. Preloaded bolted joints

2.1 Purpose of preload

A bolt is tightened so that it elongates and the clamped members compress. The resulting tensile bolt force is the preload, F_i. Preload improves joint stiffness, prevents separation, reduces alternating stress in the bolt, and may prevent slip in friction-grip joints. Excessive preload can strip threads, crush soft members, yield the bolt, or cause leakage and distortion.

A useful idealized model consists of a bolt spring and a clamped-member spring in series. Let k_b be bolt stiffness and k_m be clamped-member stiffness. Under an external separating load P, the fraction carried by the bolt is

and the changes in bolt and member forces are

The member force decreases by ∆F_m, while the bolt force increases by ∆F_b. These relations assume linear elastic behavior, concentric loading, constant stiffness, and no joint separation.

The bolt force after loading is therefore

Joint separation begins approximately when the clamping force falls to zero:

This expression is an idealization. Embedment, gasket behavior, bending, prying, nonuniform contact, and local plasticity can substantially change the actual separation load.

If F_p is the proof load of the fastener and n_p is a selected preload factor, a preliminary preload may be written as

Typical design practice often places preload near 70–80% of proof load for reusable steel fasteners, but the permissible value depends on standard, tightening accuracy, joint material, lubrication, temperature, and service requirements. It must not be treated as a universal rule.

2.2 Bolt and member stiffness

For a uniform bolt of length L_b, modulus E_b, and effective area A_b,

For a simplified uniform clamped member of length L_m, area A_m, and modulus E_m,

Real joints usually have a pressure cone rather than a uniform cylindrical compression zone. Consequently, k_m is often obtained from an equivalent-area model, finite-element analysis, or experimental data. The stiffness ratio is particularly important: a flexible bolt and stiff members give a small C, reducing the bolt’s alternating load.

2.3 Combined loading and failure checks

For a bolt subjected to axial force and direct shear, a common preliminary interaction check uses von Mises equivalent stress:

The check is appropriate for ductile fastener material under static loading when nominal stresses adequately represent the critical section. Thread-root stress concentration, bending, fatigue, and installation damage require additional evaluation.

For a bearing-type bolted connection, possible limit states include bolt shear, bolt tension, bolt bending, bearing or crushing of the connected plate, net-section tension, block shear, tear-out, thread stripping, and prying. For a slip-critical connection, frictional slip is also a limit state. The applicable resistance equations should be taken from the governing design code, such as a recognized structural steel, pressure-vessel, or machine-design standard.

Worked example 1: preload and external separation load

A preloaded joint has bolt stiffness k_b = 1.0×10⁶ N/mm and member stiffness k_m = 3.0×10⁶ N/mm. The initial preload is 18 kN. Determine the bolt-load fraction and the idealized separation load.

Thus, before separation, 25% of an applied separating load increases bolt tension and 75% reduces member compression. The result is valid only for the assumed linear, concentric joint model.

3. Tightening, locking, and service reliability

The torque required to produce preload is affected by thread friction, under-head or nut friction, thread condition, lubrication, and tool accuracy. A widely used preliminary relation is

where T is tightening torque, K is an empirical nut factor, F_i is preload, and d is nominal diameter. Because K can vary widely, torque control alone may produce large preload scatter. Angle-controlled tightening, tension-indicating bolts, hydraulic tensioning, or direct ultrasonic elongation measurement may be preferable for critical joints.

Locking methods must address the actual cause of loosening. Important categories are:

• Prevailing-torque nuts: distorted-thread or polymer-insert nuts resist rotation; they are less suitable for high temperature or repeated reuse unless approved.
• Chemical threadlockers: anaerobic adhesives fill the thread clearance and resist vibration; surface preparation, cure, temperature, and service chemical compatibility matter.
• Mechanical locking: castellated nuts with cotter pins, safety wire, tab washers, lock plates, and positive retainers prevent rotation by geometry.
• Wedge-locking washers: paired inclined surfaces create a wedge effect under vibration; correct installation is essential.
• Jam nuts and double nuts: useful in selected applications, but their preload and space requirements must be controlled.

A split lock washer should not automatically be regarded as a reliable anti-vibration solution. Locking devices do not compensate for inadequate preload, poor joint stiffness, contaminated surfaces, or unsuitable design.

4. Eccentric bolted joints

An eccentric joint carries a resultant force whose line of action does not pass through the bolt-group centroid. The load produces direct shear and a moment. For a group of bolts subjected to in-plane force V and moment M = Ve, the direct shear per identical bolt is

where n is the number of bolts. Under the elastic method, the moment-induced shear in bolt i is proportional to its distance r_i from the bolt-group centroid:

The vector directions are tangential about the centroid. Direct and moment-induced shear must therefore be added as vectors, not as ordinary scalar magnitudes. The bolt with the largest resultant is checked for shear, bearing, and connected-member failure.

For a bolt group carrying a tensile or shear force with an out-of-plane eccentricity, the same principle applies to the appropriate rotational stiffness model. If the joint permits contact opening, prying, or bolt-group rotation, a rigid elastic distribution may be nonconservative.

Worked example 2: simple eccentric bolt group

Four identical bolts form a square of side 100 mm, centered at the origin. A horizontal shear force of 8 kN acts through the centroid, and an in-plane moment of 0.8 kN·m acts about the centroid. Each bolt is 70.71 mm from the centroid. The direct shear is 2 kN per bolt. Since

the moment-induced shear magnitude at each bolt is

The moment-induced vectors are tangential and differ in direction. At a bolt where the direct and moment-induced components act in the same direction, the resultant is approximately 2.0 + 2.828 = 4.828 kN. At the opposite location, they may partially cancel. A complete design must resolve both components in x–y directions and then check the maximum resultant. This example illustrates why adding all bolt loads uniformly is unsafe or unnecessarily conservative.

5. Power screws

Power screws convert rotary motion into axial force. They are used in screw jacks, vices, presses, lifting tables, and actuators. Common forms include square, Acme, and trapezoidal threads. Square threads have high efficiency, whereas Acme or trapezoidal threads are stronger, easier to manufacture, and better suited to practical machinery.

Let d_m be mean thread diameter, l lead, α lead angle, μ coefficient of friction, and λ thread half-angle. For a single-start thread,

For a V-thread, an effective friction coefficient is often approximated by

This approximation treats thread friction through an equivalent square-thread model. It is suitable for preliminary design, not for detailed efficiency certification.

For raising a load W with a square-thread screw, the torque at the thread is

For lowering the load,

A collar or thrust bearing adds torque. For a uniform-friction collar with mean collar diameter d_c and collar friction coefficient μ_c,

Thus, total raising torque is approximately T = T_thread + T_c. The screw efficiency, excluding or including the collar as stated, is

Self-locking during lowering requires positive resisting torque, approximately

for a square thread. If this condition is not met, the screw may back-drive; a brake or separate locking device is then necessary. Vibration, lubrication, wear, and dynamic effects can invalidate an assumption of self-locking.

Power-screw design also checks compressive stress, buckling, thread stripping, wear pressure, nut length, shaft torsion, key or collar stresses, and thermal effects. For a long screw under compression, Euler buckling is a useful screening check:

where E is Young’s modulus, I is the second moment of area, L is unsupported length, and K is the effective-length factor determined by end conditions. The applied compressive load must be suitably below the critical load, with code-appropriate safety treatment.

6. Welded joints

Welding creates a metallurgical connection. Common processes include shielded metal arc, gas metal arc, gas tungsten arc, flux-cored arc, submerged arc, resistance, laser, and friction welding. The design must consider weld type, effective throat, parent-metal strength, weld-metal strength, residual stress, distortion, heat-affected-zone properties, inspection class, and fatigue detail category.

For a fillet weld with leg size s, the ideal effective throat is

For a weld length L, the nominal throat area is A_w = aL. Average throat shear is

For a weld group subjected to a moment, the elastic method distributes moment-induced throat shear in proportion to distance from the weld-group centroid, analogous to an eccentric bolt group. Direct and moment-induced components are resolved vectorially. The design standard may use a combined normal-and-shear interaction rather than a simple von Mises check; the governing code must control.

Welded joints are efficient and economical for fabrication, but residual stress and geometric discontinuities can reduce fatigue strength. Smooth transitions, adequate weld size, avoidance of abrupt termination, good fit-up, qualified procedures, and nondestructive examination are central to reliability. Oversizing a weld can increase distortion and residual stress without improving fatigue performance.

7. Riveted joints

Riveting remains important in aircraft, boilers, bridges, heritage structures, and applications where heat input or field repair constraints make welding unsuitable. A riveted lap or butt joint may fail by rivet shear, plate bearing, plate tearing across a hole, edge tear-out, or joint crushing.

For a rivet of diameter d_r in single shear, the nominal shear area is

The tearing strength of a plate strip of thickness t, width w, and pitch p is based on the net width p − d_h, where d_h is hole diameter:

The bearing capacity of one rivet is commonly screened by

These expressions are simplified and must be supplemented by joint efficiency, row interaction, eccentricity, fatigue, corrosion, and applicable structural code provisions. Riveted joints require hole-quality control and attention to access for installation.

8. Brazed and soldered joints

Brazing joins materials using a filler metal whose melting temperature is above approximately 450 °C but below the melting temperature of the base materials. Soldering uses lower-temperature filler metals. The base metal normally does not melt, which reduces distortion and permits joining dissimilar materials.

Strength depends on overlap, clearance, surface preparation, filler-metal wetting, joint temperature, load direction, and service environment. A long lap joint should not be assumed to develop uniform shear because load transfer is concentrated near the ends. Brazed joints are often designed so that the principal load is carried in shear or compression rather than peel. Cleanliness and controlled clearance are essential; excessive clearance can reduce capillary action and strength.

9. Adhesively bonded joints

Adhesives transfer load through a continuous layer and distribute stress over a broad area. They can join dissimilar materials, seal against moisture, damp vibration, and avoid holes or thermal distortion. Common systems include epoxies, acrylics, cyanoacrylates, polyurethanes, and structural anaerobics.

A first estimate of average adhesive shear stress is

where F is transmitted load, b is bond width, and L is overlap length. This is only an average. Elastic shear-lag models show that stress is highest near overlap ends, especially when adherends are stiff and the adhesive is thin. Peel stress caused by bending is usually more damaging than uniform shear.

Good bonded-joint design uses long, tapered or scarfed overlaps where practical; avoids peel and cleavage; controls bond-line thickness; provides surface preparation and cure control; and verifies environmental durability. Temperature, moisture, chemicals, ultraviolet exposure, creep, and inspection limitations must be considered. Adhesive joints may be unsuitable where immediate full strength, high service temperature, or easy nondestructive inspection is required.

10. Fatigue and manufacturability

Joints often fail by fatigue at threads, weld toes, bolt holes, abrupt section changes, and adhesive overlap ends. Fatigue design requires the service load spectrum, stress concentration, mean stress, surface condition, residual stress, environment, and detail category. Preloaded bolts are advantageous because a properly designed joint keeps external load changes mainly in the clamped members, thereby reducing bolt stress range.

Manufacturability includes tool access, tolerance stack-up, standard component availability, assembly sequence, inspection access, repairability, and process capability. A joint that is theoretically strong but impossible to tighten correctly is not a successful design. Designers should specify torque or tension procedure, lubrication condition, locking method, inspection acceptance criteria, and replacement requirements.

11. Applied case: removable gearbox mounting joint

Background

An illustrative gearbox is mounted to a steel frame by four preloaded bolts. The gearbox produces vibration and a horizontal reaction, while the mounting faces must remain in contact to prevent fretting.

Problem

A preliminary design using lightly tightened bolts experienced loosening and fretting at the interface. The load direction was eccentric relative to the bolt-group centroid, and assembly personnel used an uncontrolled impact wrench.

Analysis

The joint was re-evaluated as a preloaded friction joint. The designer calculated bolt-group direct shear and moment-induced shear, selected a preload below the bolt proof load, and checked separation under the maximum overturning load. The interface friction capacity was then assessed using the specified surface condition and a suitable design coefficient. Bolt stiffness and member stiffness were estimated to determine the change in bolt force under external tension.

Solution

The revised design used property-class fasteners compatible with the frame material, hardened washers to prevent embedment, calibrated torque-angle tightening, and a prevailing-torque retention method approved for the operating temperature. The mounting surfaces were machined and cleaned, and dowels were added to transmit locating shear without relying on bolt shanks. The procedure specified a cross-pattern tightening sequence and periodic inspection.

Outcome

The improved joint maintained contact under the design load, reduced fretting, limited preload scatter, and made maintenance verifiable. The dowels did not replace preload; they provided positive location and reduced reliance on friction for transverse positioning.

Learning points

1. Loosening is usually a system problem involving preload, stiffness, vibration, and surface movement.
2. A locking device cannot correct inadequate tightening or joint separation.
3. Eccentricity must be included in bolt-group analysis.
4. Assembly and inspection procedures are part of the mechanical design.

12. Standards, safety, and professional practice

Fastener and joint design should follow the applicable standard for the machine, pressure equipment, structural application, or transport sector. Standards define materials, dimensions, proof testing, tightening procedures, weld qualification, inspection, allowable stresses, and acceptance criteria. Traceability is important for safety-critical fasteners and weld consumables.

Engineers must distinguish nominal calculations from certified design. Where failure could cause injury, environmental release, or major economic loss, independent review, validated software, proof testing, and documented inspection are appropriate. Digital tools and finite-element analysis can reveal load paths and stress concentrations, but they do not replace correct boundary conditions, material data, mesh convergence, or physical validation. AI-assisted design may help compare standard fasteners or identify design alternatives, but final decisions require competent engineering judgment and auditable sources.

Chapter Summary

Temporary joints use preload, friction, geometry, or mechanical engagement to transmit load while permitting disassembly. In a preloaded bolt joint, bolt and member stiffness determine how an external separating load is shared. The bolt-load fraction is C = k_b/(k_b + k_m), and separation must be checked rather than assumed impossible. Fastener design includes tensile, shear, bearing, thread, fatigue, preload, and environmental checks.

Eccentric bolt groups carry direct load and moment-induced load; the components must be combined as vectors. Locking methods should be selected for the actual loosening mechanism and service environment. Power screws are designed from lead angle, friction, torque, efficiency, self-locking, strength, wear, and buckling considerations.

Welded joints require attention to effective throat, weld-group geometry, residual stress, fatigue details, distortion, and inspection. Riveted joints are checked for rivet shear, plate bearing, net-section tearing, and edge failure. Brazed and adhesive joints depend strongly on overlap, surface preparation, temperature, environmental durability, and avoidance of peel. Across all joint types, load path, fatigue, manufacturability, standards, and assembly control determine practical reliability.

Key Terms

Preload: Initial tensile force introduced into a fastener during tightening.

Proof load: Specified test load a fastener must withstand without unacceptable permanent deformation.

Tensile-stress area: Effective threaded area used for nominal tensile calculations.

Grip length: Thickness of material clamped by a fastener.

Joint stiffness: Resistance of the bolt or clamped members to elastic deformation.

Separation: Loss of compressive contact between clamped members.

Nut factor: Empirical factor relating tightening torque to preload.

Prevailing torque: Torque resisting nut rotation due to a locking feature.

Eccentric joint: Joint in which the load line is offset from the joint-group centroid.

Power screw: Threaded device that converts rotary motion into axial force or displacement.

Lead angle: Angle describing screw lead relative to the mean thread circumference.

Self-locking: Condition in which a screw does not back-drive under load.

Fillet weld: Triangular-section weld joining approximately perpendicular surfaces.

Effective throat: Effective dimension used to calculate fillet-weld resisting area.

Heat-affected zone: Base-metal region whose properties change during welding.

Riveted joint: Permanent mechanical joint formed by a rivet installed through aligned holes.

Brazing: Joining with a filler metal melting above about 450 °C without melting the base metal.

Adhesive bond: Joint formed by an adhesive layer between adherends.

Peel stress: Stress tending to separate an adhesive joint normal to its interface.

Joint efficiency: Ratio of joint strength to the strength of an unjointed reference section.

Review Questions

Short Answer Questions

1. Why is preload introduced into a bolted joint?
2. Define the bolt-load fraction C and state what it represents.
3. Name four possible failure modes of a bolted plate connection.
4. What condition approximately produces self-locking in a square-thread power screw?
5. Why is peel generally undesirable in an adhesive joint?

Long Answer Questions

1. Explain the spring model of a preloaded bolted joint and derive the expressions for bolt-load increase and separation load.
2. Describe the analysis procedure for an eccentric bolt group carrying direct shear and an in-plane moment.
3. Derive or explain the principal torque components of a power screw and discuss the effect of a thrust collar.
4. Compare welded, riveted, brazed, and adhesive joints in relation to strength, fatigue, inspection, and manufacturability.
5. Discuss tightening accuracy, locking methods, and the relationship between preload and vibration loosening.

Analytical / Application Questions

1. A joint has preload 25 kN, bolt stiffness 0.8 MN/mm, and member stiffness 2.4 MN/mm. Calculate the bolt-load fraction and idealized separation load. State the assumptions behind your result.
2. Design an initial analysis plan for a four-bolt gearbox flange subjected to direct shear, overturning moment, temperature variation, and vibration. Identify the required strength, fatigue, preload, locking, and inspection checks.
3. A bonded lap joint is being considered instead of a welded joint for a lightweight machine cover. Evaluate the choice for static load, cyclic load, temperature, moisture, repair, and nondestructive inspection, and recommend additional validation tests.

Multiple Choice Questions with Answers

Question 1

In the linear spring model of a preloaded joint, the fraction of an external separating load carried by the bolt is C = k_b/(k_b + k_m). What happens to C when the clamped-member stiffness increases while bolt stiffness remains constant?

A. It increases

B. It decreases

C. It becomes exactly one

D. It becomes independent of stiffness

Correct Answer: B. It decreases

Question 2

A joint has bolt stiffness 1 MN/mm and member stiffness 3 MN/mm. What is the bolt-load fraction?

A. 0.20

B. 0.25

C. 0.50

D. 0.75

Correct Answer: B. 0.25

Question 3

Which condition approximately gives self-locking for a square-thread power screw during lowering?

A. μ < tan α

B. μ = 0 for all lead angles

C. μ > tan α

D. α = 90°

Correct Answer: C. μ > tan α

Question 4

For a fillet weld with leg size s, the ideal effective throat is approximately:

A. 0.25s

B. 0.500s

C. 0.707s

D. 1.414s

Correct Answer: C. 0.707s

Question 5

Why must direct and moment-induced loads in an eccentric bolt group be combined as vectors?

A. Because all bolts have different material strengths

B. Because their directions vary around the bolt-group centroid

C. Because preload is always zero

D. Because moment has no units

Correct Answer: B. Because their directions vary around the bolt-group centroid

Question 6

Which locking method provides positive geometric prevention of nut rotation?

A. Castellated nut with cotter pin

B. Plain flat washer only

C. Unlubricated thread only

D. Oversized clearance hole

Correct Answer: A. Castellated nut with cotter pin

Question 7

A primary design concern for a long power screw under compression is:

A. Optical transparency

B. Euler buckling

C. Electrical conductivity only

D. Plate net-section tearing

Correct Answer: B. Euler buckling

Question 8

Which adhesive-joint loading mode is generally most damaging and should be minimized?

A. Uniform compression

B. Pure hydrostatic pressure

C. Peel or cleavage

D. Symmetric in-plane shear only

Correct Answer: C. Peel or cleavage

Question 9

The nominal tensile stress in a threaded fastener is normally calculated using:

A. The nominal diameter squared without qualification

B. The tensile-stress area

C. The washer outside diameter

D. The nut height only

Correct Answer: B. The tensile-stress area

Question 10

Which statement best describes a major advantage of brazing?

A. The base materials must always melt completely

B. It can join dissimilar materials with relatively low base-metal distortion

C. It requires no surface preparation

D. It eliminates all fatigue concerns

Correct Answer: B. It can join dissimilar materials with relatively low base-metal distortion