Fasteners, Joints and Power Screws

Introduction

Fasteners and joints are essential to machine design because individual parts must be connected into safe, serviceable assemblies. A joint may be permanent, as in welding and riveting, or detachable, as in bolting and pinning. The designer must ensure adequate strength, stiffness, fatigue resistance, sealing, manufacturability, and ease of inspection and maintenance.

This chapter develops the design principles of threaded fasteners, preloaded bolted joints, riveted and pinned joints, welded and brazed joints, adhesive joints, and power screws. Particular attention is given to eccentric loading, joint separation, fatigue, friction, efficiency, self-locking, and buckling.

Learning Objectives

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

• distinguish temporary and permanent joints and select an appropriate joint type;
• identify common thread forms, fastener failure modes, and bolted-joint preload principles;
• design bolted joints under direct, eccentric, fluctuating, and separating loads;
• analyze riveted, pinned, welded, brazed, and adhesive joints;
• calculate the torque, efficiency, and self-locking condition of power screws;
• check power screws for compressive stress, torsional stress, and buckling;
• apply standards, safety factors, and good engineering practice to joint design.

1. Classification and Design Requirements of Joints

A temporary joint can be dismantled without destroying the connected parts. Bolted, screwed, keyed, and pinned joints are typical examples. A permanent joint is not normally dismantled without damaging the joint or components; welded, brazed, soldered, riveted, and bonded joints belong to this class.

The selection of a joint depends on load type, temperature, corrosion, required stiffness, production volume, access for tools, inspection requirements, and whether disassembly is expected. A joint should transmit the required load while limiting deformation and avoiding local damage such as bearing failure, tearing, thread stripping, weld cracking, or adhesive peeling.

Important design requirements include:

1. Strength: the joint must resist static, impact, and fatigue loads.
2. Stiffness: excessive slip, opening, or rotation must be prevented.
3. Reliability: preload loss, corrosion, vibration loosening, and manufacturing variation must be considered.
4. Manufacturability: tolerances, accessibility, welding position, and assembly sequence matter.
5. Inspection and maintenance: critical joints may require torque records, proof testing, nondestructive examination, or periodic replacement.
6. Standards: thread geometry, bolt grades, weld quality, and allowable stresses should be based on applicable standards such as ISO, ASME, ASTM, or national codes.

2. Threaded Fasteners

2.1 Thread geometry and terminology

A screw thread is a helical ridge formed on a cylindrical or conical surface. Important terms are pitch, lead, major diameter, minor diameter, pitch diameter, flank angle, crest, root, and helix angle. For a single-start thread, lead equals pitch. For an n-start thread, lead is n times the pitch.

The helix angle λ at the mean thread diameter d_m is defined by

where L is the lead and d_m is the mean diameter. The angle is dimensionless, and all diameters must be expressed in the same unit.

Metric ISO threads are commonly designated by nominal diameter and pitch, for example M12 × 1.75. Coarse threads generally provide rapid assembly and greater tolerance to damage, whereas fine threads provide a larger tensile stress area and finer adjustment but are more sensitive to damage and contamination.

The tensile stress area A_t is used instead of the nominal shank area when estimating tensile capacity. For a metric thread, a commonly used approximation is

where d is nominal diameter and p is pitch. This approximation is applicable to standard metric V-threads and should be replaced by the tabulated standard value for final design.

2.2 Bolt strength and failure modes

A fastener may fail by tensile fracture through the threaded section, shear, bending, thread stripping, bearing, fatigue, or hydrogen-assisted cracking. The connected member may fail by plate tearing, bearing, punching, or excessive deformation.

For a tensile load F_t, the nominal tensile stress in the threaded section is

where σ_t is tensile stress and A_t is tensile stress area. The design is acceptable only when the resulting stress is below the appropriate allowable value or when the factored resistance exceeds the factored load according to the governing design code.

A preliminary proof-load check may be written as

where F_p is proof load and S_p is proof stress. Proof stress is a material and property-class value, not a universal constant. The actual bolt grade and standard must therefore be identified.

For a bolt simultaneously subjected to tensile and shear stresses, a ductile-material von Mises check is often used:

where τ is the shear stress. This relation assumes a homogeneous, isotropic ductile material and a suitable static-yield criterion. It does not by itself address fatigue, stress concentration, preload uncertainty, or brittle fracture.

3. Preloaded Bolted Joints

3.1 Purpose of preload

A preloaded joint is tightened so that the bolt is placed in tension and the clamped members in compression before the external service load is applied. Preload improves fatigue life, prevents separation, limits slip, and increases joint stiffness. The external tensile load does not usually act entirely as an additional bolt load because part of it relieves compression in the members.

The bolt and clamped members can be represented by two springs in series. Let k_b be bolt stiffness and k_m be member stiffness. The joint constant, or load fraction carried by the bolt, is

For an external separating load P, the increase in bolt load is

and the reduction in compressive member load is

The bolt load and member clamping load are therefore

where F_i is initial preload, F_b is total bolt force, and F_c is remaining member compression. These equations assume elastic behavior, an axially loaded joint, and a load path that can be represented by linear springs.

Joint separation begins when F_c = 0. Thus the separation load is

A properly designed joint maintains a positive compressive clamping force under the maximum service load, unless controlled separation is specifically permitted.

3.2 Bolt and member stiffness

For a uniform bolt of length L and tensile area A_t,

where E_b is the bolt Young’s modulus and L_b is the effective elastic length. For members of equivalent area A_m and thickness L_m,

Real joints have pressure cones and nonuniform contact; therefore A_m and L_m are effective quantities. Detailed stiffness models or finite-element analysis may be required for critical joints.

3.3 Torque-preload relationship

A simplified tightening relation is

where T is tightening torque, K is the nut factor, F_i is preload, and d is nominal bolt diameter. The nut factor incorporates thread friction, bearing friction, lubrication, surface finish, and geometry. It is not a material constant. Typical values vary widely, so torque alone provides an uncertain preload unless friction is controlled or preload is directly measured.

A more explicit approximate relation is

where φ = arctan μ_t is the thread friction angle, μ_t is thread friction coefficient, μ_b is bearing friction coefficient, and d_b is the effective bearing-friction diameter. This expression assumes a square-thread-like friction model for the thread and neglects several geometric details; standard tightening procedures or calibrated data should be used for final work.

Prevailing-torque nuts, thread-locking compounds, lock washers, safety wire, castellated nuts, and mechanical locking devices may be used where vibration loosening is possible. A locking device should not be treated as a substitute for adequate preload.

4. Bolted Joints Under Eccentric and Fatigue Loading

4.1 Direct and eccentric loading

Suppose a bolt group contains n bolts and is subjected to a direct load P through the group centroid. If the load is shared equally, the direct force per bolt is P/n. If an in-plane moment M acts about the centroid, the additional force in bolt i is proportional to its radial distance r_i:

where the summation includes all bolts and the force is tangential to the circular distribution about the centroid. The vector sum of direct and moment-induced forces must be performed for each bolt. The most heavily loaded bolt governs.

For a tensile bolt group subjected to a moment that opens the joint, a simplified elastic distribution is

where y_i is the distance of bolt i from the neutral axis. This equation assumes a rigid connected plate, elastic bolt response, small deformation, and no contact loss. Once separation occurs, the load distribution becomes nonlinear and the model is no longer valid.

4.2 Fatigue of preloaded bolts

For an external load varying between P_min and P_max, the bolt-load range is

and the alternating component of bolt force is

The mean bolt force is

The corresponding nominal alternating and mean stresses are σ_a = F_a/A_t and σ_m = F_m/A_t. Fatigue assessment must include thread-root stress concentration, surface finish, mean-stress effects, corrosion, preload scatter, and the relevant S–N or strain-life data. Goodman or Gerber relations may be used only when their material assumptions and design-code requirements are appropriate.

A major practical principle is that a stiff clamped joint, with a small C, reduces the alternating bolt stress. Increasing preload within safe limits also keeps the joint closed and reduces separation-related impact loading.

5. Riveted and Pinned Joints

Rivets are permanent fasteners used in aircraft structures, boilers, bridges, and sheet-metal assemblies. Pins are usually detachable and are used for locating, transmitting shear, or forming pivots.

For a riveted lap joint, possible failure modes include rivet shear, plate tearing across a row of holes, bearing failure, and edge tearing. For a single-rivet joint carrying load P, the nominal rivet shear stress is

where n_s is the number of shear planes and A_r = πd_r²/4 is the rivet cross-sectional area. For a single-shear joint, n_s = 1; for a double-shear joint, n_s = 2, provided the geometry actually produces two effective shear planes.

The net-section tensile stress in a plate of thickness t and width w containing one hole of diameter d_h is

The average bearing stress between a fastener and plate is approximately

These average-stress equations do not capture local plasticity or stress concentration. Pitch, edge distance, hole quality, corrosion, and load eccentricity must also be checked.

Pins may fail in shear, bending, bearing, or by fatigue at grooves and shoulders. A pin carrying transverse load should not be treated as a pure shear member automatically; short pins often develop substantial bending because load is not applied through idealized planes.

6. Welded Joints

Welding creates a continuous or intermittent fused joint. Common processes include shielded metal arc welding, gas metal arc welding, gas tungsten arc welding, submerged arc welding, laser welding, and resistance welding. Design must account for weld size, throat, length, electrode or filler strength, residual stress, distortion, heat-affected-zone properties, inspection class, and fatigue category.

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

for an ideal equal-leg fillet weld. If the effective weld length is L, the throat area is aL. Under direct load P, the average throat shear stress is

For a weld group subjected to an in-plane moment, the direct shear and moment-induced shear must be combined vectorially. The weld-group polar second moment is used to distribute moment loading according to distance from the weld-group centroid. For eccentric transverse loading, both direct throat stress and bending-related stress may occur.

Weld fatigue is often governed by the weld toe, root, or discontinuities rather than by the nominal static strength. Therefore fatigue design should use the applicable weld classification and stress range method. Nondestructive methods include visual inspection, dye penetrant, magnetic-particle, ultrasonic, and radiographic examination.

7. Brazed, Soldered, and Adhesive Joints

In brazing, a filler metal melts above approximately 450 °C but below the melting point of the base materials. Soldering uses a lower-temperature filler. These processes can join dissimilar metals and thin sections with limited distortion, but joint strength depends strongly on clearance, surface preparation, wetting, filler selection, and service temperature.

Brazed joints are strongest when loaded in shear or compression over a substantial overlap. Peel and cleavage loads should be minimized by geometry. The nominal average shear stress in an overlap joint is

where b is joint width and L is overlap length. Actual shear stress is nonuniform, especially near overlap ends, so the average equation is suitable only for preliminary sizing.

Adhesive joints transfer load through chemical adhesion and mechanical interlocking. Their advantages include joining dissimilar materials, sealing, damping vibration, and distributing stress over a large area. Limitations include sensitivity to temperature, moisture, surface contamination, creep, aging, and peel stress.

For a simple lap joint, the average adhesive shear stress is P/(bL), but a proper design must consider elastic shear-lag, adherend stiffness, adhesive thickness, cure condition, and environmental degradation. Scarf joints and stepped joints reduce peel stress compared with abrupt lap-joint ends.

8. Power Screws

Power screws convert rotary motion into linear motion or transmit large axial force. Applications include screw jacks, presses, vises, lifting mechanisms, and machine-tool feeds. Common forms are square, Acme, and trapezoidal threads. Square threads are efficient, while Acme or trapezoidal threads are easier to manufacture and better able to withstand wear.

8.1 Raising a load

Consider a screw with mean diameter d_m, lead L, helix angle λ, and friction angle φ. For a square-thread screw carrying axial load W, the torque required to raise the load is

Since tan λ = L/(πd_m), this can also be written in terms of lead and diameter. The torque to lower the load is

provided the assumed friction model applies and the sign indicates the direction of impending motion. If φ > λ, the screw is self-locking: it will not descend under load when driving torque is removed. If λ > φ, the screw is overhauling and may rotate under the load.

For a V-thread or Acme thread, the thread friction is increased by the included-angle effect. If α is the half-angle of the thread, an approximate effective friction coefficient is μ′ = μ sec α, and φ′ = arctan μ′. The square-thread equations can then be used with φ′, subject to the limitations of the approximation.

8.2 Efficiency

The ideal torque for raising a frictionless load is W L/(2π). Therefore the raising efficiency is

For the square-thread model,

Efficiency is reduced by thread friction and collar friction. If a collar of mean friction radius R_c and coefficient μ_c is present, the collar torque is approximately

and must be added to the thread torque. A thrust bearing or low-friction collar can substantially improve efficiency.

8.3 Screw stresses

The screw is subjected to axial compression or tension and torsion. The nominal axial stress is

where d_r is the root or minor diameter. The torsional shear stress in a solid circular section is approximately

where T is the applied torque. A ductile-material equivalent stress may be estimated by

The root diameter must be used because it is the weakest section. Thread-root stress concentration and wear may require a design factor or a code-specific calculation.

8.4 Buckling of power screws

A long screw in compression can buckle. The Euler critical load for an ideal slender column is

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. For a circular root section,

Euler theory assumes a straight, elastic, initially perfect member with ideal end restraints. Real screws have imperfections, thread clearance, eccentricity, and possible yielding. If the slenderness is not sufficiently high, a Johnson or inelastic-column method, manufacturer data, or a design code should be used.

A practical design must satisfy both strength and stability requirements, for example

where n_b is the buckling safety factor, while also satisfying the combined stress limit. The smaller allowable load governs.

9. Worked Example: Preloaded Bolted Joint

A steel joint uses one M16 bolt with tensile stress area A_t = 157 mm². The bolt is tightened to an initial preload F_i = 20 kN. The bolt stiffness is k_b = 1.0 MN/mm and the member stiffness is k_m = 3.0 MN/mm. The joint is subjected to a separating load varying from 0 to 30 kN. Determine the maximum bolt load, minimum member compression, and whether separation occurs.

The joint constant is

The maximum bolt-load increase is

Thus,

The member compression reduction is

Therefore,

A negative calculated value means that the members would separate before the full 30 kN load is reached. The separation load is

Hence the joint requires greater preload, greater member stiffness, additional bolts, or a revised load path if separation is unacceptable. The maximum nominal bolt tensile stress before separation is approximately 27,500/157 = 175 MPa, but fatigue and preload scatter must still be evaluated.

10. Illustrative Case: Joint Selection for a Vibrating Pump Base

Background

An industrial pump is mounted to a steel base. The assembly experiences vibration, periodic maintenance, oil exposure, and occasional overload during starting. The base must be removable, while a nearby guard requires a permanent lightweight attachment.

Problem

An initial proposal uses lightly tightened bolts for the pump and a thin adhesive lap joint for the guard. Field experience shows bolt loosening and peeling of the guard joint.

Analysis

The pump bolts are exposed to fluctuating transverse and separating forces. Light tightening produces little clamping force, allowing slip and impact. The guard adhesive is loaded partly in peel because the overlap ends are abrupt and the adherends are flexible.

Approach and solution

The pump joint is redesigned with properly sized high-strength bolts, controlled preload, hardened washers, and a joint stiffness arrangement that keeps the interface compressed. The transverse load is resisted primarily by friction generated by preload, with bolt shear checked as a secondary load path. A locking method compatible with the maintenance procedure is specified, and tightening is verified by calibrated equipment.

The guard is redesigned with a longer overlap, rounded or tapered load-transfer ends, cleaned and treated surfaces, controlled adhesive thickness, and a mechanical backup where failure could create a hazard. The adhesive is selected using temperature, oil-resistance, and fatigue data rather than nominal room-temperature shear strength alone.

Outcome

The redesigned pump joint remains closed and resists vibration loosening. The guard joint experiences lower peel stress and has improved environmental reliability. Inspection instructions identify bolt preload verification and adhesive surface preparation as quality-critical operations.

Learning points

Joint design is a system problem rather than a simple fastener-strength calculation. Preload, stiffness, load path, environment, assembly control, and failure consequences must be considered together.

11. Design Practice, Standards, and Limitations

A professional design process should:

1. define loads, load combinations, temperature, environment, and required life;
2. identify whether the joint must be detachable, sealed, electrically continuous, or insulated;
3. select a joint type and establish the load path;
4. calculate static strength, stiffness, separation, slip, fatigue, and stability;
5. select standardized fasteners and compatible materials;
6. specify tightening, inspection, surface preparation, and replacement requirements;
7. verify tolerances, accessibility, corrosion protection, and manufacturability;
8. document assumptions and obtain testing or code approval where necessary.

Safety-critical joints require traceability, qualified procedures, controlled materials, and inspection. Welding procedures may require qualification and certified personnel. Adhesive bonding requires control of shelf life, mix ratio, cure cycle, surface preparation, and environmental exposure. Fastener substitution should not be made merely because nominal diameter appears identical; strength class, thread pitch, coating, length, and compatibility may differ.

Computer-aided design and finite-element analysis are valuable for eccentric joints, pressure cones, weld groups, and adhesive stress distributions. However, numerical models do not automatically provide reliable results. Contact definitions, preload steps, nonlinear material behavior, mesh refinement, and validation against hand calculations or test data are essential. Digital torque tools and ultrasonic bolt-length measurement can improve preload verification, but their calibration and uncertainty must be managed.

Challenges and Contemporary Developments

Modern joint design increasingly addresses lightweight materials, mixed-metal corrosion, high-temperature service, electric vehicles, additive-manufactured components, and disassembly for recycling. Hybrid joints combining adhesive bonding with mechanical fasteners can improve load distribution and fail-safe behavior, but their load-sharing mechanism changes with temperature, aging, and damage.

Sustainable design favors standardized fasteners, repairable assemblies, reduced material use, low-toxicity coatings, and joints that can be separated at end of life. Artificial intelligence can assist with joint-type selection, anomaly detection from torque data, and predictive maintenance, but engineering judgment and physical validation remain necessary. AI-generated recommendations must be checked against standards, material certificates, and failure-mode calculations.

Chapter Summary

Joints must be designed as complete load paths, not as isolated components. Threaded fasteners are governed by tensile stress area, preload, thread strength, friction, and fatigue. In a preloaded joint, the joint constant C determines the fraction of external separating load added to the bolt; separation occurs when member compression falls to zero. Eccentric bolt groups require vector combination of direct and moment-induced forces, while fatigue design must account for preload and stress concentration.

Riveted and pinned joints require checks for shear, bearing, net-section tearing, bending, and fatigue. Welded joints are designed using effective throat and weld-group mechanics, but fatigue and inspection often govern. Brazed and adhesive joints perform best when loads are distributed in shear and peel is minimized.

Power screws transform torque into axial force. Their design requires raising and lowering torque, efficiency, self-locking, collar friction, combined stress, wear, and buckling checks. Standards, controlled assembly, environmental effects, inspection, and life-cycle considerations are essential to reliable joint design.

Key Terms

Preload: Initial force introduced into a fastener during tightening.

Tensile stress area: Effective threaded area used to calculate bolt tensile stress.

Joint constant: Fraction of an external separating load carried as additional bolt load.

Joint separation: Loss of compression between connected members.

Nut factor: Empirical factor relating tightening torque to preload.

Thread stripping: Failure caused by shear rupture of engaged threads.

Eccentric loading: Loading whose line of action does not pass through the joint-group centroid.

Rivet: Permanent mechanical fastener installed by deformation.

Bearing stress: Local compressive stress between a fastener and the surrounding material.

Fillet weld: Triangular weld joining two approximately perpendicular surfaces.

Effective throat: Minimum effective dimension of a fillet weld resisting load.

Brazing: Joining process using a filler metal melting above approximately 450 °C.

Adhesive joint: Joint in which an adhesive transfers load between adherends.

Power screw: Threaded mechanism that converts rotary motion into linear force or motion.

Lead: Axial advance in one complete revolution of a screw.

Helix angle: Angle representing the inclination of the thread helix.

Self-locking: Condition in which a loaded screw does not rotate backward without applied torque.

Overhauling: Condition in which the load can drive the screw backward.

Effective length factor: Factor K used to represent column end restraints in buckling analysis.

Joint stiffness: Resistance of a bolt or clamped-member system to elastic deformation.

Review Questions

Short Answer Questions

1. What is the purpose of preload in a bolted joint?
2. Define tensile stress area and explain why it is used instead of nominal shank area.
3. What is the difference between a temporary and a permanent joint?
4. State the condition for self-locking of a square-thread power screw.
5. Why should peel loads be minimized in adhesive joints?

Long Answer Questions

1. Explain the spring model of a preloaded bolted joint and derive the expressions for bolt-load increase and member-compression reduction.
2. Discuss the principal failure modes of riveted and pinned joints and describe suitable checks for each.
3. Explain the design of a fillet-welded joint under direct and eccentric loading.
4. Derive the torque and efficiency relations for a square-thread power screw, stating all assumptions.
5. Discuss the factors that influence fatigue life and preload reliability in bolted joints.

Analytical / Application Questions

1. A preloaded joint has F_i = 15 kN and C = 0.30. Determine the separation load and the bolt load at an external load of 20 kN. State whether the joint remains closed.
2. A power screw has W = 10 kN, d_m = 30 mm, lead = 6 mm, and friction coefficient μ = 0.10. Calculate the helix angle, approximate raising torque, and determine whether the screw is self-locking. Neglect collar friction.
3. A four-bolt group carries a direct in-plane load and an eccentric moment. Describe a systematic vector method for finding the most heavily loaded bolt, and identify the assumptions that would invalidate the elastic bolt-group method.

Multiple Choice Questions with Answers

Question 1

For a preloaded joint, the fraction of an external separating load carried as additional bolt load is represented by:

A. The nut factor K

B. The joint constant C

C. The friction angle φ

D. The safety factor n

Correct Answer: B. The joint constant C

Question 2

If bolt stiffness is 1 MN/mm and member stiffness is 3 MN/mm, the joint constant is:

A. 0.20

B. 0.25

C. 0.50

D. 0.75

Correct Answer: B. 0.25

Question 3

A preloaded joint has F_i = 20 kN and C = 0.25. Its separation load is:

A. 5 kN

B. 20 kN

C. 26.7 kN

D. 80 kN

Correct Answer: C. 26.7 kN

Question 4

For an ideal equal-leg fillet weld of leg size s, the effective throat is:

A. s/2

B. s

C. s/√2

D. √2s

Correct Answer: C. s/√2

Question 5

A rivet in a double-shear joint has two effective shear planes. Compared with a single-shear joint of the same rivet area and load, the average rivet shear stress is:

A. Twice as large

B. Half as large

C. Unchanged

D. Four times as large

Correct Answer: B. Half as large

Question 6

A square-thread power screw is self-locking when:

A. λ > φ

B. λ = 90°

C. φ > λ

D. μ = 0

Correct Answer: C. φ > λ

Question 7

The ideal frictionless torque required to raise load W through a screw of lead L is:

A. WL

B. WL/(2π)

C. 2πWL

D. W/(2πL)

Correct Answer: B. WL/(2π)

Question 8

For a circular screw root section, the second moment of area is:

A. πd_r²/4

B. πd_r³/16

C. πd_r⁴/64

D. πd_r⁴/16

Correct Answer: C. πd_r⁴/64

Question 9

In a preloaded joint, increasing member stiffness while holding bolt stiffness constant generally:

A. Increases C and bolt-load variation

B. Decreases C and bolt-load variation

C. Causes immediate separation

D. Eliminates the need for preload

Correct Answer: B. Decreases C and bolt-load variation

Question 10

The most appropriate general strategy for adhesive lap joints is to:

A. Maximize peel loading

B. Use abrupt overlap ends

C. Transfer load primarily through distributed shear

D. Ignore surface preparation

Correct Answer: C. Transfer load primarily through distributed shear