How to Pick the Right Bolt Size?

Fastener selection

As mechanical engineers, fasteners are integral to nearly every project. Particularly in machine design applications, selecting appropriate fasteners and establishing their quantity can be intricate. It is advantageous to step back and articulate your requirements while creating a project outline. In this spirit, we—at Five Flute—design a requirements-oriented project utilizing issues to draft a design requirements list for bolted and riveted joints, which, while quick, proves immensely beneficial.

Slow down, think about requirements

So, what are the essential requirements for a bolted joint?

At a minimum, consider these critical factors: What is the fastener's purpose in the application? What loading conditions should the joint expect? Which of the following drives the design: static strength, stiffness, or fatigue? What does the worst-case scenario entail? What is the targeted safety factor? What materials are involved? Is corrosion a consideration? Are thermal stresses a concern? How will assembly occur? Must it be disassembled or serviced? How long should it last? What are the cost considerations?

Each application may necessitate additional considerations, yet dedicating 30 minutes to addressing these questions significantly enhances your efficiency as a designer.

Materials

Key determinants for bolt material selection include strength, corrosion resistance, temperature environment and cost. In most non-aerospace applications, bolts predominantly consist of carbon, alloy or stainless steels. Low carbon steel is favored for low-cost options within low temperature, non-corrosive environments. As carbon content escalates above 0.25%, heating treatments can achieve significantly higher strengths at the expense of ductility. Be mindful that uncoated steels will oxidize eventually, even with commonly used black oxide coatings, which offer a thin oil film delaying oxidation for a limited duration. Zinc plating represents the other widespread coating used for low carbon or alloy steel bolts, aiding in corrosion resistance in wet environments. The unique property of zinc plating allows it to migrate toward scratched areas in a “self-healing” manner, nonetheless, it remains sacrificial and won't endure indefinitely in highly corrosive settings. The table adapted from NASA's Fastener Design Manual serves as a practical guide, relating fastener materials to coatings, temperature, and strength at ambient conditions.

Design Guidelines for Bolted Joints

Bolts play a vital role in machine design and product engineering; most use cases won’t necessitate in-depth analysis. However, sudden design requirements involving low safety factors due to strength or weight dictates will demand meticulous bolted joint designs. While hand calculations can pose reasoning challenges, efficient finite element models are often inaccurate if not configured using appropriate inputs. Given the intricate nature of bolted joint design, numerous fastener-related failures manifest in practical applications. General Motors recently recalled around 500,000 vehicles across multiple models due to fastener failures. Furthermore, the new eastern span of the San Francisco-Oakland Bay Bridge faced severe fastener-related issues shortly after its completion.

Because of the complexity involved, we cannot exhaustively cover all design scenarios here. Yet, through experience, the following design guidelines equip engineers with foundational joint design toolkits, ultimately enhancing areas that warrant deeper investigation (empirically or via nonlinear contact FE models).

Design for Shear Transfer through Friction

Typically, designing a slip-critical joint stands as best practice. This approach ensures the bolts generate enough clamping load across the joint so that shear is transferred through the joint member faces, avoiding direct shear through the fastener. Though self-evident, it merits repeat emphasis: bolts are intended to establish clamping loads between components, not to function primarily as shear pins or bending devices. Hence, assuring proper preload across a bolted connection assumes critical importance. Our role as engineers is to grasp and manage loading conditions across structures we design while recognizing that assembly significantly impacts outcomes.

Insights into bolt preload demonstrate differences in loading conditions through a double lap joint secured by a sole bolt. The illustrations portray stress flow in this joint, demonstrating variations with and without further preload.

In a double lap joint with preload

In a double lap joint without preload

The absence of preload presents three significant disadvantages:

• Contact Stress. Hertzian contact stress at the bolt-plate intersection distributes across a considerably smaller surface area than the shear overlap of the joint, culminating in large stress concentrations. In softer materials, this can lead to plate deformation due to stresses shifting beneath yield.
• Bolt Loading in Shear. Instead of contingent primarily on tensile loading within the bolt, load transfer occurs via shear at the joint overlap planes. As connection sloppiness increases, additional bending moments apply to the bolt, inviting tensile stress across the thread notch. Although loading in shear may appear benign, understanding this context requires applying the Von Mises failure criterion to relate yield stress to shear stress. From this perspective, shear strength approximates 58% of yield strength, varying based on fastener materials. Thus, it results in a weakened joint while dismissing the implications of stress concentrations and bending.
• Fatigue Considerations. From a bolt's fatigue lifespan viewpoint, insufficient preload constitutes a disaster in waiting. Ideally, a properly preloaded joint circumvents cyclical loading through the bolt when cyclical structural loads run parallel to the bolt’s radial orientation. Yes, that's correct—zero cyclical loading occurs without preload. If absent, the bolt experiences fully reversed shear and bending loads when loaded cyclically. Fatigue lifespan predominantly hinges on stress amplitude exceeding mean stress. Thus, while preloading a bolt may notably amplify mean stress, it can diminish stress amplitude altogether. Illustrations below differentiate between mean stress and stress amplitude.

For applications where fatigue lifespan is vital, aim to incorporate a target preload across the joint, document necessary bolt torques, and establish quality control procedures for validating proper bolt torque attainment.

Stiffness Matters

Bear in mind that every mechanical component behaves akin to springs; their mutual stress response during loading conditions hinges on their respective stiffness. This topic holds considerable depth, impossible to explore fully within this post. Nevertheless, fundamental guidelines can elucidate common pitfalls worth monitoring.

To illustrate the importance of bolt and member stiffness, envision a basic springs-in-parallel model.

Two parallel springs (of varying stiffness) produce differential load incentives for an equivalent displacement (delta x) correlating with individual stiffness. This principle aligns with Hooke's law.

Now, applying this rationale to a bolted joint comprising a pattern of fasteners wielding distinct grip lengths and diameters reveals that fasteners with shorter grip lengths and larger diameters would handle more axial loads during member displacements. Variance in stiffness across fasteners leaves the stiffer fasteners prone to overload under specific conditions.

A beneficial guideline for bolted joints emphasizes maximizing joint member stiffness (the elements being bolted) while equalizing and minimizing fastener stiffness tailored to a predetermined target preload. While minimizing fastener stiffness may sound counterintuitive, consider implications of member displacement and vibration. For a specific preload, a joint with pliable fasteners will experience lesser variations in preload despite clamping member displacements. This design also promotes a more balanced axial load distribution among fasteners under dynamic loads, thereby diminishing localized failures.

Fastener Patterns and Positions

As engineers, we devise bolted and riveted joints incorporating multiple fasteners. The positions of fasteners often follow uniform patterns for convenience in developing simple linear arrangements within CAD applications. Nonetheless, when addressing installed stiffness or lower safety factors, meticulous attention towards fastener layout is imperative. Above all, keep in mind that the positioning of fasteners in relation to applied loads determines how much load each fastener bears. This principle underlines the prior recommendation to amplify member stiffness. A stiff component fastened down will facilitate more even load distribution among fasteners, remaining independent of their positioning.

The risks of inadequate fastener layout concerning applied loads culminate in distinct failure modes discussed below.

For extensive insights, visit Friction Bolt.

Unzipping

An axial failure mode termed unzipping transpires whereby a fastener situated near the applied load bears the majority of this load. The failure of this fastener triggers a load transfer to the next nearest fastener, which may similarly fail unless loading is moderated. Depicted below, this failure pattern risks cascading down a line of fasteners, effectively "unzipping" the joint. Note: the illustrations below feature rivets, though the failure modes engage both bolts and screws alike.

Unbuttoning

Unbuttoning bears similarity to unzipping but stems from shear loads (radial relative to the fastener). Once again, improper arrangement of fasteners and inadequate stiffness in clamped members see a fastener positioned proximally to the applied load accepting the majority of the shear load. The subsequent figure highlights conditions that can lead to unbuttoning failure.

Galvanic Corrosion

In instances where bolts and joint members consist of disparate materials, galvanic corrosion emerges as a pertinent issue. For prototypes with limited lifespans, this may seldom pose a problem; however, solutions warrant consideration for production assemblies with extended expected lifespans or exposure to harsh environments (e.g., marine products). Effective electrically isolating dissimilar materials by means of paint, powder coat, insulating washers, plating, and other surface coatings like anodizing represents the best resolution. If these solutions prove unfeasible, minimizing the surface area of the anode material becomes essential. In moist environments, particularly those of saline nature, insulating methods are indispensable.

Bear in mind dissimilar materials exhibit differing galvanic potentials. Thus, identifying the anode (most active material) and cathode (least active) is worthwhile. Material will transition from anodic to cathodic elements in the galvanic cell. A galvanic ranking of common materials is included below, arranged from most to least active. The greater the separation of two materials on this list, the larger the potential galvanic difference they possess.

Bolt Preload

Proof Load

How much torque will a bolt tolerate? As with other mechanical components derived from ductile materials, bolts exhibit yield strength. Presuming the nut or threads coupling with the bolt showcase adequate strength, excessive torque can cause the bolt to tear itself apart. Clearly, this approach falls short of optimum for most scenarios, indicating a tight yield as poor design practice. The question arises: What less-than-yield target should we aim for with our fasteners?

To prevent over-tightening, manufacturers frequently publish proof loads or torque charts for their bolts. Proof load signifies the maximum force a bolt can endure without exhibiting elastic deformation, typically ranging from 85% - 95% of yield load. Proof load delineates the absolute upper limit fasteners should encounter. Presented below is a typical stress-strain curve for a ductile material (such as low carbon steel), illustrating both yield stress and proof stress along the curve.

Why Not Proof Load?

If our goal revolves around designing slip-critical joints, necessitating increased clamping strength for effective shear transfer, what precludes us from always utilizing proof load? This arises from the fact that alongside fastener forces, joints will also subject fasteners to static and dynamic external loads. These loads could exert axial, radial, torsional, and bending forces on fasteners. Reliance on proof load consistently raises the likelihood of yielding since fasteners possess no stress reserve or safety factor in these scenarios.

This predicament represents perhaps the most formidable aspect of bolted joint design—pinpointing the optimal preload and corresponding torque for each bolt in the joint. Knowing that the ideal bolt preload falls somewhere between zero and proof load, the challenge lies in finding it precisely. Achieving such equilibrium involves balancing mean load induced through preload against dynamic or cyclic load fostered by external forces across the joint. The accompanying visuals illustrate the influences of mean load and cyclical load next to the stress-strain curve.

The preceding example illustrates selecting a preload, ensuring cyclical loading experienced by the fastener doesn't exceed proof strength. Visualizing the correct resolution seems simple, yet uncovering it poses significant difficulty upon introducing additional design constraints (such as weight, stiffness, etc.).

Choosing the Proper Preload

Determining accurate torque and preload for fasteners represents the primary challenge in bolted joint design, often necessitating an iterative approach. This involves establishing a joint design, selecting the fastener and layout presumed effective (sometimes merely based on intuition), executing an analysis, and refining fastener selection alongside layout and preload. Load conditions can greatly impact analysis complexity. A few noteworthy examples to consider include:

• Static Axial Loading Only. Generally, this presents as the simplest load case. With no shear loads impacting the joint, the design challenge typically reduces to selecting fasteners adequately sized to withstand minor initial preload while accommodating any additional static loads.

• Static Shear Loads. Similar to the previous scenario, yet friction coefficients within the joint members require consideration. Again, the target is to engineer preload sufficient for shear transfer occurring between joint member faces, negating incidences through bolt shear.

• Combined Static Shear and Axial Loading. Effectively a combination of the preceding load scenarios, requiring preload calculations that factor in axial loads. Occasionally, axial loads may act in a clamping direction, thereby enhancing joint resilience against shear forces without slippage. Conversely, axial loads may prompt separation within the joint, diminishing effective preload. In such situations, it is essential to assess both fastener stiffness and joint stiffness for computing the actual preload after applying the axial load. Subsequently, one must verify this preload suffices to counter any supplementary shear loads entering the joint.

• Combined Dynamic Shear and Axial Loading. Incorporating fluctuating shear and axial loads, one must ascertain worst-case scenarios within the anticipated load range. Analysis parallels the previous case, albeit with multiple potential worst-case scenarios introducing varied failure modes (for example, joint slippage versus fastener overload).

Bolt Preload Methods and Torque Error

Once the target preload is established, determining the exact amount of torque needed on a bolt to achieve this preload proves crucial. Several methods exist for procuring bolt preload, each associated with some degree of error. The NASA Fastener Design Manual features a useful chart cataloging the inaccuracies associated with various preload application methods, revealing that a torque wrench achieves only ±25% accuracy!

Note: It may prove necessary to account for torque error as preload error within loading conditions. As torque error likely distributes symmetrically, employing root sum square or other statistical methodologies (Monte Carlo) for aggregating torque errors across multiple fasteners along a joint could be beneficial. For single fasteners, accounting for preload error is essential. However, with a fastener pattern comprising 10 or 20, the stochastic nature might allow neglecting error due to expected balancing outcomes across the joint.

Computing Torque from Preload

When implementing torque control to procure preload, the friction coefficient between the bolt and nut is paramount. Lubricating bolt threads can substantially reduce friction, yielding considerable elongation and preload for specified torque. Once again referencing the Fastener Design Manual, one can apply the following formula for calculating bolt torque:

Torque coefficient K can be derived from the following chart.

In all instances, scrutinizing joint materials and selecting conservative values for friction coefficients, along with appropriate preload application methods factoring in safety, proves crucial.

Rivets vs. Bolts

Rivets and bolts fulfill analogous roles; however, equating them is ill-advised. Rivets possess distinct differences outlined in the following table.

Generally, rivets should be employed in sheet metal applications characterized by extensive fastener patterns and predominant shear loading.

Rivet Joint Failure Modes

Given that rivets typically join sheet materials, alloying various failure modes merits attention. As design engineers, familiarity with each failure mode delineated below and understanding governing failure criteria is essential. A thorough analysis of each mode far exceeds the scope of this post; nonetheless, both Shigley’s and Roark's Formulas for Stress and Strain serve as commendable references for grasping these failures.

Rivet joint failure modes illustrated. Starting from the upper left and progressing clockwise: sheet tear out, rivet pull out (non-head side), rivet pull through (head side), rivet shear, sheet deformation.

Tensile vs Shear Loading Case Study

Although specific rivet types (e.g., hot-driven button head rivets in structural steel) excel under tensile loads, it is generally advised to load rivets principally in shear. To elucidate the significance of managing loading conditions on rivets, consider two simple bracket designs accommodating a bearing load applied to an eyelet integrated into the bracket.

Design 1: Angle bracket with tensile loaded rivets

Design 2: Flat bracket with shear loaded rivets

Despite Design 1 and Design 2 appearing comparable, they invoke vastly different loads imposed on the rivet groups employed. Visualizing section views clarifies this divergence. In Design 1, the rivet mid-plane aligns parallel to the applied load via Section A. In contrast, Design 2 witnesses shear plane interactions between the bracket and the attached flange, represented by Section B.

Section views at rivet shear mid-plane.

Within Design 2, rivet loading emerges purely as shear. The shear loads distribute evenly among the rivet group through the application of force F and corresponding couple (F x r) at the centroid of the rivet group G. Thus, both left and right rivets accommodate shear loads stemming from the moment, as illustrated below. Note: The Five Flute Fastener Shear Analysis Template is available for shear loading calculations on personalized designs, along with several guiding examples.

Rivet shear forces stemming from applied bearing load.

Conversely, Design 1 subjects all rivets to combined shear and tensile loading. While the shear distributes uniformly, the right-side rivet carries the bulk of the tensile load. A detailed derivation remains outside the current scope; nonetheless, users can envision the bracket pivoting at its leftmost contact point. The right rivet possesses the largest moment arm in relation to this pivot point, ultimately absorbing the majority of the tensile load. This resulting uneven loading distribution is illustrated below.

Rivet tensile and shear forces resulting from applied bearing load.

Shear Strength is Greater than Tensile—Is This a Contradiction?

Astute readers might discern this presents contradictory advice regarding the tension and shear loading paradigms. The explanation lies in the fact that static ratings for rivet strength in tension often surpass their shear strength. Consider a high-strength structural pop rivet available through McMaster; it boasts a tensile strength rating of 750 lbf and shear strength rating of 600 lbf. One may infer using this rivet under tension appears advantageous. Yet, static load ratings don't portray the complete picture.

Fundamentally, understanding that a rod in tension possesses superior strength compared to shear remains valid. Nonetheless, this principle does not translate seamlessly to rivet structures. Rivets typically feature a domed or countersunk head on one side with a deformed shank on the other. The interference fit at the clogged rivet shank's non-head side triggers stress risers causing local yielding. While this slight yielding may remain manageable under static loading conditions, amalgamation of tensile and axial loads—especially under dynamic or cyclical conditions—invites joint slippage below established static load ratings. This slippage could cause rivets to loosen rapidly or succumb to fatigue.

Guidance concerning riveted joint fatigue behavior tends to vary considerably since the performance hinges on distinct joint parameters, including material thickness and fastener placement. A cautious rule suggests never to subject rivets to tensile loads exceeding 10% of their rated shear load capacity. This remains especially true when experience cyclical, fully reversed, or highly dynamic loading. To obtain in-depth design guidance on rivet application within sheet metal and aerospace structures, examining Practical Stress Analysis for Design Engineers by Jean-Claude Flabel may prove beneficial.

Takeaways

The paramount takeaway from this discussion underscores that fastener design dilemmas should never be disregarded or underestimated. The ubiquitous presence of fasteners, combined with the understanding that their strength often doesn’t represent limiting factors, can lead engineers to overlook necessary joint and fastener loading evaluations when they are fundamentally essential.

Subsequently, maters should adhere to sound design practices throughout bolted and riveted joint creation. Employ a conservative approach, mindful of numerous factors potentially impacting joint strength, such as stress concentrations, fastener strength variance, friction coefficient uncertainties, preload discrepancies and installation oversights, among others. Consider the stiffness of joint members and fasteners, utilizing this information to determine fastener material, grip length, and diameter. Understanding the significance of bolt preload corresponding to distinct loading conditions proves crucial in designing bolted joints. Go beyond just referencing maximum preload values on bolt torque charts; instead, develop a sound engineering rationale to substantiate your preload selections. Follow through on this design choice by detailing the preload application strategy, being acutely aware of its assembly implications.

Lastly, validating the correct preload achieves success is equally essential in ensuring optimal joint performance in real-world applications. In high safety factor cases, engineers can reasonably trust their analytical outcomes. However, with diminished safety factors or high failure consequences (e.g., aerospace applications), empirical testing often represents the sole approach that assures confidence in the joint design's ability to withstand anticipated loads. Thank you for reading, and best wishes on your designs! Should you have questions regarding this article, feel free to reach out—I would be delighted to discuss!

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For reference and further comprehension:

(1) NASA

(2) Assembly Magazine

(3) Structure Magazine

(4) Fasnet Direct Rivet Guide

(5) Eng-Tips Forum

(6) NASA Technical Reports

(7) Advances in Aircraft and Space Science Journal

(8) Riveted Lap Joints in Aircraft Design

(9) Shigley’s ME Design

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