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Bolted Joints by the Numbers

Preload, tightening, separation, fatigue, threads, shear, eccentric loads, gaskets and temperature, on one cylinder test rig

How to design, tighten and check bolted joints: preload and joint stiffness, torque, stretch and angle, separation and fatigue, threads, shear, bolt groups, gaskets and heat.

10 chapters · About 100 minutes · Free to read · Intermediate mechanical design and maintenance engineering

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KEVOS® LibraryENGINEERINGT1T2T3Bolted Joints bythe NumbersKEVOS® ORIGINAL BOOK10 CHAPTERS

About this book

A bolted joint looks like the simplest connection in engineering: a hole, a bolt, a nut and a spanner. It is also one of the least understood. A bolt is a spring, stretched when it is tightened, and the parts it clamps are springs too, squeezed by the same force. How that pair of springs shares the loads the joint later carries decides whether the joint stays tight, leaks, slips or breaks its bolts, and almost none of it can be seen once the nut is on.

This book shows how to design, tighten and check bolted joints with numbers. It starts with preload and joint stiffness, then covers the three ways of setting preload, by torque, by stretch and by angle, and how accurately each one works. It then checks joints against separation, proof load and fatigue, sizes threads, tapped holes and screw lengths, and moves on to joints in shear, bolt groups under eccentric loads, brackets in tension, gasketed flanges and joints that change temperature. It finishes with hole patterns and the records that show a joint was made as designed.

It is for mechanical design and maintenance engineers, machine builders and fitters. It assumes engineering or trade training and comfort with force, stress and stiffness; the joint models are explained as they are used. Each chapter works the running case with real numbers, includes one plausible mistake and how it was found, links the KEVOS® tools that do the chapter’s calculations, and ends with an exercise and its worked answer.

The running case

Every chapter follows one machine. This is an illustration. A hydraulic repair shop in Mackay, Queensland, that rebuilds cylinders for mining equipment is building the CT-1, a test rig that pressure-tests rebuilt cylinders and cycles them for endurance before they go back to site. Its bolted joints include:

  • Test head: a steel head closing a 125 mm bore test chamber, held by eight M20 property class 10.9 cap screws into tapped holes, cycled from zero to 25 MPa.
  • Frame: a welded steel frame with a bolted splice in its main beam, which carries the cylinders’ reaction loads in shear.
  • Brackets: a rod-end support plate bolted to a column web, and a load cell bracket bolted to a column flange.
  • Hydraulics: an aluminium valve manifold held by M10 cap screws that runs warm, and a gasketed return-line filter housing.

Pressures, dimensions, materials, property classes, friction and nut factors, gasket factors and test figures are the shop’s working figures or are calculated from stated assumptions. They do not describe KEVOS® work or any real business, equipment maker or supplier’s data.

How to use the book

Read Chapter 1 first: it sets out preload and joint stiffness, which every later chapter uses. Chapters 2 and 3 cover tightening and should be read together. Chapters 4 and 5 check tension joints. Chapters 6 to 10 can be read in any order once Chapter 1 is familiar.

Every calculation in the book was checked by running it, and the KEVOS® tools linked from each chapter were checked against the calculations they perform. Nut factors, friction coefficients, gasket factors and allowable stresses are typical figures for illustration; a real design uses the fastener, gasket and coating makers’ data and the applicable standard.

Source limits and professional responsibility

This book is educational. Joints in pressure equipment, lifting equipment and structures are designed and checked to their codes and standards, such as the pressure vessel and structural steel standards that apply in Australia, by competent engineers. A pressurised joint must never be loosened or tightened while it is under pressure. Decisions about real joints remain with the competent people responsible for them.

Who this book is for

Mechanical design engineers, machine builders, maintenance engineers and fitters who design, specify, tighten, inspect or troubleshoot bolted joints in machines, rigs, frames and pressure equipment.

What you will learn

  • Explain how preload and the stiffness of bolt and members decide how a tension joint shares an external load and when it separates.
  • Set and check a bolt's preload by torque, stretch or angle, and allow for nut factor scatter, wrench adapters and measurement.
  • Check a bolted joint for separation, proof load and fatigue, and size thread engagement, tapped holes and screw lengths.
  • Check shear joints, eccentrically loaded bolt groups, brackets in tension and gasketed flanges for their loads.
  • Allow for temperature, plan hole patterns and tolerances, and keep tightening records that show a joint was made as designed.

Inside this book

Chapters

  1. 01Preload and joint stiffness: how a bolted joint carries loadWhy a bolt and the parts it clamps act as two springs, how preload and their stiffnesses share an external load, when a joint separates, and what the joint constant means.
  2. 02Tightening by torque: the nut factor and its scatterHow tightening torque becomes preload through the nut factor, why friction makes that uncertain, how lubricants change it, and how to correct a torque wrench for an adapter.
  3. 03Stretch and angle: setting preload closer to the bolt, and checking itHow bolt stretch and nut rotation relate to preload, why the snug point matters, how torque-angle tightening narrows scatter, and how measured stretch verifies preload.
  4. 04Designing a tension joint for separation, proof load and scatterHow to choose a target preload that survives its own scatter: separation at the lowest preload, proof load at the highest, fatigue, and why 75% of proof can be too much.
  5. 05Bolts that cycle: fatigue in tension jointsHow a cyclic external load becomes a small alternating stress in a well-preloaded bolt, why separation and soft members destroy that protection, and how to check bolt fatigue.
  6. 06Threads, tapped holes and screw lengthsHow long a thread must engage so the screw breaks before the thread strips, how to design a tapped hole, and how to choose a screw length that puts full thread where it is needed.
  7. 07Joints in shear: bearing type and friction gripHow bolted joints carry shear: by bolts bearing on their holes or by the friction their preload creates, how to check each, and what painted faying surfaces do to slip.
  8. 08Eccentric loads on bolt groups and bracketsHow a load applied away from a bolt group's centre loads its bolts unequally: the elastic method for in-plane loads, bracket bolts in tension and shear, and the most loaded bolt.
  9. 09Gasketed flanges: seating the gasket and holding the pressureHow the bolts of a gasketed flange are sized: the load to seat the gasket, the load to hold it tight under pressure, gasket factors, bolt area, and an old empirical rule compared.
  10. 10Temperature, hole patterns and the joint registerHow differential expansion changes preload in a warm joint, how to plan a bolt circle's holes and position tolerances for clearance and tapped holes, and what a joint register holds.

Apply This in Practice

Use these KEVOS® tools to try the method from this reading with your own numbers.

References and source notes

The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 1 November 2026.

  • A. Altland and B. Simons. Concepts of Theoretical Solid State Physics (2001). Lecture notes released for verbatim copying only, so treated here as a protected work. Used only as a map of ideas: the harmonic approximation, in which bonded parts act as springs about an equilibrium position, and the way a preloaded system shares an applied load between its stiffnesses. No text, equations, figures or problems are reproduced, and all cases and calculations are KEVOS® originals.
  • R. G. Budynas and J. K. Nisbett, McGraw-Hill Education. Shigley's Mechanical Engineering Design, tenth edition (2015). Background for bolt and member stiffness by the frustum method, the joint constant, separation, the torque–preload relation, metric property class strengths and fully corrected endurance strengths of bolts, and the Goodman fatigue check, used in Chapters 1 to 5.
  • J. H. Bickford, CRC Press. Introduction to the Design and Behavior of Bolted Joints: Non-Gasketed Joints, fourth edition (2007). Background for nut factor scatter, torque, turn and stretch control of preload, ultrasonic measurement of bolt stretch, relaxation and the effect of temperature on preload, used in Chapters 2, 3 and 10.
  • E. Oberg, F. D. Jones, H. L. Horton and H. H. Ryffel, Industrial Press. Machinery's Handbook, thirtieth edition (2016). Background for the length of thread engagement by shear areas, tap drill sizes, bolt and screw thread lengths, the turn-of-nut relation and the empirical working strength of bolts in packed joints, as used by several of the KEVOS® tools in Chapters 3, 6 and 9.
  • International Organization for Standardization. ISO 898-1 Mechanical properties of fasteners made of carbon steel and alloy steel, Part 1: Bolts, screws and studs (2013). Named by number and scope only, as the standard that defines metric property classes such as 8.8 and 10.9. The proof and tensile strengths used in the book are taken from Shigley's tables and labelled as the case's working figures.
  • Safe Work Australia. Model Code of Practice: Managing the risks of plant in the workplace (2022). Named in Chapters 1 and 9 for the duties to manage the risks of plant, including pressure equipment and the release of stored energy when joints are opened.

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