3.4.1 Uppercase variables
For the purpose of this document, the following uppercaser variables apply:
| Variable | Meaning |
|---|---|
| A | Cross-section area of a joint part (in the plane perpendicular to the fastener axis) |
| As | Effective cross-sectional area of a fastener for stress analysis |
| Asm | Effective cross-sectional area of a fastener for stiffness calculations |
| Ath | Area of the (cylindrical) surface assumed to fail during thread pull-out |
| A0 | Minimum cross-sectional area of a fastener shank |
| A3 | Cross-sectional area of a fastener based on the thread root diameter, d3 |
| C | Transverse width of an eccentric joint (see Figure 8-7) |
| D1 | Minor diameter of the female thread |
| Davail | Available diameter for compression zone spreading (see Section 7.7) |
| Dh | Nominal diameter of a hole |
| Dlim | Maximum cone diameter of compression zone spreading (see Section 7.7) |
| Duh,brg | Outer diameter of the under-head or under-nut bearing surface (see Section 7.7) |
| E | Young’s modulus |
| F | Force |
| FA | Axial force transmitted by joint |
| FQ | Shear force transmitted by joint |
| FV,max | Maximum preload |
| FV,nom | Nominal preload |
| FV,min | Minimum preload |
| FZ | Maximum loss of preload due to relaxation (includes all sources, e.g. embedding, creep, etc) |
| Fb | Tensile force transmitted by a fastener |
| Fc | Compression force transmitted by the clamped parts |
| FCL | Shear force capable to move fastener shank by a distance equal to the hole clearance |
| ΔFb,A | Increment in fastener tension caused by the application of the external axial load, FA |
| Variable | Meaning |
| ΔFc,A | Increment in clamped parts compression caused by the application of the external axial load, FA (negative for increased compression) |
| FK | Clamping force acting at the interstice between two flanges |
| Fth | Axial force transmitted by the thread |
| FΔT+ | Maximum (most positive) increment in a fastener’s axial load due to thermo-elastic effects |
| FΔT− | Minimum (most negative) increment in a fastener’s axial load due to thermo-elastic effects |
| Gc | Radius of gyration of the effective interface area between clamped parts |
| Ic | Second moment of area of the clamped parts interface area |
| K | Stiffness of a joint part (N/m) |
| Kc | Critical stress intensity factor |
| KISCC | Critical stress intensity factor for stress corrosion cracking |
| L | Length |
| Lj | The joint length. The combined thickness of all clamped parts (measured without any externally preload or applied load). |
| ΔLb | Change in length of the fastener |
| ΔLc | Change in length of the clamped parts |
| M | Moment / Torque |
| Mapp | Peak torque applied to the fastener or nut during tightening (includes the prevailing torque, MP) (Mapp is also called ‘installation torque’) |
| MB | Bending moment transmitted by joint (see Figure 5-4) |
| MP | Prevailing torque (also called ‘running torque’) |
| MT | Torsional moment transmitted by joint (see Figure 5-4) |
| Mth | Torsional moment transmitted by the thread (does not include prevailing torque, MP) |
| Muh | Torsional moment transmitted by frictional forces at the under-head or under-nut interface |
| RS | Shear strength ratio |
| RZ | Average surface roughness |
| P | Probability |
| Smt | Mean strength |
| Sreq | Required strength |
| Sr | Slip resistance of a joint |
| Variable | Meaning |
| Tworking | The working temperature of the joint (specified with upper and lower bounds) |
| Treference | The reference temperature (generally taken as the assembly temperature) |
| ΔT | Change in temperature |
| Wp | Polar section modulus |
| W′p | Yield-corrected polar section modulus |
| Variable | Meaning |
| a | Load eccentricity (distance from joint axis to axis of applied load) |
| ak | Distance between the edge of the under-head bearing surface and the point of load introduction (used for eccentric joints, see Section 6.6) |
| aR | Shortest distance between the edge of the bearing surface and the edge of the clamped part |
| ai | Edge distance (measured from hole axis to edge of flange) |
| b | Effective longitudinal width of the joint (see Figure 8-8) |
| c | Empirical coefficient |
| d | Nominal diameter of a fastener |
| dmin | Minimum thread diameter = d3 |
| dS | Effective diameter of a fastener for stress calculations |
| dhead | Diameter of fastener head |
| dsha | Diameter of a shank segment |
| dsm | Effective diameter of fastener used for stiffness calculations |
| duh | Effective diameter at which under-head or under-nut frictional forces act |
| duh,brg | Outer diameter of the under-head or under-nut bearing surface |
| d0 | Minimum diameter of a fastener shank |
| d2 | Pitch diameter of a fastener thread (assumed diameter at which torsion forces are introduced within a thread) |
| d3 | Diameter of a fastener’s thread root = dmin |
| f1 | Deflection of points of action of the external load |
| fz | Plastic deformation of the joint due to embedding |
| fΔT | Thermal elongation of an item |
| Variable | Meaning |
| fb,v | Elongation of fastener due to preload |
| h | Thickness of a flange (referred to as a ‘length’ for compliance calculations), or: Height of thread |
| hk | The distance between the point of load introduction and the interstice (used for eccentric joints, see Section 6.6) |
| kar | Parameter for describing the effect of the component height on the load introduction factor |
| kdh | Parameter for describing the effect of the hole on the load introduction factor |
| kdw | Parameter for describing the effect of the bearing area diameter on the load introduction factor |
| m | Number of fasteners in a joint |
| n | Loading plane factor |
| nG | Loading plane factor of the basic body |
| nG* | Loading plane factor of the basic body whose parameter ak/h is reduced |
| nM | Moment conduction factor |
| n2D | 2D loading plane factor |
| p | Pitch of a thread |
| pi | Horizontal distance between holes |
| S | Clamping eccentricity (distance from joint axis to fastener axis) |
| Si | Vertical distance between holes |
| sf | Safety factor |
| sw | Size of wrench (measured ‘across the flats’ of a head or nut) |
| x | Number of faying surfaces that resist the shear load |
| Symbol | Meaning |
| α | Coefficient of thermal expansion for a material |
| β | Bending compliance |
| ε | Uncertainty factor used in the typical coefficient method (not applicable to the experimental coefficient method) |
| γ | Coefficient of utilization (ratio of preload stress to yield stress) |
| Symbol | Meaning |
| λ | Under-head bearing angle (see Figure 5-6) |
| ω | Torque wrench accuracy used in the experimental coefficient method (expressed at a ± value) |
| φ | Compression cone half angle (see Section 6.6) |
| ϕ | Thread helix angle (see Figure 6-1) |
| ρ | Local friction angle at thread interface |
| θ | Half angle of thread grooves (see Figure 6-1) |
| δb | Compliance of the fastener (see Section 6.5) |
| δc | Compliance of the clamped parts (see Section 6.6) |
| σV | Axial stress in fastener due to nominal preload, FV,nom |
| σV,max | Axial stress in fastener due to maximum preload, FV,max |
| σV,min | Axial stress in fastener due to minimum preload, FV,min |
| σy | Yield stress |
| μth | Friction coefficient at the thread interface |
| μuh | Friction coefficient at the under-head or under-nut interface |
| μs | Friction coefficient at the slipping interface (the interstice between the loaded flanges) |
| σbr | Bearing stress |
| σv.m. | Von mises stress |
| τ | Shear stress |
| Φ | Basic force ratio (assumes n=1 and a concentric joint) |
| Φn | Force ratio of a concentric joint including the loading plane factor effect |
| Φe,n | Force ratio of an eccentric joint including the loading plane factor effect |
| ΦC | Force ratio of a joint with cantilever flanges |
| Ω | Fatigue damage |
| Ψ | Inversion compliance (used for circular flange compliance, see Section 7.3.1) |
| Subscript | Meaning |
| A | Axial stress |
| apex | Peak |
| av | Average |
| avail | Available |
| b | Fastener (or bolt, screw, etc.) |
| ben | Bending |
| br | bearing |
| brg | Bearing strength |
| c | Clamped parts (refers to the net elastic properties of all the clamped parts in a joint) |
| comb | Combined (loads) |
| con | Concentric |
| crit | Critical |
| crush | Crushing |
| e | Eccentrical |
| eff | Effective |
| eng | Engaged |
| free | Used for fastener or clamped parts lengths to indicate that the measure is in the absence of applied loading |
| g | Gasket |
| h | Head |
| lim | limiting |
| n | Nut |
| nom | Nominal |
| net | Net tension |
| max | Maximum |
| min | Minimum |
| Q | Shear |
| req | Required |
| S | Shear |
| sha | Shank |
| slip | Slipping |
| sep | Separation |
| SO | Shear out |
| sub | Substitutional |
| T0 | Reference temperature |
| TW | Working temperatue |
3.4.2 Lowercase variables
For the purpose of this document, the following lowercase variables apply:
Figure description:
- Text: ECSS
- Graphic: A blue-bordered parallelogram divided into two sections.
- Left section: Blue, italicized letter "E" on a white background.
- Right section: White letters "CSS" on a blue background.
3.4.3 Symbols
For the purpose of this document, the following symbols apply:
Figure description:
- Text: E CSS
- Description: A parallelogram graphic with a blue border. The left side has a white background with a blue italicized "E". The right side has a blue background with "CSS" in white.
Figure description:
Text: ECSS Entities: Letters "E", "C", "S", and "S". Visual Details:
- An italicized blue letter "E" on a white background.
- White letters "CSS" on a blue background.
- All elements are contained within a blue-bordered parallelogram.
3.4.4 Subscripts
For the purpose of this document, the following subscripts apply:
Figure description:
Text: ECSS Details: Italicized purple letter "E" on a white background, followed by white letters "CSS" on a purple background. All elements are enclosed within a purple-outlined parallelogram frame.
Subscript: Meaning: ti: Tightening th: Thread tot: Total (or overall) uh: Under head ult: Ultimate V: Preload y: yield