Proof Load / Tensile Strength of Bolts
The nominal capacity of a bolt to resist axial load is dependent on the cross sectional area of the bolt and its material properties. The most commonly used measure of fastener strength is the proof load, also referred to as the nominal tensile strength, which is a function of the cross sectional diameter of the bolt and the nominal yield stress of the material. This page is divided into the following sections:
- Introduction
- Nominal Tensile Strength
- Ultimate Tensile Strength
- Reference Values of Nominal and Ultimate Tensile Strength
References
- ISO 898-1:2013 – Mechanical properties of fasteners made of carbon steel and alloy steel. Part 1: Bolts, screws and studs with specified property classes – Coarse thread and fine pitch thread
- EN 1993-1-8:2005 – Eurocode 3 – Design of Steel Structures – Part 1-8 – Design of Joints
- E. Moore, F. Wald – Design of Structural Connections to Eurocode 3 – Frequently Asked Questions
- G. L. Kulak, J. W. Fisher, J. H, A. Struik – American Institute of Steel Construction (AISC) – Guide to Design Criteria for Bolted and Riveted Joints, Second Edition
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Bolt Strength / Strength of Fasteners | Nominal Shear Capacity of Bolts |
1. Introduction
The nominal capacity of a bolt to resist axial load is dependent on the section properties of the bolt (i.e. its size) and its material properties. The most commonly used measure of fastener strength is the proof load, also referred to as the nominal tensile strength. Other measures of bolt capacity are related to, for example, shear strength and bearing strength.
2. Proof Load / Nominal Tensile Strength
The proof load (or nominal tensile strength) of a fastener is determined based on the appropriate cross sectional diameter of the fastener and the nominal yield stress of the material. As explained on the page discussing bolt classifications (grades) the nominal yield stress of ISO fasteners in accordance with ISO 898-1:2013 [1] is related to the class designation system (e.g. Class 8.8, 10.9 etc). It should be noted that the nominal yield stress for a given ISO fastener classification is lower than the minimum permissible manufacturing yield stress stated in the standard ISO 898-1:2013 [1]; however it is normal to use the nominal values for design. For example, the nominal values for use in typical design are provided for use in Eurocode EN 1993-1-8:2005 (Design of Joints) [2].
The proof load of a bolt, S_{p} is calculated as:
(1)
Where:
= | the nominal tensile stress area (mm^{2}) | |
= | the nominal yield stress of the bolt (N.mm^{-2)*} |
*For convenience, I use the notation for nominal yield stress (f_{yb}) given in Eurocode EN 1993-1-8:2005 (Design of Joints) [2]. It is assumed that this is one of the most common design standards relevant to users of this website.
2.1 Calculation of Nominal Stress Area
The tensile stress of a threaded fastener could conservatively be calculated using the cross section of the root area, defined by the minor diameter (d_{3}). This is often used as a good estimate of fastener strength. However, threaded fasteners exhibit strengths greater than that predicted by the root area. In fact, they behave as though they have a larger cross sectional area. An empirical formula has been generated that accounts for this phenomenon which determines the nominal tensile area based on a diameter midway between the pitch diameter (d_{2}) and minor diameter (d_{3}). The nominal stress area is calculated using the following formula:
(2)
or alternatively:
(3)
The variables d_{2} and d_{3} are defined on the page discussing the basics of bolted joints.
2.2 A Word of Warning
Readers should note that estimating the strength of a fastener based on the are prescribed by the nominal diameter, d, is un-conservative and should be avoided unless you are making very rough scoping calculations. When using the nominal diameter for strength calculations you will over-estimate fastener strength by anything from 2.3% to 70.7% (!) depending on bolt diameter and thread form. This is potentially a huge discrepancy; however it should be noted that the average error is approximately 5-10%. I have made this mistake myself in the past and have been unpleasantly surprised to discover that when finalising a set of detailed calculations I then had to increase bolt size. I was designing an assembly within a tight space envelope and had laid out plate stiffeners in a beam connection around a certain bolt spacing. Increasing bolt size resulted in increasing bolt-spacing and then re-configuring the assembly. I have observed other engineers making the same mistake and encourage you not to follow in our steps by making a similar, unnecessary, but perhaps not so obvious oversight.
3. Ultimate Tensile Load
The ultimate tensile load of a fastener is determined based on the appropriate cross sectional diameter of the fastener and the Ultimate Tensile Stress (UTS) of the material. As explained on the page bolt classifications (grades), the UTS of ISO fasteners is related to the class designation system (e.g. 8.8, 10.9 etc). It should be noted that the nominal UTS stress for a given ISO fastener classification is lower than the minimum permissible manufacturing UTS stated in the standard ISO 898-1:2013 [1]; however it is normal to use the nominal values for design. For example, the nominal UTS values are provided for use in Eurocode EN 1993-1-8:2005 (Design of Joints) [2].
The Ultimate Tensile Load F_{m} is calculated as:
(4)
Where:
= | the nominal tensile stress area (mm^{2}) | |
= | the Ultimate Tensile Stress (UTS) of the bolt (N.mm^{-2)*} |
*For convenience, I use the notation for UTS (f_{ub}) given in Eurocode EN 1993-1-8:2005 (Design of Joints) [2]. It is assumed that this is one of the most common design standards relevant to users of this website.
4. Reference Values – Proof Load and Ultimate Tensile Load
Table 1 presents the nominal proof load and nominal tensile loads for typical bolt sizes across the common bolt classes in accordance with ISO 898-1:2013 [2]. All bolts in the table are of the more commonly available coarse thread form. When nominal fastener diameter is greater than 39mm (M39), care should be taken when using the proof and ultimate tensile loads stated in the table. The ISO 898-1:2013 [2] classification system only applies to fasteners up to M39; however the classifications can be applied, provided that all applicable requirements in Clauses 6 and 7 of the standard are respected. If in doubt, check with your supplier to verify the mechanical properties for fastener sizes greater than M39 before using them in a design. Generally, yield strength of steel reduces as thickness increases above around 16mm, especially if the material is hot rolled and this is should you should always be aware of.
Nominal Diameter (Major Diameter) | Thread Pitch | Nominal Stress Area (Tensile Area) | Class 4.6 | Class 8.8 | Class 10.9 | Class 12.9 | ||||
Nominal Stresses | Nominal Stresses | Nominal Stresses | Nominal Stresses | |||||||
Ultimate: | 600 MPa | Ultimate: | 800 MPa | Ultimate: | 1000 MPa | Ultimate: | 1200 MPa | |||
Proof: | 240 MPa | Proof: | 640 MPa | Proof: | 900 MPa | Proof: | 1080 MPa | |||
Nominal Diameter (Major Diameter) | Pitch | Nominal Stress Area (Tensile Area) | Ultimate Tensile Load | Nominal Tensile Proof Load | Ultimate Tensile Load | Nominal Tensile Proof Load | Ultimate Tensile Load | Nominal Tensile Proof Load | Ultimate Tensile Load | Nominal Tensile Proof Load |
D, d (mm) | P (mm) | Aσ (mm^2) | (kN) | (kN) | (kN) | (kN) | (kN) | (kN) | (kN) | (kN) |
1 | 0.25 | 0.460 | 0.18 | 0.11 | 0.37 | 0.29 | 0.46 | 0.41 | 0.55 | 0.50 |
1.2 | 0.25 | 0.732 | 0.29 | 0.18 | 0.59 | 0.47 | 0.73 | 0.66 | 0.88 | 0.79 |
1.6 | 0.35 | 1.270 | 0.51 | 0.30 | 1.02 | 0.81 | 1.27 | 1.14 | 1.52 | 1.37 |
2 | 0.4 | 2.073 | 0.83 | 0.50 | 1.66 | 1.33 | 2.07 | 1.87 | 2.49 | 2.24 |
2.5 | 0.45 | 3.391 | 1.36 | 0.81 | 2.71 | 2.17 | 3.39 | 3.05 | 4.07 | 3.66 |
3 | 0.5 | 5.031 | 2.01 | 1.21 | 4.02 | 3.22 | 5.03 | 4.53 | 6.04 | 5.43 |
4 | 0.7 | 8.777 | 3.51 | 2.11 | 7.02 | 5.62 | 8.78 | 7.90 | 10.53 | 9.48 |
5 | 0.8 | 14.181 | 5.67 | 3.40 | 11.35 | 9.08 | 14.18 | 12.76 | 17.02 | 15.32 |
6 | 1 | 20.120 | 8.05 | 4.83 | 16.10 | 12.88 | 20.12 | 18.11 | 24.14 | 21.73 |
8 | 1.25 | 36.609 | 14.64 | 8.79 | 29.29 | 23.43 | 36.61 | 32.95 | 43.93 | 39.54 |
10 | 1.5 | 57.990 | 23.20 | 13.92 | 46.39 | 37.11 | 57.99 | 52.19 | 69.59 | 62.63 |
12 | 1.75 | 84.267 | 33.71 | 20.22 | 67.41 | 53.93 | 84.27 | 75.84 | 101.12 | 91.01 |
16 | 2 | 156.670 | 62.67 | 37.60 | 125.34 | 100.27 | 156.67 | 141.00 | 188.00 | 169.20 |
20 | 2.5 | 244.796 | 97.92 | 58.75 | 195.84 | 156.67 | 244.80 | 220.32 | 293.76 | 264.38 |
24 | 3 | 352.490 | 141.00 | 84.60 | 281.99 | 225.59 | 352.49 | 317.24 | 422.99 | 380.69 |
30 | 3.5 | 560.591 | 224.24 | 134.54 | 448.47 | 358.78 | 560.59 | 504.53 | 672.71 | 605.44 |
36 | 4 | 816.728 | 326.69 | 196.01 | 653.38 | 522.71 | 816.73 | 735.05 | 980.07 | 882.07 |
42 | 4.5 | 1120.917 | 448.37 | 269.02 | 896.73 | 717.39 | 1120.92 | 1008.83 | 1345.10 | 1210.59 |
48 | 5 | 1473.124 | 589.25 | 353.55 | 1178.50 | 942.80 | 1473.12 | 1325.81 | 1767.75 | 1590.97 |
56 | 5.5 | 2030.029 | 812.01 | 487.21 | 1624.02 | 1299.22 | 2030.03 | 1827.03 | 2436.03 | 2192.43 |
64 | 6 | 2675.987 | 1070.39 | 642.24 | 2140.79 | 1712.63 | 2675.99 | 2408.39 | 3211.18 | 2890.07 |
72 | 6 | 3459.764 | 1383.91 | 830.34 | 2767.81 | 2214.25 | 3459.76 | 3113.79 | 4151.72 | 3736.54 |
80 | 6 | 4344.072 | 1737.63 | 1042.58 | 3475.26 | 2780.21 | 4344.07 | 3909.66 | 5212.89 | 4691.60 |
90 | 6 | 5590.828 | 2236.33 | 1341.80 | 4472.66 | 3578.13 | 5590.83 | 5031.75 | 6708.99 | 6038.09 |
100 | 6 | 6994.664 | 2797.87 | 1678.72 | 5595.73 | 4476.59 | 6994.66 | 6295.20 | 8393.60 | 7554.24 |
110 | 6 | 8555.580 | 3422.23 | 2053.34 | 6844.46 | 5475.57 | 8555.58 | 7700.02 | 10266.70 | 9240.03 |
125 | 6 | 11191.478 | 4476.59 | 2685.95 | 8953.18 | 7162.55 | 11191.48 | 10072.33 | 13429.77 | 12086.80 |
140 | 6 | 14180.805 | 5672.32 | 3403.39 | 11344.64 | 9075.72 | 14180.81 | 12762.72 | 17016.97 | 15315.27 |
160 | 8 | 18264.134 | 7305.65 | 4383.39 | 14611.31 | 11689.05 | 18264.13 | 16437.72 | 21916.96 | 19725.27 |
180 | 8 | 23369.054 | 9347.62 | 5608.57 | 18695.24 | 14956.19 | 23369.05 | 21032.15 | 28042.87 | 25238.58 |
200 | 8 | 29102.293 | 11640.92 | 6984.55 | 23281.83 | 18625.47 | 29102.29 | 26192.06 | 34922.75 | 31430.48 |
220 | 8 | 35463.850 | 14185.54 | 8511.32 | 28371.08 | 22696.86 | 35463.85 | 31917.46 | 42556.62 | 38300.96 |
250 | 8 | 46184.283 | 18473.71 | 11084.23 | 36947.43 | 29557.94 | 46184.28 | 41565.85 | 55421.14 | 49879.03 |
280 | 8 | 58318.432 | 23327.37 | 13996.42 | 46654.75 | 37323.80 | 58318.43 | 52486.59 | 69982.12 | 62983.91 |
NOTE: Check with your supplier to verify the mechanical properties for fastener sizes greater highlighted in orange as they are not automatically covered by ISO 898-1:2013 [2].