WRC 542

WRC 542

WRC 542


Stud and Nut Structural Tension Capacity Matching

Publication Date



F. Kirkemo

Publication Type


Number of Pages



This WRC bulletin addresses the issue of stud and nut structural tension capacity matching to ensure that stud fracture occurs prior to nut thread stripping.  Industry standards such as ISO 10423 (API 6A) [1], ISO 13533 (API 16A) [2], and ISO 13628-4 (API 17D) [3] allow the use of low strength heavy hex nuts, i.e. ASTM A194 [4] Grade 2HM, to be applied together with high strength studs, i.e. ASTM A320 [5] Grades L43 and L7, ASTM A453 [6] Grade 660, and ASTM A193 [7] Grade B7.  However, common industry practice outside ISO 10423 [1] (API 6A) is to select heavy hex nuts with similar strength and/or hardness to the studs, e.g. ASME VIII Div. 2 [8]/Div.3 [9], ISO 13628-7 [10] (API 17G), and ASTM A320 [5].


In practice it has been found that the behavior of different stud/nut assemblies may vary when tightening to failure or loading to failure in service.  In some cases the assemblies fail in tension through the stud threads while in other instances the threads of the nut strip.  Tensile failure of the stud is easily detected.  The initiation of stripping failure, though, is difficult to identify because the stripping develops gradually, some tension remains in the stud, and there is little or no visible damage.  Since replacement of damaged fasteners is essential for sound and safe joints, tensile failure of the stud is required.


Codes and standards have been reviewed and the following design requirements are found to be applicable for a nut in a stud/nut assembly:


a) The nut shall have a design capacity equal to or greater than the stud design capacity, e.g. the limit load of the nut shall be equal to or greater than the limit load of the stud, see ISO 10423 [1] (API 6A), ISO 13628-7 [10] (API 17G), and ASME VIII Div.2 [8]/Div. 3 [9].


b) The nut shall meet the proof load requirement.  For heavy hex ASTM A194 [4] nuts, the proof load capacity of the nuts shall be minimum 1.4 times the minimum ultimate tensile capacity of the high strength stud and minimum 1.5 times the minimum ultimate tensile capacity of the low strength stud, respectively; see ASTM A320 [5].  These requirements imply that the strongest stud in a stud/nut assembly will always physically break before the weakest nut fails by stripping.


The most severe condition shall govern the selection of nut material grade and hardness.  Note that tension capacities for studs and nuts are given as actual capacities in kips (kN) and not given as material strength in ksi (MPa).

In order to check the structural capacity of studs and nuts, design capacity formulas are needed.  In this technical note, formulas for stud tension capacities are found in the textbook, An Introduction to the Design and Behavior of Bolts and Bolted Joints [11], and nut tension capacity formula is established.  The nut tension capacity formula is based on the formula given in Annex B, ASME B1.1 [12], but slightly modified to include radial deformations due to radial thrust from threads and load carrying effectiveness of partial threads in the countersinks (or chamfers) at the ends of the nut threads, (VDI [13]).  The modified ASME B1.1 [12] formula which accounts for radial deformation of the nut is validated by highly-detailed axisymmetric elastic-plastic finite element analysis in Appendix A [12].  The formula is a simplified version of the Alexander's formula [14].

It should be noted that both stud and nut tension capacities are reduced during torquing compared to direct tension capacities without any torque, Viner et al [15].  Typical values may be in the range of 5-20% dependent on the coefficient of friction between contacting bodies during make-up.  These reductions are caused by torsion stress in the stud and torsion stress in the nut threads.  Torque effects are not considered in this note.


Hardness spot check tests and proof load testing (up to and including 1 ½") are used to ensure that nuts have sufficient structural capacity.  In this study correlations between hardness and yield/ultimate tensile strength for nuts are assumed to establish yield and tensile strength for the nuts.  These approximate correlations are used with the structural capacity formulas to validate minimum hardness requirements to meet the proof load capacity requirements in ASTM A194 [4].


The structural design checks, i.e. limit load checks, show that the 2HM nut limit loads are less than the stud limit loads for all sizes ranging from ½" UNC to 4" 8-UN.  For example, a design factor of 0.83 is applied for pressure testing in ISO 10423 [1] (API 6A), i.e. allowable stud stress is 83% of stud yield strength or equivalent allowable tensile load is 83% of stud limit load during pressure testing.  For a 2¼" stud/nut connection with Grade 2HM nut and Grade L43 stud utilized to 83% of the limit load during the pressure test, the nut is utilized to 100% of the nut limit, hence not fulfilling the ISO 10423 [1] (API 6A) design requirements, and is outside normal industry practice.


Calculations performed for nut proof load capacities indicate that the minimum hardness for nuts applied with low strength studs (A320 Grade L7M and A193 Grade B7M) should be in the range of 200 to 220 HBW and not 159 HBW as required in ASTM A194 [4].  If low grade nuts are proof loaded and reduced from 1.5 to 1.4 times the minimum ultimate tensile capacity of the stud, i.e. the same factor as is used for high strength nuts, 200 HBW seems to give sufficient proof load capacity up to 2".  200 HBW is the same minimum hardness that is required for A320 Grade L7M/A193 Grade B7M studs.  The minimum hardness requirement increases with increasing sizes.  For nuts equipped with high strength studs (A320 Grade L7/Grade L43) the minimum hardness should be 250 HBW up to 2".  Larger nuts seem to require higher hardness.  For larger size nuts, it is important to select nut material with chemistry which ensures through the thickness hardenability as hardness is measured on the outside while thread yield and tensile strength are governing the nut load carrying capacity.  This may not be the case for ASTM A194 [4] Grade 2HM nuts which have a relatively thin chemistry and limited hardenability.


Based on the calculations and evaluations performed in this work the following is recommended to ensure that the ASTM A194 [4] heavy hex nut meets the design requirements (Items 1 and 2 above):


a) Low strength nuts like ASTM A194 [4] Grade 2HM heavy hex nuts shall not be used in combination with high strength studs like ASTM A320 [5] L7/L43 as allowed by ISO 10423 [1] (API 6A).


b) Studs shall be equipped with heavy hex nuts with a grade and minimum hardness of steel similar to that of the studs.


c) Proof loads of nuts shall be based on the stud grade, e.g. ASTM A194 [4] Grade 2HM nuts applied to ASTM A320 [5] L43 studs shall be proof loaded as ASTM A194 [4] Grade 7 nuts.  This issue is not addressed in ISO 10423 [1] (API 6A).


d) Low strength heavy hex nuts like ASTM A194 [4] Grades 2HM and 7M shall have the same minimum hardness as the low strength studs like ASTM A193 [7] Grade B7M and ASTM A320 [5] Grade L7M.  This means that the minimum hardness of the matching nuts shall be increased from 159 HBW or 84 HRB to 200 HBW or 93 HRB for low strength nuts.


e) The proof load test requirements in ASTM A194 [4] appear to be somewhat higher than the calculated minimum ultimate tensile capacity of the nuts, especially for large diameter (> 2") low strength nuts (ASTM A194 [4] Grade 2HM/7M).


The derived nut tension capacity formula is also applied to evaluate nut thread stripping for a few ISO 898-1 [16] studs and ISO 898-2 [17] nuts with 8.8/8 and 10.9/9 property class.  In ISO 898-2 [17] proof load capacity is the minimum ultimate tensile capacity of the stud (typical).  ISO 898-2 [17] nuts have much lower proof loads relative to stud minimum tensile capacities than heavy hex ASTM A194 [4] nuts.  This may explain why thread stripping sometimes occurs with ISO 898-2 [17] nuts, Hagiwara and Sakai [18].  The calculations indicate that property class 8 style 2 nuts seem to have low hardness to meet the proof load test requirement.  Note that ASME B1.1 [12] indicates similar nut tension capacity requirement to ISO 898-2 [17] be applied for noncritical design.


Preload loss due to stud loaded beyond its preload level (67% of stud yield) has been calculated by 2D axisymmetric elastic-plastic finite element analysis with modeling of stud and nut threads.  Stud/nut assemblies preloaded to 67% of stud yield capacity start to lose significant preload when loaded in excess of 75% of the stud yield capacity.  The loss of preload increases with increased load level in excess of preload, reduced nut yield strength compared to the stud yield strength, and for increased stud axial stiffness.



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