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IS20

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i

NASA/TM—2012–217454

Aerospace Threaded Fastener Strength

in Combined Shear and Tension Loading

B.E. Steeve and R.J. Wingate

Marshall Space Flight Center, Huntsville, Alabama

March 2012

National Aeronautics and

Space Administration

Marshall Space Flight Center • Huntsville, Alabama 35812
ii

Available from:

NASA Center for AeroSpace Information

7115 Standard Drive

Hanover, MD 21076 –1320

443–757–5802

This report is also available in electronic form at

<https://www2.sti.nasa.gov/login/wt/>

Acknowledgments

The authors would like to gratefully acknowledge Dr. Michael Dube and the NASA Engineering and Safety Center 

for their support and funding of this test effort, Myron Tapscott for his effort manufacturing the test fixtures, 

and James Hodo for his work executing the tests.
iii

TABLE OF CONTENTS

1. INTRODUCTION ............................................................................................................. 1

2. DESIGN FAILURE CRITERIA ....................................................................................... 3

3. TEST CONFIGURATION ................................................................................................ 7

4. TEST PROCEDURE .......................................................................................................... 9

5. TEST RESULTS ................................................................................................................. 10

5.1 Thread Stripping Failure Mode .................................................................................... 12

6. DATA ASSESSMENT ....................................................................................................... 14

6.1 Effect of Preload ........................................................................................................... 14

6.2 Shear Plane Location .................................................................................................... 14

6.3 Existing Failure Criteria ............................................................................................... 15

6.4 Modified Failure Criteria .............................................................................................. 17

6.5 Specification Versus Actual Strength ............................................................................ 20

7. CONCLUSIONS ................................................................................................................ 21

APPENDIX—TORQUE-TENSION TEST DATA ................................................................ 22

REFERENCES ....................................................................................................................... 23
iv
v

LIST OF FIGURES

 1. Maximum normal and shear stress failure criteria ..................................................... 4

 2. Threaded fastener failure criterion ............................................................................. 5

 3. Test fixtures installed in test machine grips ................................................................ 7

 4. Bolt and nut configuration ......................................................................................... 8

 5. Bolt and insert configuration ..................................................................................... 8

 6. Fractured bolts with the shear plane in the body. Loading angles of (a) 22.5°, 

(b) 45°, (c) 67.5°, and (d) 90° ..................................................................................... 11

 7. Fractured bolts with the shear plane in the threads. Loading angles of (a) 22.5°,

(b) 45°, (c) 67.5°, and (d) 90° ..................................................................................... 12

 8. Tension load only bolts with thread shear failure ...................................................... 12

 9. Tension load only bolts with bolt failure in the threads ............................................. 13

10. Ultimate bolt shear and tension load results .............................................................. 14

11. Ultimate bolt shear and tension stress results ............................................................ 15

12. Ultimate shear and tension ratios .............................................................................. 16

13. Relative displacement of test fixture faces in bolt axial direction ............................... 17

14. Test data versus failure criteria for shear plane in the body ........................................ 18

15. Chesson and test data versus failure criteria for shear plane in the body .................... 19

16. Test data versus failure criteria for shear plane in the body in the threads ................. 20

17. Fastener with nut torque-tension data ....................................................................... 22

18. Fastener with insert torque-tension data .................................................................... 22
vi

LIST OF TABLES

1. Test matrix ................................................................................................................... 2

2. Test result summary ..................................................................................................... 10
vii

NOMENCLATURE

Abody area of full diameter body section of a bolt

At tensile stress area of the threaded section of a bolt

Fult_test maximum applied test load at rupture

K ratio of bolt allowable shear load to allowable tensile load

k ratio of ultimate shear stress to ultimate tensile stress

P axial tensile load applied to a bolt as a result of tensile load applied to a joint

Pallow bolt allowable ultimate tensile load

Pallow_thread bolt allowable ultimate tensile load based on failure in the threaded section

Pult bolt tensile load at failure

Rs ratio of applied shear load to allowable ultimate shear load =V/Vallow

Rs_body ratio of applied shear load to bolt body allowable ultimate 

shear load =V/Vallow_body

Rt ratio of applied tensile load to bolt allowable ultimate tensile load

(neglecting preload) =P/Pallow

Rt_thread ratio of applied tensile load to thread allowable tensile load =P/Pallow_thread

V shear load applied to a bolt as a result of shear load applied to a joint

Vallow bolt allowable ultimate shear load =Vallow_body or Vallow_thread

Vallow_body bolt allowable ultimate shear load based on failure in the full diameter 

body section

Vallow_thread bolt allowable ultimate shear load based on failure in the threaded section

Vult bolt shear load at failure

q loading angle relative to the bolt axis

s normal stress

t shear stress
viii
1

TECHNICAL MEMORANDUM

AEROSPACE THREADED FASTENER STRENGTH IN COMBINED

SHEAR AND TENSION LOADING

1. INTRODUCTION

The strength capability of aerospace threaded fasteners is typically specified as a minimum 

tensile strength or minimum double shear strength in either a standard part or procurement specification. These values are usually derived by multiplying the thread tensile stress area by the design 

allowable ultimate tensile stress of the fastener material or by multiplying the area of the full diameter body (herein referred to as the body) by the design allowable ultimate shear stress, respectively.

Acceptance testing is performed on manufacturing lots to verify that each lot of bolts is at least as 

strong as the minimum specification values.

The specification strength values are only applicable to fasteners that are loaded in either 

pure tension or pure shear. For bolted joints that do not have a design feature to react applied shear 

loads, the bolts are required to carry a combination of shear and tension loading. Load interaction failure criteria exist for members in combined shear and tension loading,1 including a commonly used criterion specifically for threaded fasteners.1–4 However, a survey of literature reveals 

that there is little data available to validate these failure criteria for aerospace bolts in a typical 

preloaded joint installation. Furthermore, these existing failure criteria are intended for instances 

where the shear plane is at a smooth, constant cross section and do not necessarily apply to 

a threaded fastener with the shear plane through the threads.

A test program was initiated by Marshall Space Flight Center and sponsored by the NASA 

Engineering and Safety Center to validate existing combined loading failure criteria and to quantify the effect of threads in the shear plane. The testing consisted of a series of 46 tests of individual bolts. The bolts were loaded to failure at several angles relative to the bolt axis, similar to 

test method MIL-STD-1312-2,5 using a custom designed test fixture. The testing included a group of 

fasteners with the shear plane passing through the full diameter body and a group of fasteners with the 

shear plane passing through the threads. Both of these groups were further divided into fasteners that 

were installed with zero preload and fasteners that were installed with a high initial preload. Table 1 lists 

the complete test matrix.
2

Table 1. Test matrix.

Condition Shear Plane Load Orientation

Assembly 

Preload

Quantity 

Tested

1 Body Tension-only 0° None 6

2 Body Shear-only 90° None 3

3 Threads Shear-only 90° None 3

4 Body Shear-only 90° High 3

5 Threads Shear-only 90° High 3

6 Body Shear and tension 45° None 3

7 Threads Shear and tension 45° None 3

8 Body Shear and tension 45° High 3

9 Threads Shear and tension 45° High 3

10 Body Shear and tension 22.5° None 2

11 Threads Shear and tension 22.5° None 2

12 Body Shear and tension 22.5° High 2

13 Threads Shear and tension 22.5° High 2

14 Body Shear and tension 67.5° None 2

15 Threads Shear and tension 67.5° None 2

16 Body Shear and tension 67.5° High 2

17 Threads Shear and tension 67.5° High 2
3

2. DESIGN FAILURE CRITERIA

The criterion typically used to predict the ultimate failure of a member in combined shear 

and tension is based on the maximum normal stress and maximum shear stress theories.1 For the 

case of combined shear and uniaxial tension loading, the maximum principal and shear stresses 

are given as follows:

σ max = σ

2

+

σ

2

⎛

⎝

⎜ ⎞

⎠

⎟

2

+ τ

2 (1a)

and

τ max = σ

2

⎛

⎝

⎜ ⎞

⎠

⎟

2

+ τ

2 . (1b)

If the allowable stresses in shear and tension are given as tult and sult, respectively, then 

let Rs=τ/tult, Rt=s/sult, and k=tult/sult. If failure is defined when the maximum shear stress is tult

or the maximum principal stress is sult, the above equations can then be written as the following 

failure criteria:

1 = Rt

2

+

Rt

2

⎛

⎝

⎜ ⎞

⎠

⎟

2

+ (kRs)

2 (2a)

and

1 = Rt

2k

⎛

⎝

⎜ ⎞

⎠

⎟

2

+ (Rs)

2 . (2b)

These two equations are plotted in figure 1 for k values of 0.5, 0.6, and 0.7. For values of k

greater than 0.5, the bounding failure envelope consists of a combination of the maximum normal 

and shear stress curves. It is convenient and conservative to use the maximum shear stress criterion 

equation with k=0.5, and this is the criterion usually cited for a member loaded in combined shear 

and tension. When k=0.5, the maximum shear stress failure criterion simplifies to the following 

single interaction equation, where Rs and Rt are the shear and tension load ratios, respectively:

Rs

2 + Rt2 = 1 . (3)
4

The failure criterion given by equation (3) is a stress-based criterion for a material at a given 

point. Often the form of this criterion is used as a load-based criterion for compact sections by 

changing the normal stress s to a normal load P, the shear stress τ to a shear load V, and material 

stress allowables sult and τult to load allowables Pallow and Vallow, respectively, as shown in 

equation (4):

Rs

2 + Rt2 = V

Vallow

⎛

⎝

⎜

⎞

⎠

⎟

2

+

P

Pallow

⎛

⎝

⎜

⎞

⎠

⎟

2

= 1 . (4)

k=0.7

k=0.6

k=0.5

k=0.5

k=0.6

k=0.7

Max Normal Stress Criterion

Max Shear Stress Criterion

1.6

1.4

1.2

1 

0.8

0.6

0.4

0.2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Rs

Rt Figure 1. Maximum normal and shear stress failure criteria.

The failure behavior of a threaded fastener with the shear plane passing though the body 

of the fastener is determined by the shear strength of the body and the tensile strength of the 

threads. Since the tensile strength of the threads is less than the tensile strength of the body, and 

the shear and tensile failures occur at different locations, the criterion of equation (4) cannot be 

used as a single equation criterion for threaded fasteners with the shear plane through the body.

The failure criterion commonly used for threaded fasteners in combined shear and tension 

loading is given by equation (5). References 1–3 indicate that this criterion was originally developed 

for the AN series aircraft bolts, and references 1 and 3 indicate it is based on testing; however, the 

test data have not been located in a survey of the available literature. Equation (5) is the failure 

criterion that will be used to compare against the test data herein for the test configuration with the 

shear plane through the body:
5

Rs _ body

3 + Rt _ thread2 = V

Vallow_body

⎛

⎝

⎜

⎞

⎠

⎟

3

+

P

Pallow_thread

⎛

⎝

⎜

⎞

⎠

⎟

2

= 1 . (5)

The criterion of equation (5) can be compared against the maximum normal and maximum 

shear stress criteria by introducing an effective shear to tensile allowable load ratio, K=Vallow/Pallow. 

For a threaded fastener, the ratio of the tensile strength of the body to the tensile strength of the 

threads is given by the ratio of tensile area of the body to the tensile stress area of the threads, which 

for a 0.375-24 UNJ bolt is given as 1.161.6–8 If the material shear to tensile allowable stress ratio is 0.5, 

as assumed for equation (4), then the bolt shear to tensile allowable load ratio K=0.5×1.161=0.581. 

The maximum normal and maximum shear stress failure curves for k=0.581 are shown in figure 2. 

Equation (5) is also plotted in figure 2, and it can be seen that this equation approximately follows the 

failure envelope defined by the K=0.581 maximum normal and maximum shear failure curves. Therefore, while equation (5) is an empirically-based, single equation failure criterion, it is similar to the 

failure envelope predicted by the maximum normal and maximum shear stress theories.

k=0.5 k=0.581

k=0.581

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Rs

Rt

Rs 3+ Rt

2=1

Max Normal Stress Criterion

Max Shear Stress Criterion

Figure 2. Threaded fastener failure criterion.
6

There is no unique combined shear and tension load failure criterion intended specifically 

for threaded fasteners when the shear plane passes through the threads. For this condition, it is 

often assumed the criterion of equation (4) applies, where the allowable loads are the shear and 

tensile strength of the threaded region as shown in equation (6). Equation (6) will be used to compare against the test data herein for the test configuration with the shear plane through the threads:

Rs _ thread

2 + Rt _ thread2 = V

Vallow_thread

⎛

⎝

⎜

⎞

⎠

⎟

2

+

P

Pallow_thread

⎛

⎝

⎜

⎞

⎠

⎟

2

= 1 . (6)

The combined shear and tension load failure criterion in reference 4 has the same form as 

equation (5) but the shear and tensile load allowables are “based on the cross section at which the 

combined loads occur.” The resulting failure criterion is given in equation (7). This criterion is not 

in agreement with the maximum normal and maximum shear stress theories, nor is it based on test, 

and it is less conservative than equations (4) or (5). The use of this criterion with shear and tensile 

load allowables from the same cross section is not recommended.

Rs

3 + Rt2 = V

Vallow

⎛

⎝

⎜

⎞

⎠

⎟

3

+

P

Pallow

⎛

⎝

⎜

⎞

⎠

⎟

2

= 1 . (7)

The failure criteria presented above assume the only significant loading at the failure cross 

section is shear and tension. Bending moment is assumed to be zero or insignificant. For bolts 

under shear loading, moment does develop within the length of the bolt but it is nearly zero at 

the shear plane. Since the failure plane of all the test bolts with shear loading occurred at the 

shear plane, moment is not considered. If moments are not insignificant at the shear plane due to 

the nature of the applied loading, or if the configuration of the joint includes shims or gaps, then 

moment should be considered. However, it is outside the scope of this Technical Memorandum 

(TM) to determine the influence of moment on the combined loading failure criteria.
7

3. TEST CONFIGURATION

The testing reported in this TM consisted of 46 tests of individual bolts to failure. The testing was performed using a load frame with a set of fixtures that can orient the load over a range of 

discrete angles from 0° to 90° relative to the bolt axis. Pure tension corresponds to a loading angle 

of 0° and pure shear corresponds to a loading angle of 90°. Figure 3 shows the fixtures installed in 

the load frame with the loading angle set at 45°.

90° 67.5° 45°

22.5°

0°

Region of

Speckle Pattern

Ftest

V P

θ

Figure 3. Test fixtures installed in test machine grips.

The bolts were installed into the test fixtures using interfacing pucks as the bolted joint 

members. The pucks transferred the load from the test fixture to the bolt and were sized to be able 

to install the same size diameter and length bolt with either a nut or with an insert. The pucks in 

the nut configuration were sized to place the shear plane through the body of the bolt, and the 

pucks in the insert configuration were sized to place the shear plane through the threads of the 
8

bolt. For the insert configuration, a threaded heavy-duty, key-locked insert was installed into an 

aluminum 7075 alloy puck. All other pucks were made from 440C stainless steel. Figure 4 shows a 

cross-section sketch of the bolt and nut configuration, and figure 5 shows the bolt and insert configuration.

 

Figure 4. Bolt and nut configuration. Figure 5. Bolt and insert configuration.

All of the bolt specimens were 3/8-in bolts of type NAS1956C14 and were procured from 

the same manufacturing lot. The bolt material was A-286 corrosion-resistant steel heat treated 

to a minimum of 180 ksi ultimate tensile strength and 108 ksi ultimate shear strength. The nuts 

were of type NAS1805-6, and the inserts were of type NAS1395C6L. The washers were of type 

NAS1587-6 or -6C. A lubricant was applied to the faying surfaces of the pucks to minimize the 

transfer of shear load by friction.
9

4. TEST PROCEDURE

The loading of the bolts was performed by the tensile load frame operating under displacement control. The loading rate was ≈0.024 in/min for all tests. The data collected for each test 

included the load frame load cell force and the cross head displacement. Additional displacement 

data were obtained using a video displacement measuring system. This system measured displacement of the test fixture face adjacent to the pucks by monitoring a speckle pattern of paint applied 

to the surface of both fixtures as indicated in figure 3.

The bolts were installed into the pucks with either no preload or a high preload. In the nopreload tests, the bolts were installed by hand until the bolt was just seated. In the high-preload 

tests, the bolts were intended to be installed with a torque wrench until the torque reached a value 

corresponding to a preload level of ≈8,000 lb (47% of the bolt minimum specified ultimate tensile 

strength) based on results from previously performed torque-tension testing (see appendix). The 

target torque was 400 in-lb for the nut configuration, and the target torque was 1,200 in-lb for the 

insert configuration. During bolt installation into the second insert test article, the fastener broke 

before reaching 1,200 in-lb. The failure was attributed to tensile overload thought to be a result 

of large variability in the torque-preload relationship for this fastening system. Subsequent insert 

configurations were then installed to a torque value of 600 in-lb.
10

5. TEST RESULTS

A summary of the test results is listed in table 2. The ultimate load listed is the maximum 

applied load that was achieved during the test, Fult_test. The bolt ultimate tension load Pult is 

Fult_test×cos(θ), and the bolt ultimate shear load Vult is Fult_test×sin(θ). Figures 6 and 7 show 

representative fractured bolts with the shear plane through the body and through the threads, 

respectively, at four loading angles.

Table 2. Test result summary.

Condition

Load

Orientation,

θ (deg) Shear Plane

Installation 

Torque

(in-lb)

Ultimate

Load, Fult_test

(lb)

Failure

Location

1 0 Body 0 17,366 <1>

1 0 Body 0 17,679 <1>

1 0 Body 0 17,465 <1>

1 0 Body 0 20,164 Threads

1 0 Body 0 20,529 Threads

1 0 Body 0 20,229 Threads

10 22.5 Body 0 18,829 Body

10 22.5 Body 0 19,081 Body

6 45 Body 0 15,267 Body

6 45 Body 0 15,319 Body

6 45 Body 0 15,316 Body

14 67.5 Body 0 13,626 Body

14 67.5 Body 0 13,615 Body

2 90 Body 0 13,339 Body

2 90 Body 0 13,346 Body

2 90 Body 0 13,489 Body

11 22.5 Threads 0 15,084 Threads

11 22.5 Threads 0 15,100 Threads

7 45 Threads 0 11,997 Threads

7 45 Threads 0 12,046 Threads

7 45 Threads 0 <2> <2>

15 67.5 Threads 0 10,415 Threads

15 67.5 Threads 0 10,377 Threads

3 90 Threads 0 10,163 Threads

3 90 Threads 0 9,995 Threads

3 90 Threads 0 <2> <2>

12 22.5 Body 400 18,746 <1>
11

Condition

Load

Orientation,

θ (deg) Shear Plane

Installation 

Torque

(in-lb)

Ultimate

Load, Fult_test

(lb)

Failure

Location

12 22.5 Body 400 18,423 <1>

8 45 Body 400 15,382 Body

8 45 Body 400 15,343 Body

8 45 Body 400 15,292 Body

16 67.5 Body 400 13,599 Body

16 67.5 Body 400 <2> <2>

4 90 Body 400 13,337 Body

4 90 Body 400 13,373 Body

4 90 Body 400 13,302 Body

13 22.5 Threads 600 15,170 Threads

13 22.5 Threads 600 15,122 Threads

9 45 Threads 600 12,070 Threads

9 45 Threads 600 12,088 Threads

9 45 Threads 600 11,636 Threads

17 67.5 Threads 600 10,255 Threads

17 67.5 Threads 600 10,529 Threads

5 90 Threads 1,200 9,706 Threads

5 90 Threads 600 9,785 Threads

5 90 Threads <3> <3> <3>

<1> Specimen failure mode was stripping of the threads.

<2> Test data file lost.

<3> Specimen failed during application of 1,200 in-lb of torque.

Figure 6. Fractured bolts with the shear plane in the body. Loading angles of

(a) 22.5°, (b) 45°, (c) 67.5°, and (d) 90°.

Table 2. Test result summary (Continued).
12

Figure 7. Fractured bolts with the shear plane in the threads. Loading

angles of (a) 22.5°, (b) 45°, (c) 67.5°, and (d) 90°.

5.1 Thread Stripping Failure Mode

Five of the tests resulted in a combined bolt and nut thread stripping failure mode. The five 

tests were the first three tension-only tests and the two tests with high preload, shear plane in the 

body, and loaded at 22.5°. The three tension-only tests failed at an average value of 17,503 lb when 

using the NAS1805 nut. Figure 8 shows these failed bolts and nuts.

Figure 8. Tension load only bolts with thread shear failure.
13

The tensile-only tests were repeated using higher strength H20-6 220 ksi alloy steel nuts. 

These tests resulted in the tensile failure of the bolts in the threads at an average load of 20,307 lb. 

Figure 9 shows the failed bolts. For comparison, the specification minimum tensile strength is 

17,100 lb, and the lot acceptance tensile strength is 21,871 lb.

Figure 9. Tension load only bolts with bolt failure in the threads.

The two tests that failed by thread stripping and loaded at 22.5° also had the NAS1805 nuts 

and failed at an average load of 18,584 lb. This corresponds to an average tensile load of 17,170 lb 

and an average shear load of 7,112 lb. The minimum failure load was 18,423 lb, which corresponds 

to a tensile load of 17,021 lb and a shear load of 7,050 lb. This minimum tensile load is just under 

the specification tensile strength of the bolt and nut of 17,100 lb.
14

6. DATA ASSESSMENT

6.1 Effect of Preload

The bolt shear and tension ultimate load for each test is plotted in figure 10. It can be seen 

that the addition of preload did not affect the ultimate external load capability of the bolts. This 

result is consistent with the findings of other studies.9,10 The mechanisms behind this behavior 

are understood to be joint separation prior to bolt failure under tensile loading and relaxation 

of preload due to plastic deformations under shear loading. 

24,000

22,000

20,000

18,000

16,000

14,000

12,000

10,000

8,000

6,000

4,000

2,000

0

0 2,000 4,000 6,000 8,000

Shear (lb)

10,000 12,000 14,000 16,000

22.5°

45°

67.5°

90°

Body Shear Plane—No Preload

Body Shear Plane—High Preload

Thread Shear Plane—No Preload

Thread Shear Plane—High Preload

Tension (lb)

Figure 10. Ultimate bolt shear and tension load results.

6.2 Shear Plane Location

Based on the 90° test results, the average shear strength of the body section is 13,364 lb, 

and the average shear strength of the threaded section is 9,912 lb. The ratio between the thread 

and body shear strength values is 0.742. The cross-sectional area of the body is 0.1093 in2 based 

on the minimum diameter of the body,6 and the cross-sectional area of the threads is 0.0811 in2

based on the minimum minor diameter of the threads.8 The ratio between the thread and body 

minimum cross-sectional areas is 0.742. Therefore, the difference between the thread and body 
15

shear strengths can be completely explained by the difference between the cross-sectional areas 

when using the minimum body and thread minor diameters.

The net section stress at failure for each of the tests is plotted in figure 11, where the failure 

stress is determined by dividing the failure load by the original area of the failure plane. The failure 

behavior of the bolts with the shear plane in the threads is consistent with the behavior of the bolts 

with the shear plane in the body under combined shear and tension loading. Simply accounting for 

the reduced cross-sectional area of the threads is sufficient to determine the ultimate capability of 

fasteners with the shear plane in the threads under all combinations of shear and tension loading. 

No additional adjustment to the strength of bolts with the shear plane in the threaded section 

is necessary.

240

220

200

180

160

140

120

100

80

60

40

20

0

0 20 40 60 80 100 120 140

Body Shear Plane—No Preload

Body Shear Plane—High Preload

Thread Shear Plane—No Preload

Thread Shear Plane—High Preload

Shear Stress (ksi)

Tensile Stress (ksi)

Figure 11. Ultimate bolt shear and tension stress results.

6.3 Existing Failure Criteria

Based on the average of the test results, the following allowable shear and tensile strengths 

are determined for the body and threaded sections of the test bolts: Pallow_thread=20,307 lb, 

Vallow_body=13,364 lb, and Vallow_thread=9,912 lb.

The loading ratio results are plotted in figure 12 using the allowable loads listed above. 

The failure criteria of equations (5) and (6) are also plotted. The combined loading data points 

for the body shear plane tests fall within the relevant failure criterion of equation (5). The combined loading data points for the thread shear plane tests fall within the relevant failure criterion 
16

of equation (6). Therefore, the existing combined loading failure criteria overpredict the strength 

of the bolts in this test program.

It is proposed that the source for this discrepancy is bending that developed during the testing. The application of tension loads caused the joint to separate before the bolt ruptured, which 

allowed some bending to develop due to the simultaneously applied shear load. Joint separation 

was observed during some of the tests. The displacement of the faying surfaces was not directly 

measured during testing, but the video photogrammetry measurements of the fixture faces indicated relative displacement along the bolt axial direction of up to 0.079 in at failure for the 22.5° 

loading angle. Figure 13 shows the relative displacement between the two fixtures in the bolt axial 

direction for each loading angle from representative tests without preload. During the pure shear 

load tests, the fixture faces moved towards each other, so there was likely no separation for the 90° 

loading angle.

Figure 12. Ultimate shear and tension ratios.

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Rs_body3+ Rt_thread2=1

Rs_thread2+ Rt_thread2=1

Rs

Body Shear Plane—No Preload

Body Shear Plane—High Preload

Thread Shear Plane—No Preload

Thread Shear Plane—High Preload

Rt
17

20,000

18,000

16,000

14,000

12,000

10,000

8,000

6,000

4,000

2,000

0

–0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

90° 67.5°

45°

22.5°

Applied Load (lbs)

Relative Axial Displacement (in)

Figure 13. Relative displacement of test fixture faces in bolt axial direction.

The testing performed by Olson subjected smooth titanium and steel bars to combined 

tension and double shear loading.9 The failure criterion of equation (4) matched the results from 

Olson’s testing quite well. Olson’s double shear test configuration does not allow joint separation, 

which indicates that the discrepancy between the results of this TM and the failure criteria of equations (5) and (6) is likely due to the joint separation and bending that occurs under the single shear 

configuration.

6.4 Modified Failure Criteria

The test ultimate loading ratios for the bolts with the shear plane in the body are plotted 

against the failure criterion of equation (5) in figure 14. Equation (5) overpredicts the test results 

for the combined shear and tension loading conditions by as much as 7%. A modification of the 

criterion of equation (5) that better matches the data with the shear plane in the body is given by 

equation (8) and is also plotted in figure 14:

Rs _ body

2.5 + Rt _ thread1.5 = V

Vallow _ body

⎛

⎝

⎜

⎞

⎠

⎟

2.5

+

P

Pallow _ thread

⎛

⎝

⎜

⎞

⎠

⎟

1.5

= 1 . (8)
18

(Rs_body)

3+ (Rt_thread)2=1

[(Rs_body)

3+ (Rt_thread)2=1] specification 

(Rs_body)

2.5+ (Rt_thread)1.5=1

1.1

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Rs

Rt

Body Shear Plane—No Preload

Body Shear Plane—High Preload

Figure 14. Test data versus failure criteria for shear plane in the body.

Similar combined single shear and tension testing was performed by Chesson et al. using 

high-strength A325 bolts.11 The test data from both Chesson and the results reported herein, with 

the shear plane in the body, are plotted in figure 15. Both sets of data fall short of the capability 

predicted by equation (5) but match equation (8). 

The modified failure criterion of equation (8) is a potential criterion for all bolts in joints 

with no gaps or shims, a single shear plane in the body, and loaded in combined shear and tension, where the joint is expected to separate before the bolt ruptures. This criterion accounts for the 

bending that develops after joint separation and does not require the determination of the applied 

or allowable bending moment. For bolts in joints that are not expected to separate prior to rupture, 

the criterion of equation (5) is expected to apply.
19

(Rs_body)

3+ (Rt_thread)2=1

(Rs_body2.5+ Rt_thread)

1.5=1

Body Shear Plane—No Preload

Body Shear Plane—High Preload

Chesson Data Body Shear Plane

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Rt

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Rs

Figure 15. Chesson and test data versus failure criteria for shear plane

in the body.

The test ultimate loading ratios for the bolts with the shear plane in the threads are plotted 

against the criteria of equations (6) and (7) in figure 16. The failure criteria given by equations (6) 

and (7) overpredict the ultimate load capability of the bolts by as much as 10% for equation (6) 

and 16% for equation (7) at the 22.5° loading angle. A modified failure criterion that provides 

a good match to the test data is given by equation (9), which is also plotted in figure 16:

Rs _ thread

1.2 + Rt _ thread2 = V

Vallow _ thread

⎛

⎝

⎜

⎞

⎠

⎟

1.2

+

P

Pallow _ thread

⎛

⎝

⎜

⎞

⎠

⎟

2

= 1 . (9)

Like equation (8), the modified failure criterion of equation (9) is a potential criterion for all 

bolts in joints with no gaps or shims, a single shear plane in the threads, and loaded in combined 

shear and tension, where the joint is expected to separate before the bolt ruptures. For bolts in 

joints that are not expected to separate prior to rupture, the criterion of equation (6) is expected 

to apply.
20

Rs_thread3+ Rt_thread2=1

Rs_thread1.2+ Rt_thread2=1

Rs_thread2+ Rt_thread2=1

1.1

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Rs

Rt

Thread Shear Plane—No Preload

Thread Shear Plane—High Preload

Figure 16. Test data versus failure criteria for shear plane in the threads.

6.5 Specification Versus Actual Strength

While the failure criteria of equations (5)–(7) overpredict the capability of the bolts under 

combined shear and tension loads when the actual strength of the test bolts is used as the allowable, the criteria are conservative when the minimum specified strengths of the bolts are used as the 

allowable. Figure 14 shows the failure curve for equation (5) using the minimum shear and tension 

strengths from the bolt specification, normalized to the average measured strengths from the test 

specimens.
21

7. CONCLUSIONS

The results of this test program confirm that the application of an initial preload does not 

affect the ultimate strength capability of a bolt in shear, tension, or combined shear and tension 

loading when the joint separates before the bolt ruptures under pure tension loading. 

The decrease in shear strength when the failure plane is in the threaded section compared 

to the body section is accounted for by the change in cross-sectional area between the body and 

the area of the threaded section based on the minor diameter. No other strength adjustment is 

required.

The common existing failure criteria used to assess bolt strength overpredicted the strength 

of the test bolts in combined shear and tension loading when using the actual fastener strengths. 

The likely cause is due to separation of the joint, which allowed bending to develop within the 

fastener under the simultaneously applied shear load. 

Modifications to the existing failure criteria are proposed that match the results of this 

test program and can be considered candidate criteria to be used for bolts under combined single 

shear and tension loading when joint separation before rupture is predicted. The modified criteria 

account for any bending that occurs under combined loading, thus avoiding the need to estimate 

the applied and allowed bending load. 

The common existing combined loading failure criteria have extensive successful use in the 

aerospace industry. One contributing factor to this success was demonstrated in the test results: the 

actual shear and tensile strength of the test bolts were significantly higher than the minimum specified strengths. All of the common criteria would conservatively underpredict the capability of the 

test bolts, under all load combinations, when using the specification strengths.
22

APPENDIX—TORQUE-TENSION TEST DATA

The torque-tension test data for a fastener for a with nut is shown in figure 17 and for a fastener with insert in figure 18.

12,000

10,000

8,000

6,000

4,000

2,000

0

0 100 200 300

Torque (in-lb)

400 500 600

Fastener: NAS1956-C14

Nut: NAS1805-6

Washer: NAS1857-6 & -6C

Lube: Dow Corning 321 Dry Film Spray

 Applied to Threads and Washer Facing Nut

Nut1 Cycle 1

Nut1 Cycle 2

Nut1 Cycle 3

Nut2 Cycle 1

Nut2 Cycle 2

Nut2 Cycle 3

Force (lb)

Figure 17. Fastener with nut torque-tension data.

9,000

8,000

7,000

6,000

5,000

4,000

3,000

2,000

1,000

0

0 200 400 600 800 1,000 1,200 1,400

Fastener: NAS1956-C14

Insert: NAS1395C6L

Washer: NAS1857-6 & -6C

Lube: Dow Corning 321 Dry Film Spray

 Applied to Threads and Washer Facing Head

Torque (in-lb)

Insert 1Cycle 1

Insert1 Cycle 2

Insert1 Cycle 3

Insert2 Cycle 1 

Insert2 Cycle 2

Insert2 Cycle 3

Insert2 Cycle 4

Insert1 Redo Cycle 1

Insert1 Redo Cycle 2

Insert1 Redo Cycle 3

Force (lb)

Figure 18. Fastener with insert torque-tension data.
23

REFERENCES

 1. NASA TM X-73305, Vol. 1, “Astronautic Structures Manual,” Marshall Space Flight Center, 

Huntsville, AL, 1975. 

 2. MMPDS-04, “Metallic Materials Properties Development and Standardization,” FAA, 2008. 

 3. Bruhn, E.F.: Analysis and Design of Flight Vehicle Structures, Jacobs Publishing, Carmel, IN, 

ISBN: 0961523409, 650 pp., 1973. 

 4. NSTS 08307, Rev. A, “Criteria for Preloaded Bolts,” Johnson Space Center, Houston, TX, 

1998. 

 5. NASM 1312-2, “Fastener Test Methods, Method 2, Interaction,” Aerospace Industries 

Association of America, 12 pp., 1997. 

 6. NAS 1954, “Bolt, Shear, Hexagon Head, 108 ksi Shear, Long Thread,” Aerospace Industries 

Association of America, 1986. 

 7. SAE AS5054, “Areas for Calculating Stress or Load Values for Externally and Internally 

Threaded Fasteners,” SAE International, 2005. 

 8. SAE AS8879, “Screw Threads—UNJ Profile, Inch, Controlled Radius Root with Increased 

Minor Diameter,” SAE International, 2004.

 9. Olson, S.M.: “The Effect of a Tensile Load on the Ultimate Shear Capacity of a Fastener 

Shank,” Structural Integrity of Fasteners, ASTM STP, Vol. 1236, May 1995. 

10. Wallaert, J.J.; and Fisher, J.W.: “Shear Strength of High-Strength Bolts,” Journal of the Structural Division, Proceedings of the ASCE, Vol. 91, ST3, June 1965. 

11. Chesson, E.; Faustino, N.L.; and Munse, W.H.: “High-Strength Bolts Subjected to Tension 

and Shear,” Journal of the Structural Division, ASCE Vol. 91 ST5, p. 40, October 1965. 
24

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Aerospace Threaded Fastener Strength in Combined Shear 

and Tension Loading

B.E. Steeve and R.J. Wingate

George C. Marshall Space Flight Center

Huntsville, AL 35812

National Aeronautics and Space Administration

Washington, DC 20546–0001

Unclassified-Unlimited

Subject Category 39

Availability: NASA CASI (443–757–5802)

Prepared by the Spacecraft and Vehicle Systems Department, Engineering Directorate

M–1330

Technical Memorandum

NASA/TM—2012–217454

threaded fastener, bolt, strength criteria, combined loading, shear, tension

01–03–2012

UU 36

NASA

U U U

A test program was initiated by Marshall Space Flight Center and sponsored by the NASA Engineering 

and Safety Center to characterize the failure behavior of a typical high-strength aerospace threaded fastener under a range of shear to tension loading ratios for both a nut and an insert configuration where the 

shear plane passes through the body and threads, respectively. The testing was performed with a customized test fixture designed to test a bolt with a single shear plane at a discrete range of loading angles. The 

results provide data to compare against existing combined loading failure criteria and to quantify the bolt 

strength when the shear plane passes through the threads. 

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