TORQUE Program

Example Calculation - Metric Units

Presented below are the results from TORQUE for a M12 Grade 8.8 bolt with a nylon patch type locking device that creates a prevailing torque. (These calculations are in metric units, the TORQUE program can also work in units of inches and pounds and work with the unified thread form.)

TORQUE TIGHTENING ANALYSIS RESULTS Example calculation for a M12 bolt. Torque tightening analysis for a M12 bolt. FASTENER DETAILSFastener Diameter = 12.00 mmFastener Shank Diameter = 12.00 mmThread Pitch = 1.75 mmIncluded angle between the thread flanks = 60.00 degreesThread Pitch Diameter = 10.863 mmThread Root Diameter = 9.853 mmDiameter related to the Thread Stress Area = 10.358 mmThread Stress Area = 84.264 mm²Thread Root Area = 76.248 mm²Bearing Area under Nut/Bolt Head = 99.620 mm²Fastener Outer Bearing Diameter = 17.20 mmFastener Inner Bearing Diameter = 13.00 mmFastener Clearance Hole Diameter = 13.00 mmEffective friction diameter of nut/bolt = 15.20 mmFastener Yield Strength = 640.00 N/mm² JOINT ASSEMBLY DETAILSBlack oxide steel external thread, no finish on steelinternal thread, no lubricant. Black oxide steel nutor bolt, no oil, machined steel bearing surface. Prevailingtorque caused by a nylon/polyester patch on the threads.Thread Friction Value = 0.120Nut/Bolt Head Friction Value = 0.120 TORQUE TIGHTENING ANALYSIS RESULTSYield Point Tightening Factor specified = 0.90Total Tightening Torque = 83.64 NmThis torque is composed from:Torque needed to extend the fastener = 8.98 NmTorque needed to overcome thread friction = 24.26 NmTorque needed to overcome nutface friction = 29.40 NmPrevailing Torque Value = 21.00 Nm FORCE ANALYSIS RESULTSFastener Preload = 32239.37 NDirect Force that would Yield the Fastener = 53928.91 NPreload as a percentage of Yield Force = 59.78 %

MAXIMUM STRESSES INDUCED INTO THE FASTENERPercentage of the yield strength utilised = 90.00 %Von-Mises Equivalent Stress = 576.00 N/mm²Tensile Stress due to Preload = 382.60 N/mm²Torsional Stress due to the applied torque = 248.59 N/mm²Surface Pressure under the Nut Face = 323.62 N/mm²

Bolt Preload Calculation

Question:  How is bolt installation preload calculated?

Answer:  Bolt pretension, also called preload or prestress, comes from the installation torque T you apply when you install the bolt.  The inclined plane of the bolt thread helix converts torque to bolt pretension.  Bolt preload is computed as follows.

    Pi = T/(K D)        (Eq. 1)

where Pi = bolt preload (called Fi in Shigley). T = bolt installation torque. K = torque coefficient. D = bolt nominal shank diameter (i.e., bolt nominal size).

Torque coefficient K is a function of thread geometry, thread coefficient of friction t, and collar coefficient of friction c.  Look up K for your specific thread interface and collar (bolt head or nut annulus) interface materials, surface condition, and lubricant (if any).  ("Torque specs for screws," Shigley, and various other sources discuss various K value estimates.)  If you cannot find or obtain K from credible references or sources for your specific interfaces, then you would need to research to try to find the coefficients of friction for your specific interfaces, then calculate K yourself using one of the following two formulas listed below (Shigley, Mechanical Engineering Design, 5 ed., McGraw-Hill, 1989, p. 346, Eq. 8-19, and MIL-HDBK-60, 1990, Sect. 100.5.1, p. 26, Eq. 100.5.1, respectively), the latter being far simpler.

    K = {[(0.5 dp)(tan   +  t sec )/(1  –  t tan sec )]   +   [0.625 c D]}/D (Eq. 2)

    K = {[0.5 p/]   +   [0.5 t (D – 0.75 p sin )/sin ]   +   [0.625 c D]}/D (Eq. 3)

where D = bolt nominal shank diameter. p = thread pitch (bolt longitudinal distance per thread). = thread profile angle = 60° (for M, MJ, UN, UNR, and UNJ thread profiles). = thread profile half angle = 60°/2 = 30°. tan = thread helix angle tan = p/( dp). dp = bolt pitch diameter. t = thread coefficient of friction. c = collar coefficient of friction.

D and p can be obtained from bolt tables such as Standard Metric and USA Bolt Shank Dimensions.

The three terms in Eq. 3 are axial load component (coefficient) of torque resistance due to (1) thread helix inclined plane normal force, (2) thread helix inclined plane tangential (thread friction) force, and (3) bolt head or nut washer face friction force, respectively.

However, whether you look up K in references or calculate it yourself, the engineer must understand that using theoretical equations and typical values for K and coefficients of friction merely gives a preload estimate.  Coefficient of friction data in published tables vary widely, are often tenuous, and are often not specific to your specific interface combinations and lubricants.  Such things as unacknowledged surface condition variations and ignored dirt in the internal thread can skew the results and produce a false indication of preload.

The engineer and technician must understand that published K values apply to perfectly clean interfaces and lubricants (if any).  If, for example, the threads of a steel, zinc-plated, K = 0.22, "dry" installation fastener were not clean, this might cause K to increase to a value of 0.32 or even higher.  One should also note that published K values are intended to be used when applying the torque to the nut.  The K values will change in relation to fastener length and assembly running torque if the torque is being read from the bolt head.

One should measure the nut or assembly "running" torque with an accurate, small-scale torque wrench.  ("Running" torque, also called prevailing torque, is defined as the torque when all threads are fully engaged, fastener is in motion, and washer face has not yet made contact.) The only torque that generates bolt preload is the torque you apply above running torque.

A few more things to be aware of are as follows.  Bolt proof strength Sp is the maximum tensile stress the bolt material can withstand without encountering permanent deformation.  Published bolt yield strengths are determined at room temperature.  Heat will lower the yield strength (and proof strength) of a fastener.  Especially in critical situations, you should never reuse a fastener unless you are certain the fastener has never been yielded.

1.1   Bolt Preload Measurement

If a more accurate answer for bolt preload is needed than discussed above, the specific combination and lubricant would have to be measured instead of calculated.  Measurement methods are generally involved, time-consuming, and expensive, and are beyond the scope of this article.  But perhaps one of the simplest and least expensive methods, to test specific combinations and lubricants, is to measure the installed fastener with a micrometer, if possible, and compute torque coefficient K as follows, per Shigley, op. cit., p. 345, para. 2.

    K = T L/(E A delta D)        (Eq. 4)

Where T = bolt installation torque, L = bolt grip length, E = bolt modulus of elasticity, A = bolt cross-sectional area, D = bolt nominal shank diameter, and delta = measured bolt elongation in units of length.

Bolt Torque Chart

Suggested Starting Values

The below estimated torque calculations are only offered as a guide. Use of its content by anyone is the sole responsibility of that person and they assume all risk. Due to many variables that affect the torque-tension relationship like human error, surface texture, and lubrication the only way to determine the correct torque is through experimentation under actual joint and assembly conditions.

Learn more about torque and tension.

ASTM A307

Bolt Size TPIProof

Load (lbs)Clamp

Load (lbs) Tightening Torque (ft lbs)

Waxed Galv Plain

1/4 20 1145 859 2 4 4

5/16 18 1886 1415 4 9 7

3/8 16 2790 2093 7 16 13

7/16 14 3827 2870 10 26 21

1/2 13 5108 3831 16 40 32

9/16 12 6552 4914 23 58 46

5/8 11 8136 6102 32 79 64

3/4 10 12024 9018 56 141 113

7/8 9 15200 11400 83 208 166

1 8 20000 15000 125 313 250

1 1/8 7 25200 18900 177 443 354

1 1/4 7 32000 24000 250 625 500

1 3/8 6 38100 28575 327 819 655

1 1/2 6 46400 34800 435 1088 870

1 3/4 5 68400 51300 748 1870 1496

2 4 1/2 90000 67500 1125 2813 2250

2 1/4 4 1/2 117000 87750 1645 4113 3291

2 1/2 4 144000 108000 2250 5625 4500

2 3/4 4 177480 133110 3050 7626 6101

3 4 214920 161190 4030 10074 8060

3 1/4 4 255600 191700 5192 12980 10384

3 1/2 4 299880 224910 6560 16400 13120

3 3/4 4 347760 260820 8151 20377 16301

4 4 398880 299160 9972 24930 19944

SAE GRADE 2

Bolt Size TPIProof

Load (lbs)Clamp

Load (lbs) Tightening Torque (ft lbs)

Waxed Galv Plain

1/4 20 1750 1313 3 7 5

5/16 18 2900 2175 6 14 11

3/8 16 4250 3188 10 25 20

7/16 14 5850 4388 16 40 32

1/2 13 7800 5850 24 61 49

9/16 12 10000 7500 35 88 70

5/8 11 12400 9300 48 121 97

3/4 10 18400 13800 86 216 173

7/8 9 15200 11400 83 208 166

1 8 20000 15000 125 313 250

1 1/8 7 25200 18900 177 443 354

1 1/4 7 32000 24000 250 625 500

1 3/8 6 38100 28575 327 819 655

1 1/2 6 46400 34800 435 1088 870

ASTM A325 / ASTM A449 / SAE GRADE 5

Bolt Size TPIProof

Load (lbs)Clamp

Load (lbs) Tightening Torque (ft lbs)

Waxed Galv Plain

1/4 20 2700 2025 4 11 8

5/16 18 4450 3338 9 22 17

3/8 16 6600 4950 15 39 31

7/16 14 9050 6788 25 62 49

1/2 13 12050 9038 38 94 75

9/16 12 15450 11588 54 136 109

5/8 11 19200 14400 75 188 150

3/4 10 28400 21300 133 333 266

7/8 9 39250 29438 215 537 429

1 8 51500 38625 322 805 644

1 1/8 7 56450 42338 397 992 794

1 1/4 7 71700 53775 560 1400 1120

1 3/8 6 85450 64088 734 1836 1469

1 1/2 6 104000 78000 975 2438 1950

1 3/4 5 104500 78375 1143 2857 2286

2 4 1/2 137500 103125 1719 4297 3438

2 1/4 4 1/2 178750 134063 2514 6284 5027

2 1/2 4 220000 165000 3438 8594 6875

2 3/4 4 271150 203363 4660 11651 9321

3 4 328350 246263 6157 15391 12313

ASTM A193 B7

Bolt Size TPIProof

Load (lbs)Clamp

Load (lbs) Tightening Torque (ft lbs)

Waxed Galv Plain

1/4 20 3350 2513 5 13 10

5/16 18 5500 4125 11 27 21

3/8 16 8150 6113 19 48 38

7/16 14 11150 8363 30 76 61

1/2 13 14900 11175 47 116 93

9/16 12 19100 14325 67 168 134

5/8 11 23750 17813 93 232 186

3/4 10 35050 26288 164 411 329

7/8 9 48500 36375 265 663 530

1 8 63650 47738 398 995 796

1 1/8 7 80100 60075 563 1408 1126

1 1/4 7 101750 76313 795 1987 1590

1 3/8 6 121300 90975 1042 2606 2085

1 1/2 6 147550 110663 1383 3458 2767

1 3/4 5 199500 149625 2182 5455 4364

2 4 1/2 262500 196875 3281 8203 6563

2 1/4 4 1/2 341250 255938 4799 11997 9598

2 1/2 4 420000 315000 6563 16406 13125

2 3/4 4 468500 351263 8050 20124 16100

3 4 567150 425363 10634 26585 21268

3 1/4 4 674500 505875 13701 34252 27402

3 1/2 4 791350 593513 17311 43277 34622

3 3/4 4 917700 688275 21509 53771 43017

4 4 1052600 789450 26315 65788 52630

ASTM A354-BD / ASTM A490 / SAE GRADE 8

Bolt Size TPIProof

Load (lbs)Clamp

Load (lbs) Tightening Torque (ft lbs)

Waxed Plain

1/4 20 3800 2850 6 12

5/16 18 6300 4725 12 25

3/8 16 9300 6975 22 44

7/16 14 12750 9563 35 70

1/2 13 17050 12788 53 107

9/16 12 21850 16388 77 154

5/8 11 27100 20325 106 212

3/4 10 40100 30075 188 376

7/8 9 55450 41588 303 606

1 8 72700 54525 454 909

1 1/8 7 91550 68663 644 1287

1 1/4 7 120000 90000 938 1875

1 3/8 6 138600 103950 1191 2382

1 1/2 6 168600 126450 1581 3161

1 3/4 5 228000 171000 2494 4988

2 4 1/2 300000 225000 3750 7500

2 1/4 4 1/2 390000 292500 5484 10969

2 1/2 4 480000 360000 7500 15000

2 3/4 4 517650 388238 8897 17794

3 4 626850 470138 11753 23507

3 1/4 4 745500 559125 15143 30286

3 1/2 4 874650 655988 19133 38266

3 3/4 4 1014300 760725 23773 47545

4 4 1163400 872550 29085 58100

Notes:

1. Values calculated using industry accepted formula T = KDP where T = Torque, K =

torque coefficient (dimensionless), D = nominal diameter (inches), P = bolt clamp load, lb.

2. K values: waxed (e.g. pressure wax as supplied on high strength nuts) = .10, hot dip

galvanized = .25, and plain non-plated bolts (as received) = .20.

3. Torque has been converted into ft/lbs by dividing the result of the formula by 12

4. All calculations are for Coarse Thread Series (UNC).

5. Grade 2 calculations only cover fasteners 1/4"-3/4" in diameter up to 6" long; for

longer fasteners the torque is reduced significantly.

6. Clamp loads are based on 75% of the minimum proof loads for each grade and size.

7. Proof load, stress area, yield strength, and other data is based on IFI 7th Edition (2003)

Technical Data N-68, SAE J429, ASTM A307, A325, A354, A449, and A490.

Methods of Tightening Threaded FastenersWe have a web site dedicated to training, have a look at www.bolting.info - the material on this site provides additional information on this topic.

One of the major problems with the use of bolted joints is the precision, with regard to achieving an accurate preload, of the bolt tightening method selected. Insufficient preload, caused by an inaccurate tightening method, is a frequent cause of bolted joint failure. It is important for the Designer to appreciate the features and characteristics of the main methods employed to tighten bolts. Presented below is a brief summary of the major bolt tightening methods. Note however that whatever method is used to tighten a bolt, a degree of bolt preload scatter is to be expected.

There are six main methods used to control the preload of a threaded fastener. Specifically:

1. Torque control tightening.

2. Angle control tightening.

3. Yield controlled tightening.

4. Bolt stretch method.

5. Heat tightening.

6. Use of tension indicating methods.

Torque Control Tightening Controlling the torque which a fastener is tightened to is the most popular means of controlling preload. The nominal torque necessary to tighten the bolt to a given preload can be determined either from tables, or, by calculation using a relationship between torque and the resulting bolt tension.

When a bolt is tightened the shank sustains a direct stress, due to the elongation strain, together with a torsional stress, due to the torque acting on the threads. Most tables of bolt tightening torques ignore the torsional stress and assume a direct stress in the threads of some proportion of the bolts yield stress, usually 75%. For high frictional conditions the magnitude of the torsional stress can be such that when combined with the direct stress, an equivalent stress over yield can result, leading to failure. A more consistent approach is to determine the magnitude of the direct stress which, when combined with the torsional, will give an equivalent stress of some proportion of yield. The proportion commonly used with this approach is 90%.

Torque prevailing fasteners (such as Nyloc, Cleveloc nuts etc.) are often used where there exists a risk of vibration loosening. The prevailing torque has the effect of increasing the torsional stress in the bolt shank during tightening. This affects the conversion of the tightening torque into bolt preload and should be allowed for when determining the correct torque value for this type of fastener.

As can been seen by study of the above chart, a fundamental problem with torque tightening is that because the majority of the torque is used to overcome friction (usually between 85% and 95% of the applied torque), slight variations in the frictional conditions can lead to large changes in the bolt preload. This effect can be reduced by the use of so called friction stabilisers. These are substances which are coated onto the fasteners to reduce the frictional scatter. Other ways to improve the accuracy of the method are:

1. Do not use plain washers; their use can result in relative motion to change from the nut to washer, to washer to joint surface, during tightening. This as the effect of changing the friction radius and hence affects the torque-tension relationship. If, because of excessive bearing pressure, a larger bearing face is required, thought should be given to the use of flanged nuts and bolts.

2. Determine the correct tightening torque by the completion of tests. Strain gauges can be attached to the bolt shank and tightening completed on the actual joint. A load cell

under the bolt head can be used, however it is not as accurate as strain gauging, since the joint characteristics have been changed.

3. If it is not feasible to establish by testwork the actual tightening torque, determine the tightening torque using the best information available i.e. fastener finish, nut head bearing surface size and prevailing torque characteristics, if applicable. (The computer program TORQUE developed by Bolt Science can allow for all these effects.)

4. Ensure that the tightening torque value is specified on the assembly drawing. Quotation of a plus or minus 5% tolerance is good practice. More unusually, quote that a calibrated torque wrench is to be used to check the torque after installation. The method used to tighten the bolt has a significant influence on the preload scatter (see below).

Angle Controlled Tightening This method, also known as turn of the nut method, was introduced for manual assembly shortly after the second World War when a certain tightening angle was specified. The method has been applied for use with power wrenches, the bolt being tightened to a predetermined angle beyond the elastic range and results in a small variation in the preload due, in part, to the yield stress tolerance. The main disadvantages of this method lie in the necessity for precise, and, if possible, experimental determination of the angle; also the fastener can only sustain a limited number of re-applications before it fails. Yield Controlled Tightening This method, developed by the SPS organisation, is also known under the proprietary name "Joint Control Method". Very accurate preloads can be achieved by this method by minimising the influence of friction and its scatter. The method has its roots in a craftsman's "sense of feel" on the wrench which allowed him to detect the yield point of the fastener with reasonable precision. With the electronic equivalent of this method, a control system is used which is sensitive to the torque gradient of the bolt being tightened. Rapid detection of the change in slope of this gradient indicates the yield point has been reached and stops the tightening process. This is achieved by incorporating sensors to read torque and angle during the tightening process. Since angle of rotation and torque are both measured by the control system, permissible values can be used to detect fasteners which lie outside their specification (having too low a yield for example).

A small degree of preload scatter still results from this method due to the influence of friction. The method detects the yield point of the fastener under the action of combined tension and torsion. The higher the thread friction, the higher the torsional stress, which, for a given yield value, results in a lower preload due to a lower direct stress.

The method has been used in critical applications, such as cylinder head and conn-rod bolts, in order that consistently high preloads can be achieved (which can allow smaller bolts to be used). However, because of the cost of the tools necessary to use this method (a hand wrench incorporating the control circuitry costs many times more than a conventional torque wrench), widespread adoption of this method is unlikely. (Although manufacturers may be able to invest in the equipment, unless service staff have similar

equipment, the Designer cannot depend upon high preloads being maintained in the field.)

Bolt Stretch Method A problem relating to the tightening of large bolts is that very high tightening torques are required. Although this can be partly overcome by the use of hydraulic torque wrenches (the reaction of the torque however can be a problem), the use of hydraulic tensioning devices is commonplace for bolts over 20mm in diameter. The method uses a small hydraulic ram which fits over the nut, the threaded portion of the bolt/stud protrudes well past the nut and a threaded puller is attached. Hydraulic oil from a small pump acts upon the hydraulic ram which in turn acts upon the puller. This is transmitted to the bolt resulting in extension occurring. The nut can then be rotated by hand with the aid of an integral socket aided by a tommy bar.

Control of the hydraulic pressure effectively controls the preload in the bolt. A small amount of preload reduction however does occur when the pressure is removed as the nut elastically deforms under the load. Removal of nuts corroded to the bolts can be a problem with this method.

Heat Tightening Heat tightening utilises the thermal expansion characteristics of the bolt. The bolt is heated and expands: the nut is indexed (using the angle of turn method) and the system allowed to cool. As the bolt attempts to contract it is constrained longitudinally by the clamped material and a preload results. Methods of heating include direct flame, sheathed heating coil and carbon resistance elements. The process is slow, especially if the strain in the bolt is to be measured, since the system must return to ambient temperature for each measurement. This is not a widely used method and is generally used only on very large bolts.

Tension Indicating Methods This category includes the use of special load indicating bolts, load indicating washers and the use of methods which determine the length change of the fastener. There are a wide number of ways bolt tension can be indirectly measured and the discussion presented here is not exhaustive.

Special bolts have been designed which will give an indication of the force in the bolt. One such fastener is the Rotabolt which measures bolt extension by the use of a central gauge pin which passes down a centrally drilled hole in the bolt. Underneath the head of the gauge pin, a rota is retained which is free to spin in a very accurately set gap. The fastener stretches elastically, whereas the gauge pin does not move since it experiences no load. As tightening continues, the bolt will stretch sufficiently to eliminate the gap and prevent the rota from being able to be rotated. This is the indication that the bolt is correctly loaded. Another proprietary fastener uses a similar method. The HiBolt uses a pin located centrally down the bolt as does the Rotabolt except the pin is gripped by the slight contraction of the bolt diameter; the pin being locked when the correct preload is reached.

The use of load indicating washers is widespread in structural engineering. Such washers have small raised pips on their surface which plastically deform under load. The correct preload is achieved when a predetermined gap is present between the washer and the underhead of the bolt. This is measured using feeler gauges. Generally they are not used in mechanical engineering, but are, extensively, in civil engineering.

The extension which a bolt experiences can be measured either using a micrometer or by a more sophisticated means such as using ultrasonics. The extension can be related to preload either directly, by calibration, or indirectly, by calculation. If ultrasonic measurement is used then the end of the bolt shank and the head may require surface grinding to give a good acoustic reflector.

To assist the Engineer in overcoming the problems associated with the use of threaded fasteners and bolted joints, Bolt Science has developed a number of computer programs. These programs are designed to be easy to use so that an engineer without detailed knowledge in this field can solve problems related to this subject.

Suggested Tightening Torque Values to Produce Corresponding Bolt Clamping Loads

    SAE Grade 2 Bolts SAE Grde 5 Bolts SAE Grade 7 SAE Grade 8

Size

Bolt

Diam.

D(in.)

Stress

Area

A(in²)

Tensile

Strngth

min psi

Proof

Load

psi

Clamp

Loa

P (lb)

T

Dry

Tor-

que

Lub.

Tensile

Strength

Proof

Load

Clamp

Load

T

Dry

Tor

-que

Lub.

Clamp

Load

Tight

Dry

Tor-

que

Lub.

Clamp

Load

T

Dry

Tor-

que

Lub.

4-40 0.1120 .00604 74,000 55,000 240 5 4 120,000 85,000 380 8 6 480 11 8 540 12 9

4-48 0.1120 .00661     280 6 5     420 9 7 520 12 9 600 13 10

6-32 0.1380 .00909     380 10 8     580 16 12 720 20 15 820 23 17

6-40 0.1380 .01015     420 12 9     640 18 13 800 22 17 920 25 19

8-32 0.1640 .01400     580 19 14     900 30 22 1100 36 27 1260 41 31

8-36 0.1640 .01474     600 20 15     940 31 23 1160 38 29 1320 43 32

10-24 0.1900 .01750     720 27 21     1120 43 32 1380 52 39 1580 60 45

10-32 0.1900 .02000     820 31 23     1285 49 36 1580 60 45 1800 68 51

1/4-20 0.2500 0.0318     1320 66 49     2020 96 75 2500 120 96 2860 144 108

1/4-28 0.2500 0.0364     1500 76 56     2320 120 86 2880 144 108 3280 168 120

5/16-18 0.3125 0.0524     2160 11 8     3340 17 13 4120 21 16 4720 25 18

5/16-24 0.3125 0.0580     2400 12 9     3700 19 14 4580 24 18 5220 25 20

3/8-16 0.3750 0.0775     3200 20 15     4940 30 23 6100 40 30 7000 45 35

3/8-24 0.3750 0.0878     3620 23 17     5600 35 25 6900 41 30 7900 50 35

7/16-14 0.4375 0.1063     4380 30 24     6800 50 35 8400 60 45 9550 70 55

                                     7/16-20 0.4375 0.1187     4900 35 25     7550 55 40 9350 70 50 10700 80 60

1/2-13 0.5000 0.1419     5840 50 35     9050 75 55 11200 95 70 12750 110 80

1/2-13 0.5000 0.1599     6600 55 40     10700 90 65 12600 100 80 14400 120 90

9/16-12 0.5625 0.1820     7500 70 55     11600 110 80 14350 135 100 16400 150 110

9/16-18 0.5625 0.2030     8400 80 60     12950 120 90 16000 150 110 18250 170 130

                                     5/8-11 0.6250 0.2260     9300 100 75     14400 150 110 17800 190 140 20350 220 170

5/8-18 0.6250 0.2560     10600 110 85     16300 170 130 20150 210 160 23000 240 180

3/4-10 0.7500 0.3340     13800 175 130     21300 260 200 26300 320 240 30100 380 280

3/4-16 0.7500 0.3730     15400 195 145     23800 300 220 29400 360 280 33600 420 320

7/8-9 0.8750 0.4620 60,000 33,000 11400 165 125     29400 430 320 36400 520 400 41600 600 460

                                     7/8-14 0.8750 0.5090     12600 185 140     32400 470 350 40100 580 440 45800 660 500

1-8 1.0000 0.6060     15000 250 190     38600 640 480 47700 800 600 54500 900 680

1-12 1.0000 0.6630     16400 270 200     42200 700 530 52200 860 660 597 1100 740

1-1/4 7 1.1250 0.7630     18900 350 270 105,000 74,000 42300 800 600 60100 1120 840 68700 1280 960

1-1/4 12 1.1250 0.8560     21200 400 300     47500 880 660 67400 1260 940 77000 1440 1080

1-1/4 7 1.2500 0.9690     24000 500 380     53800 1120 840 76300 1580 1100 87200 1820 1361

1-1/4 12 1.2500 1.0730     26600 550 420     59600 1240 920 84500 1760 1320 116600 2000 1500

1-3/8 6 1.3750 1.1550     28600 660 490     64100 1460 1100 91000 2080 1560 104000 2380 1780

1-3/812 1.3750 1.3150     32500 740 560     73000 1680 1260 104000 2380 1780 118400 2720 2040

1-3/8 6 1.5000 1.4050     34800 870 650     78000 1940 1460 111000 2780 2080 126500 3160 2360

1-1/2 12 1.5000 1.5800     39100 980 730     87700 2200 1640 124005 3100 2320 142200 3560 2660

Notes:

1. Tightening torque values are calculated from the formula T = KDP, where T= tightening torque. lb-in. K=torque-friction coefficient; D = nominal bolt diameter. in; and P = bolt clamp load developed by tightening. lb.

2. Clamp load is also known as preload or initial load in tension on bolt. Clamp load (lb) is calculated by arbitrarily assuming usable bolt strength is 75% of bolt proof load(psi) times tensile stress area(sq in.) of threaded section of each bolt size. Higher or lower values of clamp load can be used depending on the application requirements and the judgement of the designer.

3. Tensile strength (min psi) of all Grade 7 bolts is 133,000. Proof load is 105,000 psi.

4. Tensile strength (min psi) of all Grade 8 bolts is 150,000 psi. Proof load is 120,000 psi. Ref.:Fastening Reference, Machine Design, Nov 1977.

What is the Proper Torque to Use on a Given Boltby Joe Greenslade

"What torque should I use to tighten my bolts?" is a question suppliers of bolts are frequently asked by end user customers. Many times I have been asked if a chart is published on the recommended tightening torque for various bolt grades and sizes. I do not know of any. This article provides such a chart for "Initial Target Tightening Torque. It See Figure 1. The formula for generating these values is explained below.

The widely recognized engineering formula, T= K x D x P (to be explained later in this article), was used to provide the chart's values, but it must be understood that every bolted joint is unique and the optimum tightening torque should be determined for each application by careful experimentation. A properly tightened bolt is one that is stretched such that it acts like a very ridged spring pulling mating surfaces together. The rotation of a bolt (torque) at some point causes it to stretch (tension). Several factors affect how much tension occurs when a given amount of tightening torque is applied. The first factor is the bolt's diameter. It takes more force to tighten a 3/4-10 bolt than to tighten a 318-16 bolt because it is larger in diameter. The second factor is the bolt's grade. It takes more force to stretch an SAE Grade 8 bolt than it does to stretch an SAE Grade 5 bolt because of the greater material strength. The third factor is the coefficient of friction, frequently referred to as the "nut factor." The value of this factor indicates that harder, smoother, and/or slicker bolting surfaces, such as threads and bearing surfaces, require less rotational force (torque) to stretch (tension) a bolt than do softer, rougher, and stickier surfaces. The basic formula T = K x D x P stated earlier takes these factors into account and provides users with a starting point for establishing an initial target tightening torque.

• T Target tighten torque (the result of this formula is in inch pounds, dividing by 12 yields foot pounds

• K Coefficient of friction (nut factor), always an estimation in this formula

• D Bolts nominal diameter in inches

• P Bolt's desired tensile load in pounds (generally 75% of yield strength)

The reason all applications should be evaluated to determine the optimum tightening torque is that the K factor in this formula is always an estimate. The most commonly used bolting K factors arc 0.20 for plain finished bolts, 0.22 for zinc plated bolts, and 0.10 for waxed or highly lubricated bolts. .

ThreadTensile Stress

AreaSAE Grade 2 SAE Grade 5 SAE Grade 8

Size TSA 75% Yield Strength (PSI) - 43000 75% Yield Strength (PSI) - 69000 75% Yield Strength (PSI) = 98000

    Plain Zinc Plated Waxed Plain Zinc Plated Waxed Plain Zinc Plated Waxed

  Square Inches A. lb. Ft.Lb. Ft.Lb. Ft.Lb. Ft.Lb. Ft.Lb. Ft.Lb. Ft.Lb. Ft.Lb.

114-20. 0.0318 6 6 3 9 10 5 13 14 6

1/4-28. 0.0364 7 7 3 10 12 5 15 16 7

5116-18. 0.0524 12 13 6 19 21 9 27 29 135116-24. 0.0580 13 14 6 21 23 10 30 33 15

318-16. 0.0775 21 23 10 33 37 17 47 52 24

318-24. 0.0878 24 26 12 38 42 19 54 59 27

7/16-14. 0.1063 33 37 17 53 59 27 76 83 387/16-24. 0.1187 37 41 19 60 66 30 85 93 42

112-13. 0.1419 51 56 25 82 90 41 116 127 58

112-20. 0,1599 57 63 29 92 101 46 131 144 65

9116-12. 0.1820 73 81 37 118 129 59 167 184 849116-18. 0.2030 82 90 41 131 144 66 186 205 935J8-11. 0.2260 101 111 51 162 179 81 231 254 115

5J8-14. 0.2560 115 126 57 184 202 92 261 287 1313/4-10. 0.3340 180 197 90 288 317 144 409 450 205

3/4-16. 0.3730 200 221 100 322 354 161 457 503 228

The only way to properly determine the optimum tightening torque for a given application is to simulate the exact application. This should be done with a tension indicating device of some type on the bolt in the application. The bolt is tightened until the desired P (load) is indicated by the tension indicating device. The tightening torque required to achieve the desired tension is the actual tightening torque that should be used for

that given application. It is extremely important to realize that this tightening value is valid only so long as all of the aspects of the application remain constant Bolt suppliers sometimes have customers say that their bolts are no good because they have started breaking while being installed. Thorough investigation commonly reveals that the customer has started lubricating the bolts to make assembly easier, but maintained to same torque as was used when the were plain finished

The table in this article shows that by using this formula a 1/2-13 Grade 5 plain bolt should be tightened to 82 foot pounds, but the same bolt that is waxed only requires 41 foot pounds to tighten the same tension. A perfect 1/2-13 Grade 5 waxed bolt will break if it is tightened to 81 foot pounds because the K factor is drastically lower. The bolts are fine, but the application changed. Suppliers need to understand this and be able to educate their customers to resolve this common customer complaint about breaking bolts.

The chart is provided for quick reference by fastener suppliers and users for selecting an initial target tightening torque. This chart was derived by using the formula shown earlier. An example of the calculation is as follows:

Product: 3/4-10 Grade 5 zinc plated boltFormula: T= K x D x P

 • K=0.22 (zinc plated)• D=.750 (3/4-10 nominal diameter• P=23.046 pounds

Hopefully the chart will help suppliers with an initial answer to the customer's question, "What torque should I use to tighten my bolts?" Keep in mind this is only an estimated value. It may provide satisfactory performance, but it also may not. Every application should be evaluated on its own to determine the optimum torque value for each application. Major bolt suppliers should have tension indicating equipment necessary to help their customers determine the appropriate tightening values for their specific applications. Keep in mind that if the lubricant on a bolt and nut combination is changed, the tightening torque value must be altered to achieve the desired amount of bolt tension.

Bolt Torque - Screw Torque Data

Suggested maxium torque values for different material and grade bolts &

screws.

Torque, is the measurement of the turning or twisting force applied to an object. The desired result is to hold two

parts together with a tension or clamping force that is greater than any external force that could possibly seperate

them. The part then remains under constant stress and is immune to fatigue.

These charts apply to clean and dry parts. A lubricated bolt requires less torque to attain the same clamping force

as a non-lubricated bolt.

The values are stated in Inch pounds.

Bolt SizeThds Per

Inch

Low Carbon Steel

18-8 St. St.

Yellow Brass

Silicon Bronze

Aluminum 2024-

T4

316 St. St.

Monel

0 80 1.0 --- --- --- --- --- ---

1 64 1.5 --- --- --- --- --- ---

72 2.0 --- --- --- --- --- ---

256 2.2 2.5 2.0 2.3 1.4 2.6 2.5

64 2.7 3.0 2.5 2.8 1.4 3.2 3.1

348 3.5 3.9 3.2 3.6 2.1 4.0 4.0

56 4.0 4.4 3.6 4.1 2.4 4.6 4.5

440 4.7 5.2 4.3 4.8 2.9 5.5 5.3

48 5.9 6.6 5.4 6.1 3.6 6.9 6.7

540 6.9 7.7 6.3 7.1 4.2 8.1 7.8

44 8.5 9.4 7.7 8.7 5.1 9.8 9.6

632 8.7 9.6 7.9 8.9 5.3 10.1 9.8

40 10.9 12.1 9.9 11.2 6.6 12.7 12.3

832 17.8 19.8 16.2 18.4 10.8 20.7 20.2

36 19.8 22.0 18.0 20.4 12.0 23.0 22.4

1024 20.8 22.8 18.6 21.2 13.8 23.8 25.9

32 29.7 31.7 25.9 29.3 19.2 33.1 34.9

1224 --- --- --- --- --- --- ---

28 --- --- --- --- --- --- ---

1/420 65.0 75.2 61.5 68.8 45.6 78.8 85.3

28 90.0 94.0 77.0 87.0 57.0 99.0 106.0

5/1618 129 132 107 123 80 138 149

24 139 142 116 131 86 147 160

3/8 16 212 236 192 219 143 247 266

24 232 259 212 240 157 271 297

7/1614 338 376 317 349 228 393 427

20 361 400 327 371 242 418 451

1/213 465 517 422 480 313 542 584

20 487 541 443 502 328 565 613

9/1612 613 682 558 632 413 713 774

18 668 752 615 697 456 787 855

5/811 1000 1110 907 1030 715 1160 1330

18 1140 1244 1016 1154 798 1301 1492

3/410 1259 1530 1249 1416 980 1582 1832

16 1230 1490 1220 1382 958 1558 1790

7/89 1919 2328 1905 2140 1495 2430 2775

14 1911 2318 1895 2130 1490 2420 2755

18 2832 3440 2815 3185 2205 3595 4130

14 2562 3110 2545 2885 1995 3250 3750

The values are stated in foot pounds.

Bolt Size (inches)

Thds Per Inchttc

SAE 0-1-274,000 psi

Low Carbon Steel

SAE Grade 3

100,000 psi Med Carbon Steel

SAE Grade 5

120,000 psi Med Carbon Heat T. Steel

SAE Grade 6

133,000 psi Med Carbon Temp. Steel

SAE Grade 7

133,000 psi Med Carbon

Alloy Steel

SAE Grade 8

150,000 psi Med Carbon

Alloy Steel

1/4 20 6 9 10 12.5 13 14

28 --- --- --- --- --- ---

5/1618 12 17 19 24 25 29

24 --- --- --- --- --- ---

3/816 20 30 33 43 44 47

24 --- --- --- --- --- ---

7/1614 32 47 54 69 71 78

20 --- --- --- --- --- ---

1/213 47 69 78 106 110 119

20 --- --- --- --- --- ---

9/16 12 69 103 114 150 154 169

18 --- --- --- --- --- ---

5/811 96 145 154 209 215 230

11 --- --- --- --- --- ---

3/410 155 234 257 350 360 380

10 --- --- --- --- --- ---

7/89 206 372 382 550 570 600

9 --- --- --- --- --- ---

18 310 551 587 825 840 700

8 --- --- --- --- --- ---

1-1/87 480 794 872 1304 1325 1430

7 --- --- --- --- --- ---

1-1/47 375 1105 1211 1815 1825 1975

7 --- --- --- --- --- ---

1-3/86 900 1500 1624 2434 2500 2650

6 --- --- --- --- --- ---

1-1/26 1100 1775 1943 2913 3000 3200

6 --- --- --- --- --- ---

1-5/85.5 1470 2425 2660 3985 4000 4400

5.5 --- --- --- --- --- ---

1-3/45 1900 3150 3463 5189 5300 5650

5 --- --- --- --- --- ---

1-7/85 2360 4200 4695 6980 7000 7600

5 --- --- --- --- --- ---

24.5 2750 4550 5427 7491 7500 8200

4.5 --- --- --- --- --- ---

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What Torque Should Be Used to Tighten Metric Machine Screws?

American Fastener Journal, Mar/Apr 2004 by Greenslade, Joe

1 2 Next

A lot is written about bolt and nut tightening, but little is written about tightening machine screws. It is just as important to carefully select an appropriate tightening torque for securing machine screw joints as it is for securing bolt and nut joints. Properly secured joints are directly related to the quality of the end product assembly. The means of calculating the suggested tightening torque is the same for machine screws as it is for bolts. The values are just smaller.

CALCULATING MACHINE SCREW TIGHTENING TORQUE VALUES

The most widely used formula for calculating threaded fastener tightening torque is:

T = DKP

Where:

T = Torque (inch pounds and Newton meters; 1Nm = 9 in.Ib.)

D = Nominal thread diameter (expressed in inches; 1 mm = .03937 inches)

K = Nut factor (.22 for zinc electroplating)

P = Pounds of clamping force (75% of yield strength)

There are various strength levels of metric machine screws and each has a different recommended tightening value. ISO has two predominate machine screw strength levels: Property Class 4.8 (close to SAE 6OM) and Property Class 8.8 (close to SAE 12OM). Property Class 4.8 indicates a minimum tensile strength of 480 mega Pascal (MPa). This is equal to approximately 70,000 pounds per square inch (PSI). Property Class 8.8 indicates a minimum tensile strength of 880 mega Pascal (MPa). This is equal to approximately 127,000 pounds per square inch (PSI).

DETERMINING TIGHTENING TORQUE BY TESTING

The chart below provides reasonable tightening values, but they are not the optimum tightening values for every application. A far better way to establish a tightening torque for a particular application is by conducting a simple study.

To determine the ideal tightening torque for any particular application joint, do the following:

* Make up 12 of the exact application joints being studied.

* Tighten the machine screws until something in the joint completely fails; then record every failure torque value.

The best failure is the twisting in two of the screw, but this does not always happen. The internal thread may strip; the components may crush or distort. It makes no difference what fails.

* Calculate the average torque value at which this particular joint fails.

* The optimum tightening value for the particular joint being studied is 60% of the average failure value.

CALCULATIONS ARE FINE, BUT TESTING IS SUPERIOR

The correct tightening of all threaded fasteners is critical to obtaining an end product of consistently high quality and dependability. Determining tightening torque by calculations or taking values from charts like the one provided in this article is better than just guessing at what a particular torque should be. The best approach to establishing the optimum tightening torque value for a particular joint is determined by performing the simple study described herein.

Joe Ctreimslade has been active in the fastener industry since 1970. he has held positions with major fastener producers in sales engineering, marketing, product design, manufacturing management, and research and development management.

Mr. Greenslade holds twelve U.S. patents on various fastener related products. he has authored over 136 trade journal articles on fastener applications, manufacturing and quality issues. he is one of the fastener industry 's most frequent speakers at trade association meetings and conferences. he is the youngest person ever inducted to the Fastener Industry Hall of Fame.

Mr. Greenslade is active in numerous fastener industry associations and societies holding office in several of them.

In addition to guiding the activities of Greenslade & Company, Mr. Greenslade works as a consultant with fastener suppliers and end users on product design, applications engineering, and quality issues. In this capacity he works to resolve fastener applications problems, ?? help select the best fastening approaches in new product designs, to assist in the standardization of fasteners used within an organization, and to provide training on various aspects of fastening technology and fastener quality assurance. he also serves as Expert Witness in litigation involving fastener related issues. he can be reached at: phone 817-870-8888, fax 817-870-9199 or email: greensladeandcompany@sbcglobal. net.