MadSci Network: Engineering

Re: prevailing recomended torque for machine screws

Date: Tue Aug 22 17:25:12 2000
Posted By: Bradley Kelley, Grad student, Mechanical Engineering, Colorado State University
Area of science: Engineering
ID: 966035965.Eg

Dear Miroslav,

I am always amazed at how a seemingly simple question doesn't have a simple 
answer.  Given my limited resources, I found very little information 
regarding bolts smaller than ╝".  I found some torque charts for bolts 
above that size, but most companies that produced these tables were quick 
to point out that these were recommendations only.  An unreferenced torque 
spreadsheet that shows reasonable numbers is shown at
However, it doesn't include the sizes you need.  So we will have to use an 
equation to help solve your question.

Pre-tensioning of bolts is what keeps your connection together.  A much 
better explanation of the importance of pretensioning is given at the 
following websight from Unified Engineering Inc. http://www.uni
Bolts are pretensioned by turning them until they are snug, then using a 
twisting force (torque) from a specialized torque wrench or adjustable 
impact hammer to further turn the bolt.  Since the head of the bolt is snug 
against the washer or surface, turning the bolt actually elongates it.  The 
elongated bolt acts as a stretched spring, pulling the two materials 
together.  This is the pretension force.

Most designers want to maximize the pretension force used, since using 
larger bolts at less than maximum force is wasteful and more expensive 
(unless the engineer determines a necessary degree of safety requires 
larger bolts).  This is how most tables are set up, for the maximum 
recommended pretensioning for a certain bolt.  If you do have some tables 
for the larger bolts, you will see there are two major factors when 
determining the maximum torque for a bolt.  Grade and lubrication.

Grade is the type of steel your bolts are made out of.  The higher the 
number, the stronger the bolt.  Grades 1 and 2 are the lowest, cheapest, 
and are frequently what you buy from the hardware store.  I would HIGHLY 
recommend not using these for high stress applications as they also tend to 
have a wider range of strengths.  The next major grade is grade 5, which is 
medium strength and used when grade 8, a high strength bolt, is not needed. 
 A good strength table is shown at the following websight:
This sight also gives a shortened example of the equation I will talk 

The other factor is lubrication between the bolt and the threads.  If there 
is no lubrication, some of the torque force is needed to overcome the 
friction between the inner and outer threads.  This friction then 
dissipates, meaning the net pretensioning is less.  By lubricating the 
bolt, the torque needed to get the same pretension force is less.

I won't go through the derivation of the necessary torque equation, since I 
barely understood it as well.  But here it is:  (From "Mechanical 
Engineering Design" Shigley & Mischke.  5th edition, McGraw-Hill Pg. 346).

T = K*Fi*d

T = Torque
K = Torque Factor
Fi = Preload Force
d = Major bolt diameter (ex. .250" for ╝" bolt)

The bolt diameter is the easy one to find, it is the preload force and 
torque factor that are a little more subjective.  The torque factor 
generally depends on lubrication.  Here is a quick table extracted from the 
above reference.

Bolt Condition	K Factor
Nonplated, black	.30
Zinc-plated	.20
Lubricated	.18

There are other lubrications that can reduce that number even further, but 
for general purposes a K value of .20 is used.

Then what is the max preload force?  Again from Shigley and Mischke, who 
referenced the following info from Russell, Burdall, & Ward Corp's book 
"Helpful Hints for Fastener Design and Application".  

"For reused connections, pretensioned load (Fi) should be 75% of the proof 
load (Fp) of the bolt."  The proof load is obtained from the equation Fp = 
Fp = Proof load of bolt
At = Tensile Stress Area
Sp= Minimum Proof Strength

So before I confuse you any further, lets do an example using a ╝-20 grade 
5 bolt.  If you can't find a table listing proof strength, it is generally 
90% of the yield strength.  (Not tensile strength!) (See the values at the 
bicycle websight).  Proof strength for a grade 5 bolt of this size is 85 
kpsi (1 kpsi = 1,000 psi or pounds per square inch).  Tensile stress area 
is .0318 in^2.  (The following website has tables that give the stress area 
for small bolts. Look under fasteners).

Therefore,  Fp = 85,000 psi * .0318 in^2 = 2703 lbs.

And we wand Fi to be 75% of this, so 0.75*2703 lbs = 2027 lbs.

And from our earlier equation, T = K*Fi*d.  We will chose the base K of .20 
in this case, and d of ╝ bolt is .250 (d is also found at the last 
websight).  Then we getů

T = .20*2027 lbs*.25in = 101 in.lbs, or divide by 12 and we get 8.5 ft.lbs.

The table from the first websight gives a torque for an unlubricated ╝-20 
bolt of 8 ft.lbs, so our equation seems quite close.  It is likely the 
table is a little on the safe side.

So now you have a way to figure out approximate maximum recommended torques 
for your machine screws.  Please note that this is only a recommendation 
and there can be other factors involved.  Also, the manufacturer of your 
bolts may have better strength information on their product, and be VERY 
sure about what grade of bolt you have!  It should be obvious that a low 
grade bolt could snap off at the recommended torque of a grade 8.  Best of 
luck and I hope this helps.

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