Rules-of-thumb for thread engagement typically advise: For a steel nut member: 1 – 1 ½ times the fastener diameter should be engaged and for aluminum nut members: 2 – 2 ½ times the fastener diameter should be engaged. But these guidelines frequently result in over-designed joints and sometimes these full-thread lengths just aren’t available in your new design.
So how do you configure the length of engaged threads so they are less than rules-of-thumb and still provide adequate strength and safety factors necessary? The following is an example of a Grade 5 capscrew installed into rolled threads in a ZA-8 aluminum alloy die-casting. Be aware that the following ONLY applies where the fastener is stronger than the nut (threaded) material. Other formulas apply where both material strengths are equal or the nut material is strongest.
Thread Strip-Out, Bolt Material Stronger Than Nut Material: (Note: These formulas are courtesy of John Bickford in his book, “An Introduction to the Design & Behavior of Bolted Joints”)
½-13 UNRC x 2.50” long Grade 5, hex head capscrew threaded into ZA-8 die-cast Al/Zn alloy.
As = 0.7854*(D-0.9743/n)^2 [inch fasteners only]
Le = (Sst*2*As)/(Snt*π*n*Dsmin*(1/(2*n)+0.57735*(Dsmin-Enmax))) [Nut strip only]
Ats = π*n*Le*Dsmin*(1/(2*n)+0.57735*(Dsmin-Enmax)) [Nut strip only]
The following can be found in Machinery’s Handbook and a table of Fastener Strength Designations.
As = 0.1419 sq. in., tensile stress area of the bolt
Dsmin = 0.4876 inches, minimum O.D. of bolt threads
Enmax = 0.4565inches, maximum pitch diameter of nut
Sst = 120,000 psi, ultimate tensile strength of bolt material
Sy = 92,000 psi, yield strength of bolt material
n = threads per inch
Snt = 53,000 psi, ultimate tensile strength of the ZA-8 nut material
Fi = initial preload applied, lbs.
Td = design torque to achieve the initial preload, lb-in.
Fs = Strip-out force, lbs.
Using the formulas and tabular information above:
Ats = 0.6426 sq.in., shear area at root of nut threads
Le = 0.5719 inches, length of thread engagement required to develop full strength
La = 0.647 inches, minimum thread engagement available
La / Le = ratio of minimum full threads available to full threads required = 1.131
(Note: this is the joint’s safety factor if nothing else is considered in the joint design.)
Fi = (% of bolt strength)(Yield Stress)(As) = 0.80*92,000*0.1419, Fi = 10,444 lbs. preload allowable
Torque = (k*Fi*d)/12 (torque calculations are always conducted in lb-inches, then converted)
= 0.2000*10,444*0.500, therefore the design torque, Td = 87.0 lb-ft. @ 80% of bolt yield
Fs = Snt*Ats*(La/Le), and the force required to strip the nut material is 38,526 lbs.
Fi / Fs = 10,444 / 38,526, therefore the design torque produces only 27.1% of nut strip-out.
These calculations are best done in a spreadsheet to avoid errors and allow input data modifications to see how the various joint components are affected. For example, if you change to a Grade 8 capscrew and reduce the full-thread engagement to only 0.250 inches (or 3.25 threads), a design torque of 123 lbs-ft. will develop an initial preload of 14,758 lbs., enough to begin strip-out of the ZA-8 rolled threads.
Keep in mind that the nut factor (k-value) of 0.2000 was chosen based on empirical data. Calculations are only as precise as the k-value. Otherwise, they are only a “best guess” of joint performance. For an example of how critical the K-value is, see my 11/15/20 post, “What Does the Nut Factor, “K”, Really Encompass”. ALWAYS test a few samples of the actual fasteners, materials and torque tools which will be used in production. If nothing else, you can always tighten some samples to failure for a rough confirmation of the accuracy of your calculations. If you have questions regarding other bolt and nut strength combinations, you may contact me at dmzenge@charter.net or <mobiletechengineering.com>.