14 Replies Latest reply on Aug 6, 2012 5:05 PM by Chris Fernald

    How are bolt FOS's calculated?

    Chad St.Louis

      I'm curious how bolt FOS's are calculated in Solid Works.


      My model uses 80% of proof for axial loading (pre-load) which already equates to a maximum FOS of 1.25 (1/.8). Yet when shear and bending moment are taken into consideration, putting the bolt under higher tension, I end up with a higher FOS. ???


      Can anyone explain?



        • Re: How are bolt FOS's calculated?
          Dougal Hiscock

          Are you interested in FOS for yield or ultimate strength?

            • Re: How are bolt FOS's calculated?
              Chad St.Louis

              The strength data being used is tensile strength area, bolt strength and Factor of Safety.


              For an M16 grade 10.9 bolt for example, I calculated these to be:


              .24 in^2

              120000psi (proof load stress)

              1.15 (arbitrary)


              I don't think tensile or ultimate is used in this case. Proof load is used for bolt strength.

                • Re: How are bolt FOS's calculated?
                  Dougal Hiscock

                  Chad, strength and FOS always comes down to yeild or ultimate tensile strength of the material.  Some rough calculations show you are indeed using the yield strength of the bolt material for your FOS.


                  The 16mm bolt shank will yield in pure tension around 181kN (210mm^2 area, 900 MPa minimum yeild).

                  The 14mm minor diameter of the threads will yeild (neglecting stress concentration) around 139 kN (154mm^2, 900 MPa minimum yield).


                  0.24 square inches is the 154mm^2 of the minor diameter.

                  120,000psi is 827 MPa which is roughly 93% of minimum yield.  Because 900 MPa is the minimum yield and bolts can be higher your proof stress based on ~80% yield does make sense.

              • Re: How are bolt FOS's calculated?
                Paul Kellner

                Are you modeling the bolt in Simulation?


                The FOS calcs normally used are based on uniaxial stress. An FEA model will include 3D effects.


                Bolt FOS are calculated based on ultimate strength. Frequently this means some stretch in the bolt. This implies a non-linear analysis where stress will increase to yeild and no further.

                  • Re: How are bolt FOS's calculated?
                    Chad St.Louis

                    Hi everyone,


                    Thanks for the comments. The following link explains the procedure used by SW.




                    The equations are taken from "Criteria for Preloaded Bolts", NASA Document MSTS 08307; Revision A: July 6, 1998. SolidWorks formulation is based off the formulation described in this document. It is not the exact methodology.


                    It was not clear to me how the axial, bending-moment, and shear were combined to determine an overall FOS.


                    Hope this helps.



                      • Re: How are bolt FOS's calculated?
                        Paul Kellner

                        There is only one type of element that will easily yield those values and that is a beam element. So they calculate that ratios for axial, bending and shear and combine them according to the following equation. The R values are the individual factors of safety given just that type of loading.


                        1 / ((Ra + Rb)^2   + Rs ^3) >   SF


                        For axial:


                        Ra = F/(At*S)


                        S is the allowable tensile stress for the material in the axial direction. F/(At) is the axial stress on the gross section.


                        It would certainly seem that there is something wrong with the equation because it doesn't yield sensible results in the case of a single non-zero load. For example if Ra worked out to be 1/2 and the others were zero then the calculated value  should be 2. Instead it would be 4 if you used their pass fail equation. It looks like a typo, the equation should take the square root of the denominator. I would definitely run a test case to see what is really happening.

                          • Re: How are bolt FOS's calculated?
                            Adrian Tayne

                            This is old but I found this helpful and wanted to add to what Paul mentioned. There is definitely a mistake in the SW help equations, which are still that way as of today. The error stems from a discrepancy in how the ratio values (Ra et. al.) are defined. SW defines them as not being multiplied by FOS while the aforementioned NASA  document (very useful) defines them including the FOS.  For example, NASA defines Ra as the ratio of actual load to acceptable load multiplied by the FOS.


                            Ra = FOS * (P/At*S)


                            whereas SW defined it as


                            Ra = (P/At*S)


                            So in the equation for Rcombined in the SW help, each term on the left needs to be multiplied by FOS. This then needs to be less than or equal to 1.


                            Also, NASA states that the fastener must meet all 4 criteria listed (tension, shear, bending, and combined loads), not just combined load like SW implies.


                            What I don't know is whether SW is actually calculating this wrong or if the help just has a typo. A user should take the listed bolt and pin loads and check the (4) criteria by hand to make sure.

                            • Re: How are bolt FOS's calculated?
                              Chris Fernald

                              I’ve also had issues with bolt connector FOS.  I made a post a while back about a similar subject: https://forum.solidworks.com/thread/44790

                              Regarding the help file formula, I come to the same conclusion; there seems to be an extra squared term in the SW equation. So the problem I am having is two-fold:

                              1. FOS given by solidworks is dominated by the preload, which is generally very close to the proof load.  This means the FOS is always slightly greater than 1, even when the applied load is very small.  (see hyperlink)
                              2. Even if I could separate the FOS from being dominated by preload (for example, set the preload to 0), the formula used to calculate that FOS is x^2 higher than I would expect in the simple axial case.  Therefore, it is suspect.

                              When I presented these questions to our SW re-seller I was referred to the same NASA document.  At this point, I continue stuggle with this problem, as I haven't found a clear answer.

                                • Re: How are bolt FOS's calculated?
                                  Adrian Tayne

                                  Based on my conversation with my VAR, the equations that SW actually used to calculate the bolt stresses are accurate. It's only the equations in Help that are inaccurate. Someone made a typo... So I am surprised that your numbers are coming out wrong

                                    • Re: How are bolt FOS's calculated?
                                      Chris Fernald

                                      I just checked in this thread to see if there was any resolution.  My VAR also referred to the NASA document which says the FOS has a squared relationship to load.  A few people posted that it would be a good thing to run a comparison model, so below is a basic hand calc compared to the SW results.  Since it is still not clear to me why the two methods don't match, I wanted to post this for documentation purposes.  Seems like predicting the FOS to be falsely high could be a real problem, so I hope it is either fixed or better explained in the future.