Analysis

Fastener Modeling: A FEA Approach to Pre-Tension

“What is the specified torque values for this product?” – It’s a question all too familiar as a manufacturer in the telecommunications industry. The question is not only asked often but rarely yields a simple answer. Because products are made for universal applications, the applied torque for bolting and the subsequent clamping force will vary upon application. Friction coefficients, pole diameter, tower leg size, and material differences are just a few “unknowns” that make giving a simple answer out of reach.

To the customer, the lack of guidance leaves room for confusion. We strive to not only make superior product, but to also provide a pillar of engineering support. This article wishes to help alleviate some of the confusion by clarifying our design practices for bolts and threaded rod.

A simple model was generated and analyzed with the finite element analysis software ANSYS Workbench. While the model analyzed in this article is not a product, a similar FEA approach is used often on our products; one such example would be collar mount like the RM3-HD and LWRM where the threaded rod is analyzed with pre-tensional forces.

Model Setup

U-bracket, threaded rod, and two hex-nuts were modeled in an assembly as shown in figure 1. Each plate of the bracket is 3x3x ¾ inch. The threaded rod is 6 inch with ½ inch OD and the hex nut is ½ inch. The material grade of the threaded rod is grade 5 J429 and the plate steel is A36. The contacts between the bolt and plate are non-linear and frictional to make the simulation closer to real world values. The mesh consists of hexahedral cells with a sizing of 3/16 inch sizing. The average mesh element quality is 0.94 (out of 1) and the total cell count is 8220 and total number of nodes 41698.

Pre-tension load of 6000 pound is apply to the threaded rod on the center. A fixed boundary condition is applied to the bottom side of the plate. Typical pre-load design values should not exceed 70% of the yield strength of the material. Since J429 ½ inch bolts have a yield strength of 92000 psi and the area of the rod is 0.196 square inches, the maximum force allowable would be 12622 pounds. The value for this analysis was taken as half the previous allowable value as shown in figure 2. When applying this in the field, the amount of torque applied to each nut would translate to clamping force by the equation below where torque (T) is equal to the clamping force (F) times the diameter (d) and time a bolt constant (k). For this analysis, the applied torque would be 50 ft*lbs, assuming k is 0.2.

Results

The maximum stress is located in the zone between the rod, bolt hole, and nut head. As shown from figure 3, the maximum stress in the assembly is 44641 psi. This stress concentration while below the yield of the bolt is much higher than the nominal stress. The maximum nominal stress on the bolt is 33000 psi as shown in figure 4. By using the known value of 6000 lbs of pre-tension, the axial stress would be 30487 lbs (theoretically) which makes the model in good agreement as the percent difference between the two values is 7.6%. The equivalent stress on the plate is highest, 29846 psi, on the corner between the bottom plates.

The total deformation caused by the 6000 lb pre-tension was trivial as the maximum deflection was 0.0067 inches as seen in figure 5. The scale is increased by 55 times to show the results more pronounced. An important note, as the bent plates begin to bend inward, the nut stays in contact with the face of the plate; this is ideal for bolting as nut-head separation causes unwanted stressors.

Conclusion

Because products are made for universal applications, “unknowns” during the design process make giving a specific value for torque difficult. However, utilizing FEA can reduce and eliminate issues with pre-tension design. In the model, the nominal stresses were in agreement with hand calculations. The model revealed that stress concentrations on the bolt cause it to see much higher loading than hand calculation predictions; stress concentrations are one of the reasons why designing a bolts pre-tension for 70% of yield or less is necessary.

Joseph Trimble

Joseph Trimble graduated from Purdue University-Northwest with a Master of Science in Mechanical Engineering in 2016. While a graduate student, he worked as a researcher utilizing numerical methods such as finite element analysis for structural and fluid dynamic analyses.