Thread Stripping Calculation Example
Abigail Tyrie
The size of a screwed fastener is first to be established by calculating the required tensile area with the appropriate factor of safety. If the joint is fixed using a nut and bolt from the same grade there is no need to size the nut while the standard length of the nut is such sized that the screw will fail before the thread is stripped. If the screw fastens into a tapped hole of a low strength material then a check of the thread engagement length is required.
The shear strength is defined by Fs=τ Ath where τ = shear strength of the material and Ath the thread shear area. When the external and internal thread are of the same material, the internal thread (in the tapped hole) is stronger in shear than the external thread. One of the problems in predicting the thread stripping strength is that without considering such effects as thread bending, nut dilation (effect of radial displacement) and tolerances of thread dimensions an optimistic result is calculated.
Accurately calculating the required thread engagement length is a complex problem. In an attempt to ensure that thread stripping does not occur rigorous and extensive tests can be fulfilled in which the strength is measured of a range of engagement lengths. In a similar way the length of engagement Le=0.75d of a standard nut is defined (standard nut height 0.8d>0.75d because of the chamfered hole).
The shear strength of a material is often expressed in the ratio of the shear to tensile strength, for ductile materials like steel τ/σ=0.580. With a bolt and nut of the same grade the ratio Ath/As should exceed 0.580 to ensure that the strength of the tensile area is the weakest. The stripping strength of a particular engagement length or material can be derived from the standard nut height. A material with only the half shear strength of the fastener requires the double length of engagement, Le=2x0.75d.
Threaded fasteners work by tightening and allowing both the bolt and nut materials to elongate against each other, creating a clamping force that holds two or more parts together. However, this clamping action causes stress on the fasteners, which can lead to disastrous material failure if not properly managed. This article tackles one of the common causes of fastener failure called thread stripping.
Thread stripping happens when the shear stress experienced in the thread helix surpasses the shear strength of either the bolt or the nut material used. Thus, the thread is damaged or ripped off, as shown in the illustration of a partially stripped thread below.
However, nuts are generally designed to have lower strength and hardness values than bolts of the same grade. For example, the hardness of a grade 8 nut would likely be lower than that of a grade 8 bolt. This is because, in a fastened assembly, it is necessary for the nut to yield first to ensure that the first thread does not carry the whole load solely; instead, it is distributed across the succeeding threads.
Thread stripping is a mode of failure that needs to be avoided at all costs. In general, fasteners are designed so that the possibility of failure due to breakage of the bolt body is far greater than the possibility of thread stripping.
On the other hand, thread stripping is a gradual type of failure and is hard to detect during assembly. It starts at the first thread and then gradually spreads throughout the entire thread engagement length until it breaks.
As the fasteners are tightened, the bolt elongates and the nut compresses. This causes the threads to deform and the nuts to dilate because of the radial wedging action between the internal and external threads. In general, the dilation is greater for nuts with lower yield strength and thinner walls.
The problem is that dilation typically occurs at the location of the first thread, which is also the thread that bears most of the load. As the nut dilates, the length of engagement of this thread decreases, thereby reducing the shear area and increasing the stress experienced by the thread.
Nut dilation can further be intensified by thread bending. When the strength of the bolt and the nut material is approximately equal, the bending of the threads caused by the axial load can amplify the effect of nut dilation and further increase the shear stress on the threads.
Bell-mouthing is when there is a slight taper on a threaded hole, which can extend up to about half the diameter of the hole. This is primarily caused by the instability and flexibility of the drill point during the drilling process.
When tapped, bell-mouthing results in a variable thread height along the length of the tapered hole. These variations in height cause a significant reduction in the shear area, especially in short lengths of engagement and fine pitches. Thus, it also increases the induced shear stress and the possibility of thread stripping.
The principal reason for thread stripping is when there is not enough thread engagement length to handle the shear load. This is because the cross-sectional area through which the shear occurs is directly proportional to the thread engagement length, as shown in the equation below:
It is absolutely necessary to select the correct length of thread engagement to avoid thread stripping and provide a safety factor to ensure that, in the event a failure occurs, tensile fracture happens before thread stripping.
The stripping strength of an assembly depends on the shear strength of the nut and bolt materials. Whichever has the lesser value will dictate the final shear strength of the assembly, and indicate where shear stripping is most likely to occur.
It is important to note that, unlike tensile and yield strengths, there are no published shear strength values for the different bolt and nut materials. For design purposes, the Industrial Fastener Institute states that the shear strengths of carbon steel fasteners may be assumed to be approximately 60 percent of their specified minimum tensile strengths (or proof stress for nuts).
Based on the cross-sectional shear area and the shear strength of the bolt and nut materials, the maximum shear load that the fastener can handle before thread stripping occurs can be calculated using the formula:
Based on these equations, it may appear that the maximum shear load can be increased simply by extending the length of engagement. However, it is important to note that the applied load is normally not equally distributed across the threads. Instead, most of the load is carried by the first thread, as shown in the load distribution diagram below.
Hence, there is a limit to how long the thread engagement can be extended to produce an appreciable increase in strength. For carbon steel fasteners, it is limited to approximately one nominal diameter. After that, there will be no appreciable increase in the maximum shear load the threads can withstand.
The bolted joint is among the most common joining methods -- other common joining methods include riveting, welding, press fits, pins, keys, and adhesives. The primary components of a bolted joint include the threaded fastener as well as the parts to be joined together (the clamped parts). The bolted joint works by inducing an initial clamping force ("preload") on the joint by threading the fastener into either a nut or into threads that have been tapped into one of the parts. This preload ensures that the clamped parts remain in contact and in compression throughout the life of the joint.
Washers are typically used in the joint and serve many purposes. They minimize embedment of the bolt head and nut into the clamped parts, and they aid in tightening. Since bolt holes could have sharp edges or burrs, washers are used to protect the fillet under the bolt head from scratching since this is a critical area that is prone to failure. Washers also serve to distribute the preload and applied force over a larger area, both on the bolt head and on the faces of the clamped parts. This reduces bearing stresses, helps to prevent pull-through, and helps to prevent damage to the surface of the clamped parts.
When analyzing a joint, it is necessary to know the characteristic dimensions of both the external thread and internal thread. A thread size is specified based on a nominal (major) diameter and either the number of threads per inch (for unified inch threads) or the pitch (for metric threads). The thread sizes for coarse thread and fine thread can be found in tables located in any standard machine design handbook, as well as in the thread size tables in the Appendix. The pitch, P is the distance between the threads. When the pitch is in units of inches, it is related to the threads per inch, TPI, by:
The tables below provide equations for some of the thread profile dimensions of interest for both unified inch threads and ISO metric threads. In the case of metric threads, the thread profile is based on a parameter H, the height of the fundamental triangle. The value of H is related to the thread pitch, P by:
Bolts are installed with a preload that ensures that the joint members remain clamped and in compression throughout the life of the joint. Preload is also important for joints with a cyclically applied load. The preload will increase the mean stress, but it will reduce the alternating stress.
In general, the preload force should be no less than the maximum tensile force that will be applied to the joint. This will ensure that the clamped parts always remain in contact and in compression. Because some of the tensile force applied to the joint will act to relieve compression in the clamped parts, the joint will separate at a value of applied force that is somewhat higher than the preload. This will be discussed in a later section.
Because the tensile force that will be applied to the joint dictates the required preload, then the maximum utility is obtained from a bolt by preloading it to the highest possible value. The ductility of the bolt material dictates how close to the yield strength the bolt can be preloaded. Shigley and Lindeburg both recommend the following (conservative) values of preload:
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