Design considerations of reliable screw joints

Pitch P, angle of thread 60º, pitch diameter d2=D2, major diameter of external thread d,  minor diameter of internal thread d3, major diameter of internal thread D, minor diameter of internal thread D1, root radius R, height of fundamental triangle H.

The critical areas of stress of screwed fasteners are:

The effective cross section area, or tensile area.
The shear area of the external thread (screw, bolt)
The shear area of the internal thread (nut, tapped hole)

 When a reliable design is to be achieved screw joints are such designed that the effective cross section area is determinative for the strength of the assembly, i.e. the screw fails rather than the internal or external thread strips. The length of the screw engagement should at least be sufficient to carry the full load necessary to break the screw. If not, thread stripping starts at the first engaged thread and successively shears off subsequent threads. This may take some hours to complete and so the joint may appear fine at the time of assembly but will fail in service.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. Weak materials are sensitive for galling at high contact pressure. In order to enlarge the stripping strength and at the same time to prevent galling it is possible to use helicoils.
 Case: Effective length of thread engagement Problem: Calculate the required length of engagement of a tapped hole in a casting of spheroidal graphite cast iron. The thread strength must be able to carry the full load at which a M12-10.9 bolt fails.   Given: The tolerance class of the dimensions of a standard nut are assumed to be representative for the tapped hole. The ratio of shear strength to tensile strength of the SG cast iron is taken as τ/σ=0.9, where the tensile strength is σ=500 MPa.   Solution: The ratio of shear strength of the bolt and the tapped hole is 0.58 1000 / 0.9 500 = 1.3. The required length of thread engagement becomes 1.3 0.8d = 12.5 mm.   Accurately calculating the required thread engagement length with a sophisticated program available at www.boltscience.com , in which a large number of influence factors are considered, finally results in a required effective thread engagement length of 12.9 mm.A generally used practical calculation method for the tread stripping strength is given by the formula Ath=0.5πd0L0. where d0=(d2+d3)/2. Applying this formula results in the effective length of thread engagement of L0=11.5mm.Note that the shear strength of a metric fine thread exceeds that of a standard metric thread because of the slightly larger d0-value (approximately 6%).

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