Mechanics of Loading and Stressing a Bolt
When the nut is turned in a tightening direction by the applied torque (T), the flange, nut and bolt head surfaces are eventually put in contact along planes. This contact prevents further forward advance of the nut. Continued tightening is accomplished at the expense of metal deformations. While there a combination of metal deformations involved, normally only the tensile deformation in the bolt body is used to evaluate the resulting load.
When further torque is applied to the nut, the nut threads act on the bolt threads so as to pull the bolt up through the nut. This pull results in a lateral and axial deformation of the bolt body. The tensile force causing this deformation also causes an equally compressive load to be transferred from the nut and bolt head to the flanges.
A step by step analysis of how a loading device for threaded fasteners works is as follows:
F x D = T
Where: F = Force in inch-lbs
D = Distance in inches or feet
T = Torque in inch-lbs or ft-lbs
For instance, if you were to pull on the end of a 12” wrench, distance D, with a force of 50 lbs., force F, the resulting torque would be:
F x D = T
50lbs. x 12” = 600 inch-lbs. or
50lbs. x 1’ = 50 ft-lbs
An important step, often difficult to understand is how we go from torque to bolt tension force. For a given size bolt and nut a scale can be attached and measure the force F, shown above, and with a fixed distance D, the torque can be calculated. During this operation the bolt elongates and the amount of elongation could be measured. Another bolt of the same size is mounted in a tensile testing machine. This machine measures bolt tension force versus elongation. In the former case torque versus elongation was measured. In the latter case bolt tension force versus elongation was measured. Thus, torque versus bolt tension force can be correlated.
It is important to note that friction and variability of the lever arm length (where the wrench is gripped) are all variables that contribute to the inaccuracies of using hand wrenches. Accurately translating this torque number into compressive stress requires a good understanding of the condition of the mating surfaces and friction factors involved throughout the bolted connection.