When we start tightening the screw, there are some forces which start producing, these forces are following
Tensile stresses due to stretching of bolt
The best known method to design a bolt is the direct tensile stress having large factor of safety. The reason behind taking a large factor of safety is to accommodate indeterminate stresses.
Pi = 2840.d N
This formula is taken by using experimental techniques in which Pi is the initial tension and d is the nominal diameter of bolt in terms of mm. In case of making fluid tight joint, we use the formula mentioned above. But if we don’t want to make the bolt fluid tight then the initial tension in the bolt goes half down.
Pi = 1420.d N
Furthermore it is experimentally proved that a bolt having less than 16 or 18 mm nominal diameter is not used for fluid tight joints.
During manufacturing, if the manufacturer doesn’t initially stress the bolt then we can findout its maximum safe axial load by using following formula
P = Permissible stress x Stress area
Stress area can be found by using following relation
Stress area = (π/4)x[(dp + dc)/2]2
where in the above expression dp is the pitch diameter and dc is the minor diameter.
Torsional shear stress by frictional resistance of threads at the time of tightening
Torsional shear stress can be found as following
T/J = τ/r
where in the above expression T is the torque applied, τ is the torsional shear stress, r is the minor radius of threads and J is the polar moment of inertia.
If we continuously using screw tightening and loosening, it will create scoring and ultimately increases torque applied.
Shear stress across the thread
By using formula we can get average shear stress across thread
τs = P / (πdc x b x n)
where in the above expression, b is the width of thread section at nut, n is the number thread in contact, dc is the minor diameter and P is the safe axial stress in the nut.
Compressing stress on thread
Between threads we can obtain compressing stress as following
σc = P / π[d2 – dc2]n
Bending stress when nut is not parallel to bolt axis
When nut is not parallel to the bolt axis, bending stress start producing in the shank of the bolt
σb = x.E/2l
where in the above expression, x is the difference in height between extreme corners of nut, E is the young modulus and l is the length of shank.