Bolt Pre -Load

Effect of Initial Bolt Pre - Load

In the diagram above assume that the one end of the bolt and part are welded to the support and the nut is just put on 'finger tight' to remove any play.

The deflection of a bar under axial load:

delta = P L / A E where P = load, L = length, A = cross section area and E = Young's modulus.
Stiffness = k = load/ delta, N/m, rearranging the above and with subscript p meaning part and b meaning bolt: k_b = A_b E_b / L_b and k_p = A_p E_p / L_p

P_b = part of load P carried in bolt and P_p = part of load carried in part.
P = P_b + P_p

The deflection of the bolt = P_b / k_b and of the part = P_p / k_p and these must be equal. P_b / k_b = P_p / k_p

P_b = k_b(P - P_b) / k_p

P_b k_p = P k_b - P_b k_b

P_b (k_b + k_p) = P k_b

P_b = P k_b / (k_b + k_p) and similarly: P_p = P k_p / (k_b + k_p)

Suppose that the nut is tightened so additional tensile load, F_o is placed in the bolt, then the force in the bolt: F_b = P k_b / (k_p + k_b) + F_o This causes an equal and opposite compressive force in the part, so F_p = P k_p / (k_p + k_b) - F_o
In practice F_o is applied on assembly, before the load P is applied. The initial force F_o must always be made large enough to keep the part in compression, ie F_p must be negative. This is needed to maintain a gasket seal or merely to reduce the effects of cyclic loading on the bolt.

Example calculation

Return to Module Home Page

David J Grieve, 10th February 2004.