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Aviation History
1941
1941 - 0743.PDF
MARCH 27m 1941. 243 1AIRCRAFT ^ ENGINEER No. 181. 16th Year. PRELOADED STUD ../ Importance 0/ Taking Elasticity into Account By LT.-COL. J. D. BLY .it- THE question of the effect of applying an extprffialaxial load to a preloaded bolt appears to gum riseto a certain amount of confused thought, jlnth the result that incorrect solutions of the problem.^re often obtained. / Fig. i shows a plate supported at K and L. A bolt is passed through a hole in the plate, and tJfe nut is pulled up until the reaction at each of the faces DF and GH is P lb., that is to say, until the preload is P lb. If an axial load W is applied as shown it is evident that the sum of the reactions at K and L must be increased by an amount equal to W. The effect on the reaction at the face DF is not so obvious, and it is stated not infrequently that this reaction is unchanged if P is greater than W. The proof advanced is that the reaction at the face GH is reduced to P — W, and therefore the total forces acting on the bolt and nut are P upwards and (W -\- P — W) down- wards ; and the fact that such a system of forces satisfies a condition required for the equilibrium of the bolt is held by the supporters of the theory to show that the proof i,s correct. In approaching the problem it must be realised that if the bolt and plate were perfectly rigid there could be no .preload, -since the preload depends for its existence upon ,1+he storage of strain energy and without elasticity there can be no strain. It is evident, therefore, that the elas- ticity of the plate and bolt must be taken into account if a correct solution is to lie obtained. In Fig. 2, let L = unstretched length of bolt. dL — amount of stretch. T = thickness of plate before compression. dT — amount of compression. a = area of cross section of bolt. jA — area of plate under compression. Ej = Young's Modulus for bolt. E2 --- Young's Modulus for plate. Consider first the case with preload P only. 'Since E == Stress/Strain, P „ dL . P „ dT O.B.E., F.R.Ae.S., F.R.S.A. D BOLTS '\E,a - 7 E.A" Now suppose a load W to be applied axially as shown in the figure. The downward force on the lower end of the bolt is increased by the amount W, and the bolt will stretch, reducing the preload to an amount less than P and allowing the plate to expand. Let P, = the residual preload. rfjL = the total stretch of the bolt. d T = the remaining compression of the plate. D Pj, * G L F r 1 FI&.1 D G 4 r •tL T J, FIG. 2 w P, = E dj. (W + P,)L PiT Now Therefore i and dxT — also L + i Whence *_, — ,-_, —T \ E,a From (iv) and (v), d T T whence E2A = T - d T E2A - P, W + P, -PiE,a + W + P, W(E2A - P)P, = P E2A (v) (vi) Whence dL = PL and dT = = j PT (i) (") Also, since the dimension BC is common to both plate and bolt, L + dL = T — dT (iii) From (i), (ii), and (iii), E2A This gives the residual preload for any value of W less than Wo. The reaction at the face DF is equal to the tension in the bolt. Calling this F we get F = W + P, r W(E'fl + p> • • (vii) ~F Exa +E2A " " ( J The preload is totally relieved when P, = o. If W(, is the minimum external load required to completely relieve the preload, from (vi) we get Since the preload cannot have a negative value it follows that the tension in the-bolt and the pressure on the face DF
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