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The flanges at the end of the two turbine shafts seen above, are bolted together to form a very rigid friction coupling 2

High pressure turbine casing. Note the proportion of the depth of the flanges to the bolts diameter. Note also the spacing of the bolts. This is one of the most extraordinary bolted joint. 3

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These are the heater elements used to ‘grow’ the length of the bolts. When left to cool and the bolts reaches the same temperature as the flanges, they develop the required preload 5

The stem of the bolts is held from turning while the nut is torqued up. Holding the end of the stem prevents torsional stresses being transmitted to the stem. 6

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The effect of fillets and bolt shank cross-section on fatigue strength 9

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Improvements in fatigue life by increasing radius of fillets at the base of external thread 11

A simple example of parallel load paths. Here for the spring at left, we can say because it has fewer coils, of thicker wire and of smaller coil diameter, will be stiffer than the one at right. Let the relative stiffness be: K L = 10 K R If the applied force F causes an extension of Δ, the force carried by the left and right springs are: F R = Δ K R F L = Δ K L = Δ 10 K R Where F T = F L + F R = Δ 11 K R The fraction of the force carried by either spring is proportional to the relative stiffness of that spring. F L / F T = 10 / 11 F R / F T = 1/ 11 The applied external force is divided between the two load paths in proportion to the ratio of their stiffness to the total stiffness. FTFT FTFT 12

Article from Volvo on new head bolts stiffness calculation 13

Bolted joints may use a small number of large dia bolts, with wide and thick flanges or a large number of small dia bolts and small flanges. We must also choose the shape and strength or grade of the bolt. Near one extreme we get the cheapest joint, near the other the lightest. Exactly the parameters of each is very difficult to determine without something like a ‘solver’. In individual industries there has been a tendency to select a combination and stick with it, now thanks to MS it is possible to obtain numeric optimal solution for each application. 14

Villiers two stroke engine. In low performance and low efficiency engines one finds simple means of sealing the engine head to the cylinder and thereby containing the combustion products. Here a simple paper gaskets are used both at the head and at the cylinder to crankcase joints. Paper has about 1/2000 the Young’s modulus of iron. Hence the stiffness of the assembly is very poor and the alternating loads on the bolts is not helped much at all by the cast iron cylinder 15

Coventry Climax, 2 liters 4 cyl, 62 The ‘head’ of this engine is removable. To seal the combustion products an even pressure has to be maintained all around the interface between the cylinder block and the head. By this sort of strategy the conical compression zones generated by the pretension has space to spread from the middle of the cylinder block, to all around the top of the cylinder and meet similar cones coming from the head. To achieve this the studs begin half way through the cylinder block and extend all the way to the top of the engine. Each cylinder has 4 bolts equally disposed around its periphery. Cylinder head Interface head to cylinder block. Cylinder head hold-down studs 16

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These bolts have to hold the tower segments together, when subjected to fluctuating wind loads (among other loads) 18