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# 3.5.1.2 Restraint in CAESAR II

The term restraint, although technically applicable to any of these boundary conditions of the piping system, colloquially is confined to those restraints which have a relatively rigid stiffness, and restrain the pipe in a direction other than simply in the downward direction (i.e., a hanger, support, etc.). Restraints may act in more than one degree of freedom (but less than six, which would be an anchor). Restraints may be classified yet further in terms of their direction — for example, axial restraint, or guide (a restraint in both directions of the horizontal plane when applied to a riser, or in the lateral direction when applied to a horizontal run), or in terms of their function (for example, limit stop, where a gap is closed as the pipe moves, before the restraint kicks in). Restraints may consist almost entirely of manufacturer's hardware (i.e., clamp and sway strut assemblies), or may be built up of structural steel. Restraints are coded in CAESAR II as various combinations of restrained degrees of freedom (X, Y, Z, RX, RY, and RZ). Restraints in a skewed direction can be defined with direction cosines (or direction vectors) — i.e., 0.707, 0, 0.707 is equivalent to 1,0,1. Friction can be activated by defining a Mu value (coefficient of sliding friction) for the restraint (Mu values for steel on steel typically range on the order of 0.3). Friction is represented by applying a force equal to Mu times the restraint load on the pipe along the direction of movement.

Examples of restraints are shown in Figures 3-95 through 3-97. Figure 3-95 shows a simple restraint, consisting of a sway strut. A sway strut, due to the pins at the brackets, allows the pipe to move laterally (to the strut). The clamp allows the pipe to rotate in any direction. Therefore, the strut restrains only in one degree of freedom (i.e., Z). The radius of gyration of the strut is sufficient to prevent buckling, so the strut restrains in both directions of the degree of freedom. Since the pipe does not rub against anything as it moves, friction is not modeled.

Figure 3-96 shows three restraints built up of structural steel. In (a), the restraint is only in a single degree of freedom (Y), but in two directions (both up and down). In (b), lateral restraint is added as well, giving a two degree of freedom restraint. In (c), lugs are welded to the pipe to provide axial restraint, creating a restraint in three degrees of freedom (not an anchor, since the pipe is free to rotate about three axes). In these cases (although the third case is moot), friction should be modeled, since the pipe would rub against the restraint if it moves.

Figure 3-97 shows a restraint in four degrees of freedom—X, Z, RX, and RZ, since the lugs prevent lateral translation of the pipe, and the double lugs resist any moments about the X-orZ-axes. This restraint should also be modeled using friction.

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