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ASME B31.3-2016
<br /> 319.4.4 Flexibility Stresses (c) The bending stress range,Sb,to be used in eq. (17)
<br /> (a) The axial, bending, and torsional displacement for reducing outlet branch connections shall be calcu-
<br /> stress ranges shall be computed using the reference mod- lated in accordance with eqs. (19) and (20), with
<br /> ulus of elasticity at 21°C (70°F), EQ, except as provided moments as shown in Fig. 319.4.413.
<br /> in para. 319.2.2(b)(4),and then combined in accordance For header (Legs 1 and 2)
<br /> with eq. (17) to determine the computed displacement
<br /> stress range, SE, which shall not exceed the allowable (iM�)�+ (ioMo)�
<br /> displacement stress range, SA, in para. 302.3.5(d). See Sb = Z (19)
<br /> also eq. (1d)and Appendix S,Example 3 for the greatest
<br /> computed displacement stress range. For branch (Leg 3), use eq. (20) when ii or io is taken
<br /> from Appendix D; when both ii and io are determined
<br /> SE _ OSJ+Sb)�+(2St)� (17) by experimental or analytical means, e.g., ASME 1331J,
<br /> use eq. (19).
<br /> where
<br /> AP = cross-sectional area of pipe; see para. 319.3.5 S (iiMJ2 + (ioMJ2
<br /> FQ = axial force range between any two conditions b Ze (20)
<br /> being evaluated
<br /> iQ = axial stress intensification factor. In the where
<br /> absence of more applicable data, iQ = 1.0 for r2 = mean branch cross-sectional radius
<br /> elbows, pipe bends, and miter bends (single, Tb = thickness of pipe matching branch
<br /> closely spaced, and widely spaced), and iQ = Th = thickness of pipe matching run of tee or header
<br /> io (or i when listed) in Appendix D for other exclusive of reinforcing elements
<br /> components; see also para. 319.3.6. TS = effective branch wall thickness,lesser of Th and
<br /> it = torsional stress intensification factor. In the (ij)(Tb)
<br /> absence of more applicable data,it = 1.0;also Ze = effective section modulus of branch
<br /> see para. 319.3.6. = Trr22TS; see para. 319.3.5
<br /> Mt = torsional moment range between any two con-
<br /> ditions being evaluated 319.5 Reactions
<br /> SQ = axial stress range due to displacement strains Reaction forces and moments used to design restraints
<br /> = iQFQ/Ap and supports for a piping system, and to evaluate the
<br /> Sb = bending stress range due to displacement effects of piping displacement on connected equipment,
<br /> strains shall be based on the maximum load from operating
<br /> St = torsional stress range due to displacement conditions, including weight, pressure, and other sus-
<br /> strains tained loads;thermal displacement;and,where applica-
<br /> = itMt/2Z ble, occasional loads. The reactions shall be calculated
<br /> Z = section modulus of pipe; see para. 319.3.5 using the modulus of elasticity at the temperature of
<br /> the condition, E,n (EQ may be used instead of E,n when
<br /> (b) The bending stress range,Sb,to be used in eq. (17) it provides a more conservative result).The temperature
<br /> for elbows,miter bends,and full size outlet branch con- of the condition may differ in different locations within
<br /> nections (Legs 1, 2, and 3) shall be calculated in accor- the piping system.
<br /> dance with eq. (18), with moments as shown in Where cold spring is used in the piping system,experi-
<br /> Figs. 319.4.4A and 319.4.413. ence has shown that it cannot be fully assured.Therefore,
<br /> the reactions shall be computed both with the assump-
<br /> (iiMJ2+ (ioMJ2 tion that only two-thirds of the design cold spring is
<br /> Sb = Z (18) present, and with four-thirds of the design cold spring
<br /> present.
<br /> where If it is necessary to determine the reactions at ambient
<br /> ii = in-plane stress intensification factor; see temperature, the designer shall consider loads at that
<br /> para. 319.3.6 condition, including the design cold spring and self
<br /> io = out-plane stress intensification factor; see springing of piping. Self springing may occur if the
<br /> para. 319.3.6 operating stress in the piping system exceeds the yield
<br /> Mi = in-plane bending moment range between any strength of the material or if the piping operates at tem-
<br /> two conditions being evaluated peratures in the creep range of the material.
<br /> Mo = out-plane bending moment range between any 319.5.1 Maximum Reactions for Simple Systems.
<br /> two conditions being evaluated For a two-anchor piping system without intermediate
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