Document 6y5GBgE7EGV6JXwL172OeGg9

890 CHAPTER 58 1965 Guide And Data Book Table 16 ... Thermal Stresses Due to Total Constraint Therm! Stresses, Pa Change, f Oeg Steel Wrought iron Cast Bran or Iron 'bronze Copper Abwtnum 20 3900 3800 1428 2760 40 7800 7600 2856 . 6520 60 11700 11400 4284 82SQ 80 istf 15200 5712 11040 100 19600 19000 7140 13800 * for temperature* between 83 end 400 F. 2980 5960 8940 11920 14900 2700 5400 8100 10800 13500 Table 17 .... Physical Properties for Determining Thermal Stress (fanperatoret between 32 and 400 f) Steel Wrought Coif Brass or Cop per AJtw Coefficient of Linear Expansion, o X 10*... 6.5 6.8 5.95 9.85 9.3 13.5 Modulus of Elasticity, E, psi X 10-*............... 30 28 12 14 16 10 product of aE, psi......... 195 190 71.4 138 149 135 Ezamplt: Tbe coefficient o# f-p*"*1"" tor steel " 0.0000085 in./ip. end the modulus at elasticity -- JO,000,000 psL Therefore aB m IBS ptL stricted to nominal pipe sizes 3 in. and smaller in which range commercial fittings are available. This type of fitting has gained rapid acceptance owing to its ease of installation, low cost, and ability to make a pressure-tight joint without weak ening the pipe,.as is'the case with threading. Dimensions for socket-welding fittings, in accordance with ASA Standard B16.U-1946, are given in Table 12. , EXPANSION AND FLEXIBILITY Changes in temperature cause a change in dimensions of any matter. The metals that are used for pipe have the same characteristics in that they expand with increasing tempera ture. If the metal is constrained so that it cannot expand, then an internal compressive stress is set up in the material. This stress can be calculated, just as any other stress, by using Hooke's Law. where F " force of constraint, pounds. e ~ deformation, inches. E 9 modulus of elasticity, pounds per square inch. A -- area of metal, square inches. L 9 length of metal, inches. This equation is valuable in determining the internal stress of the pipe and the constraining force: on the anchors. It assumes that the stress is less than the yield strength of the metal. In other words* the metal will return to its original dimension when the temperature returns to its original level. Materials such as cast iron are not ductile, hwnf* the yield strength is approximately equal to the ultimate strength. These materials have excellent compressive strength but poor tensile strength. For this reason, it is difficult to bend these materials appreciably. Cast iron, for example,' could be put in tendon and, from Table 16, it is seen that, for a temperature change of 100 deg, a compressive stress of 7i40 psi would be developed.- If the pipe were straight, this stress would be handled easily. If, however, the stress caused a bending mo ment, then fracture might occur. The values of stress found in Table 16 were determined by using Equation 1 and substituting Equation 2 for e e - aL&t (2) tollers a 9 coefficient of linear expansion, inches per inch. At temperature change, Fahrenheit degrees. This gives Equation 3 F - aEA&t, ' (3). Values for a and E are given in Table 17 for various pipe materials, to facilitate determination of the stress in an ac tual pipe. The following example illustrates the computation of stress. Example 1: What is the force set up by a 1-in. Schedule 40 steel pipe if the thermal expansion from a 100 deg temperature increase is fully constrained? Answer: From Table 1, determine that for a 1-in. Schedule 40 steel pipe, the metal area 9 0.494 sq in. Then, from Table 17, aB -- 195 psi, and from Equation 3 F 195 X 0.494 X 100 - 9630 lb. It is interesting to note that length does not enter into the determination of the contrasting force. This is so because the stress is a unit length function and so is the expansion; there fore, they cancel each other. In other words,-if a weight stretches a 10-foot wire 0.10 in., then that same weight would stretch a 100-foot wire one inch. In both cases the elongation was 1 part in 1200. The realization that thermal stress is in dependent of length is important, but often overlooked. Nonetheless, that concept explains the feasibility of utilizing the inherent flexibility of the pipe to take care of expansion. Regardless of the length of pipe between anchors, it is possible to provide for the expansion by putting the force of expansion into the pipe as internal stress. If the pipe is not straight, then the force of expansion will cause a bending moment. The pipe will then be under a com bined stress. The stresses will be longitudinal and transverse, and to a small extent radial. Ail of these stresses tend to fracture the pipe, and therefore must be added to make up what is called allowable combined stress. The Code for Pres sure Piping, ASA B31.1, published by the ASME, sets up very definite limits for the allowable combined stresses for various pipe materials. For temperatures below 400 F and for piping that is for neither district heating nor power, any standard pipe material may be used. For high-temperature or highpressure work, some text on expansion and flexibility should be consulted. It is beyond the scope of this chapter to de velop the theory of expansion caused by high temperatures. For tiie simpler problems encountered for temperatures of 400 F and less, which the heating enginnw is more apt to encounter, there are four methods of allowing for expansion. The first method is to use packless expansion joints. These joints include types of bellows expansion joints, rubber, cor rugated copper and other metals. Rubber-type joints are occasionally used in vacuum or lowpressure steam lines. Maximum temperature is generally 180 F. If oil is present in the line, rubber-type joints will be. attacked. Travel of these joints is often limitAd to 1 in- or less. The travel to be expected can be PAlimUtAd by using Equa tion 2. Pipe, Tube, .and Fittings 891 The second type of expansion joint is called a sltp. joint. This joint allows for expansion by a sliding of a female mem ber over a male member. The joint is kept tight by means of pairing The packing determines the limit of the tempera ture to which the joint may be subjected. The main disad vantage to this joint is that it must be continually inspected for deterioration of the packing. If the designer uses double slipjoints/the travel may go to several feet, but a single joint generally allows about a foot of expansion. It is common prac tice to use slip joints up to 250 psi. Slip joints should not be used in refrigerant piping. . Tbe most common method of allowing for expansion in heating systems is-to'use the flexible ball pipe joint. This third method was first used with screwed fittings, but it is now also used with welded fittings. With welded elbows,-this joint introduces torsional stress in the elbow and in the swing piece. This type is adequate for taking up the expansion in a header, and- preventing fracture of the riser or, heating element. The fourth method is to allow the flexibility of the pipe to absorb the stress of expansion. A technique used to reduce the stress in the expanded pipe is that of cold springing it before hooking it up. Cold springing can be used to absorb about one-half the stress.'The technique ifi to install the pipe with a stress opposite to that which would result when the temperature of the pipe changes from its installed to its oper ating temperature. For example, if the operating temperature is, higher than the -installed temperature, and expansion would take place, causing a compression stress of 2000 psi, the pipe would be installed with 1000 psi of tension. In case the operating temperature is lower than the inatallpd tem perature, and contraction would take place, resulting in a par ticular, value of tension stress, then the pipe would be in stalled with a compression of about half of this value.; . For conditions not requiring rigorous-analysis, it is per missible to use expansion bends designed by means of Equation 4. - L 9 8.1fty/D^s (4) where L 9 length of pipe, feet. ' D..= outside diameter of pipe, inches, i * 9 deformation, inches (see Equation 2) fiber stress ^ 16,000 pounds per square inch. Equation 4 can be used for bends with two fittings, regu lar U-bend, and offset U-bead, as shown in Fig. 4. It gives the length of pipe, L, that must be used in the U-bend to take L2A+B ' U bend with 4 OUings U bend with 2 fittings Fig. 4 .... Measurement of L on Various Pipe Bends Table 18 .... Equations.for Bending Stress and - Deflection between Supports Type of Support Sending Stress, Pd S Deflection, Inches . r Single span' (free Continuous line... . ,, 0.75 WLW. I _ 0.5 WL*D, s~ i ,, 22.5 WL* El y 4.5 WL*. ~ El W - total weight (pipe, fluid, etc.) pounds per foot. D, 9 outside rfi*TTHtir of pipe, inches. L 9 length of span, feet. B 9 modulus of elasticity, pounds per square inch* I m moment of inertia, (inches)4. Di inside diameter of pipe, inches. up'the deformation, e. When welding fittings are used, the radii should be six times the outside diameter of the pipe. One other restriction is that the pipe should not be heavier than extra strong. Manufacturers of pipe or pipe fittings often publish ex cellent treatises on the simplification of expansion problems. One of the publications4 which is available offers a compre hensive discussion of thermal expansion, , contraction, and alignment in piping. It is suggested that the engineer`obtain such publications and a text or handbook7 on the subject before attempting to solve a problem on flexibility. HANGERS AND SUPPORTS In the preceding section, Equation 3 was developed to give the force of total constraint. This equation is appropriate re gardless of tiie sign of At, positive or negative. It docs not, however, allow for any bending moment, but is for straight compression or tension. ` " If the compressive force is great enough, or if the line is long enough, a slight eccentricity of the load application will cause a buckling of the line. This buckling is identical to-the Table 19 .... Recommended Maximum Spacing.of Hangers and Minimum Hanger Rod Size for Steel and Copper Pipe* - Noahserf Pip* Sixe fa. 1 lX 2 3 3K 4 Maximum Spaa H 7 9 10 12 13 14 Minimum Rod : X 5. X X X X X 5 10 - X 6 17 : >' ......... x 8 19 = : . H 10 22 X 12 23 ' K. For H in. copper tabs, 9 ft spacing of hangers is recommended. r