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448 CHAPTER 31 1959 Guide Table 16 .. Dimensions of Grass or Bronze Screwed 90-Deg Eibows, lees. Crosses, 4D-Degtlbows and Couplings (Straight Sizes 125 lb) 80 ELBOW TEE CROSS 45 ELBOW CAST WROUGHT Nomine! Pipe, Sim Center to End, Eibows, feei. length of Center to End Thread, Mm 45-Deg Elbows Diameter Wrought Coupling node Diameter Band length, of Cast fitting Metal Thick- Min Band Diam eter, Mia Min Max End to End Straight Coupling Cast Wrought A B C D E f GH W 4 X H 4 .H j in m 0.54 0.71 0.82 1.01 1.18 1.43 1.69 1.84 0.25 0.32 0.36 0.43 0.50 0.58 0.67 0.70 0.42 0.56 0.63 0.78 0.89 1.06 1.22 1.30 Kb **6 842 146 14e 0.14 0.16 0.17 0.19 0.23 0.27 0.31 0.34 0.41 0.54 0.68 0.84 1.05 0.44 0.58 0.72 0.90 1.11 1.32 1.66 1.90 1.39 1.73 1.97 0.08 0.08 0.09 0.09 0.10 0.11 0.12 0.13 2 2.12 0.75 1.45 2.4 2.70 0.92 1.95 3 3.08 0.98 2.17 4 3.79 1.08 2.61 0.41 0.48 0.55 0.66 2.38 2.88 3.50 4.50 2.45 2.98 3.60 4.60 0.15 0.17 0.19 0.22 From Aatrriean Standard for Brass or Brans* Scrrved Fitting*. 125 Lb- ASA B16.15-1M7. All dimBiM riven is inebee- 0.67 0.81 1.00 1.17 1.42 1.72 2.10 2.38 2.92 3.49 4.20 5.31 0.80 0.97 1.05 1.29 1.43 0.83 1.03 1.11 1.36 1.50 1.68 1.86 1.92 2.20 2.88 3.18 3.69 Equation 4 can be used for bends with two fittings, regu lar U-bend, and offset U-bend, as shown in Fig. 3. It gives the length of pipe, L, that must be used in the U-bend to take up the deformation, a. 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. It is suggested that the engineer obtain such publications and also a text or handbook* 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 the sign of At, positive or negative. It did not, however, allow for any bending moment but was 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 with the action of a column under excessive compression. In fact, a pipe line in compression is identical to a column. Column criteria can therefore be used for selecting the action of sup ports to resist lateral thrust. A common equation' for determining safe column loads is Euler's formula: (for cast iron see Equation 8) (5) where S *= allowable column load, pounds per square inch. k = radius of gyration, inches. 1 es column length, inches. L (OP>* + (ID)* ..a" 16 Equation 5 is sometimes modified by a correction factor C to the following: S - C*B (jj (6) where C = correction factor depending on end loading in accord ance with the following table: End Conditions or Column . One End Fixed Fixed Fixed Pin Other End Fixed Free Pin Pin Value of C - 4.00 0.25 2.25 l.oo Pipe, Fittings, Welding T_Li_ t7 _ _ _ nmnnAM .Cast-Brass Solder-Joint Elbows, Tees, and 45-Deg Elbows (Straight Sires) Tahl> 18____Dimensions of Cast-Brass Solder-Joint Couplings (Straight, Reducing, end Cueuh fc Sized z 449 WJ- OM* T ts* CLAOW 90* STBCET MOW *' STnCCT CLBOW 2 COUPUNG C TO C REDUCMG COUPING CCCCNTRC OXFIMO C TO C I'lli Standard Water Tube Size Center to Ex terna/ Shoulder 90-Deg Street Show -Length 45-D*g Show . Center to Ex terna! Shoulder 45-Dog Street ETbow O XX H 46 X 46 X 4 4 46 4e *46 46 46 X 46 46 4 1 X 4 46 46 ix H 1 Kb 46 ix 1 14 4 4 2 ix m Ke X 24 14 14 4 3 14 14 X 34 2 4 4 24 5 34 6 34 8 44 `Kb 14e 14 24 From Americas Standard tor Ca*t-Bn*t Solder-Joint Fitting*, ASA B16.181950. All dimenskma given la inches. * Not standardised tor wrought fittings. Consult manufacturer for From Equation 6, l - rk CE (7) This equation is not used for column construction but is sufficiently accurate for the work of a heating engineer. The equation is modified for cast iron because of its poor tensile strength. It is generally acceptable to use one-half the value of S from Equation 5 for cast iron, so the safe column load & for cast iron is STRAIGHT SEDUCING ECCENTXfC Standard Water Tube Sire laying length* M Standard Water Tube Size laying length* N Standard Water Tube Sire laying length* W X 46 X X 4 4e ii X X 4 1 x 4 X l x4 X46 4 4 14 * 1 H 14x1 X X 4 14 x H H 14 x 4 X l 4 14 x 14 H 14 x 14 lX* 14 4 I4xi X 14 *1 `Kb 14 4 14 x X 46 2 x 14 14 2 Kb 2 x 14 4 2 X 14 `Kb 24 46 2 x 14 4 24x2 14e 3 46 2x1 4 3 x24 14 34 4 2x4 4 3 x 2 14e 4 4 24*2 46 4 x 3 2 5 4 24x14 4e 6 4 24x14 . X 8 4 24x1 X. 3 x 24 3 x2 4 x3 4 x24 4 x2 X X `Kb 14 146 6 x4 8 x6 146 14 From American Standard far Cast-Bras* Solder-Joint Fittings, ASA BIS.191950. All dimensions given in inches. * Not standardised {or xerougkl 6ttiogs. Consult manufacturer for dimension*. Answer: Using Euler's formula, Equation 5 gives St for cast iron. (8) It is permissible to allow the l/k ratio for steel to go as high as 120, but for cast iron the desirable maximum is taken as 70. It is not to be understood that a fracture will' occur at l/k ratios in excess of those given, rather it is to be understood that lateral support should be given for those ratios and for those magnitudes of stress. If an expansion joint is used, this will, of course, relieve the compressive stress. Example t: For Example 1 given in the preceding section, the constraining force for a 1-in. pipe was 9630 lb. What is a required spacing for lateral support for this pipe? bo i - tVi7s For a 1 in. Schedule 40 steel pipe k - 0.4205 in. B - 30,000,000 psi. S 9630 * 0.494 = 19500 psi. I - 51.8 in. Therefore, lateral supports on 4-ft centers are adequate. The other type of load requiring some support is the bend ing stress due to the weight of the pipe, its insulation, and of