Engineering and Contracting . 50. 370 ENGINEERINGAND CONTRACTING Minimum Thickness of Plate in the Shell. For a stack as shown in Fig. 1 (a), the overturning mo-ment due to wind pressure is M = PXDXHX12X y2H = y2l2PDHMn. , M=y2PdH=in. lb. (1) The resisting moment at any section is given byT(d*—d<)s M = ; but d= (d—2T), therefore 32dd* = (d—2T)\ giving, if we neglect powers of T higherthan the first which may be done as T is very small ascompared with d, the resisting moment,TXaxd^-Ts M = = d=Ts (2) 32dSolving Equations (1) and (2), FdH- PH= s= = (3) d=T DT or the
Engineering and Contracting . 50. 370 ENGINEERINGAND CONTRACTING Minimum Thickness of Plate in the Shell. For a stack as shown in Fig. 1 (a), the overturning mo-ment due to wind pressure is M = PXDXHX12X y2H = y2l2PDHMn. , M=y2PdH=in. lb. (1) The resisting moment at any section is given byT(d*—d<)s M = ; but d= (d—2T), therefore 32dd* = (d—2T)\ giving, if we neglect powers of T higherthan the first which may be done as T is very small ascompared with d, the resisting moment,TXaxd^-Ts M = = d=Ts (2) 32dSolving Equations (1) and (2), FdH- PH= s= = (3) d=T DT or the stress per lineal inch along the circumference PH= S = (4) DIf E be taken as the efficiency of a riveted joint, equa-tion (2) becomes, M = d=TsE (5) Solving Equations (1) and (5) for T, we havePdH- PH- T = = (6; d=sE DfE which gives the thickness of plate necessary at any sec- 100 t;§s V S ^i 300 3/e DiAncTCR or Stack in 15 ?0 ^5 30 [mciENcroFjomT WORKim 5TRE55 5 10 15 ZO DunirrR ofStack m Fect Fig. 2—Thickness of Plates. tion to resist the moment due to wind pressure, for anyfiber stress, f, and any efliciency. The unit stress at any section due to the weight of thestack above the section is, W 490TDHT s = = = (7) 24tDT 144tDTTherefore the total unit stress in the plate at any sec-tion is given by S = PH- DT (8) It is evident from Eijuation (8) that the stress due toweight of stack above the section may be neglected up toa height of over 400 ft. with an error of less than 1 percent. The weight of the lining has been neglected as it isusually carried by the foundation. In special cases itmay be carried on angles riveted to the shell. In suchcases the weight should of course of included. 100 3eo\ DiAniTlR CF Stack 15 iO ^5 FFFICItnCYOFjOITIT: 5TRe55:l6,000lk^.in.
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