IS 4998( PART 1) : 1992chimney. The enhancement in wind Loads will be due to an increase in the value of CD. The value of C, for each chimney located within a distance of 3 times the effective diameter, may be calculated by assuming the value of CD to be increasing linearly from 0.8 (for a spacing of 3 effective diameters ) to a value of 2-O ( for a hypothetical spacing of 1 effective diameter which implies that the two chimneys touch each other if they are cylindrical and identical ). These values of CD apply up to the height of the nearest interfering chimney, if the chimneys are of unequal height. It is permissible to obtain more accurate values of Cn by carrying out properly conducted model tests in wind tunnels.A-1.2Unsteady Forces on a Single ChimneyTanks elevated on staging or towers are generally provided for water storage and supply. The capacity and height to the bottom are determined from a consideration of the service of the tank. Design a circular elevated water tank for a capacity of 2, 50,000 litres. The height of the tank bottom above the ground level is8.7m. The tank is supported over eight columns and is situated at the railway station in Allahabad.solution-1. Size of tank-250m3. Assume hemispherical bottom and the height of cylindrical shell to be 0.8times the diameter of tank as shown in fig1.1 /4D20.8D+1/24/3 (D/2)3 is equal to 250 and D is equal to 6.55m. Hence height, H is equal to 0.8D=5.24m. Now thickness of plates- lets us provide 16mm power driven rivets for making the connections. Also let the efficiency of the joints be75%. Now thickness of shell plates t is equal to whd/2at=9.8110-65.241036.55103/20.75 (0.80.6250) =1.87mm. Add 1.5mm to account for corrosion .now t=1.87+1.5=3.37mm6mm. so provide 6mm thick plates in the cylindrical shell of the tank. Thickness of suspended bottom plates- h=(5.24+6.55/2)=8.515m. and t= whD/4at= only change 5.24 equal to 8.54 and result is 1.52mm. and add 1.5mm to account for corrosion. As t=1.52+1.5=3.02mm6mm. so provide 6mm thick plate in the hemispherical bottom of the tank. Conical roof- provides 5mm thick plates for the conical roof. The pitch of the roof may be kept 1 in 4. Connections-power driven 16mm (gross diameter=17.5mm) field driven rivets and double riveted lap joints have been used all through. Cylindrical shell plates- hoop stress per linear vertical height F1=whd/2=9.8110-65.241036.55103/2=168.35N/mm. Now strength of the rivets in single shear is equal to /417.520.890=17318.03N and strength of rivet in bearing= 17.5*6*0.8*270=22680N. Now rivet value, Rv=17318.03N and pitch of rivets=2*17318.3/168.35=205.74mm not greater than 60mm (10t=10*6=60mm). Rivets for horizontal joints are provided at the same pitch as that for vertical joints. 4 A-1.2.1 Hemispherical bottom plates- hoop stress per unit length in the radial joints, F2= whD/4 use 8.515 instead of 5.24 as earlier and result is 136.78N/mm. Since the force F2 is less than F1, rivets for making connections of hemispherical bottom plates are provided at a pitch of 60mm (same as calculated for the cylindrical portion of the tank) for radial as well as horizontal joints. Cylindrical shells with hemispherical bottom shell-there are no inclined or compressive stresses on the hemispherical portion and therefore connection of the two shells need not be designed again. Hence, provide 16mm power driven field rivets at a pitch of 60mm power driven field rivets at a pitch of 60mm and double riveted lap join. Circular girder- weight of water, W1=10*250=2500KN=2500*103 and self weight of tank, W2= {*6.55*103*5.24*103*6+1/2*4*{6.55*103/2}2*6] *7.9*10-5=83052.77N and self weight of conical roof, W3= /2*6.55*103[{6.55*103/2}2+{6.55*103/4}2]*5*7.9*10-5=14880.74N. When the height to top diameter ratio of the chimney exceeds about 20, the possibility of second and higher modes of oscillations being excited due to vortex excitation can be expected. Since the dynamic stresses due to higher modes of oscillations can be much higher than that due to the first mode of oscillation, it is important that the design be check-ked for higher modes of oscillations, if found necessary. The self weight of the tank and that of the conical roof may be increased by20% to account for additional weight of overlap of plates and connectors. W4=1.2(W1+W3)=1.2(83052.77+14880.74)=117520.21N. Assume self weight of girder as 1500N/m and total self weight of girder=1500**6.55=30866.14N and total weight of girder is equal to W=2500*103+117520.21+30866.14=2648386.35N is approx. Equal to 2650.0*103KN. A-1.2.2 for circular girder supported over eight columns- maximum bending moment at supports-= -0.00827WR=-0.00827*2650*103*6.55/2=-71773.26 Nm and maximum torsion(at 9degree 33 minutes)= 0.00063WR= 0.00063*2650*103*6.55/2 is equal to 5467.6Nm. Maximum shear force at supports is 2650103/16=165625N and section modulus, Zreq=71773.26*103/0.66*250=434989.8 mm3. Because of the relatively small thick-ness of the chimney at the top compared to its diameter, possibilities of covalling oscilla-tions will have to be examined if the diameter of the chimney exceeds 75 times the wall thickness at the top. Lets us try a girder section as shown in Fig1.2. The section has been built-up by using 1m depth of cylindrical shell of the tank and 2ISA 150*150*18.

IS 4998 ( Part 1 ) : 1992 Calculated by the formula:IXX= 610003/12+21048.9104+25079(500-43.8)2= 26350.45104 mm4Section modulus, ZProv=I/y=263504.5104/500= 5270090>438310 which is alright. Torsional constant, J=1/3bt3=2{1/3150183+1/3(150-18)183}+1/3*1000 63 =1168416mm4. Shear stress due to torsion=T/J*max=5467.6*103/1168416*(18+6) = 112.30 N/mm2 A-6.1 AERODYNAMIC INTERFERENCEOF TWO OR MORE CHIMNEYS= equivalent aspectratio = H/dCi c. =RMS lift coefficient to be taken as o-12L= correlation length in diameters, which may be taken as 1.0 in the absence of field data01=CLd4zezeiH1 (L/2t) 1/2Where Zei = height in m at which d%&/J t is a maximum in the it mode of vibrationThe values of a do not exactly match the variation of & factors of IS 875 ( Part 3 ) : 1987. However, they have been chosen to be slightly conservative and should be used only in A-5.3(b) and nowhere else. Calculations should begin by first taking zei = H and progressively decreasing z till a maximum in qoi is observed for each mode. However, if Vcr for any mode is more than the maximum wind speed expected at site for ze= H for the first mode of vibration itself, the chimney will not experience any significant across-wind load in that mode. For very tall chimneys roi may not show a maximum, either in first or the second mode at speeds less than the maximum expected at site. In that case, the value of ze shall be taken as the value at which the calculated Vcr equals the maximum expected velocity V, at ze. Now shear stress due to shear force= 165625/2*5079+1000*6=10.2503N/mm2 and total shear stress=112.30+10.2503 equals to 122.55N/mm2>100N/mm2(0.4*250).Hence, the section needs a revision. The next trial section is shown in Fig1.3.Ixx=618003/12+22588.7104+26881(900-56.1)2=1276861.9104mm4ZProv= 1276861.9104/900=14187354mm3> 434989.80mm3 which is all right.

8A-6.2 When chimneys in a cluster are of different sizes, the magnification factors shall be established by model tests or on the basis of observations on closely spaced dissimilar chimneys. Such interference in dissimilar chimneys need not be considered if the smaller chimney is at a distance of more than 20 times the diameter at 2/3rd height of the nearest larger chimney. For a given configuration of identical chimneys, the magnification factor obtained from Fig. 1 indicates a measure of the seriousness of the increased amplitude of oscillations due to aerodynamic interference, although the actual magnification at full scale Reynolds Numbers, of the order of lo, are 1ikeIy to be lower.A-6.3 When two or more nominally identical chimneys are located within 20 times their diameter at 2/3rd height, adverse aerodynamic interference between them can be expected. Figure 1 is to be used as a guide for assessing this aerodynamic interference. This figure gives the magnification factor by which the amplitude of transverse oscillations may increase, as a function of spacing and chimney taper and has been obtained by model experiments at Reynolds numbers of about lo6 with laminar boundary layer separation. A single isolated chimney will experience unsteady wind forces due to two main causes, namely ( i ) periodic vortex shedding, and ( ii ) unsteady force caused by atmospheric turbulence and/or wake from structures of comparable height. It may be assumed that every chimney with a height more than 3 times its effective diameter, will shed vortices of oppose-site sign alternately from opposite sides. The periodic vortex shedding is very marked at sub-critical Reynolds numbers. When the surface of the chimney is even slightly rough, distinct periodic forcing is not present in the critical Reynolds number range from 3 x lo5 to 2x 106. The alternate shedding of vortices from the two sides of the chimney will result in periodic forces both in the direction of wind and perpendicular to it. The force that is generated in the direction of wind is called, Oscillatory Drag Force and the force that is generated perpendicular to the direction of wind is called, Oscillatory lift force. Now the torsional constant=2 {1/3200183+ (200-18)} +1/31800 63= 3030048mm4. Shear stress due to torsion is equal to 5467.6*103/3030048(18+6)=43.30N/mm2. and shear stress due to shear force is 165625.0/2*6881+1800*6=6.743N/mm2 and total shear stress =43.30+6.743=50.04N/mm2