”Viiigaéééfi «1 4 . a“ .3. .H STRESS ANALYSIS . a I ‘ Q9 ‘ I STEEL COAL TOWER AND BUNKER A “animal“ Dog!” of 8.3. IICHIGAN STATE COLLEGE Leonard A Robcrt ‘ '9 I94I 7 my“ I ‘3‘". 1‘ ‘ . A I I ‘ , A . I ‘ I I ' I . I .wdwaauIW-ouul - " STRESS ANALYSIS OF STEEL COAL TOWER AND BUNKER A THESIS SUBMITTED TO THE FACULTY OF MICHIGAN STATE COLLEGE OF AGRICULTURE AND APPLIED SCIENCE BY LEONARD A. ROBERT CANDIDATE FOR THE DEGREE OF BACHELOR OF SCIENCE JUNE 1941 THESIS ACKNoumEDGmms The author is under obligation to a number of persons for their cooperation and assistance. He is particularly indebted to the following members of the Civil Engineering staff: Professor Professor Professor Professor Professor Professor C. C. C. A. J. L. L. A. Allen, Department head Miller, Dissertation Adviser Cade Leigh Meyer Smith Engineering Department, Detroit Edison Company Ruth MCFarland, stenographic I]. A. R. A J?'5(7‘3{2 11 (1‘03?! U" FOREWORD The coal tower and bunker are to be constructed by the Detroit Edison Company at their marysville plant and are to occupy a portion of a building known as the crusher house. The Detroit Edison Company supplied the attached con- struction plans, and it is the purpose of the thesis to analyse the stresses in this structure and to check their design. The library was searched but no direct information was available on the design or construction of such a structure; therefore Ketchum's text on Walls, Bins and Grain Elevators was used. In this text Ketchum explains the design of tall circular grain elevators as developed by Janssen, Airy, the Germans and others, and states that the above named are the most used and that they check actual values very closely. The connection between the stresses in a structure designed to store grain and those of a structure designed to store coal can best be explained by referring to Ketchum's text, page 308. It is quite evident that the development of the equations for pressures to be used is a purely static analysis of a granular mass confined within a circular container, and in the final analysis will not differ for any granular mass except in that of the values for unit weight, angle of repose, angle of friction and value of k; these can only be obtained for any one granular substance under given conditions by ex- periment. The value of k is approximately equal to l - sin 5 l + sin and is actually equal to L/V; where L is the lateral pressure and V is the vertical pressure. On page 214 of Ketchum's text are shown the results of experiments on coal by the Portland Cement Association and by the link Belt Company in which they have determined bituminous coal to weigh 50 pounds per cubic foot, the angle of repose to be 30 to 45 degrees depending on conditions, corresponding values of k to equal .33 and .17 and the angle of friction to equal 18 degrees. The smaller angle of repose gives the greater lateral pressure, and the greater angle of repose gives the greater vertical pressure. It is therefore advisable to design the tower and hopper for maximum conditions affecting their design. The tower is designed for a coal with angle of re- pose of 30 degrees and the hopper for a coal with angle of repose or 45 degrees. In the analysis the worst condition derived from the methods of Janssen, Airy and the Germans is used. CONTENTS Acknowledgments...........................l Foreword...00000000.OOQQOOOOOOOOOOOOOOOOOOOZ Nomenclature..............................5 PART I Analysis of tower shell...................6 PART II Analysis of tower stiffeners.............lO PART III Analysis of hopper plates................l9 PARTS IV and V Analysis of the plate supports...........22 Construction plans...................Pocket NOMENCLATURE The following nomenclature will be used. L lateral pressure hydraulic radius angle of friction L/V (a constant for any one granular material under given conditions) height weight 2.718 normal pressure pressure of coal in vertical direction supported by shell angle of friction==u' height = h vertical pressure frictional force horizontal reaction vertical reaction PART I ANALYSIS OF TOWER SHELL Janssen's: L==wfi, ~ku'h u' l - e R 1.:50 x 9.5[ -.31 x .21 x 81.j5 031 l "' e 905 L=e92# L=kV V=§9_g=2,700#/sq. ft. .33 2 2 German Practice: /‘ ( $9117 P=wR y-__B___(l-e R) k—ul P=50 x 9.5 81.5 - 2.5 , (1 - 1 ) .33"x .305 E .22 x 3 5 x 81.5; P: 12,650#/11n. ft. L = 905#/sq. ft. V = 2,7lO#/sq. ft. P= 12,650#/lin. ft. Airy'S: szd 1.1-2 l+u u+u' 2n u+u'+l.-uu' d L=kV x 5 .74—.3I+-l - (.7 x Lay/7 II = 872#/SQ¢ ft. V=§12=2,640 .33 P2812 x .205 g; 81.5 = ll,000#/lin. ft. 2 TABLE I Summary of Three Methods L‘Sg.fto vzggcgfo Pglin.f‘b. T0133]. P ’ Janssen's 892 12,420 1,492,000 German 905 2,710 12,650 1,505.000 Airy's 872 2,640 11,000 1,310,000 In analysis use L==905# V==2,710# P==12,630# When a hopper is emptied from the side, the lateral pressure on the opposite side will increase as much as four times. (Ketchum, page 351) These hoppers do not empty from the side, but they do empty from a point considerably off center; in order to com- pensate for this a proportion of actual offset to radial distance was used as a factor by which to multiply four and obtain a reasonable factor of increase for this problem. 19 144 t: 5.,300..__= .358 Use .375 12,000 .375 was used In order to show the allowable stress for material used and the actual stress imposed upon it, for the full height of the tower, a Table and Graph are included on the followingjpages. TABLE II TABLE OFJPRESSURES ACTING WITHIN THE TOWER AND ON THE SHELL Depth Pressure Pressure Weight of coal on coal Normal to supported by Shell shell, and wt. of shell 10 396 132 1,770 20 966 322 8,620 30 1,314 438 17,600 40 1,620 540 28,900 50 1,926 642 43,000 60 2,190 730 58,500 70 2,409 803 75,000 80 2,631 877 94,000 81.5 2,710 905 94,400 10 PART II ANALYSIS OF TOWER STIFFENERS Stiffeners must be used when the height is less than two and one-half times the diameter. (Ketchum, page 359) Spacing of stiffeners. (Design of Steel Structures, Urquhart and O'Rourke, page 178) d=__t__ (12,000 - s) 40 d==spacing t==thickness S==web shear #/sq. in. S: 000 12 =26d 378 x 27 x 12+5/16 x 30 x 12+1/4 x 24 x 12 d=_3__ (12,000 - 26d) 320 d==90" 89.75" was used Because the stiffeners in this structure also act as columns, it is necessary to design them in combination. Computations of floor loads is necessary. Refer to pocketed drawings 6858-3592 and 6S58-3593 which show the floor plans of all floors attached to tower and their design loadings. It is necessary to compute the load transmitted to each column or stiffener; this was done graph- ically on the plans, and the results are tabulated below. From the roof there is transmitted to column 01 and 02 29,200# and 35,600#, respectively. ie. Cl= 21.25'x (7.25'+~6.5') 100==29,000# C2==21.25 x (6.5' +-lO.25') lOO==35,600# 11 This in turn is transmitted together with a portion of the bunker floor loading to the (E) and (W) stiffeners. ie. Loads transmitted to the (E) and (W) stiffeners at bunker floor, elevation 693'. (see Drawing 6858-3592) C2='35.6 01:129. 2 10.25 13.05 10. 25 .92 l 8 6 l3. 5 8.1.9:L_ 4.92 .513. 6' .5 W= 83.28 E= 68. 10 18.7 4 RN: g x 18.74-13.OS+8.96+lO.25+4.92+_§_%x35.6+ _1__1_ x 29.2=83.28 kips \N 5 R = l3.05+—8.96-+10.25-+4.92-+11 X 35.6-Pgi X 29.2==68.10 e 35 35 kips All the loads shown are transmitted by the bunker floor except loads of 29.2 and 35.6 which are transmitted as shown by column 01 and C2. 12 There is also transmitted to each stiffener the weight of coal supported by 7.47' of shell, the weight of the shell and the weight of the stiffener. ie. wt. of coal supported by shell per stiffener 94,000# wt. of shell 7,470# wt. of 10 WP 29 81.5' long 2.360% Total 104,230# additional wt. of East and West stiffeners 896 Total 105,126# The following table shows the floor loads brought into the columns at their respective elevations and the weight of the coal and material supported by the stiffener. The tower is so constructed that the analysis of any quarter is an analysis of the complete structure. The table therefore shows only the West stiffener (W); the East stiffener (E); then, numbering from (E) counterclockwise, (A), (B), (C) and (n). A E 13 TABLE III TABLE OF COLUMN LOADING Column Loads in kips Elevation E A B C D W 693 68.38 8.27 5.09 12.75 4.91 83.28 671'2" --- 1.7 6.7 3.0 2.8 17.8 656'9" --- 1.7 6.7 3.0 2.8 17.8 641'3" --- 1.7 6.7 3.0 2.8 17.8 624'3" --- 1.9 7.6 3.4 3.2 20.1 614'6" --- 1.7 6.7 3.0 2.8 17.8 105.1 104.2 104.2 104.2 104.2 105.1 Total 173.31 120.84 143.36 132.35 123.51 279.68 The question arises as to why each section of stiffener is not studied and incremental relations of actual stress and allowable stress analyzed. The structure carries the same size stiffener from top to bottom, and therefore in checking the design it is not necessary to do so. If the in- tent is to analyze the structure in such a manner, remember that the pressures do not vary as the height but as a curve shown on graph on Plate I. In analyzing the stress in each stiffener a number of conditions must be noted. 1. The shell is welded continuously to the stiffener on either edge of the stiffener flange. 2. The shell is therefore a curved cover plate, and a 14 portion of it can be used as a supporting member. 3. The coal load and shell load are transmitted through the shell and therefore will act as an eccentric load, acting through the centroid of the curved section supported. 4. The floor loads are not in all cases brought into the stiffener but are transmitted to it as eccentric loadings and may act on one or more faces of the stiffener. The question now arises as to how much of the shell can be used as a cover plate for the stiffener. The A. I. S. C. does not give any allowable values for this condition; so it is necessary to reason out an allowable value. For columns built up of two channels and a connecting cover plate the distance between the gauge lines must not exceed 40 times the thickness of the connecting web. The outstanding leg of flanges in compression must not be more than 12 times the thickness of the material. It is quite evident that the conditions in this problem are not as favorable as the former, but are-more favorable than the latter. The former would allow a cover plate of 20", the latter a cover plate of 15"; there- fore a cover plate of 18" is used. Analysis of the lO-WF-29 stiffeners. A=8.53 sq. in. 1:157.3 111.4 depth=10.22" 15 \7047'/:4038" STIFFENER z=19 x 12 - 19 x 12 3: cos 11°15'=4.38" e= distance-from face to center of loading 81: R sin 11° 15' 11 15' R = radius 11° 15' is in radians el=l x 12 x .1 0 .1963 el=1.4l6" l - Determine the location of the neutral axis. Area of cover plate 3/8 x 18:- 6.75 sq. in. 37:541.); 8.53 + 1041;635:745" 15.28 I=157.3+8.53 x (2.34)2+ .079+6.75 x (2.96)2 =263.1"4 ie. Stiffener A l6 39.16 kip 104.2 kip - 93 .1 r—— lam—1 I utral axis lO-WF-29 neutral axis el=l.4l6" 62:10.22 " 7045: 2077" 33:2077+10416=4019" 8:13.121; A I Sm: 1&::§6+ 016 X 20 +10 .2 cl .1 15.28 263.1 ==15,920#/sq. in. S=léioi " £22.16 X 2077+1040Q 4012) iofii =" 6’OOO#/SQO in. r: 2620].. = 401 15.92 1:16 3: 12:48 r 4.1 Allowable stress 17,000 - .485 x 192 g 192 4.1 x 4.1 =16, OOO#/Sq_c in Column B, C, and N are similarly loaded, but with lighter loads; therefore they are of sufficient size. 17 Check column W 12" I=40.B# A==ll.84 sq. in. depth=12.00" width=5fi—" 1=268.9"4 105.1kip ‘— 63—..02 3...— : Elan—fl I ——neutral axis I 12" I 40.8 (IA/“W neutral axis §s=6.2§ x 12.19-+11.84 x 6 = 8.26" 18.59 I==268.9+(2.26)2 x 11.84 +.079 +6.75 x (5.93)2 I=455.8"4 61:12 " 8026:3074" e2: 3.74+1.41=5.55" = u 83 8.26 18.59 433.8 =15,966#/SQ_0 inc 5:279.7 - L83.28 3.3.114 + 105.1 x 5.15 - 91.33 8.26)8.26 433.8 = 15 .210#/sq . in. 18.59 'r 4084 Allowable stress 17,000 - .485 x (40.6)2==16,200#/sq. in. Column E same as column W but loaded differently. 0 - e e .e. €1= 12 - 8-26=3.74" e2=5.74+1.41=5.15" 3:111: + (68.21 3 2.14.4051 x 5.15) 4.11 18.59 433-8 =16,860#/Sq. in. S =l21021 " (68.21 Q014+10101 J; 501.5)8026 18-59 433-8 ==-5,830#/sq.in. A stress of l6,860#/sq. in. is allowable due to the fact that the load on the column is accumulative, and therefore the actual stress (as noted in loading table II) decreases with each foot of height and.will not exceed the maximum allowable of l7,000#/sq. in. 18 19 PART III ANALNSIS OE HOPPER PLATES In the analysis of pressures acting on the plates of a hopper, the ellipsoidal method is normally used, but because this hopper is of such odd shape a purely static analysis is advisable. This will give the same maximum but will not give the gradual decrease to the top of the hopper. The following is an analysis on that basis. As explained in the foreword the following pressures apply to the hopper. =50 x 9.15 1‘ - 1 =5,52o#/sq. ft. .17 x .31 .17 x .31 x 81.5 e 9.5 ._/ V (base)==3320-+12 x 50==3,920#sq. ft. V (analysis)==3,920+-392==4,312#/sq. ft. The value of 10% added to actual pressure is recommended to take care of added pressure caused by opening and closing of h0pper outlet. In the analysis of the plate supports the vertical pressure is 3,320# at the top and 3,920# at the bottom. An average of these, plus 10%, will give 3,982#. The average value was used as a uniform pressure on the sup- porting members. The 10% is an imperical value, so that the results obtained by finer analysis would be a waste of time. A value of 4,000#/sq. ft. is used. In the design of the hopper parts it is common practice to allow for a factor of safety of 4; this value is to take 2O care of usage. If the hopper will not be subjected to maximum wear a smaller factor may be used. This value is taken care of in allowable stress and is entirely up to the designer. An allowable stress value of l3,700#/ sq. in. is recommended by most authors. ie. Analysis of Plate 2. (see Index of Plates in pocket) (see prints 6S58-3590 and 6858-3591 for dimensions) For a horizontal projection area of 1 sq. ft. the vertical projection area: 5.98 sq. ft. The actual area T 6.17 sq. ft. The plate makes an angle of 9 degrees and 18' with the vertical.Sin ¢==.162 Cos ¢==.97 V=4,312#/Sq. ft. L==l,420#/sq. ft. N=(V s1:?¢+L 0032;!) #/sq. ft. of plate N==4,3l2 x .162 x .l624—1,420 x .97 x .97 =~l,445#/sq.ft. Maximum unsupported length==16" (see plate 6858-3590) s=mg m=y_12 c =5/l6" I=1/12 x 1 x (5/8)3= .0204"4 I 8 8 x 16 x .0204 "d H I emu TABLE III TABLE OF PLATE RESISTANCE ate, Area 9 Cos_fi Sinm§_ L V N 1 21 45-00 .707 .707 1200 3652 2500 2 1105 9‘18 097 0162 1420 4312 1445 4 18.6 45-00 .707 .707 1200 3652 2500 5 24.7 18-10 .95 .312 1420 4312 1700 6 53.5 23-40 .915 .401 1420 4312 1860 7 31.4 23-40 .915 .401 1420 4312 1860 8 53.5 23-40 .915 .401 1420 4312 1860 9 36.7 37'45 .790 .613 1420 4312 2500 0 20.8 23-40 .915 .401 1420 4312 1800 l 7.0 37-45 .790 .613 1200 3652 2110 Area per sq. ft. of horizontal projection Maximum Stress Vertical Actual pfigpan inch kips 1 1.41 16 8.0 5.98 6.17 16 5.0 5.98 6.17 16 5.0 1 1.41 21 14.6 3.04 3.21 21 10.2 2.29 2.50 19 9.1 2.29 2.50 18 8.2 2.29 2.50 18 8.2 1.19 1.56 18 11.3 2.29 2.50 18 8.2 1.19 1.56 18 12.1 22 PAR“ IV ANALNSIS OF THE PLATE SUPPORTS It is first necessary to determine the coal pressure and plate resistance balance. To do this it is necessary to compute the resistance of each plate to a maximum loading of moving coal. The vertical pressures and the plate resistances should balance in order that too great a pressure is not transmitted to the hopper outlet. Too great a pressure at the hopper outlet would cause arching and binding. ie. Computation of the vertical resistance of'plate 2 (see index of plates in pocket) and tabulation of results for the other plates. Plate 2 Average vertica1==4,000# Horizontal==l,320# N==(norma1) V==sin fl L==cosp¢ ¢==angle plate makes vertical. F==friction force N=4,ooo x .162 x .162+l,320 x .97 x .97=l,344#/sq. ft. of plate F‘=.325 x 1,344==437#/sq. ft. Rv=:vertica1 resistance per sq. ft. of plate. RV: N sin.¢—+F cos ¢ In.p1ate 2 the plate makes an angle of 9 degrees and 18 minutes with the vertical and at its center makes an angle of 9 degrees and 18 minutes with the outlet, but at its extremities the angle of discharge with the vertical is increased to 25 degrees on south and 13 degrees and 30 minutes on the north. 23 (See 6S58-3580) Therefore, the vertical resistance of the plate varies from: 1,344- X 0162+437 X 097:640 at center 1,544 x .423-.437 x .573==820 1,544 x .254+-457 x .957==750 Total resistance of plate in vertical direction.= at south end at north end RV x Awwhere A is the area of the plate. Rv of the central section==§l.61 x 2.08)640==14,200# 1. 2 Rv of south section=$(2.08 x 5.67 x(820+6401=27,500# 2 RV of north end=-2-(13.3 x 2.08) 640+150=9,500# 2 Total vertical resistance of the p1ate==51,200# The results of complete hopper analysis of plates are shown in tabulation below and on drawing plate in pocket. TABLE IV TABULATION OE VERTICAL RESISTANCE OF HOPPER PLATE.ANALYSIS Plate Normal Friction Angle at Angle at Angle at center left right 1 2,425 785 45 - 00 ---- ---- 2 1,285 416 9 - 18 25 - 00 13 - 30 3 1,285 416 9 - 18 13 - 30 ---- 4 1,285 785 45 - 00 ---- ---- 5 1,580 513 18 - 10 ---- 41 - 40 6 1,740 565 23 - 4O 41 - 40 31 - 45 7 1,740 555 23 - 40 31 - 45 25 - 00 8 1,740 750 23 - 4O 31 - 45 41 - 40 9 2,323 750 37 - 45 41 - 40 ---- 10 1,740 565 23 - 4O ---- 31 - 45 11 2,110 685 37 - 45 ---- ---- TABLE IV (CONT.) Total 1,022,850 Plate Ctr. Angle Lft. Angle Rt. Angle sin. cos. sin. cos. sin. cos. 1 0707 0707 " " " - 2 .162 .970 .422 .905 .234 .955 3 0162 0970 0234 0955 - - 4 .707 .707 - - - -- 5 0312 0950 ' ' 0665 0747 6 .401 .915 .665 0747 0525 085 7 .401 .915 .525 .850 .422 .905 8 .401 .915 .525 .850 .665 .747 9 .613 .790 .665 .747 - - 10 0401 0915 " "' 0525 0850 11 .613 .790 - - - - Resistance Per Unit Total for Center_. Left Right Plate 2,265 -- --- 67,200 611 916 696 86,000 611 696 --- 10,300 2,265 -- --- 59,700 1,240 -- 1,635 114,000 1,214 1,580 1,393 179,800 1,214 1,393 1,244 99,300 1,214 1,393 1,580 179,800 2,012 2,100 --- 122,000 1,214 -- 1,595 66,750 1,830 -- --- 21,000 Hopper outlets 1.67 x 1.67 x 4,000 x 1.5... ................... ;_1§,ZQQ Surcharge==ll§§ x 3320==942,000 4 24 Wt. of coal in hopper: End hopper (£19.41? 17.25)9.5 (1.67 x 1.67)fi712.25 845 cu. ft. Center hopper 4117.25 x 15 1.67 x 1.61712.92 735 cu. ft. wt. (735 845)50 79,000# Total pressure 942,000 79,000 1,021,000# This proves to be a good balance for the 4 section as a whole, but looking at the problem as per hopper: Area of corner hopper surcharged is 160 sq. ft. Pressure 160 x 3520 845 x 50 589,250# Resistance 612,200# There is an excess of resistance in the corner hopper; therefore it will operate satisfactorily except for a pocketing of coal under certain conditions between plates 5 and 6. The balance of the 4 leaves an excess of pressure in the center hopper of some 28,000#. Whether or not this would be sufficient to cause arching at the outlet and therefore stoppage of flow, is something of which there is no definite proof. It seems however that there is a possi- bility of such a thing happening. Rivets will be placed in these plates to increase the coefficient of friction, thereby decreasing the pressure at center. 25 26 PART V STRESS ANAIXSIS OF THE SUPPORTING MEMBERS The supporting members are stressed by a load acting normal to them and by an axial load transmitted to them by the member to which they connect to form the trough for the support of the plates. Each member carries a portion of the vertical and horizontal reaction, at point of con- nection, proportional to its angle of‘inclination to the vertical or horizontal. ie. Analysis of member #6. (see drawing plate in pocket) The vertical reaction at the hopper outlet is taken by one-half the members at 9 degrees 18 minutes and one-half at 23 degrees 40 minutes. Where the load is carried by V1 at 9 degrees 18 minutes and V2 at 23 degrees 40 minutes: V1+-V2==100% of load To find the percentage of load taken by each equate Vl sin o'to V2 sin.¢ Then .162V1,=.401V2 Vl = 2047V2 2.47 V2-+V2==lOO% V2=28.8% v1=71.273 The total vertical reaction at hopper outlet is 95.5 kips. 71.2% is carried by J; the members and equals 68 kips. The portion allotted to #6 is 68/4==17 kips. The horizontal is taken care of by an angle bar running from hopper to 27 column. For member #6 as shown by table VII is 14 kips. N = 1,285 x 22.45 = 2,170#/1in.ft. Hp: 15,700# H.o = 2,260# 700#/1in.ft. N Vt: 16,700# vP = 2,760# \H». Member #6 is supported as shown, fixed to hopper base plate at A and to a supporting member at B, acted upon by a uniform load N normal to the axis, a vertical load V at the outer fibre, making an angle of‘9 degrees and 18 minutes with the axis, and a frictional force F applied along the outer fibre through the hopper plates. member #6 is a 12 WP 53 section S'==70.7 A==12.06 Stress-=Mg==M Where M is maximum, stress is maximum 13' Maximum Bending Moment will occur at B and is equal to: 22.45 x 1,285 x 15.5 x 121,916 x 22.45 x 12 + 2 2 28 11.000 x J? x 12 + 2 14,000 x .162 x 12 x 4 +17,000 x .162 x 15.5 x 12- 14,000 x .97 x 15.5 x 12 = 740,500 in. 1b. S=18 8.00+ 0 00 :12 000#/sq. in. ' 12.06 E707 ' The truth of this is best represented by the graph on the following page. " yr I 4"". 1‘ ’1” ’ l4“‘".’. .1 ,I J“ 44!! ii?! [a ’II"" . . n ' mat/,3." TABLE V INDEX OF MEMBERS SUPPORTING HOPPER PLATES (use with plate I in pocket) MEMBER SIZE LENGTH SECTION AREA OE AREA-OFIPEKTE (feet) MODULUS SECTION SUPPORTED (sq. in.) l 12-WF-53 2.36 70.7 12.06 4.12 2 12-WF-53 2.95 70.7 12.06 5.5 3 10-WF-33 3.64 35.0 9.71 7.18 4' 8’WF'17 400 1401 500 7048 5 12-WF-53 13.3 70.7 12.06 15.5 8 8-WF-17 4.3 14.1 5.0 7.73 9 lZ-WF-45 14.2 58.2 13.24 17.85 10 12-WF-45 14.2 58.2 13.24 24.90 12 diaph. - - - 8.37 13 12 20.7 12.8 21.4 6.03 10.9 14 l2-WF-53 12.2 70.7 12.06 10.90 16 lO-WF-33 7.2 35.0 9.71 17.4 17 8-WF-l7 4.9 14.1 5.0 11.8 18 diapho "' " "' 6023 19 diaph. - - - 5.72 20 B'TVF-l'? 506 1401 500 11.35 21 lO'WF‘Zl 8 o 5 210 5 6019 1700 22 10-WF-45 11.3 49.1 13.24 20.1 23 12-WF—53 14.2 70.7 12.06 26.30 24 12-WF-53 14.2 70.7 12.06 24.90 25 lO-WF’33 905 5500 9071 18030 26 diaph. " "' ‘ 8037 27 diaph. " "'. "’ 8.37 28 10-WF-33 9.5 35.0 9.71 18.30 29 l2-WF-53 14.2 70.7 12.06 24.90 30 12-WF-53 14.2 70.7 12.06 26.30 32 10-WF-33 8.5 35.0 9.71 17.0 33 8‘WF’21 506 1800 6018 11035 34 " "‘ " " 5072 55 8-WF-21 5.2 18.0 6.18 9.82 37 l4-WF-78 15.6 121.1 22.94 26.5 38 8'WF‘21 104 1800 6018 2037 39 10-WF-33 2.0 35.0 9.71 3.19 40 14-WF-78 2.3 121.1 22.94 41 diaph. - - - 8.37 42 lO'WF’Zl 905 2105 6019 1803 43 12-WF-45 14.2 58.2 13.24 24.9 TABLE VI TABLE OF VERTICAL REACTIONS (use with plate I in pocket) MEMBER GROSS R;72 PLATE AREA MEMBER UNIT TOTAL LPLATE Rv Rv WEIGHT WEIGHT Rv SUPPORTED (kips) (kips) (kips) (kips) (kipsl (Sg.ft.) 1 2265 9.0 .1 .1 9.2 4. 4.1 2 2265 12.5 .1 .2 12.8 6.4 5.5 3 2265 16.3 .2 .1 16.6 8.3 7.2 4 2265 17.0 .2 .1 17.3 8.6 7.5 J 2265 709 ' ‘ 709 400 305 L2 2265 309 " " 309 200 109 5 630 9.7 .3 .7 10.7 5.3 15.5 6 640 14.4 .5 .7 15.6 7.8 22.45 7 790 13.5 .4 .3 14.2 7.1 17.15 8 880 6.8 .2 .1 7.1 3.5 7.73 I 910 07 ' ‘ 07 04 082 K2 540 9 08 " " 908 409 15035 K 1240 808 02 "' 900 405 701 9 1220 22.1 .4 .7 23.2 11.6 18.1 10 1230 30.8 .6 .7 32.1 16.0 25.0 11 1300 24.2 .4 .3 24.9 12.5 18.6 12 1350 11.9 .2 - 12.1 6.1 8.8 P 1380 101 ‘ “ 101 05 08 13 1300 1403 ‘ 07 1500 705 1100 14 1260 13.9 .2 .6 14.7 7.3 11.0 15 1390 28.5 .5 .4 29.4 14.7 20.5 16 1480 25.9 .4 .2 26.5 13.3 17.5 17 1540 18.5 .2 .1 18.8 9.4 12.0 18 1590 909 01 ‘ 1000 500 602 12 1620 204 04 ' 208 104 105 19 1550 8.8 .1 - 8.9 4.5 5.7 20 1500 18.7 .2 .1 19.0 9.5 11.4 21 1420 24.2 .4 .2 24.8 12.4 17.0 22 1340 27.0 .5 .5 28.0 14.0 20.1 23 1230 31.1 .6 .7 32.4 16.2 26.3 24 1230 30.6 .6 .7 31.9 16.0 24.9 25 1300 23.8 .5 .3 24.6 12.3 18.3 26 1350 1103 02 - 1105 507 804 Q 1380 08 ‘ ‘ 08 04 06 G 1560 101 ' ‘ 101 06 07 27 1350 1103 02 ' 1105 507 804 28 1300 23.8 .4 .3 24.5 12.3 18.3 29 1230 30.6 .6 .7 31.9 16.0 24.9 30 1230 31.1 .6 .7 32.4 16.2 26.3 31 1340 27.0 .5 .5 28.0 14.0 20.1 32 1420 24.2 .4 .3 24.9 12.5 17.0 33 1500 18.7 .2 .1 19.0 9.5 11.4 34 1550 808 01 - 809 409 507 G 1380 .08 04 - 102 06 06 H5 1560 101 02 " 103 .6 07 TABLE VI (cont.) UNIT TOTAL IPLATE MEMBm GROSS R v72 PLATE AREK R.v Rv WEIGHT WEIGHT SUPPORTED (kips ) (kips) (kipsl (kipsl (kips) (sq. ft.) 35 2080 21.8 22.1 11. 0 10.5 36 2060 42.0 .1 .3 42. 4 21. 2 20. 3 37 2030 55.2 .6 1.2 57.0 28.5 27.2 71 2100 3709 ’ ‘ 308 109 108 V 650 502 02 - 504 207 801 A1 2265 59.5 .6 - 60.1 30.0 26.3 38 1830 5.6 .1 - 5.7 2.9 3.1 39 1830 7.3 .5 .1 7.9 3.9 4.0 40 1830 7.9 .6 .2 8.7 4.4 4.3 41 1350 1103 ‘ ‘ 1103 506 804 42 1300 23.8 - - 23.8 11.9 18.3 43 1230 30.7 .2 .7 31.6 15.8 24.9 F2 1380 08 ‘ ‘ 08 04 06 i I i TABLE VII TABLE OF HORIZONTAL REACTIONS (use with plate I in pocket) MEMBER NORMAL UNIT R TOTALth ‘Rh/2 (Degnds) (pounds (kipsl1 _Lkips2 1 2425 1710 7.0 3.5 2 2425 1710 9.4 4.7 3 2425 1710 12.3 6.2 4 2425 1710 12.8 6.4 J 2425 1710 6.0' 3.0 L2 2425 1710 3.2 1.6 5 1285 1245 19.3 9.6 6 1285 1245 28.0 14.0 7 1285 1245 22.4 11.2 8 1285 1245 9.6 4.8 I 1285 1245 1.0 .5 K2 1285 1245 19.1 9.6 K 1740 1590 11.3 5.6 9 1740 1590 28.8 14.4 10 1740 1590 39.8 19.9 11 1740 1590 29.6 14.8 12 1740 1590 14.0 7.0 P 1740 1590 1.3 .7 13 1580 1500 16.5 8.3 14 1580 1500 16.5 8.2 15 1580 1500 30.8 15.4 16 1580 1500 26.3 13.2 17 1580 1500 18.0 9.0 18 1580 1500 9.3 4.7 I2 1580 1500 2.3 1.2 19 1740 1590 9.1 4.6 20 1740 1590 18.2 9.1 21 1740 1590 27.1 13.6 22 1740 1590 32.0 16.0 23 1740 1590 41.7 21.8 24 1740 1590 39.6 19.8 25 1740 1590 29.1 14.6 26 1740 1590 13.4 6.7 Q 1740 1590 .9 .5 G 1740 1590 1.1 .5 27 1740 1590 13.4 6.7 28 1740 1590 29.1 14.6 29 1740 1590 39.7 19.8 30 1740 1590 41.7 20.8 31 1740 1590 32.0 16.0 32 1740 1590 27.1 13.6 33 1740 1590 18.2 9.1 34 1740 1590 9.1 4.5 G2 1740 1590 .9 .5 H2 1740 1590 1.1 .5 35 2323 1830 19.2 9.6 33 TABLE VII (cont.) NORMAL UNIT R TOTALTRT (pogndsl (pounds (kipsl 2323 1830 37.1 2323 1830 49.7 2323 1830 3.3 1285 1240 10.0 2425 1710 45.0 2110 1670 5.2 2110 1670 6.7 2110 1670 7.2 1740 1590 13.4 1740 1590 29.2 1740 1590 39.6 1740 1590 1.0 TABLE VIII STRESSES IN SUPPORTING MEMBERS ER U 1E T TA NORMAL A ADS RE NORMAL SUPPORTED LOADING v F (kips LOAD (sq.ft.) (kips) (kips) (kips)/sq.1n.) Spoundsl #‘ ___ l 2425 4.1 10.0 22.3 3.2 10.5 2 2425 5.5 13.5 24.8 4.4 14.0 3 2425 7.2 17.6 15.7 5.7 13.0 4 2425 7.5 18.4 10.0 6.0 8.94 5 1285 15.5 19.9 17.0 6.5 8.75 6 1285 22.5 28.9 17.0 9.4 12.0 7 1285 17.2 22.1 1.5 7.2 10.4 8 1285 7.7 9.9 3.0 3.3 7.34 9 1740 18.1 31.5 6.8 10.3 11.6 10 1740 25.0 43.5 6.8 14.2 14.5 11 1740 18.6 32.4 12.4 10.5 13.2 12 1740 808 1503 509 500 - 13 1580 11.0 51.4 8.5 16.7 13.0 14 1580 11.0 17.4 8.5 5.6 13.0 15 1580 20.5 32.4 14.0 10.5 10.6 16 1580 17.5 27.6 13.3 9.0 10.0 17 1580 12.0 19.0 9.5 6.2 12.7 18 1580 602 908 500 302 - 19 1740 507 909 500 303 - 20 1740 11.4 19.8 9.5 6.5 13.7 21 1740 17.0 29.6 12.3 9.6 18.4* 22 1740 20.1 35.0 14.0 11.4 11.8 23 1740 26.3 45.7 20.0 14.9 13.3 24 1740 24.9 43.3 10.0 14.1 12.9 25 1740 18.3 31.8 12.3 10.3 13.0 26 1740 8.4 14.6 5.9 4.7 - 27 1740 804 .1406 507 407 "' 28 1740 18.3 31.8 12.1 10.3 13.0 29 1740 24.9 43.3 10.0 14.1 11.8 30 1740 26.3 45.7 26.0 14.9 13.9 31 1740 20.1 35.0 33.2 11.4 13.9 32 1740 17.0 29.6 18.0 9.6 15.2 33 1740 11.4 19.8 15.0 6.5 12.2 34 1740 507 909 500 303 " 35 2323 10.5 24.4 5.0 7.9 11.1 36 2323 20.3 47.2 15.0 15.3 19.9% 37 2323 27.2 63.2 30.2 20.5 12.6 38 2110 3.1 6.6 0 2.1 - 39 2110 4.0 8.5 0 2.8 - 40 2110 4.3 9.1 0 3.9 - 41 1740 8.4 14.6 5.7 4.7 ~ 42 1740 18.3 '31.8 12.0 10.4 20.5* 43 1740 24.9 43.3 26.0 14.1 16.0 *Upon checking with the designers to determine the reason for excess stress in these members, it was found that they had increased their size when making up the final bill of material. 36 I ~ j ORDER ORE/astray- - ,2.” H55 .2'flég?73'25/NE H.524; '3 ' 3‘9 #7367153 H56 24‘5": I W , I “ll“- "THE DETROIT EDISON COMPANY-- DRIPPING I SURVIVING DETROIT. 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