ML19343C899
| ML19343C899 | |
| Person / Time | |
|---|---|
| Site: | 07109086 |
| Issue date: | 03/06/1981 |
| From: | HITTMAN NUCLEAR & DEVELOPMENT CORP. (SUBS. OF HITTMAN |
| To: | |
| Shared Package | |
| ML19343C897 | List: |
| References | |
| 18680, NUDOCS 8103250520 | |
| Download: ML19343C899 (37) | |
Text
{{#Wiki_filter:I ADDENDUM #1 SAFETY ANALYSIS REPORT FOR THE HN-100 SERIES 1 RADWASTE SHIPPIf1G CASK Revision 2 March 6,1981 l HITTMAN NUCLEAR & DEVELOPMEllT CORPORATI0fl COLUMBIA, MARYLAND 21015 h B1032505
Spec. No. ADDENDUM #1 IIN-100 Series 1 Radwaste Shipping Cask ItMVISION LOG ll EV. 1)A T E ENGINEElllNG Q. A. PROJ. MGil. ECN # 0 9/11/78 fl u.y, m(1,,Qge, ~fjug(M J d ~~ d Rev. Date ENGIfiEERING Q.A. TRANSPORTATI0t! ECfi# 1 9-I3-80 WA 80-158 2 3-6-81 ' DEA h k [fg &[f[/M('g/ 81-042 v a m P00RORG, Nil
f INTRODUCTION This addendum was originally issued to increase the allowable internal load which can be transported in the HNDC HN-100 Series 1 shipping cask. As such, only the areas of the original safety analysis report which are affected by this increase were revised and submitted herein. Revision 1 to this addendum contains the analysis for modified lifting lugs to be installed on the HNDC HN-100 Series 1 shipping casks to allow the use of sharter lifting cables. packages in the series are constructed of ASTri A516 Grade 55, ASTM A516 Grade 70, ASTM A515 Grade 70 steel. The safety analysis has been revised based on the use of ASTM A516 Grade 55 steel which has the lower yield and ultimate strength of the steel used in the packages. The tiedown analysis has been revised to combine the longitudinal, transverse and vertical loads in terms of the tota' tensile force on the cable and calculates the stresses on the shell based on the vertical and total horizontal components on this tensile. The analysis concludes that the package can be operated safely with a maximum weight of contents of 14,500 pounds and a gross package weight of 50,000 pounds. The description of the package as contained in the original safety analysis report has been revised to reflect the worst fabrication dimensions and materials of construction of the casks.
1.0 PURPOSE The purpose of the following document is to provide the information and the engineering analysis that demonstrates the performance capability .and structural integrity of the HN-100 Radwaste Shipping Cask and its com-pliance with the requirements of 19 CF't 71, Section 71.21 and Appendix A.
2.0 DESCRIPTION
The HN-100 Shipping Cask is a top-loading shielded container designed specifically for the safe transport of radioactive waste materials between nuclear facilities and waste disposal sites. It is basically a top-opening right circular cylinder consisting of a cask body, cask lid and shield plug. Its principal design dimensions are 82.75 inches o.d. by 81.5 inches high with internal space of 75.5 inches I.D. and 73.5 inches high. (Dimensions vary slightly from unit to unit.) 2.1 Cask Body The cask body is a steel-lead-steel annulus in the form of a vertical-oriented right circular cylinder closed on the bottom end. The side walls consist of a 3/8 inch inner steel shell, a 1-3/4 inch thick concentric lead cylinder, and a 7/8 inch thick outer steel shell. The bottom is a 4 inch thick steel-plate welded integrally to both the internal and external steel body cylinders. The steel shells are further connected by welding to a concentric top flange. Positive cask closure is provided by the 0-ring seal and the required lid hold-down bolting. 2.2 Cask Lid The cask lid is a four inch thick steel plate which is stepped to mate with the upper flange of the cask body and its closure seal. Three steel lug lif ting cevices are welded to the cask lid for handling. The cask lid also contains a " shield plug" at its center. 2.3 Shield Plug The shield plug is a four inch thick, circular steel plate f abri-cated in a design similar to the cask lid including the 0-ring gasket and the required hold-down bolting to provide positive closure to the cask lid. The shield plug also has. lifting device located at its center to facilitate its handling. 2.4 Cask Closure The shipping cask has two closure systems: (1) the cask ' lid is closed with 30 one-inch diameter bolts and an 0-ring gasket seal, and (2) the shield plug is closed with 16 half-inch bolts and the same seal system used for the cask lid but smaller. A
2.5 Cask Tie Down System The shipping cask tie down system consists of two setc of two crossed tie down cables ~ (total four cables) and either shear blocks or a retaining ring attached to the trailer. Four to eight shear blocks are used. T1e shear blocks are either fabricated steel brackets with or without adjust-ment screws or wooden blocks bolted through the trailer deck adjacent to the steel framing members. 2.6 Cask Internals Tha wk internals consist of four separate configurations based on the typu of containers te be housed: (1) one large disposable con-tainer, (2) eighteen 30 gallon drums (including two 9-drum pallets for material handling), (3) fourteen 55 gallon drums (including two 7-drum pallets), or (4) eight 55 gallon drums (including two 4-drum pallets). All internal containers have integral leak-tight seals or closures, i.7tegral lift lugs and vertical symmetrical clearances. Drums are stacked in two tiers-or levels, each on removable pallets designed to minimize interaction between drums. 2.7 Gross Package Weights The respective gross weights of the cask components and its designed radwaste loads are as follows: Cask Body 29,000 pounds Closure Lid 6,000 pounds Shield Plug 500 pounds Total Cask Unloaded 35,500 pounds HN-100LC Disposable Container and Waste 14,500 pounds HN-100-55 (14 druns of Radwaste) 12,500 pounds HN-100-30 (18 drums of Radwaste) 11,500 pounds 2.8 Radwaste_ Package Contents a The contents of the various internal containers can be process solids in the fann hf spent ion exchange resins, filter exchange media, evaporator concentrates, and spent filter cartridges. Materials will be either dewatered, solid, or solidified. 3.0 DESIGH CRITERIA AND SilMfiARY OF RESULTS .The HN-100 Radwaste Shipping Cask was designed and analyzed in accordance with and meets the requirements of.10 CFR 71. The physical data for the construction materials. is as.follows: lif ting lugs, inner and outer steel shells.
~ are ASTM A-516, Grade 55 (Units 1, 2, 3 and 4) and ASTM A-515, Grade 70 (Unit b). The bolting material is ASTM A-320, Grade L7 or ASTM A-307, Grade A for the respective casks. The tiedown luas are ASTM A-203, Grade E (Units 1, 2, 3 and 4) and ASTM A-515, Grade 70, (Unit 5). 3.1 General Standards for all Packaging (71.31) 3.1.1 ChemicalReactions(71.31(a)J_ The package contents will consist of process waste materials encapsulated in disposal drums or containers which are placed within the shipping cask. All disposal containers placed within the shipping cask are required to have positive sealing closures. Hence, there are no significant galvanic or chemical reactions between the package contents and the shipping casks. 3.1.2 Positive Closure (71.31(b)) , Both types of specification drums (30 gallon and 55 gallon) have positive closures. The large disposable containers will be pemanently sealed with a container cap. All disposable containers are placed within the shipping cask which (itself) has positive closure for the cask lid to the body flange surface and also between the shield plug and the cask lid flange surface. Hence, there is no possibility of inadvertent. opening of either the disposal containers or the shipping cask. -3.1.3 Lifting Devices (71.31(c)) 3.1.3.1 Shipping Cask (71.31(c)(1)) Two types of lift lugs are used on these casks. The options are as follows: (See Appendix for analysis and details). Option 1 & 2: Three equally spaced lugs are welded to the upper steel flange and the outer steel shell of the cask body. The lugs may Se flat plate'(0ption 2) or rein-forced (0ption 1). The cask is lifted using a lift beam and the lugs._ The lifting lugs are designed to lift three times the weight of the cask with stresses less than yield strength. Option 3: Two lugs are welded to the upper steel flange and the outer steel shell in diametrically opposite ' sides of the cask. The two lugs are designed to lift three times the weight of the cask using cable slings with stress ess than yield strenn;h. The cask can also be lifted with lift beams or chains.
3.1.3.2 Cask Lid (71.31(c)(2)) The lif ting device for the cask lid consists of three equally spaced clevic pin lifting assemblies, attached to - stiffener bars which are welded to the cask lid. These lifting devices will support three times the weight of the cask lid with no stresses in excess of their yield stress. See Appendix for analysis and details. 3.1.3.3 Shield Plug (71.31(c)(2)) The lifting device for the shield plug concists of a single clevis pin assembly attached to a lug which is welded directly to the upper or outside of the steel plate which is the shield plug. This ' lifting device will suoport three times the weight of the shield plug with no stresses in excess of its yield stress. See appendix for analysis and details. 3.1.' 3. 4 Non-Lifting Attachments Covered or Locked (71.31(c)(3)) Both the cask lid lifting device and the shield plug lif ting device will be covered to prevent their being used to lift the shipping cask. 3 3.5 ' Lifting Device Failure (71.31(c)(4)) All lifting devices are designed such that excessive loads will result in failure at the weld joints. These types of failures will not impair the shielding or containment properties of the shipping cask. 3.1.4 Tie Down Devices (71.31(d)) 3.1.4.1 Tie Down Forces (71.31(d)(1)) The tie down devices consist of four ratchet binder or turnbuckles and cable assemblies attached from the tie down adapters on the cask to tie down lugs on the trailer body. Additionally, shear blocks 'finnly position and hold the cask on the trai'er bed. The tie down lugs have been designed to allow the cask to withstand a vertical force of two times the weight of the cask, a transverse force of five times the weight of the cask,~and a longitudinal force ~ of ten times the weight of the cask with no resulting excessive stresses. See the Appendix for the analysis and details. O. L
3.1.4.2 flon-Tiedown Devices (71.31(d)R)J. The length of the tiedown cables prevents the use of anything but tne tiedown lugs fnr package tie down. There are therefore no structural parts of the cask which could be employed to tie tne package down which do not comply with 10 CFR 71.31 (d)(1). 3.1.4.3 Tie Down Device Failure (71.31(d)(3)) The four tie down adaptors on the cask periphery have been designed so frat loads transmitted by the tie down cables under worse conditions will neither damage the outer steel shell nor cause the tie down adaptors to fail. The tie down system analysis is shown in the appendix. 3.2 Evaluation of a Sinole Package (71.34) Refer 'to Appendix A - flormal-Conditions of Transport. The cask has been designed to withstand conditions likely to occur under normal conditions of transport with design integrity being analytically verified with safety factors in excess of 1.0. Specifically, the HN-100 package meets the following separately applied conditions: 3.2.1 Heat Since the package is constructed of steel and lead, temper-atures of 1300F. will ' ave no effect on the package. 3.2.2 Cold The^ steel materials selected for forgings, plate, and - bolting each retain structural integrity at temperatures down to -400F. 3.2.3 Pressure The cask can withstand an internal vacuum of 7.35 psia. The resulting stress on the inner steel shell is 740 psi, which gives a safety factor'of 51.3. This referenced analysis is shown in the appendix. ~3.2.4 Vibration The cask tie downs firmly position the package as to minimize any vibrational effects. In addition, all cask external devices are firmly attached (either by welding or boltino) to the cask. L
3.2.5 Water Spray The cask is sealed by an 0-ring gasket seal with suitable holddown bolting to assure.it is both water and pressure tight. In addition, the radwaste is contained within sealed steel containers -in the cask void volume. 3.2.6 Free Drop The cask has been analyzed to insure its structural adequacy to withstand a one-foot drop, striking any cask surface, onto a flat horizontal surface. The analysis is in the appendix. 3.2.7 ' Corner Drop The specified condition is not applicable since the package weight is greater than 10,000 pounds. 3.2.8' Penetration The impact of a vertical steel 1-1/4 inch diameter,13 pound cylinder from a height of four feet will not puncture the cask outer steel shell. In addition, there is no externally mounted equipment on the cask, the-damage of which due to this transport condition, would limit the cask structural adequacy or hinder its function. 3.2.9 Compression This specified condition is not applicable since the package . weight is greater than 10,000 pounds. 3.3 Standard for Normal Conditions of Transport for a Single Package _ (71.35) -3.3.1 Materials Release The HN-100 cask'has been designed to prevent the release of radioactive material during normal conditions of transport as defined in ' Appendix A of -10 CFR 71. Specifically, the design closure consisting'of the 0-ring gasket seal for both the cask lid-and the shield plug closure are capable of withstanding higher temperatures and forces than-the cask experiences during nonnal transport conditions. In a similar manner, the number of bolts and o the strength of 'the bolting design for the closures assure that the bolts' will not fail during normal transport. 3.3.2' Packaging Effectiveness e The packaging effectiveness _under'" normal conditions" of . transport have been _ analytically verified to protect the contnnts from excessive heat, vibration, shock, corrosion,~ or exposure to 'the effects of weather. L
i-i 3.3.3 Pressure Increase The cask contents are either solid, solidified, or dewatered resin. The temperatures and pressures to which these wastes are exposed are not sufficient to generate gas formation. Further, the various individual containers within the cask are sealed precluding any possible interaction between waste types. Hence, these is no possibility of gas formation which might reduce cask packaging effectiveness. [ 3.3.4 Containment of Primary Coolant (71.35(a)(4)) Not applicable. 3.3.5 Loss'of Coolant (71.35(a)(5)) b-Not applicable. There is insufficient internal heat resulting from isotope decay to require the use of a coolant in this design. 3.3.6' Atmospheric Venting (71.35(c)) Under normal conditions, the HN-100 cask was designed to prevent venting of the casks' contents to the atmosphere, plus the individual waste containers in the cask void are sealed. 9 J )- r i .h. ~ + v. ,w.. -, e .e.--nw-- 4 ---g
i 4 4.0 Procedural Controls (71.24) Customers that use the HN-100 casks are suuplied a copy of the had . Services Manual. This manual describ?s the services that will be surplied and contains a section on operating procedures. This procedure describes the inspection of the cask and trailer upon arrival at the site, the loading procedures and the forms that need to be filled out prior to the cask leaving the customers' site. snspections are performed by the customer prior to loading the cask, by the driver prior to leaving the site, and after arriving at the consignee's si te. 4 Loading procedures include the opening and closing instructions for the cask and are included as part of the Rad Services Manual. Radioactive Shipment Records providing the necessary information are required to be f,illed out. Two copies accompany the shipment to the consignee, one copy is retained by the shipper and one copy is sent to HNDC. i The casks and trailers undergo a routine technical inspection at least 4 once every four months for safety items and semi-annually for all other items. i These inspections involve checking cask for contamination, damage to interior or exterie., gaskets, studs, signs and placards, shielding and tie downs. 1 4 I d m. 3 e ws-, .-..ur-% n -- -v --e.--+ ,vw v e -vpv wm, e - rw=wv,- +=w-v -=m--w-e-,-y
In all calculations below, the worst case fabrication tolerances were used. 1. Lifting Devices [ A. Cask Lif ting Lugs - With and Without Reinforcement ifor use only with lifting bars) ji 50,000 lbs \\".. 2 82 " U l~ d,-]l ~- -m-1.88*.e- + l l l Il l I I = A. 94 ---se i_ _ _ __I r 3/4" weid t i 1. Tension Stress Load = 50,00 = 50,000f 3 2 min. area = (4.54 - 1.88) x 1.0 = 3.06 in stress = 50, 0 = 16340 lb/in ,0 safety factor = = 1.84 ,34 -9 e
o 2) Shear Due to Col t L_oaJ Area = (2.82 b9 2 x 1 = 4.82 in' 2 2 Stress = = 10,373.4 lb/in Sy (shear) = 0.6 x 30,000 = 18,000 lb/in 2 Safety Factor = 1 34 = 1.74 3) Minimum Weld Lenoth_ Weld efficiency = 85% Weld strensch (3/4" fillet) = 7200 lb/in RequiredWeldLength=h[00 _~-- = 8.17 in y200 Minimum weld length = 5 + 2 x 3 = 11 in Safety Factor = -h'7-= 1.346 4) Bearing Stress in Hole Pin dia. (1-1/2" shackle) = 1.675" Bearing stress = h 00 = 29850 x Safety Factor = 2- - - = 1.005 B. Cask L_if t Luas - Modified Design (for use with lif ting bar or slings) 106,066f Weight of cask = 50,000 lb f u ber of lif t lugs = 2 f 2.124 Dia-Vertical load per lug = 2.64 2.69"R u e=45 50,000 x 3 0 = 75,000 1b Cask Cover Total load each lug (e = 450) 75,000 I sin e = 106,066 = Y +2. 94-> Cask Body a 3 Minimum length of slings = 82.75 + 6 1 y = 62.77" 2 sin e = 5.23' 12" 2.44' thick U
- 1) Tensile Stress in Lift Lug Area ( A-A) =(2.69 x 2 - 2.125)(2.44) 2 7.94 in
= I' Vertical load = 75,000 Stress = h'000 = 9,445.04#/in A z 9g-Area (B-B) = (2.69+2.94x.Y-2.125)(2.44) B = 11.52 i n' Stress = 106 6 = 9207.129/in 2 o Safety Factor = g g4 3.18 = 2) Bendino Stress in Lif t Luo Bending Stress Ic-c " ~12-bh ' 1 3 = 7-x 2.44 x 5.75 = 38.66 i n 1 d 106,066# M = 75,000 x 2 + 75,000 x 0.185 = 150,000 + 13,875 75,000 = 163,875 in-lbs g f _ MC _163,875 x 2.875 _12186.8 2" b F~ 38.66 C 4C Tensile Stress % 5.75 Area (C-C) = 2.44 x 5.75 = 14.03 in 2 2 ft* .' 3 = 5345.7 f/in Combined Stress z fT = 12,186.8 + 53,457 = 17,532.5 #/in Safety Factor = -f 75 = 1.71 3) Shear Stress in Lift Lug Area = 2 x (2.69 106 x 2.44 = 10.54 in 2 Stress = l-- = 10,063 f/in z ,/ / Yield Strength Shear = 0.6 x 30,000 / = 18,000 f/in' ' ~ - - = 1. 79 Safety Factor = p-063
4) Weld Strength Vertical Loading 75,000# Length of weld = d 106,066# 2(2.5 + 10.5) + 2.5 = 26 + 25 = 28.5 inch 0 f= = 2632 lb/in > 75,000# Bending Load with Slings g (Assume bending around upper flange) / 2.5" 3/4" fillet v 75,000# x (2 + 2 5_) h ? 9 3.25" = 75,000 x 3.25 E = 243,750 in-lbs F = 243 = 32,500 lbs 3/4" fillet 7.5" 10.5" S > Length of weld = 10.5 x 2 + 2.5 5.25" = 23.5 inch v 0 f= = 1383 lbs/in / 3/4" I Combined stress /2F32F+ 1383 = 2973 lb/in Allowable stress 3/4" weld = 7200 x 0.85 = 6120 lbs/in - Safety Factor = 6120 yg g = 2.06 -
5) Baaring Stress in tiole Pin Dia. (13/4" in shackle) = 2 in Bearing Stress = fx' 2 = 21,735 #'in 4 ,0 Safety Factor = = 1.38 4
2. TIEDOWil AtlALYSIS A. Tiedown Loads The cask tiedowns consist of four cable and turnbuckle or ratchet binders assemblies and shear blocks at the cask base which firmly position and hold the cask to the truc! pl a tform. The following analysis shows the ability of the cask t:~',wn lugs to withstand ccinbined loads due to a 109 longitudinal, 59 transverse and 29 vertical loads. 6 R ci K =w v v _ JLo JL K 6 w m mm v v _\\ v Ms 49" 33" ;< 33" ; < 49" % a n , CG 59" av. A 65" av. 40 v 9F 9P A 6 ' av. Force Diagram ~ q@- 2=49" N N 97.68 V=59" 77.8 [ / 1) Horizontal Longitudinal load = 10g Fe M [Fv d \\ 59" Shear block b RW y 41 + + -> 41+33=74 + E11 =0 9 10W (40-6) = F x 59 + f x 74 + W x 41 7 y ___ = hh 1.2 F F = y 7 (340 - 41)W = F x 59 + 74 x 1.2 F g g 299W = F (59 + 89.1) 7 =299(50,00p) F = 100,945# t 14 8.1 100 945 F = Each tiedown = = 50,473# g load = 50,473 x b7 S = 100,616# Total tension 0 109 4j 2) Horizontal Transverse Load = 5g Ft Fw f a' 59" sw 40" yw y a 6" 82 - 53.5 = - = 14.25 in + + 41" + IM = 0 b 5(W) x (40-6) = W x 41 + F x 59 + F x 14.25 t y ~ 59 [F~ t 60.T Ft= x F _= 1.025 F y y (170 - 41)(W) = 59 x 1.025 x Fy+ 14.25 Fy _ 129 x 50,000 p = 86'316 v 74.725 Fy each cable = 86,312 = 43,158 S Tension due to Sg transverse load = 43,158 x kj = 71,492#
3) Vertical For_ce = 23 2W h h W Fv v Fy. total = 2W - W y each cable = {- = 50 000 = 12,500# F Tension due to vertical load = kj - x 12,500 = 20,695# 68 4) Total Tension and Vertical and Horizontal Components Total = 100,616 + 71,452 + 20,695 = 192,763# 5 Fy = 192,763 x = 116,431# 97 68 Fh = 192,763 x h = 153,630# c B. Analysis of Tiedown on Cask Shell The tiedown loads are transmitted into the cask shell as external noments. These nonents are the product of the tiedown forces and the offset distance between the line of action of the tiedown force and the attachment plate. ML I F, <HS-- Offset 1.75" 4n NC u Fx F 153,630# = z i F 116,431# = x I Circumferential moment = 153,630 (1.75) = 268,850 #in. M = c L ngitudinal moment = 116.431 (1.75) = 203,750 #in. M = L l Reference for method of calculation: Welding Research Council, Bulletin No.107 (WRC'107), Stress in Cylindrical Pressure Vessels from l Structural Attachments. y = r/t = radius to thickness ratio (pg. 2, WRC 107) - C = 1/2 the circumferential width of the loaded _ plate (pg. 2, WRC 107) i - C = _1/2 the longitudinal width.of the loaded plate (pg. 2, WRC 107) 2 By = C /r ' (pg. 2, WRC 107) 1 B2 = C /r (pg'. 2,~WRC 107) 2 Check that 5 _ y < 100 w -y m g - +
_ ~ _ _ _ Nomenclature Appl. cable to Cylindrical 5 hells 7 1 2__ - 1 V, concentrated shear load in the dr-2 2 B + B cumferential direction, Ib 0.3 1.2 V,. concentrated shear load in the lon-gitudinal direction. Ib M, external overturning moment in the circumferential direction with re-spect to the shell, in. Ib M exte-nal overturning moment in the = t General Nomenclature longitudinal direction V,'ith re-normal stress in the ith direction on spect to the shell, in. Ib the surface of the shell, psi R. mean radius of cylindrical shell, in. shear stress on the ith face of thejth 1 length of cylindrical shell. in. r,, direction halflength of rectangular loading in c, stress intensity - twice maaimum circumferential direction. in. S = shear stress, psi halflength of rectangu!ar loading in e, t membrane force per unit length in longitudinal direction, in. N, = the ith direction, Ib/in. T wall thickness of cylindrical shell, bending moment per unit length in in. M, = the ith direction, in. Ib/in. coordinate in longitudinal direction x membrane stress concentration fac-of shell K. = 1 tor (pure tension or compression) coordinate in circumferential direc. y bending stress concentration factor tion of shell K. = denotes direction. In the case of cylindrical coordinate in circum-i o spherical shells this will refer to ferential direction of shell the tangential and radial direc-I:R, tions with respect to an axis attachment parameter s = normal to the shell through the y, e,fg, center of the attachment as e,f g, g, shown in Fig.1. In the case of R,/T; sheli parameter y cylindrical shells, this will refer C,, C, mus'.iplication factors for N, and = to longitudinal and circumferen-N, for rectangular surfaces given tial directions with respect to the in Tables 7 and 8 axis of the cylinder as shown in K,, K, coefficients given in Tables 7 and S Fig. 2- - M,, M, bending moments in shell wall in denotes tensile stress (when asso-the circumferential and longi- + = ciated with,.) tudinal direction with respect to denotes compressiv2 stress (when the shell = associated with,s) N,, N, nembrane forces in shell wali in the E modulus of elasticity, psi circumferential and longitudinal = P concentrated radial load or total direction with respect to the shell = distributed radial load, Ib normal stress in the circumferer.tial direction with respect to the shell, imi nonnat st re s in the longit udinal di- = General Equation rection with respect to the shell, In the analysis of stresses in thin shells, one pro-psi ceeds by considering the relation between internal shear stress on the x face in the o r,, membrane forces, internal bending moments and direction with respect to the stress concentrations in accordance with the follow-shell, psi ' ing: shear stiess on the o face in the x r, = ~ ,, - K. N,
- A,. GM,
, directbn with re?pect to the y h-Shell, psi.
,v . d, / I n% R w ..,r .m J. gpj N_o-4.g 14_. +p _7 +_ l... j._+... _AQ, 7- -,y- { {, _.-._ p -.-.- h-4 a_m - H_ .__.,_4, ,a._ . q. -4.._. t 9_,_+_,+,4,_+_+
- i. i.
-I-+. 4 ----- j - -.-+-+-j - -.-.-+3-+--.-. -+--t *j* < - u - m -+- .Li n_ j ! l ' 4...! 1 i4 {7 i.,.; 4 -ptthy-g. 4 + i,4 g -.1-4417, 9 -p.mp-9 4p v: _ -- { -,T, ., i i,.p_.-p. _. gp 3_r 44,m r 2 1,. 1 1 3 _ m q _, _7 9 7 1 i.,.-.,,. f -- ---- p 9 h-- .,1 ..y s . 4 4 -.- - 9.._. i -- --c .,a - 4 L n_ y p.g - 2 - _._;I_-.a-1: s- = ;;_.-- - y
- s s t:s_
.i .t .1 L: ...=._=.n 2_..:- :. :. :=.:f
- ..n..-
.t -- :. =- .1
- t..-
- : l_- . u. i t- _.. = r-? . =.:. _ _1_. _:.3 J' %jq'1M -? t
- ~
s-. 1 p Z,,- e a.. i + e _,._J I I a i * ;--f'h' 0llC i., r I I I I I i - Se Y ! v Y ! i, I I i T t-MFO -O I~-T j-7 M -1 WMw [. s. ppa. Ij.q- % -N.
- p
'-i@-fh [ (Wt--- Nr -M L-b i-M-. - - ~ ~ ; it v4 : u; i u -M pj 2
- 2 ; -+
}r .. YtO Mt*Je-@hhw h O N_M,k E w -d (iff*
- s N-N Id-I 1-} If f-h. N-j-N-M Nd-yN 4-1_.
u s ._+ -I E - c. r 1.- Q -- Q. g v.Q, l~* ..? I ! i_id_ 4 y y-m-.. v. .+ - n s= - / jd jj p
- 1 : - vi
] .4. ( "' : 2,.
- 3. r ; -.12 -. pg--
1
- wa. c
.S y,. N .. -..n: : I. .n-u
- .r
., f....,v. -.,-r %. - -..g= e,, q -,,, : %w : %a.
- -:n _
-_: aa- ,; - :_. ~. -.. 1.85 m-n -T - -- %. x m_ - z - r - at -+- . --= - .v_--- w_--+-4 . Ml,/ .f y_ g ,. 7 f - e ---~ ~.- va %, %,, 7 .c.:-~- ~, _ 1 -_ -- ~ y-.c.. g .~ .-o --..h e.c% g 2 ht,. ; _-a-4 __. nr 7 - / .q E y' *n?-rM I r ! r.I y1 m ' 4 s i i ? I t j-1 .~ _i :, i r o 1. 1 1 - i 1 L, - [] _3 _k [. i 'I S I I i i, e a 4 i .. ;. -p _4
- f. i
. A t4 r o ..-i,, f - /W/ n f.f'IT i.- - -- H
- :. n s.:..
= t -;9+:+=i=- i= rid + =M =#-i=-DM . t #1 9 i iW=F,P-il:M=i = i :3 e t =- e' 4 -i.-+ +. H - H, ; ! H M * - a j h.([.~'g,,2 r-h i M=: = - - -- - - r
- i- +
E 4t T t y JI t !![; / -Waa-V((4. Mgi.3 1 ' . J 5 i ~ e i=* i -s +=r = -b~i s -j 2 { y ut t i 2 . [/M -$ i 5,d-51( ~ [hNS -+-I. . 1 c+ - i- -- ! - E:-i rj_gT =H j < :. :- i 5 ! -. -- - -- 2 hi I- -~ _:____ r ci ~_NN -5_I5$$$_j ) ~ DN g
- _.--~-e-+.
f ---- __3 - /.----..- .1 1 ..-+4-.- e. 4 U ~w; j f- +- n -.-+ im 1 fr / s s<+7 iE'I I i ! ] v ! I i C[ ,,, L1/2f._j i */ I i i # '-i I FI__ i VI 'I i'#1 i ' 7
- i i 1
' + 3 s_ e f - W-- r f a =/ 7 a l-p_- J} :uyg_p/ gk;;: = i + 4 e i + = ; - :t:+{: =w . + 4., r g - }j'idld I - - i-i + h-i : 54 -}- F -.-- -- - - - H i -. :~. + - _:i-.- hhMM +I W j i, H H d
- ; bH
+yQ j r-fMh D FM-i MIiWie ~w t +\\- e s-gr - us = s_ L . f =Tl y I '* 4'- M' i' '. *?== W E :. bi t- + -~ l [h ihb&fbE14-TU' E_- +^25-l = i---iiE=k = ~ ~F' ' 1 % ~ - '15- :5 ~; 5.[$MYE*552=I ' EI2"I ;35545fii '-'*Hil==l:' " Ei H:EC * ~ :d ~~J j l -$,p 3 _[ -_. 51- ~ - =.:' ^ ~ ~--4 -a - - -. ~. l m,;,;,; +. L: + - ~ + -, _ _.. + .a + s _-+..-4__..._._, t 9_. ~ [t-* $.,j {^ j.. y_ 1 k i-*- W__-i I i
- t. -Y h.
7 --- . +-t i 1 "-.1.i d_4 M.h.#.4 1 _+_ w,-~ *. t t. t +!" i a .[_dd-. Q. e a _ q' lL
- i F_
L iI l L4_ _!' ' L. . _L44_.1.i_ i ?.1 'I ' I i I ' i 1 22 i*NCH -sN.$- d }i : -$ ' - *. (1. I' ! i-L~ -i ;-i=1 -- f ' -
- H I MI *-
g_ f - 'N-h hk'h h kf j-dhNbYbbN I -i;$bhN I I i i bg _% .. Lj syn i-a .i a 3 . _.3 . _ i i 4.-. q..,, k_ t ' i i is 8--- . $ l. I 5 bi 3; 4 i A s 111 2- =:H-i-i -iT f 38 - ' +' -! i ~i; -n n _- - r a - = - - ~i _.. ' : i-i-17:2 7* 2 * 'i' I .li-il l - ::- ::= =_
- _ t : : :--
= a ::: :: := -- - --- ;. g :- :: 22- .:_:: } :- 2; : n r - - - :.: -
- -_ _ =:
- _n; _ : ::n t : :-:n - _,
-- :- u 2 t : --- = r r: 1 . -- - + -.n: : ~
- 2 : rn t_: :- rn:_::: :
--- n : - -._: :run :_:..-..- n. -== .! 22 r _=. r:- : - -
_4 T
.. - + -w 4. -.q- .~.._._ j. -~ F. -.- - j,. - + -._9_._.. 1 1 1. O CCS CJO C rS 0 20 C25 03'0 0 35 043 04S 0 50 Fig. 3A4embrane force N,/(%/RM) due to an esternar circumfecebal moment % on a circUar c,4irder Shcuts bn Shells -m-m _... L
WRC 10/ E li d.h } ! - . 4 I I .4Ei I II ! I 8- - t> e i a i 3 e ._.-.,-.,.%. M 4.4_a.4 L I ~,&_.- ___ ,_,._,,_4.- 1_4. _;-4 ;_4 i_a 4-.l14.11__ e 4 ,e e a 7 i -+-+-t
- t-W f
--."-_.*- iw ^ l- - * - * - + -
- - + - + - + - * - ~-*-----*-t-*,-+-+:-6-"
- 4 : ii t - - -*+-t t 4 i - t. H y - +_ 9 -- a - j l s -I.tT- " d - h t-h'i -?-b "-rH. H,4 . - +
- H-14:- t.tr +H_-b4-4-t-H_ -i-F-,t-4-4r -
- L+_1 p} a.- y: {..i. - t e - + - + - + - - - - c e i e,_a_.,, . _.+ - p-g _.e...e.-..i , 4 .?_c. .t i e.-p.. _+..s - i - 5 _+-.s 6-. 3. w %. . - 1 6-4 _6 -4. p-a +-+. 4 e 4
- i
+ 'I4 i l l 8 I: t l... ....i D d.5._i._i. :. f..~ ~._~.... '-.i.H :...i - i - _- : ~ l :.,e. - f i. : - i..F.....'. ;. F. :.i._s..i.. .. t ,-. _. + t, -.-..._+-.__..e-w-e.--o.-.- ._4 - -_..c..o.. -o- +,e 9.-. -.e-o. e.-e..c..r e.-. ._4-.... -.4..- 4-. .-4 4 -**+*-t---*--*--+-*~, 4 --, -._. - - - - t-. - --.-.-+.. -...-+...- -6 e. .- _.-. - g- ^ t--* -*-+-' -*H t-' g 1 1. J , s . s
- 3 a 1
z i : e a s
- 1
',iii 1 6 5 i ! i i n I T e i i-1 4 j - i 4 8 i i 4 t re s s. j '. s e i n ' r ^ a a j I i 7 i 6 '.+e z 5-+--- a _M. -+t i -p. t nj i i, .t ..i i. 5 55' 8 '2 ~~ ~ ~- -I ' ! YY f 4-j. t. J & a g i
- s t
- & 1 e :
2 e 3 -+--}-... . +- . j a s S 4 e i 4 e 4 1 a E t . _ m. 4-_+ 3- . r-p. - r. h3+ t. -++- - W A-t -+-. - +. 'a ,.{.. +t 4- _p p,. r. t. n - 2
- i..
-+-~~~ +i---M{i g7 3, 4-.., [. a - t, - t-+- t r : 3_ i q. z : - E.. y. 2 T..t ' : i. - L . - L. : _ t. -. .. e. i. i -" . ;. : t. ! i..-i.. f.*! ._- - r - : _._ _f. =._r J :=:--d. ::. -.. br... :r a :- =_= := h..~..- - - :..- .... n :.t -. - k - - : ~ e : : : _:u c=4 ~.21 --2:1 : =. _ _ _ _ = t-
- =
3..____._.-._._.4_ + .-.-+ + g
- -+
a 'I I f'I i ! i i i - ! I 1 i t i I ! I r i ' ! i_1 I. a
- I 3
- i e
s i I '7! -- 44.' _m+i _.'.
- m' n,.-
a 4 ., m t.i. ~2. r ' -. + iM j
- i..
2 -4 . 4 g - t't - *-w =v-i=e=i n +iw-twi=p: E m4= mri. = y= m mm ll: W!.. l ", F-H+ t
- 3
- i+ diy-%
Q t .i. -j.sr._v r. a _ ,n b: - a f a i e __e a a . g4 y 3 11, j~
== = r +y-w- 4 = Nr $ 'b9IY I 12- -.-i I r ili iI I .I E i 1. iFM--8_'E Z I-4 ~-Il _. iis.P l % J Z.i__ 4... _.. - ..._2.. =-=_.=____==._=__=p..__.x.___--_-:=_-_.=-________=,..'.'..i._:_::U'.-~L.-.__=._=_==__=-L. .. = = . _. _. _ =... _ __:. _.--_--._._7--.-_. .__-__.--4 tm 'N
- p. i __
i = ' Nhh P-u;EC~T i rg ; : m' "M, ' :n c W k,EPT 0'032 '- 4 mW M- -Q%tf. f 7.2 -~W f~ p - - -/ -' -- e s-
mm
-n' ~~b --In s 2 s ,; a_ _.-. _- f-z.: a :_:4 _ _... -.. .--) %z.--.-- f-
- - ::... - - - -.-- m
.V.w =. c " ~ = =..-- ..._,x "g" -Q MF T M L.I 1.1..L.m-L.M-} M] i ; ' i__IT__T-il_ F. i.--
- er n g
r=
n
- - 'I ' i
.-{= s %pL- _. }. ) T. 4 4.-4 L,+ a s .,g.,, A g _ _ 2 _ t4-
- VRE
-:_ '. r -- - ;-;414- -+- : -- . 244L .=r p. 4-r i _.
- Ju,
i=4-: : 1 2 '- 1 ' * -i Y-t-- Lp + V '
- s. 3 z
_'.. t-iz j.-.:rpp rtri 4 4h .iw.
- .=
. _ l _ : _= =.: _.-_ - = =m :.... =,, 2 = _ L:. =_,. y:: :_ -= ,u:_.=.... r. m: =_._:-_n - :-:-: n:-.. :=:: n_ n:1: -:
- . = pru_ :n _:- =_
.r: _:.:r .__n___-._z.___._-.i..___:. r._..... _-:..,.. _ __ .g_.. 3 _m-m:=
- :_-_ =_ _:- __- r_- ___m_._.
y_ =. g m gh N . _.. + 2 u . m' I p.f_I Ik._._ i
- dfM,
~~ j I- [i .S !I iI I I 1 .. w_m i _ d ldm_+.. ii! > - ! t f.4 - *, - LL-+_ -i-4 i_.- _y+ L 7~ --..l -+4_,. i_.4-4-1 L L -f_I!! - L 5-hL. i t i ti fy4j; pi:: ci-. j i-q .j i : -j i ! j 2 -4 ._.y_-Q. j - j. ]_ ..... F _L j.y_ - jg A _i_._g I __[_id_La..-.i._L._.._.2,_2-b !_. d. j _d__.d_._M. *- s. .dd d_. . y,_i_.M_ L .j. 4Q M.r._id_i._ _5... r,0 2. t -.i - : 4 r. 3 .i L :. TM - 1 .i1*- - * - mg t i -~ i ! - r - -- r - --
- 4. - 1; i:
-i..; 1 tv --- - r t-
- W -
- --
2L!- ! :". ' I r _ i4_ _I.. : : :
- .: Id.i.
_i'MI:i. 2.:.iN --I !. ' _. _ i i 5 77 ~ ~my. . f ! *,_,_ g _-*1-*--- q + -. _ - .a-+ . d a -.. e.. h-. i, ~.-... f_+_.-... _._.,..... _ _ g
- -.-.4_-.-
+ -4~ ~._+ : I l, .y. - q-p O Ch5 0 80 05S C20 C 25 CM O'5 CAO 055 ON 3 Fig. IA-Moment V,/M/R.J) due to an esternal circumferential moment M, on a circular cyhncer e$lltW.* 5te 5 fun m -21b-
WRC 10/ _t._... d;4 w m.f a a. _. m... m, +4.
- 1. 2 a. __ _
- 1____. m.__;.
r_4__ ._.g.. aa. i n._ _ _. .;_, d _. i. +i I I 1 z ~I l 8 ^ .C ._. '&- g r_}
- 3., 7 s
i 1-p gprr't';,. Mn = T.- m __._ -. p,-. a-v.yg ._.g.- .- p - p ,.p.p e_. r,4, g. y _.,_ w e m_.__ ..g..,._ o u m, m g.} i.t. _L _-a Ei-j,. ; :...
- -L -
. _._u_-_ g -@ t = Nhi- - ri=i d_ i =_..;. d.=i i v +4:-d e MH-i1 .._..._=__.._..__=.=.f... . t. : - _._.._. - *. %.f* *N *.. : q; y p q_. g. %,s _..r; ^
- n; r...r.. ; ;. ; n ' ;.. :J;;:. ;.- :--..._ ; 112.
.*=: - 1 _._..-...y... :: 4.. :- m 1 _.w._, .o/ _.. _.N_..- !_..._.... !-... __ _. !..,, _. _._ _. j _. _. -. _. _. _ _. _. _ _ .zm ~ y m-m n e c + + E.J J_Ll K. 1%i_4_ _%_LhQQ_.s .e_,.. I i i 1 .M _m ___w i : q Ui r_. + w su%y-N 'I. T s o_g,_ ~ s. 4 A* r . ; Q'~d,. S +i M
- hj :j'[-
2 -+i t rW ~&nN g*g ,, i, . -m, r. 4h; - +-+N ~~heshT. 1 m p4 d,.. _iii im' / ._E
- r;! t h
' rh ,% %~ &_%,%_ -4,Q*l =. 9 f?+
- J N a --
- - N--. r.%-%f F- . _t-.; :7__._f_-. r y 'n 5 w%p m,, m%.__ m -. _5.,
- .si. ~i
.r p.= E-1_.+. 5 .. _ _.::1. ;_4. 2H... i=.i. _. ::., N. N . :y...
- _d
- c.:__.:-E.
g s __. m..:= e
==:q-3 w.= r: --- r_ --i nz u z z... -:w - a s.. _. _ _ _. m -- _. N. _.%.:
- _=n
_ r. r = .--.s__. 7-Vr i li;/ / i_ s,. -Jum im .-r .3-i ~ k-.,,i i. l t, [ v. /, i--$ 5/ '.2.i-M i ! '
- != f t-=H-
. a = E it : n a . 4. i 4 -{ _ -._d[y*'.[.[' _ o f I ' t. I t -. 4_4j i>> I, .T m*F i ).i iI I
- a
+ i i . {: -[ _i 1. :-
- b._*_Q j z.
{. '-' f 2_ r *
- 5..
.= =62~.k,~,Gy-E 2 -- -k ' 3 ' 1- 'i-'"**
- .' ' d I l_ 27'
-- m. 8 2 I EE_ NI'l-
- E-3
~ ' T - _ih 5!=iL+Eumum +1mi+F=% _=f. =~ =;.;;-u:-g = ; - we en. w
- . +-- + -f -f f-
_;n = y+._+_.i.-/ t=.--.a - ---- : -- = v,._. --+ _ '~I I 2 I g ^ [ ~-'a -._._ f ~ ~~~~'~*i l l l _ l_ . _ _ -i,-/-h-*,/ - p.- t-b+-- f 32._.. g,_; 1 } e r . j I I i 1 ITI r 1 I s 1 i j-3 + i -1 1 ], ir r-t : e 4 i f.- ry .n-: i A.. _n .+ _ - - .a 'R 1 N 'I-b i'# --F 2-- F'--~~* " '~^ 2 ~~;b '-M-5 t* aj 2 _._ y p 4 _i_j {! I ~l1 ,'* [ g.. t_ L + .g n j .p. -p J T s-,3 s i s 3.. -- -i s ((f. f._--@rl-..___ _3 ii-) iM--.
- j. i m ?
q;_;., .4 g- 'Ct:3' . Z-~~~~ 1.
- : := *=~ * :...- ~ ~ * - ~ ' ', :_ ^. :.z
..:-. z*z_r-.:_ $I 5-C : *. ' :- *. + .^.'~~-l .:~'~ ~ 2:^
- -'~r_ ; -* ;.
- * : :
Aq ~ :r _rp _rn r
- r. -- -
=:_ =.._. - - - t q a p- {' _. -._ ..4,__ . _ __L. _4_._.4y*d_L t I I l 1 1 i 4_ ; I l e._.. 4_ l,..;_ l.._ t - i _;2._ 3. 2 4 t 1_ e a ,f _p p.+_q.. l, B. .g .r ..a_. .__ 1._._ d_f t l-d,.. '_i_,_ a a .i-j i -j a j .s fd_1-,3:N:E:N ! i5*- 3 - __
- r. -
'2~- ~ ~ - n- - ; 2- ' ... _..... " * ~ ~
- = =. = :-
.= :. : : _._=._,.;;....- =. . [.. ~~~' _e ..n.e..-. ..-o+. ,9.-+.-. .--a .-e+-.-..- _.-4_ .._e 0 C 05 0 30 C AS 020 0 25 030 0 35 0 40 0 45 050 ~ Fig. 3B-Membrane forte N,/(M./RJ3) due to an enternallong>tudinal rno ner.t M, on a circular cyhnder i i 7;r P00R D M
3 0 WRC 107 ...L -i._ J-,__._ {I j-{. -}- .j_ f ,_ j._. l4jr L-- _q ad. g__h.. ..- { . y e h {_o. h- .,-._.-+ d- - 4 L {_1.j _ i pF .. 4.{ 1 d j.d_, 4 4.j_.3_I._ l I_ &_._.-.._..._..g. _i._+. .g"-~-f-4 -rt i + +. 2-g__ -:2:2 . g., ._,.. j-- -. ,t .%_y _w 7 _. y y.f. .p .3... -*-1 4 s. _l
- +t t--d-b m-;
!h' !A ' ' 14 - -t-+- -j -h-.-- 8- --? t m
- r. _,2 u
-._,-t- --t4_ + -t-)_+-+-,- -+- { -t- - 6-N,. $.y - I . N - -- N. * !- i t I J"-* t.,4 t ..I
- a. _- _.
m.... ..,... _a..: =..r. :. _... _ =.... b._....-..... .... m..._. - :.,...._.t _. u.. - ----:-=
- =_.._ = :.:.:
- -... m.. -
. +..... -,.+_l.--.. w_. -4.-.... ..1 .T_++a. + i_- - .. + .rs .+ . ~...-.... .-4-e _+ .., _. _ -+ t_,_r. e.,. - r._ .4 .. + u- -r lil !l l l --H-r_ 'i! i i =i i i i = ntj-.e= i-J_._,_ig- -f d f _3h-tz:4_- 4 _ ,*-tt-I WT e_ M M-t =E -Idkq__ _._g_._,___ d i i l_ 8..' ! i-r- Ei.~ 2 a _.y. 4 ll ... q. __p. _._..p q_._.y _..4 4 f.Qif .k && y i$i V f+ pdg;-Q y ._r! : 7_,i :t-._ r_ f 3 -f ri my i_m r,tpi. )- -[7 94 _ 4L_.-4i-p tj3 pp
- - _.1w_ _7..
-
- T 1.t
_ i._
- l. 't. d :
. E. !' -!1 : il
- i. 1
- h.._._i._2 E.
-- r.i.- 3 i.. i.. 2E u.__z _ L..i t .L. n{_ t t -"-+-*-+-+- _7-+--+- - 3 ; ;_, p
- g; ;.;., ;-
,a - ;_;; + ;+g _.,.++ +-+. ~ _n_ Mb + 1 r n I 7 ~ lm e I .I I i i 1 1 I I l i 1 I.! ! 1: 'lI i i I 't i ' !! L__ + i, m,- p + 4 + 4 .? ? E-i' -t-i- a - ---T"/mu h 5-bl' 8'i~ 5 i si 5-t -i ; IIii2 E 4!@ N % '-i-i fM! N 1 M =- z -- -N~I I i~ - + '83 '- q.ALia. q g _-p _. _. q_...._Lg_j_ _4 a . 4 0 _.,i_4_,*_i; Q % -N.M4.j_p g--g-Q [ i. jp a r 2 --M k.. ..N,- m,: +I_:.. %.m r{Lr,- h. w y:. c ;; % + 0.032 _.at : .u. m ,y
- 9.,y 2 -$-f 4 1_-
. 4_....--t-4 mm.. ___ g,. gm_.p=.=___ __ __. y =. g a. %. s__ t =_. =_. _ - 2..N r. = L..: _...m::.. r
- -- w.
+ t =.- .y.._._=._.... _ =. _ - m ro __x...
- g..
_._.s._ n. -_ ;_... _ t. _ _ ~ 2., _ w._. _ m._ma .7 K._A,. s.- _ _.__x. N.- -.w.- -+-- ._-._.-y ~ m ._ h ~ \\. \\. M. h..---%._. -$*_+-A -} g. .- p .;: - - -+.*._. - N...g-: W-. @._._ Nv,- %. q y j i .--+-t-~- g u m m e 1 _Q -MMYW WW 5WM+
- I&
~ k Y -b N i ~ 3_j i4." Q
- N o- c", y m
t Nk i7 ' r__-- E -w -e x
- m
.'c w.i, ;
, 2 z l2D =.;___; ,. UST i~[--I N _ _.}j .p, +i=i l-id-NU TDO! 'Wh Gid=EI di 'i= i ti=l = k-id b %=1- , ~ = = I 2 (g 'y - E. z \\ r - Na.. T. 33. ~!.=- '3 ; m .t m-55I = ~3 : = .b
- d. _^Nr5
~. % $.N. -N.. Ds k. t.k. : . i. _1. - i...T N. h.~ + = .:z._._..-:t y g. .p _._ y _3, p. y .__ -.,. 7-g%. m. _. _ _.. _. _ _ _ _ mm .=n=._m.= z:------ Vy Ns %__._% - ~ - w.-. m :w i % ~. - - -. w_. 3.-_ %p - i mr- .g ; -4w.- -I 5 'I [ y -- H-7 , i- + 2., -j_
- 3 a. r-Trr+arH
- h t= t=l - Ll t 51- ",4i:11 : 'WN -r d-j - =.: 4 .L Ritr-i- + 0 r:J.. x. y, .f-y -g_ _ _ y,,.Q... 3 [L_ ... i _g.. _} _- -u = -- b. 4 t.: -is..L..
- d
,..i.i-hi:E
- u. -
+ F. 0:+g . +,, _ = = - _. =. .=. qu _E. F_J.. ! }-4 Jr I-j4M la f r-t.i. t-..H. L. i f.: L t +1 _.. i. t. i [.!.0. i..j - t.:.1 2 -i l
- p. t. u..;!.
2 1 t .t. t . + _... -*_-* +. p }-;33~.rEh_. -+._ r..._. _. _l-I.. I+ ;T ~;-' . _, _...~ 1 -+ :-*-T-C HIN _3..* ?.T r*2 . _. _4_.... _. -._- _ L,. _1._,:._r + :- -: e._.._.- ~_. _ _._+.. ._._.w - _+,--._r.._ +. . _, _ _~.
- _ -- +
.r.-- n +_ O COS 0 50 OIS O h0 C h5 0 30 03S C40 04S 0'O S Fig. IB-Moment M,/(M /R.4) due to an enternallongitudinaQmoment(M on a circular cyhnder) Stress'on the longitudinal t 5 plane of symmetry) P00R OR M e -2!d-
e WRC 10/ t j!! i.b LL ...H,-H- - b !",-f t,-I-t-t- -.. L', - ' t - -. 7 - -- p } ;,.. - - -T"-j-Y m m -p r ir z;.r f. ]_ a-_ 2.- ri a M
!-#4 Mi# ! -*
- --== 4= r-#:k= 5 Fdm
-l= :: i : =h=E n iri- -r:I- ' db -t-2- 9,1x 44 Iag aq a .;.u a_L pq: W-- l :i- = = = .u Li-t' L -i Ti i I _. -.... ?tb
- f, '.,_.
1 ?- I_[ % I i . - -.;? n-- ---*-Q f-if-f%- f7-y +; 4 r -~E 'TT^ ~~ ~ ~ ~ ~ ~~ fyt t -{-- balio .E.i. i -'"i - - -._ i. 2.: - -.. i i s i! (' _.3_..-.- 8T, _-::{:= r 1 :- ::
- --_-=
- n
-/ mh. n:a - d. - ;_=: m: -/. -. ;c. r - F16at===:=: _rmr:: A f-,_ --f -- - p e__. %q 1:.:r;n..g; :2_. m .:x 2x 2r -- --.=r..t-g
- :n :- :-+- : :
- a 4- .,h 1 r. a iI I .M ~-+ -*1_ I. I-I $.37 1- 'I -If; ifI [ I' I I ] 9 (' ' N I I!-LI I I I I I T S 7* I ^ ~ r_~M' ' p1..p hj 1 iit.I - I di id..T Ns T.- .-5 +: ['I MAb i -- bhb =- ..; )-
- f. -
s-N YIN 7 Iid=N -e.-- 4 =1 u. H-
- E M
D N IV i~-I -ih EiO FI-~IF =M =r- ^ - 7+ 5 4M}g- -W d j A -@- - gr- -p y- -. r-p 2 7 F '1 A b 4 _}gIi s._.4-c . s f . f,. U. 4..- i e-i- + - p i s-3.2 =v s .s- .t s_.-. . 5 ' If-_ _ --:_ Ll/,-$ i__E ,[$
- *^
= r I }- . r-i: icf-d 1.-j_7 iiiMrir ! -M24-i: 1 M - f' f: -2; [ fdyXII: * ~M 4WiMei=" Wrts E-H=D MMEif EiMMM=E EM M 7 f-m f- ---
- g. a i-.
-. 7-g -
- 7.. -
c f*v i :/ i $m 7 .e i - v i . -r s 1 1 91 ( -'_j l' fI I 3# 4g i 1 d. A !I I~ i a,__ m f., 2 - ,e a i1 I p' il I i 1. W-i a u 0 -f>l i m y pi44 m si, ,_{.' T p / ! - f2. -i-c--/ +.;; !4 a . a-gp -4p g7 N =t ' y ? t/: :/ci = W- * -M - 14i-f p" -t 4
- Mr
- t--!+
- m g_ %y o il [ i-4. l[I l lI .-Mh t il I-[- ?/ u-- V._L r-, sa - F ' L 5p / i-L_ 5fff f. f .p -f r+ +H# 1 G J q;rp j-j /_3 /? i/- /- [th 9 _+ _ 7_j aMC:23- .-145-1- - f - _im + = i if/755 %rir/ i d i% 5:JuiEh dTi-O -biEME / +- h*EEE l N5VE-Ni-fhk
- =f
=="=5d - =*==E ' ~ ~ ~ = ~- ~~
- J-fg f_ __
f pjy. l,
- n
___. ~ _ ~., ; :, ;. _,+ n. z .._ ; _4 _. _;:r m..,,,. ..... i n _4. m. - -. y _ - _ e7 ff J. I J r M i 7 v I I i v i ct r r Ier-> ?m r, f f. f.-f.
- .t_ ~f,.ic
_i.4., y e - m _ r__ 1 ~- e_q 1 I ' l-f - M- +^r --- "= & W '+' V s_.- Ei f:/ : "/= M:+ ' -=n+ =*-% - - = - +~'=+T - = + = v F : tit 5M m - H-H / ~ -1
- u
'+ i + +- + l J f, f_ -/. -6 4 i a i, v.H. .. eq y f J f./ : /, . i 2 - q-1 2 6 e i . )_r 's - .p ~
- -! q.
u i . /- G y - E ri ; - _ ;E.- .j 9 fa t + ' l,l ,_ (_ hf-- ~ . =:. R
- W 5 '5:
- ' '~~ D. '?;-i!5Y ?t5& WN Wb Si$-]. 5 =a T-f-/ z ' _.= :-... _ 1 p1 1 ,-yl g_ _. IJ g i i 'I ? I I E f s__ _] I-c., E r : N
- I I
I I I je 4 -.., Q = - .I + ,~~. f - a-- 2 o =
- 30
" ^ 4;i: I 2 1,- w-. i. i -.i.. .7 l y, I = 4 > r r r j 1. j ~~ .-M 3=t#:M M n= R E '=
- 2. -- n.:
..: ::: r.: = r.:- - ~ - :...:.- : r = t:-:- 2u.:c -- -- :- t 8. g. -e. p .e-. . 4... e=4. - ... e.-e,, 0' 5 050 OIS OEO OitS 0 30 0 55 040 045 0 0 0'0 5 ' Fig. 4A-Mernbrane force N./(M,/R.,Y) due to an external circurnferenti l M Mr am on KW N W' M u Stucacs in Shells -2le-
e B WRC 10! t__ a-I 'I I i _.I 4_ 4Lil_L dl_L i _; t____ i J.
- 4. _,_
~ I I ! ^1 I I I 1 ! ' ' - 1 I I I f ! I
- II _il.{
1 4 P.__ . 4_,,_._ 4._i.,_ i r a - ; ; ; ' h'. I__ s-7 8- . __q.-. . _ y >.j. Ji;,I q_.. J_.j.j_f_i.}..i_ p } .4._ . 4_._, 1 ._t. >t . - 6'. 1.,- 4 ,e g s i .f .i .a.4 j .4 i i s - e==.__ t i i 1 e . t i i-t d=_! -*.- i : r .:.: 2.:_-
- .7
'~ .P
- ' O:!O
. I.l i.._...;
- n
.u. . : ne .o
- 4. s
.4.4._,4__._..s _,s_.. -.s.-s _,
- 4. #.
.. e _4_+_,e_-.. -,e eo -.+_t_p_+_-. -.e..e.4 I. -. -e.,e_.,e e e e .e a_ s. a. o..- 4 l. ._-n._ -.-.,4._.o-- -.+e_ .-.-e_._.,4. --+.m_+.. - i ; e7-. .-+ 1 .. - + _ _._.-.i .4__- 4 : .+-,_ _+ +. g_ f I I i i I ! I I I i I g I' 1 ' I I i ! I 3 8 y_ ~ i i e e + i g __ 2N- !2 pp -! t ? + .P7 t-rt-i-d-r3_-...i.{ m-T.{5:-I..
- ._-..H..
1: p' n .H.&_
- f ::ri r-H: ira.
i 2::- g_ _ _4_.. j .y } } i..; _. _L_ i 4_., l
- ? =
I .i e-e- .+ . i . H l3-r- i F.:] If -{-.Q {--h r j S- ' r_" .:.r 22 a I- .I. ! --- i- .: :n w.-- 2= pr-_ nn_ t... t 2 .;u_ _ c _: = _-
- .. :-__._ :_ n
.:;;2. :. -:.z-:: :_-
- -: : ::= ---:.:-_ :
-. = : - = : :===- n:--=-
- . t.: :__:_
a...
== m::- -. nt:. ---_---:-. n n_ i _+ : I t-e _. 1~ f I ! ! 1 l' I i ! -1 1 I I + t. - L. -1 i,i a g_. r1-7 -2 1 -i.i -}. t. i = I-t r r s. -.e s 4. , Wa
- L t-.j
_j;.-F .-t-p, + u ..I 3-4 i. .p
- i. :
2-3pT-p N n:Y PMW
- F i :L Fi M i = i-
-+H -. 6 9-F-i-
- -h t i ir
'h r A I f 4 i i , i I ,'r i- ! 6 t = _4 i W'..._, r 2 is .) + i r, . q- -s -t 9- -j i1 e ++r t -i, , 7 i. j. 1[ i'-5M :b +- 4. { -i. 1: i -19i i . ! 4 :i. d 3-h e 7 2 ::='nin:
==_3M r-2 Fre :..4
- -d. ' '
a u-:il:.i- ' _ ~ 9. 5 7:E3-.. _.' - *. 1:--i tr: . :-: rr.=.. __.:__.: _.:.. _a_ __.; ._T..__a_n.c --- ...r .. 2 u. : : :.. _. _._::: u _n,_ .... +.. -._ - ._.+-+e,+-.,e_-_. .. -, +.._.__+-.-.....,,. -+n'.... .e .,... -. _....e_._.+- 4. p pi_..._,_+.+-9.4 w..%.,. u_,._- ..I _ _+-.9.,_.y+. . _} ,4 .c. t_ . + _,,. _4_,. s w_9..,__ .4_ .. r +-% _+ _,_._._,_e e~ I I I ! !4 I ! I i i I I I i i y,, }- 4 u 2 5-i .1 3 i -i ._y mw _.; _ _ 2 m o .m A3., A..x m.mN cN. :~w--,w.;'@WT w,_ -,= --a.- m, i r tT-h 'hd,m"&, r '+ w* ~' 1 ---
- r--
.. =e,. m
- ~ 'a, 0 042 NM
. "v m_.. a. T w- %w^ N n%&wmn,0, ,._d.._-_,. a.- m t__@ ~ ~. .- {.- d.., ' % :.-___.^~ hgNy = * % _-!.-2.- ='""O* w ~~ r. 3.h .p ? ri:i: -+ j. _.xM %w@ 3, _ #=== =wMw %c __._.. %y _N. y+ p_.,g ~ '. _** -t _ e t 2 3 t: n
- s g 7 7; a+.
In W_ _, m_m_ e__ n.t c : -
- =___. =.
- .:: n mia-
_2r ~ _- 3g . -+m r gn_g__ _u ..;).. t W,,. - - J_. _- - r
- zoo
== . =... s _-.m o ,.__' [~ f l ' m, __4 2 1 1. 1 1 1 j g, __ s a t a a e 2 i Te g 1 a r m ~~Y ~ I E ._.{ ~I - ~ ~ i 4j._.?.Lp , ' I.j _{.p.Q 4.y _v. ... [_. r, z.- g_ -t 4 N r, 2 2i !_7 1._.
- 7 t
.L
- : "..^*
E__ .. - ~ ~. 4._.-._..! T. 7. _C_I.-*. : ~:~. .-**_--*1 (( $..d... 'h..._. _
- 5..d. _.d_d.-.*5r.-
'..U... B... ..,-_a- _ _ _ =. .1 _ _.......i... g 0 0 0$ oso oiS oro 0 25 030 035 040 045 0 50 Fig. 2A-Moment M./(MJR.J)[due to an extern I reumferential moment a r lar c n r -21f C,.
a WRC 107 a I f. ,, f_ h, t !(i!p-w__ _u.. y __.2-t l i -t' 1L - d. .L g _q .p- __.j.}. LL. -.y L1 a_.--._ a. _p, i,
- v..: ! -
. g c-j b .l,; !+ .j q [. y 2., . n.. 7.. :q..
- _ r. :n e
t - f. :j ju.,...p =3 .--._.~ r .... m . :1..;. :. _ .. T..:... +::.. _t. :. : ;... ; _......
- : a.: n.- :v::; :-:.
- t.r..:::. =_.
y _.- .. - ~ E-~ - -~. m.-+-.-.-. -- <
- .-+..-.
- ?--- --
- s. 3.0
_ ~. ~ - - ". -. + -. + . -4 +-- - -_-_4._--_ - - - - + - ~-.!.,_%; i y ; _, i._,_ ' ' i_ iggo,_, ' !_j_4 I I I I I i ! l ! I I I I 3 i !*~ f!f i s__. '!'I-r4 n,, !. r2.Weot-, ~ n. i, - y 23-- .; [. , ;r _j j- - ).- 3 -1. s_I _ft f ]lf ] ~~ ~~ E [-s MUfd -iq ~~ --+ j i ' 4 ~ 24 , ~ ~ '- .- : a e ^ g'. :..7. _-- '.4 2 ..N~ .:t.:y}. u_ .L'. Y' L i _ _ _
- c _
- .:-....::_.n... -. : :-
_ _._ ; +-.r
- .. :. :.-. 4
- . r. --:
-l.=.
- r L.n 1*8
~ " - '.. '~: : ;~.:-;
- h& ~ 'C^
'E
- ===-
- ==
- La== =
- =:-
. ~ ' ....,y _. ~. -, - - '-l-* R - ~ ' - * * *
- _. ia.
~; ---t- .-4_._- .+- __.,. +-. M ;-, L. - -,. __.- p -p - -y + t -. . +, _ y -w,.., -. -. -t -+ 1 A - .- u. .-.-...,_+,-e*-r._.. 4- -+- -* ' -L + - - - + - -+- r./ f f. .! / r '/;-i e r f~ ~ ~ ia ii i-i E ti t-4 s ~ T-'. i~ '. ~" r [' 6 . F[ ' id y j [ - O -4 " F~ -Y - 3 -- E l :.i-~i ~! [
- r y
. f. !
- i A*
.-4 Lptj..-4_ _.L1 T7> . T~~p.' ( l l 1 g_ = * .,1 ^*"' -/i / ni ? a = *, e e !i!. i !i! l i ir .i Nf ' Tf y/.f.f ; d2.j l' T - {: i .i t - pf -= t f.. 3-- f :.. @-' p. --*~~ :y-p k g
- t. 3W3
_ Q g <... i. -[_r F:;/__. 9. -i. i. .1:yi.f .22.H..:.l:E 1 sf 5 P f. .~;_c_. 3. i.c
- h. :. : I!
g -- ' - r r-rp_ f-.:.. / =-y ..::== = :~ = = =. 2 ~---*-*r ' -- ~~- .z 4- - - '.L--- p'.; : : =r . T : n --'
- rn*; -.~~-+r
- /. +._. r ~f.-. jt_ ,,r m _n... _ ~- r g_
- . p-f-._f... -p_. j i
- g.. -
I r i 4 i 44 _ 4._.. t j g i I t I iI I I i I I I 11_ e I' f I f y4 t 2 2 +i 6. . j-j. f3 _ 4-ti: + z a -. j. i-
- r..
i 5 f5 ' / ~ E=U Y V- 'I'~- 4 =- ~ ~ Y' = E ~- ~ -"-[f-i- h '. f, I j [ i b -t~ ' -~ i--[- ~ i i e-;- t I 4y t4 g-d F. -1 J i -- re. t.
- .r
_4 ,j.. 'I 3 + r .y- ' /- :, / ;-i.. r-i i H-d-i jf f.-'__-H 9-i -E 4 9.1 d 'c y
- 3s l'
_ - n n- -_.___:_. C r:.= ;. ' :=. nC-T : t-: :: r/ .n.-
- n.-
..-2 .;;--~ - I~~*~-~-~ --- - 2'I = ~ I~5=ZE 2-~IE ^
T'
~~~ ~ p-p.. ' n -- -. ~C " ~~ ~ _a [j. W..I^ I IEI I I e IL '..t 3 s,,,.. I I 't 4
- ' g g
- - x a, p__ l2 x a n G pl. ; =.
- E-.
Q i 1 I } -l =. = ..[ [ M L+.t -{
)--- ].Q I
-s ,_] f.'.. n-
- 4-.
a +
- 4 y
i_j-[_ .. l--
- 'i.
! -i c 4_ t--- .g-3 .. - : n.
- n. :.:.._-
.ci. h:.:. .=.... -._.- ~. ..-8 c-. x m:- m :~. : :::.
- - * =n c
.......s -,.a ..u -...,.. r.,.- -. .. _..~....-.... - + n .e-m -.-. 7,-.- n.7 s-..- -..,. +. y, 0 00S Oio CIS O'20 025 030 O '3S O'0 845 0 'S0 4 Fig. 4B-Membrane force N./(M /R.9)due to an enternallongitudinal mornent Mo on a circular cytmder t P00R D E A e- - -219-
URC 10/ _ j._l - . lI lI i I I I ' i'Q IL I Jd-j i P ,. +- -'I-',"---- -b b f E- *- - { -- "i--- "W L' .. T-4 b y r s-Y I' e -- . _j j ..]. _1. p g q _ -- l l a- - q
- 9. p 7 m. q..h~_ 7-q,-.H_
p _] } ! q. 9.,
- j. l
- -j
' _j }l s- _ q-a_ a___ -g _a_. -t. _t.d 4._ i. - L. d.: ,, I I I~ J-t- -t:: -l4-8
- 3.
-..2. 2.-- .g s . *'*~ .:1_
- _* * :.:.
21._n
- -._ u.
- :._..
e.- _. L_.:. 2__1._:_ __:.__ _+- t_ b. M _4_.,4._ - -.4. 4.-. -t--+-++-+- -e-.- -+. 4 -....v..--.- ..m-_._ _... - - + _.. +. . _ ~. - - - _ _-._ _ + - +. _, -. _ - 1 l I I I I I T I i ! T I g f I '~ i i i i t l l i i i- -e H. .y y 4 ..: y 2 i - = - 4 = -ll: ~- M -izii 14-U:" iH I-E
- ==I*
F- + - :b ~.g ll l l 4.Ly 4 7-j p_j "_ - N 2~ .~ I i . 4 i i. I?tb r-- + -'~.r r y 3 :r--- - :r- -i i r+-- 7 - + -i - r 41 722 4ksi_ W r- - d-E. _r : .,.2
- 2==
:n.
- 3 _2_.,_;; Uhk - ! i-H: b -*- - ' "i - h 4-i -- i ti -i
- gJg-.
g2 mm E== 1-
- =_
- -:_ nur 2
- ::- n
- =-
+_ 3__ em - -- h-_ a 1 ^ j ~, e 2 i a p h Q-T b c 'm im.O -,i _._2 ir ~w - - A i: m:i-N r_ .Li -r -i 4 g:a Q ~ a - u = i-J 9=i _.T 2 4g, =#MVi t N;W,Vg h-i_4:1-VM < y,. s -
= E -T- = l-b = - M i
=- T N-1 T 4 -e h %- \\j -La QI 3 ?' cK %L i O %. ri w- : c. - 3 EM-is-H. -iT-l iki:M; d= -iEC ;-i= ::--f w t..:th-( yli : :- : N _% ' 3 prairp riS + i: h: n --- - -- --:=-_n:M:x;;u:-. 3 q:_. % r:.._..u-s' x._,- 1 . E ~ A FA @ i-. _. i xn ~ - - - - - - - - a _- - - - - -_u,_;-.1 d N:=:. =v._ q _.- g %]-*--
- ;;-l_s -------S y%q - --- -
"c.c.J=. gym t -+-- h.__4 - s-3 -r_+ m.. 1C% ' <d c hu 't :gir i% I I A A _s -N -N. s-w >w w '[ \\ A h r."."T E 3 7 @gNi 70 l^i ='D' % 85 ~ g g ., e g.
. i =r-p y M_. 4- .,s p ; m; - i4
- j 3 3
- =1 3:2.i H: =- tt- ----
3 -di .p+my -- N -Ms h -N_- %y. + - iN- -- f - - ca
- =-=
u_:zu i-..- %sp - L Y %-t-i-N-- - !-~ _: - - - - 8 7y -- [!- gN._'hi- +i l.[ h $j g -- qTg
t
_i -4 i .. t w_.3 . p is 'I' j, f: : ;p .N -j in-, ._4_ ; - %j' Q- . j.4 .[d:- i 4. [-i. .e , q f_, 3 r --g Q.3 k fir Q' '(j
- j
- -
ri l l $si-Hii"si N -li- -h -l-t =.in ? m-iS:@- r=_M;_m _=__-D D y* rt si N,4 :+b T _ isr= :- - ,_=y, t -*t ^ - ~ %}g= - 2 qr_. L. "=:-.g. _ L .. _.n _T = .-__._.._.. _. s._. y.^ ._.s...___ ~'._%'y s s. l' i .] ,. I. I,.L .I.i _ r 3 ii e 9 n !i g __ l i
- ' - i I'%
17:- - F 1-I-. 4 r. i -L i - "~~ _._. ].}_ {.Lj 4 I p._ y '--r p .j4; '"~~ ~ . ; -T.' =j a - _-m = _ p n ,. =,, e. L a _+-. . - _ ~ _.._ _. _m_,_.-~.__., .... +._;_._ . +.. .~ I ' -*,--m ...t.+-'- - -+--- " - t-* r 0 0 OS 010 0 15 020 025 0 30 035 040 0 45 o 50 Fig. 28-Moment M,/(M./R.8) due to an externallongitudinal moment M, on a circular cylinder (Stress on longitudinal i " plane of symmetry) i ,4frrwn in.Nhrifs -21h-
Computztlon Shut for Local Stressas in cylindrical Shstis .P -qM L M V C
- 1. A,.a.
4 L. 4.* 3. c..... e.... v...
- .hg "k"
e.4..t t.. s. P. _ O is. .m L/2 y 0d '7 h' f~ v' e.4F264 16. T ,,,',3,_'m. i-C.... m.... m L.... m... .t yM3ZD... i6. s s - O. /6 Dts \\, e O T.........
- v. JUd~. is, g
AT TACHWENT Au g, sm. L. 4 s sa L. 4 vL :/4t= U/ib. - ~ -[ 3 e
- 2. c
.,..6....i...... _L y0
- s..... c e. e...... s....
T -- g yi e v............ ,. a.f r 6
- .-*,i.-d.==
1-Rm L Cu C L
- not E. E -... i s 4.....s.....
V....!
- 4...,
R.g W.3... .....d.....oh..ga....e=*. g F *.* R 4....e. C... ..b..l 6 1, 4 E $ $ t 5 -. 8 te.d......... 6...m................ F. S. 6.e o w.....d ea... e e..H. a, at 3, og c, ct o,, j pg 3C or ud_ ,, / "0 ). P_ l s m., a.1 s ] {e r .64 [ \\,M 4, {L 4. g F T. i +/ K w, a,,,g' "* ( ?, g'I'$,w .s .O \\* m;; I.2150l A]5C / m s..s g p}g \\,... a;< / ..n ft s <1l $O k's Y $% "?S f ~1/$0 ~~})$1 .a p get u,y : n 6/. ' s,; ' ' X, .... v,Q "..... (s...;< sn '#3(oSoo ) $ ['G$;6 l K TX WX t')W ~O) lx; / ...., = n s o -9w -s, nma,;g.vi%:;,w " na 0 es ~, >, L ~- ...s y .c...,, M_MWM
- :.:..a,.% "L : )
..',7,. =,90 0 >^0 +11 0 +71s0 -?r:0 ~ au.r. ..n,i .se..... n4 -t1.1x + 3 Loo 11.126a -3(.00 -3 9:,tt:yl D r 1173 -MG Jc or I _ a._ . / _ a..i.P ,.s i i ie., m ., x ..l...s 3 '-(.., :,,,)..~.;, = 3 7go MM&% 37sz uys: +37.a +3 7.x . 7..a & "( L )..,. =>3 os s$$QM r'bi[BBQ is a% s+a,s 73o:s- =a
- t
- 1 a +/403 5 4. % ml4-3.n ?h, *' w~ wz mu..>3 j'*9 \\ s..u o) *..s(< s
- f f.oD ~/Qs ~l600 1/(,.30 b
';;;.:..e4.9 ~ L ::,,) .'?,. = ygoo yu +ws: +yqu -yy.n k;5Qh,','W'Qik -....-...i...- .ax..... a. e -(C00 +2$O0 t(oC00 S00 */(.77$*9215 t,e.,l5' c ',, w [ w.s m. t .2 4 2...;,1 7 m., .. 4 v, .. df,a. ' 8;? Vt's T& 977-
- 6D8 +6frID '$230 ~b300 $h
- 4. v.
- 1. <$
e 4Ge _ ' '50 " ' ' - (%,['<,.;g /,~'4'& pia ' S4%-..5!$,i C1ttn
- l-s.~... e g.0 99% T? x}
vL y /00 y */cm . * * = *. v L S/cs n y-S S au a1, ..n, s.- en r ......g a +4530 tLk00 -lit.3 - (,V00 - S*/ob -S/co +S/00 + S*/ 00 e COMBI! ICD STRESS INTR;SITY - S 3 'i' - G $.o 4c g /< KSI o
- 3 o
.o
- 1) When T / 0, S '= largewt abr.olute macnitude of either
+0 i /(O - 0.)2 + 412]or/(O - 04)2 + 4T S=1/2[O 2 4 x x p x
- 2) When T = 0, S = largest absolute magnitude of either S=0x, 04 or (O - 04 x
6
Sumary At the highest stress location the worst case stress is 30.0 KSI. for ASTM 515 Grade 55 Yield is 30 KSI Therefore the factor of safety is 1.0 for ASTM 516 Grade 70 Yield is 38 KSI Therefore the factor of safety is 1.3 - 21j -
d C. AtlALYSIS OF CASK TIEDOWft ADAPTER The Hil-100 Series I cask tiedown adapter is analyzed for a 10, 5, and 29 combined loading condition. 9 9 Mounting Plate Adapter lug \\A f N 1.00 + 3.12 dia. yv M i b=9.94 P 3.75 P " " (Ref.) t 1.75" 1.44 f wP M N ji The adapter is constructed of either ASTM A-203 Grade E alloy steel er ASTit A-515 Grade 70.Since the ASTM A-203 Grade E has a lower yield strength it will be used in the following analysis. The ASTtt A-203 Grade E steel has a minimum yield strength of 40,000 psi and a ultimate strength of 70,000 to 90,000 psi. The loading on the adapter will be 192,763 lbs. 1) Bearing stress in pin hole: f = h 7633,44 = 42,904 #/in 2 x Safety Fa ctors (yield) k0 = 0.93 gr (ultimate) 70,000 4'2T904 = 1.63 ~ e e. 2) Tearing stress (in Plane M-M) f= '1'2T(~ m T
- 47'469 #/i"'
(5 Safety Factor (yield) l_0 - = 0.84 (ultimate) = 1,47 4
- Safety factors less than one based on minimum yield strength are considered acceptable since:
(1) energy absorption by the cable and trailer has not been included; (2) yielding of the adapter would not impair the safety of the package; (3) loads of tnis magnitude would not be encountered in. actual operations since they would destroy the trailer to which the tiedowns are attached. i
- 3) - Weld Strength Analysis Stresses in-the adapter lug to the mounting plate are a result of
- the direct shear load. The direct shear stress.c 192,763 = s 1 x 0.707 x 25.82 10,559 #/in' o = s i z -The allowable shear stress is 15,600 #/in Safety Factor = hh = 1.48 L e - 4 g e -*=w y--, _y., p g ,-w s --wy-s-m.- -%'m.---p ---e w --w y&-- --,we++m-r% .y,--wi---- yp-- r%
I e . o i F e 3. OilE FOOT FREE DROP t.'.ALYSIS The cart body must absorb the total kinetic energy. Th kinetic energy to be absort;d by the cask body is: Ek - mgh = 50,000 x 12 = 600,000 in-lb. i i i The volume of steel required to absorb this energy is: E Y = s Sy Material is ASTM A5:5., Grade 55 (Sy = 30,000 psi) 4 600,000 V * ' 0,000 = 20 in.3 s Corner Imoact This config' ration of the H'i-100 cask corner is: u l I e-3 "-> l 7/8' + 4--* e - 3/8" / b \\7. H U p 4-2" \\ t IL il R=41" i At an impact angle of 450 the steel corner will be defortred in the shape of an ungula and the volume of the deformation is determined by the following equation: s = R3(sins - '5I" - 0 cos 0) Y - 3 f(e)=h=f,h,k= 0.000290 0 = 0.2967 radians = 17 y y , - =,,,,. ,ms.,_ ,,,,-__,m-
',,.o e 1 l R / u ,a 1 b k ) \\ k n b .e--- b-. .e-- b = R (1-cose) b = 41 (1-cos 170) = 1.79 in .i b c = y = 1.27" 1 .I The effect on the cask body due to the corner impact event is show? on the above sketch. Neither the inner ner outer shells are'affected 4 by the corner impact. // / I / // / / / /,l/> L / y l////// //////// v b = . 2BS80 - - -}}