Solutions to Design of Weldments - Blodgett
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,-;_, - . 0 . 0 W.1 I I f l= N II _.J \ ... "\ \ .. . 1:.. -oj lo- T d=Zo" l ' . '-• .. f, The serviceability of a product or structure utilizing this type of Information Is and. must be the sole responsibility of the builder/user. Many variables beyond the control of The James F. Lincoln Arc Welding Foundation or The Lincoln Electric Company affect the results obtained In applying this type of Information. These variables Include, but are not limited to welding procedure, plate chemistry and temperature, weldinent design, fabrication methods and service requirements. y I
Transcript of Solutions to Design of Weldments - Blodgett
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The serviceability of a product or structure utilizing this type of Information Is and. must be the sole responsibility of the builder/user. Many variables beyond the control of The James F. Lincoln Arc Welding Foundation or The Lincoln Electric Company affect the results obtained In applying this type of Information. These variables Include, but are not limited to welding procedure, plate chemistry and temperature, weldinent design, fabrication methods and service requirements.
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APPLYING THE SOLUTION GUIDE The Lincoln Electric Csmpany ,seminars offer an excel
lent opportunity for engineers to discuss problems that are common to many different areas of design.
Orner W. Blodgett has compiled solutions to these problems and others that have been generated for companies in an attempt to share the ideas that have been gained.
In order to limit this publication to a reasonable number of pages, only a portion of each design is shown and each full sheet has been reduced 75% to allow up to four problems per page.
Inclusion of a design problem does not necessarily mean approval of the design, in some cases the author was asked
to estimate the capacity of thfl ·'iJJ!Idment based upon the size of existing welds. In other cases, a failure was involved and the weldment was analyzed to determine the cause and a correction was suggested. This booklet is not meant to be critical of any design.
The table of contents lists problems by subject matter and the end of each problem is noted by a bold rule line. Readers desiring related information should refer to Design of Weldments published by The James F. Lincoln Arc Welding Foundation.
Richard S. Sabo Manager of Educational Services
TABLE OF CONTENTS
WELD ALLOWABLES- PROPERTIES OF WELD
Permissible Stress on Welds . . . . . . . . . . . . . . . . . . . 1 Types of Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Welds Treated as a Line . . . . . . . . . . . . . . . . . . . . . . 3 AISC Fatigue Allowables . . . . . . . . . . . . . . . . . . . . . 4
CIRCULAR WELDS
Moment of Inertia & Polar Moment of Inertia of Welds 5 Weld on Trunnion .............. , . . . . . . . . . . 6A Circular Welds in Bending . . . . . . . . . . . . . . . . . . . . 6C Coupler in Steel Mill Roll . . . . . . . . . . . . . . . . . . . . . 7 Circumferential Welds in Bending & Torsion . . . . . . . . BD Butt Weld of Auger . . . . . . . . . . . . . . . . . . . . . . . . . 9 Circumferential Welds in Torsion ................ 10 Circumferential Welds in Tension .......•....... 11 B
WELD SIZE EXAMPLES
Fillet Welds - Parallel Loading ................. 11 C Fillet Welds -Transverse Loading ............... 11 D Base of Signal Tower· ........................ 12A Circular and Elliptical Welds in Tension ........... 12B Fillet Welds on Gusset Plate . . . . . . . ............ 12C Circular and Elliptical Welds in Bending ........... 12D 750 Ton Press Frame ....................... 13A Lugs on Fork of Lift Truck ................... 13C 3 Dimensiona~ Welds on Storage Rack ............ 130 Bracket$ on 400 Kip; Extrusion Press ............. 14A Bracket on D~iU Rig- 200 Kip Load ............. 14D Transferring a Moment ...................... 15C. Welding Attachment to Hold-Down Platten 17A
(temperature difference) .................. . Sign on Tension Flange of Girder (stress difference) .... 17D Bracket on a 3 High Steel Mill Roll (stress difference) ... 18A Critical Fillet Weld Size and Shape ............... 18C Welds on a 1000 Ton Press .......•......•....• 19A Welds on a Crane Base ....................... 19D Link Support Bracket of Injection Molding Press ..... 20 Links on Fork Lift Truck •....•..•............ 21 Attachment for Ripper Tooth on Bulldozers ........ 23 Welds on Rail for Rollers .........•...•..•.... 24D Stresses in Shell of Pulley ..•......•........... 25 Welding'bf Masonry Plate on Spandrel Beam ........ 30D Stresses in Double Discs of Roll ................ 31 Welded Pulley Block ........................ 33D Socket and Shank of Coal Auger ......•......... 35 Welds in 7,145 Kip Hold Down Box Ring ......... ; 38 Welds in Support Box Ring of Basic Oxygen Furnace .. 41 Flange Welds of Vibrator ..................•.. 43D Welded Rock Crusher ....•.................. 45
LONGITUDINAL SHEAR
Crane Runway Girder ............. : ......... 49A Fabricated Columns with Wind Moments ........... 49D Plug Welded Cantilever Beam .................. 50A Platten for Press . . . . . . . . . . . . . . . . . . . . . ...... 50B Built-Up Ends of Continuous Beam .............. 50C Outrigger Beam of Mobile Crane ................ 50D Longitudinal Shear - 6 Sided Section ............ 51 Longitudinal Shear'- 8 Sided Section ............ 52A Longitudinal Shear -Circular Section ............ 52C
CURVED MEMBERS
Basic Curved Beam Formu Ia . . ................. 53 Curved Beam Problem ....................... 54A Welded 2 Ton Press ......................... 55D Transfer of Moment Into Press ................. 56C Weld Stress in Curved Portion of Lamp Frame ....... 58
TORSION
Torsional Members ......................... 59A Torsional Resistance- Closed Tubular Sections ...... 59B Torsional Resistance- Diagonal Bracing ........... 59C Frames Under Torsion ....................... 59D Member Failing in Torsion .................... 60
TUBULAR MEMBERS
Welds for Tubular Structures ....•............. 61 Tubular Structures Fatigue Allowable ............ 63 Dihedral Angle Charts ....................... 64 Example of Tubular Connection ................ 65
SHOCK LOADING
Shock Loading- Basic Information .............. 67 Shock Loading- Basic Formulas ............... 68 Girder to Absorb Energy •.•.................. 69A Welds on Car Bumper - 5 MPH Shock Load ........ 69B Ore Striking Bumper Plate .................... 69C Weld on Trailer Hitch- Shock Load ............. 72 Trailer Hitch - Road Conditions ................ 74 Axle Mounting Bracket ...................... 75D Welded Eccentric for Vibrator ................. 76
DISTORTION
Distortion of Spandrel Girder .................. 77 A Diametrical Shrinkage of Butt Weld on Pipe ........ 77B Angular Distortion- Single Vee Groove Butt Weld .... 77C Angular Distortion -Single Bevel Groove Butt Weld ... 77D Distortion of 90 Foot Long Bars ................ 78A Longitudinal Shrinkage of Girder ............... 78C
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Stress Allowables for Weld ·Metal Type of Weld Stress Permissible Stress Required Strength Level I 1 )(2)
COMPLETE PENETRATION ~ROOVE WELDS
Tension normal to the effective throat. Same as base metal. Matching weld metal must be used. See Table below.
Compression normal to the effective throat. Same as base metal. Weld metal with a strength level equal to or one classification (1 0 ksilless than matching weld metal may be used.
Tension or compression parallel to the axis Same as base metal. of the weld. Weld metal with a strength level equal
Shear on the effective throat. .30 x Nominal. Tensile strength of weld metal to or less than matching weld metal may
(ksi) except stress on base metal shall not be used.
exceed .40 x yield stress of base metal.
PARTIAL PENETRATION GROOVE WELDS
Compression normal to' effective throat. Designed not to bear - .50 x Nominal Tensile strength of weld metal lksi) except stress on base metal shall not exceed .60 x yield stress of base metal.
Designed to bear. Same as base metal.
Tension or compression parallel to axis of Same as base metal. Weld metal with a strength level equal to the weld. 131 or less than matching weld metal may be
Shear parallel to axis of weld. . 30 x Nominal Tensile strength of weld metal used .
lksil except stress on base metal shall not exceed .40 x yield stress of base metal.
Tension normal to effective throat. (41 .30 x Nominal Tensile strength of weld metal lksil except stress on base metal shall not exceed .60 x yield stress of base metal.
FILLET WELDS 13)
·stress on effective th.roat, regarle&s of .30 x Nominal Tensile strength of weld metal direction of application of load. lksil except stress on base metal shall not Weld metal with a strength level equal
exceed .40 x yield stress of base metal. to or less than matching weld metal may
Tension or compression parallel to axis Same as base metal. be used.
of weld.·
PLUG AND SLOT WELDS
Shear parallel to faying surfaces. .30 x Nominal Tensile strength of weld metal Weld metal with a strength level equal lksil except stress on base metal shall not to or less than matching weld metal may exceed .40 x yield stress of base metal. be used.
(1) For matching weld metal, see AISC Table 1.17.2 or AWS Table4.1.1 or table below. (2) Weld metal, one strength level ( 10 KS I) stronger than matching weld metal may be used when using alloy weld metal on A242 or A588 steel
to match corrosion resistance or coloring characteristics (Note 3 of Table 4.1.4 or AWS 01.1 ). (3) Fillet welds and partial penetration groove welds joining the component elements of built up members (ex. flange to web welds) may be
designed without regard to the axial tensile or compressive stress applied to them. (4) Cannot be used in tension normal to their axis under fatigue loading lAWS 2.5). AWS Bridge prohibits their use on any butt joint (9.12.1.1 ),
or any splice in a tension or compression member (9. 17), or splice in beams or girders (9.21 ), however, are allowed on corner joints parallel to axial force of components of built up members ( 9.12. 1.2 ( 21. Cannot be used in girder splices (AISC 1.1 0.8).
MATCHING WELD METAL AND BASE METAL Weld Metal BOor 70 70 80 100 110
A36; A53, Gr. B; A106, Gr. B; A131, A131, Gr. AH32, OH32, EH32, AH36, A572, Gr. 60, A614 [over A514 [2·1/2 Gr.A,B,C,CS,O,E;A139,Gr.B; DH36, EH36; A242; A441; A516, Gr. 65; A537, 2·1/2 in. (63 in. (63 mml A381, Gr. Y35; A600, Gr. A, B; A601; 65; 70; A537, Class 17; A572, Gr. 42, Class 2; A63, mmi];A709, and under];
Type of A516, Gr. 55, 60; A524, Gr. I, II; 45, 60, 55; A588 (4 in. and under!; Gr. E Gr. 100, 100W A517; A709, Steel A529; A570, Gr. D, E; A573, Gr. 66; A595, Gr. A, B, C; A606; A607, Gr. [2-1/2 to 4 in. Gr. 100, 100W
A709, Gr. 36; API 5L, Gr. B; API 5LX, 45, 60, 55; A618; A633, Gr. A, B. C, (63 to 102 [2·1/2 in. (63 Gr. 42; ABS, Gr. A. B. D, CS, OS, E D (2·1/2 in. and under); A709, Gr. 60, mmll mml and
60W; API 2H; ABS Gr. AH32, DH32, under] EH32, AH36, DH36, EH36.
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J'n.LU IIBUI LOliDI!D IR .111ft' DDIIC'rlOJ!
Shall not overatzeae the baae metal.
PAR'l'IAL PENB'lRATIOII G!!90VB !!1!LDS
SREAII (pulled parallel)
Allowable ahear on weld • • 30 BXX Shall not overatreaa baae metal in shear... • .fo 0y
TBIISIOII (pulled aomal)
Allowable cenaioa om weld • • 30 BXX Sball DOi: overatreaa base metal 1D tension. • • &0 0y
L.ower atrength weld metal may be uaed at ita lower allowal»le.
SHEAR PARALLEL TO AXIS OP !!§I,D
1.~1: ~M" '• p~n•.tnJ'tlotJ
~-·· ..... d
Allowable shear ~ veld • .30 2XX on Uroat. Lower atrenvth weld metal 11ay be u.secl at lta lower allowUle ..
Shall not overat.reaa the base metal in ehear.
TBHSIOR OR COMPRBSS!O! PAJW.L!L fO AXIS OP tmLQ
p>rtio.l
f:!~=~ &llawllble of ... ld ia the .... u l>aee •ul. Lowv eU""9t9> weld -1 •Y 1>a uBIId.
- 2.
i!.ll-le- weld 1.8 the .... ae baoe metAl.
llatcbi"'J -ld .... tal ..... t bl lleed.
AllowUle ahear 011 weld • .30 EXX om tbroat. Lover atre119t:h weld: metal may be used at ita lower allowable.
Sball DOt overat.reaa the base metal in abear.
'l'RIJSS JOINT - COMPLE'l'E PBIIBTRATIOII GROOVB NELliS
71\e teDaion COOipOAeftt would require matahl D9 ""lei 118tal.
AllowUle on ftlcJ is the aame aa baae -tal.
Ma'tahl119 weld metal 'IIU&t be ueed ..
C9!!PI!BSSIOII IIOlUUIL TO AX.IS OP IIELD llot reooaended uleaa absolutely 118CBeaary blcauee of exce•'l.ive u01111t of welcl metAl.
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A Propertt~ ot v ldad conneotlaa tre•ttnc \he veld as a ltne • -
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c• .&;:{ 2.
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L' b+d r.·1f(~) s..•-i(n•") '>.off:".;t-, r:.•Jc,•.c, r,.~(~i ~·-H ... ••) -s,,.f(t;jf) c,•/c:•c~ ~ ~ &.. !!( .... \ JL "(til!) J= + "f tll't"d. Cr· j ~ .. ,.I.~ 't'alttd) t:.~,..a- 'i " ..
:r~· ft(,btc!) s,· t(~oi>+dl ;r-~~)~\('"••i) - . 2ibtd I
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L• b•zJ s.~,·"T Tid
r.L r.,• fz(b+<>d) Sy• -l-!bt,d) 3. \t~)+,lo+lod) "'· btZd c• /N.'+O.J'
L· ~'>•o) r,• /t•>td) ~·t(~b+.l) .. J=¥ Xy• J/(bt !.I) Ytlbt"34)
c-~ z.
L· bud r,•tl~) ~ .... ~(zb•d) \,·f!~) ' \. ' d( r,· £ vf c;.·.f.a c,· ~)
j•~i'WJr)t~ C •f<,'+l"t.JL
£...-2(·,..;•) :r,.. t lt!;lt) '>.,• tt~b•d) ~-.·+ 1~) I 1 ;: f. ~,. t Gr* -.(:~ .. ) Co•t{WJ-) J• f-lwt-)+ t c:. Jc.,• + l"'>>"
L-: :.t 1 ~.~~o; T,•-ll 3b +d) ~.· 4£!b-td)
r,:f -;,· j ib'<d' J"=f{!.btd)•~ C.=-z.--
':>·11" r'
L..: 1r r cT• r(t-*") Ce• ;:
I,' rYlf- ~) Iyr _r;1L
L• Z(1tr -t-d)
-·-1·/1~ 1<-D~ ~dt .,jew
r • 11"r • { ) ) ..>y--;r /r~
.r.·-n-/(a'+Zit) .r. "-n:Q.(c!'H o') 7.: 2 Jd'+fJE
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prggnrt;y gt H''ded qonpogym - trutfn• - weld .. a line
1 1.• 2r(}
·-~--r· •zt~ ,.,_ i. _ .ltr_ ~ _ •· :z;,= r'(tH ~} \ 'r
Oif-b-11~·~
*- Q!. I.. • >.S b' J• ZI
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e _ r tin9 ··-r
L• r(1tn)
L• t'(1f+2-2 I')
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detallsattaahedby lilletorfiRICM!welds a<2" c 7'<a<4"or12b Q) a> 4" or 12b E)
~ ~~~~ ~R@
TR klbe
fillet welded
M (/
© ~ friction on gross section
-'"!!on net """'""' M
M
other than M HSbofts
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M
TR@)
w set)
to connectton of any rolled sectKlM
Curved arrow indicates region of application of fatigue allowables
-- Straight arrows indicate applied forces Grind in the direction of stressing only (when slope is mentioned (ex. 1 in 2-1/21 this is always the maximum value. Less slope is permissable.
AISC allowable fatigue stress (asr and 75rl (kips) -also used by AWS Structural Welding Code (Sect. 8- Building) •
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lilii1J~jl A 60 36 24 24
NJ~ B 46 27.5 18 16
~~. c 32 19 13 Stnm
0 27 16 10 7 r E 21 12.6 8 5
F 16 12 9 8 Shear "sue..
•at toe of stiffener welds on girder webs or flangea.
but shall not exceed steady allowables
allowable fatigue stress
"max or Tma• = maximum allowable fatigue stress
~ .. y
O.r or T., = allowable range of stress, from table
Omin Mmin Fmin Tmin Vmin K =--=--·--·--·--"max Mmax F,.... '~"max Vma•
S = shear T = tension R = reversal M = stress in metal W " stress in weld 1 = allowable steady shear stress
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nut aoment of inertia of a croas aectlon 1s referenced to an axis vhlch ~
~or the aeatton. It ie aa though the plana or tbls sect.lcm t.eDda t.o revol•e about
·tht.a ax,s, aee figure (a)., The basic moment ot tnert18 la a un.lt area mult.lplle4 b7
the square or tho dlet.anee or this al"'!a 1.o the reterer:ace ala, see tlgure (d).
Fisurea (a) and (d) reproeaent t.he moment ot i.nert.la about the (x-x) ax1a, and ripee
(b) aad (e) represent the moment Of ioertl.e about t.be (7-y) axle.
'l'he polar moJIIEillt of tnertla ot a erase sect.lco ls referenced to an axil normal to the
~ oJ.' the oroos secUcm.. It 11 as tbou.lh the plana ot thLs s~~"Ctloa teads to rotate
about this axis, see figure (c). The baaic polar J¥1msnt ot inertia is a unit area
~t~~lt.lpll.ed ~ the square of tbe rolar dlet.Gnce· t.o this area (~), see tltJ"U"8 (t).
Since the SQU.Ve or tbis polar distance la equal to the SWII Of the &q\Y:res or the
d1atances to t.he (x•x) and (;y-7) axea 1 lt. can be shown th11t thenpoler moment ot lnertla
is equal t.o the sum or the moments or tnertla taken about cny t.vo axes at 90° to ••ch
other. S!nce axea (x-x) and Cr•r) •re 90° to etch oth•1 the 8WII or the moment ol
inert.le aboat t.he (x-x) axla and the moaen.t ot lnertla about the (r-r) axlllll 1s equal
to the polar moRent or inertia about axis (s-z)1 normal 1.o both axes (x-.a:) and ()'•7).
or r,... I,. .. r 7
y
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z : m \ I • J
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1r /; -!\ : dp •
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\:· t'L ___....,...---; ' X
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--- \ .- \-
y
\ 'z
...i----1 K l 1
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CD ly
~·Ad;• I.,t-I1
It la possible t.o bave a condttlOQ la vbit:Jb the axU ot revGlutlon neit.her Uu11 tn tha
plane or the section (1110ment or lDertl.a) nor 18 normal to the plrme ot the aect ion (polar
mollldlt or lnertla),
In tbe tollow1ag welcled aGMectt.on., oCOISlatlng or Wo el.ra.WI!'erentl.el velds 3o1n1n1 ~
trunnion ot a abaft t.o tvo end dlsce• tbe a.ls (z-z) F&&slns thi'OUSb the center ot snvlt-7
or tbe welda 1s t.ba az1a abou:t vhich the two velds tend to rot.at.e because ot t.be beodlns
act.lon or the t.runnlcD (vartloal bearlns 1"88ctlan X the moment an.). Notice that the
retarence axis {z-z) lies parallel to tbe plane of eaah veld. P'o-.ap, but does not lle
vlthln eltber plane.
U ve cCilSider tbe t.vo clrcumterentl•l-velds (a) ~ (b) u conoentr~Wd at t.helt aent.era
or aravity, th8D lt ls seen tb3t the ret'ereaoa uls (z-•) Ls ncmu:l to the plane 01' these
'"4&ld groups, therefore ve could. call tbls properf.J' ot the :;~ect10JI1 polar IROIIMJft~ or 1nert1a •
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z
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4 ]'.: {de) e•
y
··-0':· /a .. ts) 1 ( .,.__~ Y,
X
e"= Y'+~t a/$t> y: r Sin .I. So e'&= y ..... sin\Lib1
¥
IVe .,,;,11 9ef the same resuttif>vr ~o~.se the·pqr«lle/ aJttr theorem. First f,h,J ~ a66ut tUI'S{z,-z,) t:hen -shift para lie I t!J d1ste1ncP or(%.) -ilJ eo(i~ (2-z),
J" •• r .. + A("A/ Iz,= (2wetcls Y1r "r1)
A~ k weldi)(z'llr)
J. • C! 1t r "t 'l'lrr( ~)' • arrr\'!T"rb"-
1 Jz = 'IT"r~-~r: .. ~
tt •ee DW'S P•'!e z.2-8 Dw f'A'Ie z:s-1"
b...t- lle<f lee t (t)
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;r.:!.~~nry7r-~~~~7T.ni~n7~~
~T~~~~~~~~~~
I-- a" /o•··--=~-1~• =~~:=::~=== raoment arm • IS •
P"'perty of l,<ldd, - ~... bc"d1nq 4b.. .. t ~~nter oF "fi'<IUity of we/Js
J..= 'IT'r-(zr'+b"") • '!r-2"·1Z(2j.T-('''"J• z?'·~in"
horiuntll./ compen .. nt p~ b<rndtnq (. M c: ... Qo.Dt>olbt• lll•Y2.th) .. DLI()'> d,,. rh T 2.?(.,5' 1hl · -,-, , • 7111
uertt~l component ef beadmq
r • !1ft. jlooorJO 1/n•I'S•nXJtn) /{) ~ rv :r. 2'1'-S" ,;i~ " /,'I •5 ,;,
vert iea.l 'hea.r
'"h.:t•4~<e "u .. -l.re for f.'llet welrl1
A
a~ •-t•ID~cyoM Wid r<lflllt! K<=-1 ,...•nol IS 1'= 'IS'DOp.,· on thrMt
- bto),!l,C"·""' . ~
c
---· -·~-----------------·--~·-·
low •-• 'Ills tnlllnlao tllmo "' 200 IPII ond raqlllrea 100 81' to drlve 1•,
T " c.'!lpoo HP .. 43.oooXtco). '3/ fi'OD · !6 R Pfo\ Zoo ' ' 1
" $
'ltd • 'It 'I ~ pro pert'( of. weld J~ = T • T ~ liO. 27 in..,
. ~or one we(c{ or
J.· z.(so.2'1)~ IIJO,fi'itl'(t~Jo"J•/ds) u.nit ~ore e "" weld
f • TC. /1>t,S'OO ,;, ll>s){2 in)_ 6. z ~. 'f 'itt;, t J.~ /OO,fi' /h"S -
r ~· )'!7.'!fl.r,;.
r ~.· I'IID.S t;',p
~""" ~.· '9'10. "!I,,,;, f,· (.H..ttU.It,;
B
6
r ... • r2, + A[i)~ .r~,· {i. w~ld~{lr"'l~ A" {z we.lcls)t2'11'r)
I2
"' Z 'lt't" ~ f 't'rtr(_j}'l.
Tz = 11"1 ( 2 r .. + b")
.,.. , .. e l)W'i> p"-'le "l.Z-8
DLV p<~~e 'l,"J•I'b~<t ne91er.t' c~)
Ex&~mele M .. ~ .. ; 111 • In /<ops
i" tu:tr<:& he.au.., pipe • bw 11. 1rr E?Owe/d
A• /l.e in" t.•.!lJin oD• :~.-zS'• r='f.lur I• 10~ in4
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• It: is cU.ffiCNll: ~ give a dir..,t .,...,.. on the design of thie welded coupler. Although the ral:ed - of the clriving 1110~ land Ua RPHI are given, there is aome quenion in my mind aa ~ whether this ie th8 11uiJDIIDI ~rque or c:oulcl U: raverae inatant:ly? Could this be a ahoal< loed? COUld thare be any miaalig-nt in this C011pler7 If so, thia aould introdllaa very high bending 11101181\t& on tbe eo~~plar.
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•
I am DDt certain ao ~ the type of applioation of the load -steady, fatigue, or oboe!<. U fatigue, then the life axpeoted
!..r:r .... ::. ~~r.' :ld "=.!~e.~~.::'"::: :r~=~o::.::~ of the wlda, Por erample, with B70 weld metal - going frOID a valaa of f • u,aso v for ateady loads all the way dovn ~ F • 3180 v for a complete reversal fatigue 1oa4 over 2, DOO ,ooo cyale•.
On aheat l&l , I have checked the fillet -ld le9 alae for ~oion only. 'fbe aiae,variea from two 3/8• fillet• Lor a atea4y load~ t110 7/8' fillets if complete reveral in fatigue.
On sheet IS) , I haVe aonaiclered the additiQI\81 problem of •vertical llialignllant 1.010 incbesl if the -. (discs) are as.- to be -fectly r,id. Of c:ourae, thio aondUion would
:t :!::..~~ ~. ·';3,, i= ;, ~lf::. ~:.:::a f!:"~!i:lte in~ couiderat:ton •
Two c.h-cum Ferenz'lq/ fillet wekls IAJ(Jt.ld have c:2 ~/4.~ .'Tl~rne·rrt of ;nertti:l of- (treatti79 weld as a /he)
J.,-=2{-"ti·'): 1fi-'~. 7r(:_r.lm zr...sso. ,;.,"
,. .. J} .,.. F.· .If:..." [o;.,oo.~X/.3) _ 't:...., 1•1;::. • <t 2'-, Sc5"0 - z.:; "" " -··--··-----------------For steady /()adtt?r and .£ 70 -,.,efd mdttl, the ,:;,_~t.--a!A· 'S
~ "'(.3oY'Io.ooo'f'!"7)-=- 1'/,'ii'.SO 161,;.,
/, ~ O.'' e9 517--e w~ ~= .17o •
but because of the z?./dts'c I lASe t 1-1'0
. 7.
M ----...::.-.:.:::
as-sume A,.. 010 ,;,
---__ .....
M ~ "{3o•tc•X&&9s-){. 010),.. (71) ...
Fortl.l.nQtely the end d1sc<:. arf!" not 100?, r/9/d, t!Jere \!-Jill be ::.ome venciin~ in the dr'~s ana the moment(MJ V1ill be much lower.
r.a.
-11
,. "'-r,
F.• f, r,ll(• f. 'Yr.
14nit force on welcled e<>nnedton F.·ffi 'S = ~d~ •1tr~ (treated as a ltne)
f ~ • ~ • ::."1,. pricJ. ~~ fit~Nr InCh)
5iart IAnth a ~ertrie.l dtspl~tcement Qnd um;rier ends f ,jc.,cl • c:ldermlne end momedt th tut.e
L -----:101~ conclt'tkm ®
c
D
A ,_,. 111/A>111 end dries 'to n:~~te (~) s.. there /S nt> 1!'nd tr10ment lh tde
---'9..1--·1 I
Fz· '~F' (~·+~
..., 1~ {/JJi ..!QS~ 6c1 1$ !lfptJI;?.e oncr ,~rFa':t~"i nNJm•nll rcac-t,"rr :..~-,.. t
'50
.,,., '•l s•~n .
,. t) t>owe\IE'r -To>---;r ~ A,= 6j,r; and f',_ • trr.r-..
A (,F t'(~ "'' 11' r; r ... c b" 7i b + ""'
itA. be.
,tt~~ H·;s.
"' ... • 'lrr.r. t'E 8..(:2r.t b) c>r IY~'I''tJ. ,Zbl I
,,,. ~--t;i-
and t?· e. t e. ,.,.., Vft b'
e • i7Y + :ii'lt:-:r.~. r.lf.""t •""E"'c"':~""r; +""b'""~
or
alt.o <r<>tnq bo.clc l.o the 1,.-j:..-~ o" o;heef@
M .. • 2 ~:r.. ('~I :as) bw.t L· !Jt A.· e r;
~.0:..1 bel'<;.:; a. u.nit lei"CC-i ~ o' ""''d.-d conneet,On
B
. 8.
example
r,= 13.0,,; r~· l'.S in
·~f A. r ,()(0 1;,
L~7/,;,
b•/3.5'111 t • ~~, ,;,
c
l:=z~/ h d t".lc: . 1. Q-=s-=s_ec_m_e _ ___J_-L.:.._:
,--- dll' 2,... 1
fb•~• 2~;: • /II.{() /Jyq, h" F'y._,..,_,.• '3c>S lbltn f, • IC,<t(> !ft • .(.._.,. ~~..,1([))
~ .. • jr;,...;if,' fll'it>'t 305'0
• ZC.YO~ "' 2.890 16/fir
~rom ~l>eet(i), fa1t'l.""' a/iowa bit',·~ ~·1teo her>ce k'l -:.ru ..uo .. !d b .. w• 1f~g.,. 9o~· or@
T __ l____ : d,,. :
J ·-----~! . ___ IIi.:- .. ··--·'
tn••ta11t 11n:t fo.-c<." on ""ld
lr' jf,'• fb'• f,' • /.n'+ z.z~·+ z.~s· ::: 1.51"''~ u~i> Al'SC. Fat•cjut> Allowabln
life N= lfXJ. 000 l!f(Cfe~ E'IO WEld mrtal
cat<'qt>ry@ '"'" '!i{re-:;, "'"''If! k • rna. -0
<11/c>wable 1'.,.., ~ ~ • ~· = J$"51 b.i not fD P<ef"•~ 21 .,,
le1 -,,z ~ .,f f,'flti .... ~·d
•
•
•
•
•
~r~----------~l=zoo,~U--------------------------~j7 ~k-------....Qa. ,,.,•::..· ---------~,k!f----b c s'""' ----~:JI
f I l \ I I 1 1,\ ' ) \I\ \ ~ \ \ \ \ \\'A\•\1\f·"t\~' AA AA~IIAt.t.~
. V \J {\/ v If\' 1 J \· 'I 'I ~~~V V V V V V . /!s.~t"/t· orZ.ill"f.;, ) ¥1/f~ ,, 3.'15 ~n
Ze>.l 'Ytt or 1,6&!1.;,~
I.U•/,,811tr ••
HH+H::oj .IE .. 11¥. ---il
t.."lt:I0"-
1"1,• ¥ft·1<}: (I.,S~IIY)(zoo-1/<f)"
herc e• D
, ... : •.. j
~- ~(1a ib)•(,,qs)ls~:Nz.,u4+8') = lt• 2L 2(>Da)c(
R,=r~.<r~ ·~.)(8'-···)-H,.f lbs'
/1,: f f '1'3.~ a, 3 '/ s: ,;, b-.
TN only t.arque an thla cunnac:U~m waulcf be that portion eppllad to tna auacnad aacUon, hOwever we 1111111 ue• Ule full value af tnat supplied by tha ddVII unit, aesu•ln; the ather and 11 stuck,
f-------4--:r T" "'·0()() liP - fi,UJDOxlt~) a 12,8'1:? I.? ll> RPM • '1'1
, .,../,_,, J . ,.1!.9... ~ • ..,·c.. 'f a
unit torce' on weld
b~rrdtng ~ • tj • 2.2,S'?S' : b 'S., ~-'
tfOO, :6 /!:.,
~ f = I£. (iz,a1o ')(-,,;,) = t ~ 3'10
I I 3. !;/··:·
resu.lt Qni unit force r--.~b ~t'
hv /(+ ~~ .... '"(}()\tiS' '1/6 16h_.;
A c
Slnca tnle part ratet••• U •lght ba wall ta u•• tf'la AWl f et1Que • aftiiUlM rar tN allaweble at tllil fillet weld.
For
lr/00 4J
1- "Yz
3VOO C(J
• /2Z
IJJ.o..i baou:e .of the .• 'i~'l ml:h {h,C.( P!Re 1 AWS wo!.l.ld trG>urre a m•mmu•n o~ ~4>~b
lf tnla ware ahaek loading, tnla rarca could double. I believe the biliKiaat unknown load waul.d be the b6:~d1ng ar tna IIYJUrlal to be canvaved, lllhleft tPDuld rorca the ac:rBtu upward ln the central poi'Uon.
....,._ 12.4£): 50 ,., - '-..
tnsume an averape t!Jiiness of the tuhe 1!• • 4>¥8,/, and o.D. "r;,o,;, , then :r"' 3~ 7 /n-r
It the sc.rew were ~reed !A.pward A." /.Chn
/VT"' (iz){J)()o~lo•Y39.1)"' 3 ~7, 3oo. ,;,;6, (:).Oo)'l.. 1
8 D
. 9.
th/r. would <UUtse a unit /;end;na farce on tr .. -:: weld of- ·;.7
f =~; 3s-?;300 .. ~ .,.., u •. , ~
the steaclf( alhwable on a ~~ 1:::. E 70 IS:
F= //,ZOO W 2 //,:J.OO{f16) ... E 'i>;i;) -the Fatt9tt(> a//tJwa~le on 4 ~6h F10 1S'
F ~ S/00 1.t.>
1-%
As ,a me:d't'er of 1nterest the b(!ndm9. str~ss m t-he ru.6e under tl11's tJt7nd, 'tton tS-
"Jtnce N/ = ~ Rna /if= IZ ~ . ._"·I
12.4 E"C. tr"' L.._
Tn1a would lndlcat:a 'Lhat: two 5/16 inch fillet walda would prabably provide the raqubad at.rangt:h af tha tullaa far the ~ loa.da involved; hQtQe¥81' U aat1111 nt:al'lal al'tould bind end fare. the BC.f'tl¥ up.rard, tor pample juJt: 1 tnch, the load on the weld as ~~~rell aa tha etraee .1n the tube wauld be varr hlgft.
A
!lJ{ !It CtRC!JMFE!!!:NTlAb FILLET !!:ilo£ !!! ~ ~ There ilr• men~ methode to c•lcul•ta the allawMtlle. tcorqua ldi1Lh l!llr~ be
@ tJ'..n&fernd by a ct.rcWDhnnUal fl.llet lftld araunei • shaft,. PFi"NP51 the
almpleat h to tn•t the weld aa a Una iiMd aaaume thilt U '& ncUu1 1a tha su.e
aa that af the ahaft.
I t
®
lenqih o{ w~id • 2.1t r -lorau.e arm : r llr,it )orce c.n ·~.octd' ~101 £tJ i
1'
.l
Torlll~<t: trrtnsferted by ..,.td
Dr I T~ /l1r T 1u t • I o<
u. obtain the Blllhl: result U' WI' tre•t the weld lis a line lind usa at ... nG .. rd
design farmul••·
where
and F •.7o7 wT or ~T., = ,?()? 1.u l
Fr0111 thh.we me~ salve dinctly far weld size far • glv~m tui'QUII and welD
lllcwabh.
ln tnl' above, (A) and (B) 1 we nan 111.etde two assumptions, first we nave assumeD
that tna sneer stress 11 un1fotml~ dhtributed tnrout;~hout tne eatlre tnrollt
ana, sat.and we nave use~ the rddlua or th'l anart EUI the l'ddius or tnr llna or
the ..,.ld. Actually tne anear Eo tress ls sllqntly Qteehr at tne outer flLBI' of
tne tnruat. Tnh meana tnP atresa is t;~reater than the average 11111 h•\o'& used, or
laokirlg at it tne otner ...av, tne lnn.r pnrtlon af t.nr throat has a lower airess
end thtrnfore tne torQue transferred by tne weld will be allgnUy lees tnim
calculated. By ueing th• ndlu9 of the &haft far tt\a ~a~ald, wa are c:onaervatlve,
ths 11'18 ar tt-e weld 111· at e sllgntly gneter radius.. Thase_ two Bfio&unptlons
tend to offset eacn othl!i'r. As the redlus or the snaft incredt:l!l wltn re~pect
to tne sln or the w&ld, the error ln using these two assumptions decreases.
Fer the usual sln of shaft end weld, tl"lls metnad is adequate.
Far 11 &fllall shaft aand rat,_r.large ~~~t~ld, 1t Dd.c,ht be will to uu • m-tnoa
....,len Qlvea a IJIDre true picture or tne prabhm. In the next methud, ll!f' .... 111
u&e 4 tetter v111lue far the radi'ua af t••• we!ld.
@w. C4ft u&e ti'IP tt•act radt.ue or tne weld,
or
len'lth of weld • e 1T ( rt "'11.) torQue arm : (r ... "'/~) 11nit ~tell! on weld • .'to? w r
'T•21T(d~)(r + "'f.,V_.7o'l "'T)
-(t_ 'Shaft
but ln order tu obtain thP fillet weld elze (tD) • we mua.t be vtlll to sche
the fall011·1ng cubld •aw. tlan ..
[0arw~-t-t~:>r..,- ~""0 I Although thh cau!d be Dana, .u mtght be batter ta make .. t"ble or rnalsUr•g
taraue ln t•l".fll& or &hlllt racllua (r) 11nd leg al.ra ar f"ilht wPla (w).
B
. 10.
In thll next &oathodt we shall J'ACagniu the entln thi'Dilt: ea hevlng dlfferent
® redl1 t bu~ we shall aaaume a uniform d1strlbut1an of ehear etre11e tnruughaut
the lllltld.
T w
l r
c
1-.ho.H ct_ : 2:11"(t-t.?D'IX)
-!Dr<;ue arm :(r1.?11?1t) ,.,.;t stress on aru • .,...
AT•ZV(t+o'lll'l•)(dx)T(t+.'/D71C) , 21tT (rt-.'IO'JX)~(dx) .... ,,.,au T• 21TT" r'tr'+ Ji rr. t tz.i<')dx •
1.-~
( • rw ~) T· IZ 11-r"' r t -r i- 12.
~ ln thh oaet~ad, '>~e shall also recoqnln the Vilrlable ahtuilr &treH across thl
\!;_} throot of the ""'10, T T w
l 'l.:....-t~
_I I•M'Ifh ()I weld • 21t (r-t .1o'l><) torQue arm rt.'IO'P' unit stres'S at 6<) • 'T: = i(r+·""'~~) IlL ,... h_C&)
D
~ ! tu= ill' W'l'z'' w:.l'' c.u:- tc,•·
r-•Z" rsz" ra Z'" ra z.o''
anJ@ T·IZ7rTwra. '7~!183 18~S7J ?>73,/iJ.) ~3~:S;· :.:; -·-
@ r~ (i. trTw(r+"'4)' 9'1,/(ICJ '10,:,.).) '1'/1.~!>0 1, '.3~.~.\)
® 0
-·#·- --·-- ---··· T• ,ll11'Ti<J(r'tl:jl 1-Jt{} 9'l,:J40 ~/0,6'10 •n:J:;tu 9. 387,3-tl
T• 7f~r+~ · ~.,J I
"fC.SSO I
J99.fi'IO Lf!J ·~ "1..)1 'l,l}~,.M:) --- ..
Although method (E) h more involved, 1t gives tne 'bBst picture ar the loading_
ar tnP weld 1 and th11 010st accurate valuaa.
ttethod (D) requires as much worll:, but 1s not quite as accur&te because we hava
assumed a unlfal'ffl stnse dlstribl.lt:lan acrose tha throat ana.
Mtlthod (C) t..~hlch tnats the weld as a line gave al1110st the &881e nsui Ls as
method (D).
Method (A) ar (B) (;~re really tha same method) treat the weld aa a line and
~a• the &811111 radlua for the weld as the shttft. Tney QB1Je vsr~ good ra~ul u ror
tha lart;~er diameter shaft and ameller W!Plds. The only problem la ln very smell
ahafte and rather hr~a welda, in this case it does nat give ~;~au tna full va.lue
af thll' taraue because the smaller radius of the ahert is used rather th&n the
larger radlu& ar the line of tM weld.. Pfotica far tt111 2° radius shaft and the·
P fillet w.ela, the result 1a a torque or l13 1 10D incn ~ounds 1 whenee tha villue
should be "ltl, 1)0 inch oaunds •
•
•
•
•
•
I
... 0
Circum £eren rial Weld It!... ""T;cs,'fJn
C-r K• ~ K • .L.. ' r. ,. r.
To tor~ue l~t 1" • weld sbe:rr allowable OSSIUII~ 'If' thtrJQt ~ t~qx
_., r 1>- --lw 1'-
T [i ' tH: ] 'IT ;;r:\ = (1+ 1<, tKJ- lrl(, +K, 6.{a T .. r. r--
[ K~(3t !',) + (H' ... ) .. (z1 ~ .. )] ~ v = r."'
For minimum t::~PIDUDt of weld rneta.\1 do no-t bev•l.
0 ,01 .o~ .01 .o'f OS .o, 0 .01/~3~ -~~~~· -"~~ ·'7'15'3 ·'-'1.'1'1'1 .'l.'l~
.I .tlfsqq • S0)88 .ssDO'I .S'i'IS3 .r.'/S)~ ,r.1'U'l .'l'·llqq
.z :1~1'-S !mi' U1t.8 /,0,0 t.mr 1.186~ W11~
·' J.I.J'I'-8 /.~'t'fS I.SS2.'1 u.os'l J.lo5'12 •m-ar '·""" ,'I /.'18?'1 2.0~" 1.0'1'15 2.1Sb/ 3.:>.1~'1 'l.a'ID:I. 2,'!>3.,8 .5 15',/b ~.UIO ~-'"!WI 2WD'1 2.8012 ~~?0. 2M.?.1
·" 3.1'1/7 [:ll3~1S ,,,.,,.,. '1.3&.11 mn 3.'1'110 ~~ss-w .'I 3.£~201 188'11 ~.'15'!5 """'" 'j-Oq{)h '1.15"1'11 'f.~ .a 'l.soe'l I ,,SSOI 'f,!.S11 '1.12.~ '1-'1'16.!1.. 'f.fl(,'tl '1."1'1~
,'1 S.2YtJ3 15.'\IS'f 5,'\'fi<l 5,'1,8'1 :;.5'1153 r.r.~ 1 ~. Oo5
I.D ,.ou.'l "'0~~ ,.17'11 '-'-5'8'- &.H'fi "-'1118 6..50~~
M '-113'12 ,,ql~l '/.OO,S 'l.O'tS'f .1818 1·'-lo&'l '1.35"1 1.2 '1.?/0l. ?.8005' '1.8'11{) '1.'!1111 ~.O'Ill 'a.lh~ '6.;1:1'
L\ ~ ,,, $.7~?? fl.8~33 'il.'ll"'l "1,016/ "·"':1. q:'1110 J,q .,,,012 "'.?tm, '!.'iO&r. 'f.''IID/ IQ,OI:L IO.IIS to.'-16 loS /ll<i% , 14 'IY'i. to.ca~q /Q.'iSt. II.Of>~ "·''" ''· '-etJ
Va/u""" of {_!(,)one! {K,) for minimum wo.ld m ... tal (~r.') and a 9/ven w~lcl throat area ('Yr.~)
F· terrsi/e force~ T.. A i.,• v.eld shau- 41/owa.b/
,{)'I .'M6o&>~
.'l'llli' '1,'1'108 ~82.1'1
~?.85"1 ~~ ,.,.. .. 'li,I!J'Iq S.Olb'?i 5.77ff~
&.5'8'1~ 'l.~q'IO
~~Ob <J,y)'l,t /M1~ ll.?><ro
A
.08 .{), .~1.11'- .'fo'IU .~1 ,e8'181 1-\'1~ II·~ l.&'llo'l ,;q~l\ 2.4'1'10 2.5~ 'M'46o'l 3.1lX!O 148'1,. ~'IH'I 't.Wt8 i'lo't'~&l 5.tAo6 6'.1!.5~ 5;~5'/5 $'1~'1
"-lt'IO& "'"5'1'1 '1633-S .,.,,, i-'111'11 9.5381 'l.'lo80 <?.50'1:1
"·"~ ID.!i31 1/.500 li.&>ID
B
A· weld thrrxd area::---:olotLf:l-l--+r±Yr:H--t---±1~·8'1
,82.~
--1----l-.81 _; ~
y.eo "
c V')
~ Q
G:l • II s Jl ....
V) c ell ~ ~ Ill
~ "' (.0 ~
~(\J
L i
t
t r
~""' "l 1.1); <r.
:::jl") "1. ::)
Lt.. '"! I
~ <::
"! q.. '1 "! ~
f·.; D I• ·•·. I '
0
~ ·.;::
e ell
~§ ~~ Q: '- 1\J 1.1)
""'
~
";
~
'q
-J -J VII ;r,
~ I'<) .,, l
<: 0
"'.
<:: -. !\j ?~ 111 "'·. ~ "! ::r: "1 "! ~ -· ----..
31 ....
- 11 •
A ~ U. tule\ velA et.ae tor tbe baae ot • alpel. tovw, aanme vtnd pressure ~~
:_.1111~ ~ !:;.:'..:., • V: 2~\#f' ~J!.":' ..ue per hOUI' Iliad, ••- tt>l.o mm-S'"stdl'!. ---;;[5• 1 • ._ l
or 3 .. 0'
0- I,..•'frl"1a1T(~~~ !.tal r ..
"r ISOO , • IlL S...· ;;-· ~s-·J'f,.. In
ta.mt actt.n.g c tower due to wind presaare ·
M• ,Z08~0)+ 1!ijld(z88)~~z"-)+(~'-XIC.O.SXz'l-.')+ ('\)(:lll.~o-~~.:_2oD.o:r:> "-~· ~00~ k;p
S...4111& ·-· Ln pipe tile. (zooino;p)(~~ln). 2.~ G. l<~t
a-•y :18./'lln.. •
Jatlsue aUanlala for veld. min ·
)c.=- 1nii •0
1\ISC: <ondttti>r> ® 1 c&de<jor'l @ N• 2.•10~ c.'lcfn
B
Vol•m• o~ we(cl il t.Ued O>lcolate.J ~IZP • ?.(.3DJ)'('Io.o6")• t 83'? in'
-12-
c
•
~ para/lei (orce r: F. 19.09 ~ 3 IG 1£;1;, fp:' IT: 2.• IS =
~.
-f;aL- ~. r
••• ~Ai@ tc~ulta;.t a~ ~-:;;!t@
~r" }J, t fSt ~,': j(~34+z&.'l3f+ (~36.)' =- 337o 16;1;,
D • r-da/()8°~
A..·~11'r•Z'II"(,'II!') •YD.Or. ,;,
r ... rrr"• rr (,¥:J' • 8'13. '1'1 ,.,
bendit!t f,;l'f:.l"'l:r..ft~· f.l/0 ., ..
IP211ze of tt"Het weld li?O -kl meta./
•
, ..
•
•ert!. b• .:1= 01.'1 ,:, ::r;•L' GS. 3 30 .... ~b (7S0T•n•2'{13/.9••)
"'"' ~"<' 17.- • ~· · ·t~,3,5. ··o~
(••b,.t •·• ••I•) jo-- _n•· -----..j
r tr;t.
lmtp\Udlllal ·- ln tho veld clepeDdll - tla value or tho aboar (V) ln \he sbAar d!.aCI'aiDo Thora \a a ahoar ot V • 'ISO lr:ipo \a tho top aNI bot.toa horlsonwl portlons ot the traM, tnl'\ notice tber'e 11 no abear in ,._ two vertlcal partl.ans. 'l'b.ls lllBBQ8 1 theoreticaU,, no weldlnc b needed in these portions. Bovever t.o be practlcel1 w will uae the mln.l111W1J weld sbe1 vblch in the c:ase ot tbe .1a· inch \hick tlance pla\e voul.cl require llL!J!eb tUlot vel!b,~.·
(uatul O<Jrtuin") for t.he borll:~t.al port1caa... r-
1/.BO "lone~
t.ransverae un1'\ bearlnJ' f'orce (aseWIIB r p ISOO .:,. '•'"L" ~· IZ.so "linch
f.)~: + fL '"_ jcu.ao)'"t ~":_:!!:.___ ~2 ·~ 'i_'ji, F~ USC ta'\lpe valuea, 1bear and traAaveraa baartna use eoadU.lat (37)1
.... 11"1'7 (O), aveHp qcle .. ort S mlmlwo - 12/br. " 8 ~~~ " 200 ~/year :K 20 7Bara • 384,000 cycles 01' a Ute ot l001!JOO to S'001000 ct)'ales
.!.. ,z,.,,; ( ) 1".,.,. ,_,. • 7=0 • IZ, 1<.~ 1 bu:( not to e~c. .. e.! steod'f a lfowa~ It> , : ;:.1 •~i
t.v• /7./'f "lti• - f,()fv or use ~ each ~·de of ~:e b ~'ld!Xih,~l ... lciS) - ~
A
B
·----------·--- ------·----·. - ·----Qrog!e voldo AISC f"lau• valul, condlt.1al (16)1 ea'"&Wl' (0)
1'",. .. • ~· ~~~~ •Ill'·~• (ht not to e;u<>d '>ie<>aq alt..,.>l• of pL>.t< of 1'16"/<':.i)
• r·· -t __ l --------l
-13-
She of tlllet nld 011 Ufi1Dc u-• of forir -
Tba IIIIIXlOIIII copoolty lo ...-4 w a appllecl •• tho w\ar tRill of tho torlr, th1a vbole 11Dl \ tends to pbo\ abcN'\ tbe lonr ooraer vbere 1 '\ been liP apW\ \lui 1- """" bor, Tho •-1\batl horloODWl r_. <rb) •• tho R_. tRill of t1u1 tori< lo takeD b"T \be top -· -· Tho ., ... - le 11ildo4 to tile vonloal - ot tiJa ll.f\batl al-t.
T Fj, Us·)· P(3d') /5° fn• 2 p • Z.(LI ~oj>)• 6,0 K\p
l In th1e case tbe bgriscmt.al toroe (rhl la applled e\ tbe Up ot tbe bar at 808111 ec:oen\rlott¥ (e) w the o8ftter ot pvit;y ot the veld carmeatton.
Tbla eubjaot.l: t.ha aODMOt.inl veld to IOJDit bend.t.na f'OI'Cel as vell as UDlfcmlJ d1stribvte4 trarmvene forces and. ver"lcal tOJ'Cel.
t-ret.J t weld as o ;,;,,
l l>b-1 B I :·.~· weld S..•bc!+"• fs'•'l'+~·. 7.83 in .. ---- ---- --··---
bend.lq Ioree
transverse Iaroe
vert.lcal Iaroe
I ~IHHHH L='"lein--oj
weld d . I I
®® I,..•l'(2o.•b){if~~\=(2AHvti.f= J(6o.+1b+d)
~or "X"r, ~<~e re~ere.nc:e aJli~ (z-z.)
____ o!-_. d\ .. t M zd 0 0
---'!..a_ ~--~2 a a' Zl> Q. za.b
(z.a+b".!4) Z•C4+b)
'1'tiutw (ver;tt.oall
'ertia•l •bar
:I: J:~
0 0 a• a"' a a.• I> 0
~(ZCl+3b) T
C4•~•:..(::!·!f!:!l •/.O?m
r,• r•:r,-f·-'f<ui1b)- ~:'ft:i
c
D
A 'I M•AY I.·MY :r, .. 2•4" /2.() -~ .-3-~- _!J_Dj ___ ~' -b ~· s.s 0 () 0
" 2•'1" 8.0 -Ia -IVY +26'12 /4.7 d S'l'l s.s -lD -110 +:1200 -
tot.. I '3t:o - -2'f() '1"1'17
.!We !!!a
r.7, ~ .~ ..,. ,,111x•.o) •. 06 ~
vohunc• IS,S'Ji7" V.olume:= 8/7 ;,,
1011' cbeak ta aee 1t the tube U cwerat.reaaed: trosa the foJ'Q8:8 or t.ha supports.
shell
realotw-
Pl• z.( ~ e ~.{t + f)+t{f.)"f] • ~ (dte){d-1 :ae)_
e=/¥
l!! l!!!! J!l!l'!!
t. t.fl. I)?.S") • IZ "8 «1,· 'l> (21a &.16){zotz•or.~) • '"
as a '?"'de,.,,.
m4~im.IJI Mni~ ,.J,..I ~ M sht!ll F,.,. bt~~cKer
B
·14-
"·""" - -. 1, "'loal.p ot ~to" pop lo.7•)
k -- ... --- - IIIZllllll beldiJic _, ·~ -M• K,fr •(+.l"){l~t.B){t.fr.) • 10.77 ,;,11
~t.ol -.u. force ID oh8l1 ot -
T= K, t • (.sDDX,12.t.'l)• '-'34 k
F. ~'~·. I \_
f: ;.: ~
0t -· ""' braolat u .WI'F thlok IS 1/2•) ODd tbio vi.U opnod tho farce oot •• lt l.o looo -\ntod, I doD't lloUon tho bolldi.Da otreoo In t.ba aheU vlU be 111 bi.ch ae ta4lcaWd abave. Also tbo tblak ~ .. .- vi.U otUten and atreu~t.m the oholl 1a tbl.o nstaa.
It thNB beDdlDa otreooeo 11'11 hlch, tbea a oUttCIIDs ri.Da lfllf7 llo oddod, u.p ODd ~ttom, -d tbo obaU oad ~...-.
Cbe fobrion!Da probl.oa vW llo ptti.Da a .tit.-ap ID tbo 3D1Dt - tho tbiok bracket oad tbo ........t .-... of tbo olloU. . Tile odp of the - lfllf7 - t.o llo ... biDod t.o prorlde • load fit.
b· z .:1• ID
m • 1'n' 'i
- -F, P· ZOOt<
9• 'fS"
F,.n s;-· F.,m --;;;--.
p•oper h of weld· treat,J liS a h;,e
s . fkl~l. ('lll•O\+ln~( n.H ;, .. ., s T
~'l. in
n P CDS6 ('IJ?t»~)MSYS" --r.- . Sit' " "·"' t.;
m P-sin 8 l~XztJoll)'>,;,ys• ~· sui • "'/,Z8 "1,;,
c
•
•
• b-en clrit'f
J?!l""lle I l¥4
bend•nq
l!!!ra!/,/l,a&
,, -str-a.r'tthi u.p (,.Au F,n ~f.aoo~<('f) t, ,., '5,. .,., ";
( ~ .!f. • 1-DO~ t'l A., ?.'1
• f).OO ~<;,;,
(, . I f •• + f; . I 6.00' t f,,. 0 1'/,/C. "II.~
F.· n P N~l2 li("J.t>O K} L"O~ I'J()' , - c;, ",,~ "J,,.: . H~" <;...
~ /Q,OS'S Kf,,' m ,~,;,s V..( ,.oo ~<}1Jilno• . f: =s;- .
5'3.~~
p <'Mb • 11>0 I( I"IJS JJO' - £1)-7 ~<;,,; F ••
"'"' ;1.4
~DO t< ,,;, 130' + .:.. 3b' 4 ~,,,; r -;,;,e • t_rt~mver1e i4ad F4 = A..,
~4
I
I
t ... ., "'.ie af fjllet wt'kl !71) luL"!d 1!11!''0:il htmrf~ I.Mtl}
~ :~.c:..t.;~.s-"lm • t,'/93/, "r !~"A w f""1fl11<St)
i~ r.M port1a/ ~,;,t penetMf--on 9r""""" weld
t ~ 1 '·6 :~~-. ..,.,,; • !,Zr.,?,;. or Iff, 1i?d, tlmJa't '-I K~l
A
- 15.
c
she<~r applied to web pletfe.
Re,.ttu;'l doaqona.l compre~s•oil f::•1Jc, -tv h< kle '"eb P 1.l~f -
hold she.ar stres~ to T=.'tooy
IA.nit ~orce on w•lds (welds on lltJth 51de:. of web plate)
( • f .-fh-- • ~ r.. ~ u,a, Z. A..
D
TRANSFER OF MDqfNT AROUND CoRNER USING DIAGoNAL 5T!ffNf/(
~===>r==========~~~·~ • d.
that f-e9 tmn5 ferrecl. b'f weld-s ore f. • -!!!.L F. D /WI d..
b d.J d.: tO: .. db/ t!:td:
A
1RANSFER OF MOMENT f1tlm OA!c ,MEMBE-li W ,4.":;ru~ I<
F,
~ e ~ I l di D 1 II I
. . L_ _______ f~;:===~ '• ·----- -----l~C ==-:::!!::::======f.....S-.
weld@
~"''"'' ~illat o.ueld on bDth ~td.as e>f "'"!> plc..te
r • .J.L, li.dv. ~ ra 1d1 • '-d~d, z.c1, d,
weld @)
B
l'BANS FER Qf MOMENT FROM oN£ MF~BfR To ANtJTH€1?
-16-
Omer W 8/Dd!'J.,.ft April /tJ,I!i'/'1
P• d.d,-zd,d •• ~(d.-:l.d,' .a a, zd, . 'J
(P -t d3) d1 ( •Zd d t cl,) d, ...i·~. d;+d~
T4!tke tn<>ments a6C>ut pD/nt ® - z f-. d, + z v ...l =o
wel4s®ancl®
we.td®
f4 • fb• zero
(_ lli-~ rb: z d,- 4•ct,
v MJ,. f.," zM•~ " d,d..d,
shear 5tres'3 ,;, wei> p/4te.
c
•
•
• /weld "ide taffa.<.hment
,_.-- au11.me at: ~f)()·f"
T L.
1
"""" ... !. ~.-__ _~Pf
IDo:roaoe 1n le,.tb of platten over laqtb (L) duo to a ~oroture dltferiiiC8 of 300"r
e, • L T ,.n;-• We am.st place a loqi tu.dtnal u:lal eccentric force em this att.achmeat to equl t.ble maveant
QX •'a/ stress
RIOf oet tb~ IIQDOl to ..,;. ~0 Ia l.enc\b of tbe platten ...... tbe l.eiiPI> (L)
e, • e., F-L. (j_ t3W)• J. T &.•ttr~ Et W t'"
A
B
Notlao tbot tblo 10118ltwllael force (J'J) ...... tbe attachlnl plate to bond ... ord Cesl,
~ 17)oment <ll"gra!\1
F •
....(8' : T I 1..
', l -; f'e,
r~
liow W8 f'lnd tbe t1'8D8Yerao !'<roo (Fr) Daoded to poll tho attachln& plate baclc to I straight poeitlao, aaBWD1n1 a oanoantrated bearlns: fane.
l 1 e • (z F.,.)l • .5..L.
,. ~eEr z.,e-r
"'"• ~F.W' r.,. z. L.
HGV resolve tbeae forces toaetber
I_ fr • jF..• + F/
- 17-
c :1ft tbla .,..,.la
L= 4o''
f. ('JOo'F)(lO•m')(ltBY,"I().:j. 1 'f,l70. lbs or I q,l1 l<tps ,• .!o/1 X')
F,• I 1~1~ ••'p J ('io)' + \(4)' ~ I 'f.' 5"' lq ps
f c £c.. • 11:1.4,1; J<tP• r ;o. '17 K 1/n • t 1"/e In
f1J,'17Itffio ~ n~u.rrt>d 1brD<tt t,.• ~,. .'t"'i 1n or~ Tbla aJIOOI1t ot nldla& OD tile enda abODld ho adiiQuate to tranofOJ' tho for .. doe to tbo ....,..., boltlag ot tbo platt... and attaehl.nc plata, addl tlooal valcla 111117 bo nee e....,. trw other 1oadl!l.
It ea:n ba abam. 1t the burl..nc npport la eeSWDid to be ID1ltDrmJT dletrlbutad OVOJ' - tblrd \he leDatll, tbat.-
Fr • f. j L'-+ Z, 'S w•
or 1n tbla IIZIIIIPla Fr• I"/, '7 !<.,p ..
-~: .. • . s-o ,,;ch
I~ ... be ohom lt tbo boOJ'lna aupport la IHUIIad to be IDilf.....tT distributed ... r tho ontlM lanatb, tbot.-
F,.• ~ j L'-+ s:?4 w• 01' 1n tblo UOI!Iple Fr• ao,4.l<tp's
t,.•, .. 18mch
mornent dio<jrnrn
It la •- 1n tbla •""''IPla, tbat tbo ezact botrlnl d1at~lbut1oo boo ll~tla lnt1uoltce on tbo ruultlna force IDd 11814 alae,
A alp 1a attoobad to tho tana1oo £lenp ot a plata alrdor hotoro OJ'eotion. »otarllllao tbo force on tbe OODDeotln& volda at tho OPCI ot tbe olgn, boldtna lt to tba girder - tbe 111nt... 1a etreooad to zo kill,
(.4) u.ni form loo..c!
~------x----------~
mp11ement' of Slfft
F u"A""
/19'9 te..t equq.l
r b = ..... ~ .. ~~./"' ... Yb') AI!' . >EL' ,.
or ... ,-F_•_f_L_1_{_l=~ .. ~-=4-b'-)'9'-~
0
It ia nOOOOIIII'J to rid - ._unc bl'ackeloo to the ... 111
!r'"":. ~::!!!"LIIl.~m!~::..1'=: ~-~~4:.~: .. "l'here 11 very little l.Dad en the bnciiAt, bUt t.ba elesttc IIICJI'emaDt of tbe fl'ame vtll caue &OJDB ra"'e to enter ttae braakat tbi'Cqh tha cCIII'Iecttna vel.de. StAoe the comaect1ng welda I"WW across the tall vt.d.th of the braoket, we vtll cCID81del" cmlJ a 1 inc:h thick aecttcn. We vtll neglect 8lf7 reet.raiDiDI aat1Cil ot the bracket u.paa the main h'ame.
c.anatclar tbe eannectlng Velda to be eDt eo tbs fraM ta fTee to 1111:n1e, lt1e llaal.de face wtU elAstlaallJ' al.oDgat.e •
€·f Bow ·~ the IGZ'Ce ot the cOJmeottng veld to the brncket, Ptrat oona:tdar the effect or the Yertlclll torce-Vert.tcal llov••nt --au. lii"iiii'""axlRl lDad·
o-•}•-\:: E•f•ft 6.·~d·;~ duo to bonc11D1
-~~·lJa E·f·* 6··'d·W total Aa •.O..""Ab• ~fbd
~~ Tbe d1sUnee of point (a) or the med;Jer to the taqont of point (b) of the ...-r equals tba lllOJII8D't. or the a rea 'Wider t.he mC'Illl8llt diagrara tokan about polllt (a) dlvlded 1>7 EI. see 2,9•7 Deatp of \faldiiBDU
Rw ve vUl PQ.t all or tnt.s together-
Example
0 • ,6,-L:Ir h-a.-.• bra.<.lle't
or
or
A, = ,o.- t:lt.~ ha.me. br-A. .. krt
.....
tT= 3.1; I<.Si b• IB ,;, d. ~0 ;,
i,• ta-b • -t{U 1Ui){l11~) r '" MJfr,
~' ~. (. (1~Si¥teip\'. '32,'1 ~,,;. • -,cr- 7 '0 /~) r ~f' jJ'-'+32.'1' ~ 'fB.'-1 "'It;. Ir".J~. t r. •
ihrot:c ~
1 f,~ ta-b ~~n·~l
A
8
tr= ..&...,. 'P eo.e t . f:"
11ormal sifrj$ {tensile)
p ____.,..
i - ...£:._- E..Ji.!!.i_ - t - ~
'iJiur stre n It ve CGDI1del' the IIII%1Dum cCIIIblned et.Haau, t.blll becaa.e-
{:.{+ }<fl'vr&,. ~ + j(~)\(Vflf o;..,., J.[ cos 9 + j co, .. 9 + '{sin"B]
(!) or i =-p- [ C..s 8 + JCDs~ + ~ Sin" al = Q_f. 2 o-..,, ~ o;;. ..
. 18.
( PCos9)\ (Psip(/ = .1_ j cos•e +'I si/1"6 2T"" t- l Zt- -
ai.P • 'f..,.
co>& + &'eH SJn'e e Jib•'!:! iqs.:.'e 2 "
3o' zo• 10' 6' • ~~--·~+'--~.----
~c:;~~~\1-8ot- ----~~~
cl. ('> -0 000
~ 0 .!10
-- "'ff --------' -- - I
~ 0 ...... ' I-- t( f. ) -----1 !; ~) afi!::J~ .J"'l~S;-t =t, tcz~ t;..:"J.. t!::r=,•=:, (!:""~"';)the ohsar st.reas ( T) ls vi thln tba all<orabla,
t
l
The tact.ore 11s\e4 in t.he above table can be usecl In these two !Ori!Dllas to arrive at ttw proper tbroat atze.
'l'be thr<>st at e • 0 11011ld bo equal to the plate tltlclolus (t),
For a 1/2 lnch thlck Aldil plate Co;.. • 50 kal) st..,.. to the allowable of IT• 30 klll, the aolt force aotbl1 alon1 the edie of t.he plata (and t.he weld) would be l$ lrip:~ par linear lnoh. The all011ablA &hear on. the throat ot 110 veld 111eta.l 1a 21 kat, plate ts 20 kal. The HqUi.red 'throat at 8. 90° would be• o·
: t (f) • ~2 ;~ ( ~00 ~~~) " • 7 5 in '
fbla eBIIUIIISS a anltona dlatributtcm of atreas almg t.be tbroat and nepecta alqf aecandart bendl.Dg stras reault!Ds trom an:t eccenV1c1ty. The ~entr1c1ty would probabll' increase tba ......,.1 stress (tanolla) bnt ID the repon where tllis !!!lpt - (aboot& • 00), tbe throat cwmot ~ increaaed DmCh above the tb:l.Gkneaa ot tbe plat.e.
For e jo!Dt In Vl>lcb tba plat.. lntereect •• en ""f!le of 67 l/2°, use tbe- date tor e. 700 .. """ tba rcmmuas vltll e. 67 1/2°, title........ [f.;. e-?o' ..... qssl
t= /;Jr-..'9-+~ sin•EJ • zfhl~'"h"+~slrf~'lt.· ~ .708 U.ch ~·'¥ ~·.?16.mu.
c
•
•
•
•
A
0
... ,... ot ""' - ~ lA o..,.i-"'1 Ule eve .. .., the \bl'aot ot o vold, oopeeioll;r rem ool.Uplo loo<IIAa, uri..,. ei- ot ... 1do ....s p-VF or .-uoa, we will V..t t11o volA •• • l.llll ....s ..... l.dor t11o uait r- on tbio liAI,
Ia tllio euoq\11, Uae ald nrt.oa IJl tno ond aloe, eo t11o llao vlll alao ttrt lA NlaU..., oioa, !Ma 11 .s- b7 .-l-"'1 tllo otomlud veld to have a tllroet ot 1 laoh, md uta& tile ratio ot ao-1 tllroat to t.11o 1 tach at.andord •• tile rolatlYe alee ot tile liAI,
lt t.llo .U•obla alloor ... - t.llroat ot ... 11'10 vold 11 ,)0 or m, or.,.. -21 kal, tllla beaoMI ... allwable 'IIDlt to:rae ot t • 21 ktpa per linear inch tor the standaJ'd lt.Da ot vol4 (1 laob tllroatl •
_ _t;. H~'-1
~ •elaft ;., • l 01>1
'Sl2f!' •
~ relottv•. I ~ ~tz.. ·•
A II • II
8 ,8 828.
toto1 1.97.9 17,b79
CG -u• 1• n,";h'l• • 'B. I" ,q
k"· t-tt:+l~
~ ~~tt!"' • "Z.IZ I
I,,lv• I,t ~- '1 = I:,-tr,·C6•M.' 9'f1,"30.·{3S.1'.(/~¥7'f) r 32?,"'0 iP" I A 11•11 I,•ltl
C6toaW= ~: '4~• '3."/'1''
i..,,. ly+I,- '1/• I,•:r,- CEo•M• /'f,l:l'/-~.f/'1){19''1) • 1/,J'I'I.in'
B
- 19-
UPW V!ld at tr'1; (Y TVlatla& b<ml>oatal)
(vertical)
.J,.• L .. I,· ~''l"oO+ U,?/l't = 3~8, ~'10 m3
A.,• 'fq?."J ,;, (/e"''th o~ weld.)
Fo~ ~ /000 Ton'$ • 2,000 (op's
moment arm .. ~'ltn+IOin-1·q'fill" 30.tJ6 in
Vertioal oheer ~.• f., • 2.~~~., • "i.JS >J;p
Reoultoat ~· j ~: + ( ~- f,'j • J (to.O"')•t ('f.IS-.?0)' : IM>t. l<lif1
fhio roaultoat unu roroe or 10,66 klpo per llaeor taoh ie based upon a atand>rd ot
c
l bleb tbroat. !o trans1'0nl ~l.s unlt. force intO • aU, 8"t.ft8St 8~ divide tlr tbe thl'oat. abe. ill t.hls cue 1 l.nch. llaace t.bla VOD.ld CGJTeapond. t.o a unit atreaa of 10.66 lml.
'1'ba all01111ble att. atre&8 tor the tbraa\ of • veld UDdar st.ea~tr loadl.ng 1s 2lksl. (E'IO veld neta1),
T~e prea101t AISC ratlpe all..,obleo, oandUioa (16) or ()?), cate8017' (O), viti> K • iata/lm: • HrO, 1IOUld allow the tolloulaB•
lS kal tor 100,000 o;roleo U kat tor SOO,ooo eyolea ? kat tor 2,000,000 070lao a kel tar orer 2.ooo.ooo c;rala
~ veld at point ® The :rawl:t.ant. un.l\ terce oa. the weld 1a lwer htJI'8 and vOdld. aot. cca.Vol the desiBD•
lolounn !wit !!._j\2_~
z c.blf&•Z1DO."'...;,
i f,•'fll.11-lp
f,· '1. 15' ~,,.,
~"'pcrt.ft 2t I!!!!!! i. • Z(zb) • .<(z•s.:>"l• zao.i• T.,.• 2. if'. '<D" j s:.r."f lj'll, loS, .r.3
r,·z f· Wf!1- 'f4r.r.7. ,;,>
D
~~· J.• r.•IY·'~l.; <il.~t.VI'f'1,87Q.•n" -~~
14.,•2l'lo.ma;•
noitt. lilr.d ..,.,(d on z !<.." t '" I'.' t:.
In ctleclil:ln9 tP'Ie weld a he af tne above Llnlr. Suooart B.rack.et, members (A), (8), iNS. (0) fal'lll a curved besm at the (.Qrners. Thla means that the neutral Bk1& will t~nift tl\lil8rd, tharPDV lncreaatng the bending '8treas an ttle l'lner race, and ascnulng tna handing str .. a an tna outer fac:a. As the radius gr cur\lut.~o.~n or thla tnware~ earner ls increased, this candiUan becamaa lees se~o~rn ana tne bending &tress ls reduced. In thll fallowlng IIIDrk, we ha\le aaslollned ta start witn, t."at tne partial penetnhan 9roowa weld on tne lnslde corner is 2 112• dri'ap cna rsJnrorced with It 'Ulet ~o~eld which wlll pravlda a radtus of curvature of 1/211 •
1~2~ !InA systf!?ln
t:~.tt«n•ri to mtvdiP dte plrzte
S.A "'A,'( ~'t ').~·) ,.. :2,1/'f• 171dui.s of f~ fit• ~= tt.'N(I.1• l§'.)t"Jf"O·~ ~ 11eutr4/ uit~ ~endio.9 ~~~ inQer f~~-~f.--weld-·
ab,M(r;-r(> .. /l.1"'"·1'1&"{:~.il'f.t&.") _ A (r1- r. )r, !(, W (!u~·} (u39•-.l.ll'l'?l~·) •
J";; i,..eld in com~<>IJ
'/'------------.(~we\4 in 'fens/1;,
,'~'-+~-----------------
7, 3 '-/ k:si
•7.3'fl<1i , ['- ns14trat ll.~tti: rhifn
Jinuucl a:t t:ltrVI!' benuin3 ·~,;, '-'"' Slnoe 'he t.ho laoldo veld oxMndo ll8ylll<l tile neutral az18 Crnl• tho ~ Of tiWI weld I.e In the 0-0J.m 1'8fl.Cilo bonco \bare U DO DO\ob (""ot or veld) In the \elsiCil ret1Cil aad o01114 poull>J;r aee the taUpo all-ble tar a •"'''le"' ponet.nUao .......,. weld.
A
B
• 20-
HIN89"er tbere U a horizontal taroa ot ZOO klps aet.tng en t.h.ll!l joint. 'fhe resulting unlt. baarbla preaeue is -
F zoo.r<ops au"· cr= A"· ,:r·. 1' 'At·· 1• ~ ,s,
ApplTinl \bia w the pr,..101UI -dlq etreoo, t.hla vlll have the effect ot sbUtlng the reference oxla \a tbe rlst>\ b7 tile ......,\ ot 1.. 8L kol,
q
Air a l!llde tor the allowable tatlpe atrua, ve vl.ll ue the US: vat.uea. Uoln1 taUaue aondiUOII (16), partul pC~e\reU'"' ..-. veldo In e.oi!SI
~ teaalao tranavene, oateaory (O), the tau ... t......W. .wid be q_. ,-.::;r-Tha parttcu.lar load. eycle vlU produce a etreaa raop or I • o., huce Di.u~&.oKsl
Dfottee t.h.e lftd.Lcate4 \aDdle ~ e\reaa OD tbe l.aDer •urtaoe 111 7.31l kill. VbaD the azlal campresaln toroe la add.ed1 tbls tan&lle bllld.tnc atrua 1a l'ttduced. to S.SO ksl, wblcb La vltblll t.be 1'at.lpe all.ollable of B.o ksl tor a part.ial penet.ratlGD P"OOI'B veld.
Suppc~~e the reeultat atreu wa ewer the fatlpa allovable• tar SUIIPle to. 0 ksi.., In t.bu partlcular problelo, ,.klntl t.ha veld 1a....,.. (Jur lllc1'88oin1 U' • throat) vould not hel,p because t.bla would ollllp]l' oxt.oad the root ot the .. u fUrther ln\o t.be compresalcn area. fbe tensile area vhicb caratrols *be at.reaa 111 tbe teeld. la determl.ned. by the cll.atan.ea from the sbl ft.ed neo.tral uta to the surface, and Wa vlll oot ehanp •IJqplJ' by ~~aldlla the veld deeper. IA tbt.. eaae, lt vDUld be necuaary to increase t.he t.hlckneu ot the bracket so that t.be dlattmoe of tbe sbltt.ed aeutral uls to tbe aurtace VOiald beei:IDB c:nat.a:r.
Jlot.lce tbet th.e inward. veld. axt.en.da ap tbrQucb tbe ahltt.ed: neutral axU, tbte •ana the\ u doea not tenainste In 'he '-lle rep.on, All of t.ha ooterlal above \hla sbtftacl IWlt.l'al u.ls la aaswaed. to be ln cGJIJpl'fiUI.ciD..
bearln& (tronsvene)
~.--t;.~:. '1.1/"fit<
vort.laal obear (parallel)
f.·f;-~ .... 35'"11;.
Allowbla tetl.pe otreoo on t.hroo\ ot ""ld, ...., AlSC tonoolaa, oODclhi.Gn :rT, ~ (O), ovOl' z,ooo,ooo 070les, taUpo t......W. lo
1: .. ~ bare I • rdn/max • 0 beDae "tma.w !;" 8.0 t("S. ,· IM.,. 1-1<. but. aot to axoeed. etoa value of 2_2.0 kat
-!.red veld tbroo\ I.e ccm<ll~iml 16
t• '1.8'l"M •.C.IIi• e>r ~1nCb 8.0 &'Sol
requll'ed leg alae ls condlttca 37
• 'f, &"'~I@ • i6o5" or '1b. ii!C b w(.?o?)(B.o .. t) ' 'r:>
c
•
•
•
•
0
~p • ..:...:.:1
refr&.c'f~d
P"~it,(m
!hie tOJ"k Wt t.NCk baa a ec1aaors deYlce which aU.OW. tbe tork and ita loed. to -.. out -ioon~, flSW'fl l.,
fho too dlapnal ...,.ben (a) and (b), CtSW'fl 2, ore pimled togotbar at polnt (5), One - [a) la pimled at lta 1-r end to the 1lf1obla portion or the t.nck, polnt (2), lta upper 0114 elldaa vortl.QalJ¥. along the uppor 0114 of the fol'l< support, polnt (h), fha - ........ (b) U pimled at lta lower ODd to tho lower 0114 or tho foJ'k oupport, point (1), lta upper end olldaa vartlcdq along t.ho upper and of the 1lttlng portl.on or tho-· point (3),
It 11 neceasaJ7 to deteralna the a1101111t of veldlDI reqm.red. ai'Oillld the pin et \be center or tho --· polnt CSl •
In the abGvo fliiOI'• ), notice that the vortloa1 load (P) ot (1) o•=ot tnnoter wt ot (l) or (k) booaooo of t.ha ellde wblob oalT tnnofon a borloonto1 fol'Oe, Ja order to
i:;!:::., ";:.:! ~ 8P!:"J..~!'!o (~~~ !! ::!\f!:"' pen tbl'oagla tho pin at (S),
A1oo the horiaonto1 forooo on- (a) ot (2) and (k) oro oquol 01111 oppoalta to tba horhontal forooo on -er (b) ot (1) 01111 (3), :fb.aa -t tronarv tllroltcb tbo pln at (S).
We can aee tbat the 98Z'"oal torea on t.be piA i.e P and. the horlzoAta1 Ioree le
F,• Pi i P('¥)· P(~)
Pom! 2bh •- n1ue of 1!. eon be obtained 117 uelng the '"'""'"'"' or porollel torooo or the aumatlcm Of tile t.ruavei'IN!I tONu on e1tber MJibNt to be SBI'O.
A
8
• 21 .
c
p ~ ;...e 't
S fXI"'II•I !,rces on member ( hj ~ zero 0
left skle of Ftqu.re 6.
- p ( ~) eo~s + r, eMf)- F. Stiff) t PsinB- Pf coss ~ o
0 cr F,"'Fy JM + P(kf/-}-PfV/, + Pj-
:£ tn:ume~e for~es"" membet {b) •zero
+ P[~).,m8-f;etn6-l'j,51n8t}>fs,;,t9.,. 'PcosQ~o
@)or f;,= P(~)-Fv ~ r P£ + P~ noUJ ie t eA~ua 1
In the Slime munner f.tom(j) F. oti>61o- p(~)$08 ~If, I!!OSS + psine- Pi c..oseo
F. = _ d••e) ~ ~ F. ~ f p -p e <'<>:>$ ,. '1. -a- 'Sih7f h 'ShoS tiT S'iR9
or F;,: p{ b~'e)
wct.l -treated as" lthe.
, ¥ ..6... o,an.lh ~ to A,.. IZ,S1PI
res~tl1emt
t'tmst der f~t 1iu.e lt:Htt:l,;q - £70 weld metQ.{ A'S~IItne a httd euery S tninl(tes, ~hn p4r dtt'(
5" dtt9 wee/( 1 fiO wee/<~ per 'fear for lo year'
{t'-'{B'/S"Xsofzo)~ '18-0,ooo. e~alt-~
C't:d~")Df'f @ SOO, 000 C'fc/es /{:-;;~aD tZ ~I
5tres5 "' I='F: :- I :z. /<5.1
A
B
_,.,
...... ·~ ®1-r : •• 1' s• opin:·o~• : ' 1 . ' : : ' I ... __ ,.1
~l<tt:i.l eom pf1(!'5S(D i7
&f><ti.l ferrs~n
A~
I"
max tensttJ'n {net S«t"ttPI'/)
90&31!.. tt1Jt1AI /pttld (paml/el)
l.O in"
'1.1!i in" (net uette>n)
~ /Z, 308 P''
- 3,0Z8 p1.1
-(b)
• 22.
<.SilJI. z· ...... !b1~ ""'
' ,.B,Il. ' bcndoi!ct lottd (tRinsverse) elJ<tQI lead (par411el)
; ... A • t,.o m
I· zr.. to+ •
ft1r /O,&JZBib {lfOrh) :- /t:J'f,Zf!JO p. !6 if
Q¥141 CtH'II]JferNbr'
4~ I iJ I tenst~n
_Me .,(?o9.zec>){3) '='
.rTb· I 2'-
max tenst,n (net seetroPn) =
OWB-234
c
•
D •
•
•
•
. . . . 2lte·· !
1
A
: 11 f.rotn '/Aotlr ... ewp1•4J. dttWct; 1311
!,' , to <:n$1. bear-. A p.rt10n Df tiJtt I(F;-Fio) ,·fl. tntns~er-red 1nio J : s~o.pptirt/119 butl-do~er blade qs(FJ.),
/ • t'lii reiiiG'tnin~ ~rt1im (Fa) " <'' J 'tr4n'$ ~errfd 1rito the member-
·"~ '•, 1 . • rn'wttnq tn G. bendtriq moment: .,"'·,''~',\.,@I ,l·
.. , ,/:,,.. ')·\ '\: ""j·'
{ FF~()()().,.. ,/:_.:: . .....•.•• .r··v '"" En<t;·,.n~l fore"" in e•rcle(\.~re appluod to member
uitetnAl f.,rc•";, SIIIIA,..[J 11re I"Q'ioi\tecl b., member
e.. .. ntcr WISe ra'taftin C+) 8 <!00$1.der force'$ F., 8. F".,- t~..i su.ppor-"t ~-.. ... u. •. ,.,, f+)
:E~"'o t- £o,a(x/{33")- Fr(7.o) = o
Fr'" ,o,ooo~~) .. 99,oc;o'*'-
a. Mb.,. o ~,o,ooo( t3") - F; ~o) ~ o
F; .. ,po .ooo'&~) ... "3'1, CJod"'
noVJ '-"9-n"ider }orce'!.r,F. ll F', appl1ed io member "-"-:.-:,CA.tttC" member ux.ed)
2'111c. ... o +~o.ooo('-t~·)- F.{B~) F,.,. ~o,ooo1¥f-J:::. ;s-~ '16 o.'*'
-- ·- --- --.
~.hl"·o -tt.o,ooo•(n")- ;:;{8~) ""C:>
F1 u tlio~om).. 9~ '1~ o."' ~ H~;, .. o F, + F-a. t Fr = o
F .. --- f;-- F, ~ -(- 'l'!,t:JeJO) -(+ t~I,U,!r} • - ~.z.,'l·~
beca.u.~e of the Qepl ted force'!, the mem 6er 1i 'SIA.I> jec. ted io bend ttlCf
~ F,~ 39,000.
. 23.
c
mtJment- em sec"t!~'r,{c--Ja~ member
.Me-e. .. F, ( 11?a.).. 39,""-'-•(;;k':)· '1"18, roo."* \
ehec.k this -
Me-c.: Fa(Bfz)• S'176S"(Bi)•
ol<
'(~8, oOO'* _/
From ihe:,e ~or-ces, de'5Jqi1 -the rnember
bencla~<t 'Sec.·f:-t~n ~-c.) I .® -T· Ct•3.9"~ l!( 4'~---.ll
-t~~~~~~ If"
+~~~hi I~
..... -til
0
0
D
max comp~s,'ve ~~~ ~~ 4Ft{c-c)
c:r=.!!!... ... .lf'{&~mi.St 11,2oo P"'' . S.. zt:..l?in"
('heck t:dltJwahle eompresst~e
A l '5 C '3t> c. I. s. /,'IS"'
tr = [;.o - &:t J. &..o t7y 2 Cc Cb
Ce" j 2. ~aE' • /2{..,/
L:. zoH
y.
benrJuir; stress
i~ A~l. 'Steel
we I d l~"' o~ /~"•' er- brad:eis ft:, 2uuer- bar -
torc.e Fa. • sz, ?~S 16s
{Dtz:J lenptll ~f. ft'//d IDeJ:I 8 .. 2~· • :zo,:,
~· iS :l,?j.;" 2. &. '-ID lb/t~
le~~ ~e to.. 1M~: "' , ~ ~10" or uu ~ . [be= ... ~ th"'" """)
weld 11;19 o~ &:!wer- b1'1:1Ckts t~:~ web of- member-
fcrc.e F,._= S2,'l's- lbs ~I lem,tlr of f/1/e:i weld 8"~e :1." =/~,,;
('. ~ .... ) 300 lb;,:, r ''
let srz.e. w• /fi~g =- • '-~~" or tA.ae.@
A
8
wei d1~9 of -b:.p kr- t-o web cf member- a'f@
~orc.e F, = 3 -,, Ot:JO fb
i.-1.1 /en9 t-!1 o ~ weJcl. 9 " '3~"" IY ~
-24-
r: 3ftOOO = ~ 7 'If 0 1~;,;., r 19
~hec/{ hort zon'6:d shear 'Stress ,;, we·b of. member-
14." fi = s-:., 7~ 'I lb ~ 5'1, ?{,L/
'f"= ~ • ,_._ ~··If•... i3, !'TO p-:.i <. . Yt' "f.,,.. ~~; ol<.
ratl&ae au-blo '"' Qld - AIBC - -ti.CD (37), cate11017 (0), k • lllln/""" • aero - 2 r' at -111 .,. ueh pau or L qc1ea per trip • 1 trl.p .. _ S mlmltea or 11 • 12 :a: z 200 z 10 • 7681000 qcla lD 10 :rears. haDae ue a,ooo,ooo qalea.
't. • ~ " 'I k\l .. 'It<~ i 'b•:t n.t t • .o.ce•"' Z-t .... ) .... ~~ 1-.o ~
c
•
D •
•
•
I
I
A pulley ta very .:aplp and cflff1cul t kt CDIIJil&t:ely llft&lyze. I ltave found very llUla lnFol'llatian an the deaign ar pulleya.
A
In pal't @ I ttave chackH U.a fDKn tram tne beU: an \tie pulley and Htatnea a
::C.~~s;:.:::c..: ~= ::-:.~ toba~:. '::~. (f r) D w.ll u the raeultant af She
In part @ I have conaldand en. pulley kt be • alalple bHJI, euppor:ted !ly UQI twa: beerlnge ihG obtalftad tu rnulttng bending IIDMftt an en. aullay,
In pert @ I neve gone rurtl'lar lind conailllera th8 bllftdlng ar • pulley llll"'ich ~tea a lll"'aft irw1H.
In part (!) I n.va trnaed the pullq Mall n a r.lftv. uaing a t• wlda atl'lP. Tile uU eppUee•
e) radial forces b) tenoanUel force•
to ttta rlng.
Tna rln:g ie eupportad by•
c) tangenUel ahaer d) a"'eer perelhl to the reaul tent Df the twa belt tanetan farces.
~~~&)• .:!Jl:: ::.~:.:d; .. :~l:!,. t:.~==~~.!~=d 1~ ·~=-o:.:~:tn~S:~tng aamanta.
1 ... auld augoeat you Check 'the warJc end the 11ethod Far accurac:w. 1 cauld neve •ada a mletske, I have not rechecked t.he work.
Wa wUl nat~~ treat the ehell es a ring and find t.he tJending atrueu on a 1 in~ t~~ia alice or tha ahell.
The ring will be dlvliHid ln'ta l8 parts, avery 20 d&QJ'UB.
------------------------------------·-----1ha Shear on t.ha ring cauaed tJy t;he torelan fi'DID t.he llel t t.ansiona-
·-·-·-----·-. -- .. ·------·-----this farce camaa fralll thll belt. and ac:t.a in • counter-.claekwlae dlrect.ton.
B
The HBhtlng shaer from tha a!'jacent. snell, act.a around tha entire circumference or 18 segment&• in a clack w1Ba direction
I~!'/ - 'I "j, '/ 1';/-;e9ment .. - !~_.:_ __________ _ This meane there is a net ahear force undar tne belt. or-
..... ~ "'- f.ot I& ,~· 1'18 ~ I? 50' :12l "'$ '"' so• :1" /bs If ?D" ~D'l I~• 1'/ <Jo• 3Sl lb<
bYr: 13 no· -~"16 !(.,s /2 no· 'I'S" 1&. li /50" '18'1 lb• /0 no• Sl'( {~·
F .. "'
no· 'i'rO .:,:
8 ?to• 6> I~ :~s
-25.
c !: ~:;:1 :~:' .~~~ :ra!:' ,:~~:r!, a;~~:a::: !~~. '!:r~::~~· .m1 dtecf"
F.,"2.2,'1''i ~~ .-:::" ~,~ -?··
• 'U '4'15" fb '·' "''•~"'~ "'
F,.•IF.'t2F;~ coset tFi•
,.q, ,,
F;.•f(9J,'I¥F)£U('I/.'•I'Ir'/.2'1,Y6<f'J,"') + (211'1"}& = /I)~ 800 16
/ei. Sop "' a 11 '3 l!.;,.;.,h ,;., wrdth S"2,;., ... ~e
The ""alumn Analogy 118thad 111111 be used ta detesina the banding atreesu wl thin tne ring.
1) The ring ia cut at. aame aoint ea that. it beCDIIIte ataUciSlly datennlnant ..
2) The forces are applied to tna ring enc1 the tlanding mament determined.
0
3) lhla mament diagram naw bec:amea the load an an analogous column. lhta anlllogaus calumn has the same aut...ard dlmenelane as t.ne real ring, ttawaver Ua thlekneas ia equal ta liEl of the real ring.
&. ) Thla loiHI (bending moment of the reel 1'1ng) naw ia treated aa
a) en adlll. force b) a bendtnQ moment abaut h-•l axle c) e bending ~~Ga&nt about h-y) ada
S) The thraa •stresses• on the analcgaus column-
a) Pial G8
b) bending stress a~t b•d a;• c) bandln9 atresa about <v-v> §Y
nDIII Dacoma ttut corrective mamanta wt\ieh -.111 bri"9 t.ha at.attcallv dataminent ring back t.a the initial staUclll.ly inaeterminant ring. Their eigne will ba chqed and then added diractlv t.o tha lniUIIl. bending moment.
Each mD11811t. 1& found by muUiPlving t"'a particular force Dy tna distance Hblun a Una through this fDrce and tna POint in quast.19n on the rlng. Mrment.a are considllrad to be poslthe if thev are in a clackwiae direcUQII. rnaaa diatencaa are ecaled orr of tne drawing.
To get. the IIICYB8nta on aecl'l segment. cauaed bv the !I!!!!! rorces, U ia necaasarv to di'I!IW a great. dlltiDBt.er t.hrougl'l the paint Of eppl1cat1an Of tl'le fo.rce 1n thll ring and measure tne anarteat dietance rroa thie to thll center of the ugmant ln queat1an. Un t.hls figure paint. a).
Ta get the momenta an asctt &&QIIlBnt caused by the !!!!!!: farcn, 1t is necesserv to d1'11W e tangent t.hs'ough the paint or aPP).icetian of the farc;e 1n tne r1nt llftCI measure thll ahort.eat alatance frOfll th1& ta the canter of the BI!Qm&nt in question (in ttale i'igure &eQAJeRt a).
.,(i\ .. · .. tt"""t
. . ::::
\'
to gat the IIQmllflt& an ncn aei)Dll!n't caused by- the ~ faJ'cea, U 1e ftllceaaary ta draw a alngla Iliii"'tiiiough the canter af the B&Qmant tn QUB&tlon (hera paint a), at an engle of 32 Clegreaa ( tnil 1a the angle of the reaul tant farce of the twa belt tenelon fDI'cn). The attona,.t distance b&tldllen each paint of B121211Ci1Uon of farce to thla tine h maa&~Jred and 111 tha moment ar11,.
lpaint (a)l
£!!I.U1 18 •178 X le.9 • • 81) 17 •222 a U,O • - J,107 16 -266 • 21.6 • - 5, 7!10 15 -:1119 • 26, ........ 110 lit -l52 • 28.,0 • - 9,150 ll •HI x 26.6 • •101070 12 ··l5 • 21,6 • ~ I,.UO 11 ........ 14.0 ... 6,785 10 •527 • • •••• 2,51111 9 •570. "·'. + 2,790 a +61" x t•.o • • a,&DO
·•5,1!10
l!ll!t _.,,, • ,5 • • 2• -.9. l.l.. 118 ....... 10.0 • - ,.,, -46.9 x 11.0 • • Itt&
::.::: : ~~:g : : ~:~t -46.9 • 4!1.6 • - l,lltQti:: -.9 • 52.0 •• 2,"0 ~ ·•6.9 • 55.l • • 2,600 I -"'·' .. 55.] .... 2,60D
~:: : ~~:2 : : ~:~}-+7]., 7 • 37.5 •• 2, 760 +7),.7 X 26.,0 • + 1 19J7 ~ +7l. 7 • 18.0 • + 1,327 ~ +7l. 7 x 10.,0 • + 7J7 , ... •''·'. ].8 • • 280 .. +7l,.7. .5 • + 37
-6,l06 Total M8 • •1,519 inch paunda .a,;
!paint (b)j
l!I!U! 17 •222 .... , • - 1,0&1 l& •266. t•.o ... J,7tl 15 ·l09 lC 21,6 ... 6,675 lie •.JS2 X 26, .. c • IJ1 JQD 1l -JH • 28.0 • -11,100 12 -435 • 26 .... -11,500 11 -•a. • 21.6 • -1o,•so 10 •527 x llt,D • .. 7,!90
9 •570 X lt,9 a + 2, 790 8 .&lit X 4,9 • + l,D12
-55,454
!!!!II. -"'·' • .s • ... z• -46.9 • ],8.- 178 -46.9 • lD.D • • U9 -.9 • liKD • • eu .. 6.9 • 26.0 • - 1,222 ... -'-'·'. l7.5 ... 1,760""
=:::: : ~~:~ : : =:~ ~ -1.6.9 • 55.3 • - 2,600' _,.,,, • ·55.] • - 8,680 .,,,,. st.o .. • J,7ss+7l.7 ... 5.6 .. + J,J55 +7), 7 X )7 ,5 • + 2,. 760 .., +7), 7 X 26.0 a + 1,917 ~ +73, 7 x 18,0 • + 1,327 f" +7l,7ll 10.0 • + 7)7.,. +7),7. ).8 * + 280
-ne Total "aJ • +1,780 tn.:h pauna1 or..
•117,) ·117.) -117,) •117.l +117,.] +li7.l +117,) +l17.l +117,) +117,) +117.l +117,) +117.3 +117,) +l17.l +117..,) +117,) +ll7.l
•117,) • +117.l • +117.l +117,) +117,.) +117.l +117.l +117.l +117.l +117,tl +117,3 +117.l +117,) +117.l +117.J +117.) +117,)
2.5 .; • 29. •• , • • 505 J,O • • l52 1,7 • + 200 •••• + ll0l2
18.0 • + 2UI5 27.6 • + l,21t0 36.7 • + .,lUI ""·' ~ .. 5,200 .9 •• "+ 5,800 51,4 •.• 6,DWJ
~:~=N::~ ll.6 • .,5JO 29.6 • ,,.75 19.7 • + ,Jl2 10.5 • + ,2J2
l.D • + l52
.7.- 82
·'. + 82 s.z • + 610 12.5 • + 1,467 21.7. + 2,51t5 l1,2 • + l,66U ItO.) • + ... 7.30 ltB.D • + 5,637 53.1 • + 6,210 55.1 • + 6,'-60: 53.1 •• 6,310 49,.4 • + 5 1 8DO 42.1 • + .. ,835 33.2 • + l,IOD 23 .... + 2, 745 lle,.2 • + 1 1 667 6.7 • + '716
+57,)82 ""
A
8
. 26.
lpolnt (o) J £!!I.U1
16 -26& • ..., .• - l,lOl 15 ·309 .• 14.0 ... 4,325 14 -352 • 21.6 • - 7,600 ll ·396 x H .. lt • -1D,470 12 .. , • 28.0 • -12,190 11 ......... 26,.4 •. ·12,800 10 -521 • 21.6 • -11,•00 'tiJ +5'JO • 14.0 •• 7' liS
8 +614 " ... 9 • + 3,012
·•9,091
!!!!II. ·46.9 a .s • - 24 -4&.9 • .s • - 178 -4.6.9 " 10.0 • - '59 -•6.9 • 1e.o • • e•6 ... ·•6.9 • 26.0 •• 1,222"' -1.6.9. 37.,5.- 1,7&D""' -46.9 • 45.6 ... 2,1..0:::: •ltf.,.9 X 52,.0 a • 2,1eltCJ I
~:; : ~==~ : : ::::-+73.7. 51,.0 •• 3,755 +73. 7 • 45.6 ... 3,355 .. +73. 7 Jl 37.5 •• 2, 7&0 ' +7),. 7 • 26,.0 •• 1,917 • ... +73 .. 7 • 18 ... 0 •• 1,327 !:" +73 .. 7 • 10,.0 • • 737 ...
+6,1'7?
fatal Me: • +15,61el inch pounda tM
15 •J09 • ••"'·•--U•JI/5 lie •J52 x lle.O • • 4 1 9lD ll ·39& " 21 .. 6 •• 8,560 12 -le» • 26,.4 • •11,500 11 ..... 28.0 •. •ll,580 10 ·527 • 26 ••• •ll,920
9 .,70 • 21.6 • +12,320 8 +614 x U.O • + B,&DD
- 'l'l, o£1)
-.9 • .s.- 2• -46.9 • ),.8 • .. 178
::::: : t~:g : : :~: ~ -46,9 • 26.0 .. - 1,222"' ·46.9. l7.5.- 1,760~ •46,.9 X 45,.6 a - 2 1140 I
~:; : ~=~ : : ~:~:-+71 .. 7. 55.] •• 4,065 ) ... 73.7. Sl.O II. 3,755). +71.7. 45.6 •• 3,355 ~ .. +71.7. 37,.5 .. + 2,7&0 I'll
.+7l. 7. 26.0 •• 1,917 ... +7l. 7 • 18.0 •• 1,327
T a till Md • +l2, 21e2 lndl pounds """
ltaaint (e)!
£!!I.U1 u •l52. 4.9 • - 1,723 u -J!16 • a.o •• 5,5411 12 ··l5 • 21,6 •• 9,~ 11 ..... 26 ••• -12,800 10 -527. 28,.0 • •llt,'78D
9 +5-?0 • 26.4 • +15,Di0 8 +&lie • 21.6 • +13,280
-JS,'D3
!!WI -•6.9 •U.9 •U,9 .... , .... , .. 6.9 -.9 +7],.7 +73.7 +73 .. 7 +7],.7 +73.7 +7),7 +73 .. 7
,5 • • 2• ],.8. .. 178
10.0 • - • ., 18,.0 • - 8le6: 26,0 • - 1,222 .. l7.5 • - 1,760 .s leS.6 • - 2,140 , 52.0 • + l,llld'" 55.,3 • + lt,D&5 to-55.l. + •• 0651:
:~:~ : : ~::: :· 3'7,.5 • + 2, '760 .,. 2'6.0 • + 1,117
Total M • .,...4,037 lnch paunda CltL
lealnt cr>l US!!l
13 -396 .... 9 • - 1,960 12 .... )5 • 14.0 • - 6,090 11 -r.e4 • 21,.6 • -10,1t8D 10 •527 x 26,.t. • •13,ft0
9 +527 x 28.0 • +15,960 8 +614 • 26 ••• +16,220
- ,J ')t).
!!WI
=:::: : 3:: : : ~~: : -U.9 x 10.0 • • 469 :.. -46.9 x 18.0 • ... 8'-6 ~ -'-6 .. 9 • 26.0 • - 1,222 • -46.9 A 37,.5 •- 1,"0 •73. 7 • 45.,6 ... l,J55-+73. 7 • 52.0 •• l,llD ... +73,.7. 55.].+ 4,065 CQ
:~~:~ : :~:~ : : ~:= 2 +7). 7 • 45 .. 6 •• l,l55 : +73.7. 37 .. 5 •• 2.760
l!!!S!!2!! +117.3 • 1,.3 • • l!U +117 .. 3 a s.e • • 6&1 +117.3 • ll.l .. + 1,5)8 +117,.) • 21.3 • + 2,500 +117.3 x 31,.8 • + l, 730 +117 .. ) • 40.9 •• 4,810 +117.]. 48,.6 •• :i,700 •117.]. 5].7. + 6,310 +117.] • ss. 7 •• 6,540 +117 .. ] • 54.5 .. + 6,400 +117.3 • 49.9 • + 5,860 +117.] • u. 7 •• 5,015 +117,.]. ]),7 •• 3,955 +117,.) X 24.,0 ID + 2,817 •117,.]. 14.7 •• 1,725 +117,.] x 7,.D .. + 821
.sa,ss5'*"
.l'.esl!!l!l_ +117.] •. 2r.8 • + l29 +117,]. 10.0 •• 1,17] +117.]. 19.] •• 2,262 +117.] • 28.8 •• 3,380 +117.3 • li,.O • + 4,460 +117.] • 45.6 • + 5,!150 +11?.] • 50.6 .... 5,930 +117.3. 52.7. + 6,190 +117.] • 51,.] • + 6,020 +117 .. ] • 46,9 •• 5,510 +117.]. 39.7 • + 4,660 +117.3. lD.7. + 3,600 +117 .. ] • 20,9 .•• 2,455 +117.] • 11.7 • + 1,374 +117.3 x ~e.o • • ft69
• Sl,Uol. "'
W5!!!m +117.3. l.8. • .. .. 6 +117.]. 13.2 •• 1,550 +117.3 22.7 •• 2,663 •117.1 n .. e •• l, 7lo +117.3 ll.t. •• t.,620 ·117.3 4'-.6 - + 5,225 +117.3 1..6.6 • + 5,t.60 +117.] 45.2 •• 5,310 +117.1 ~eo.a · •• t., 790 +117.3 3t..t. • • t.,040 +117 .. 3 2t..4 •• 2,862 +117,.] lle.8 •• 1, 737 +117,) 5.6 • + 657 •ll7.J 2.2 • • 258
~ ~z,e.\il. ....
.Ell!li.!!9!l +117.3 • ...a . • S6t. +117.3. lle.l • + 1,678 +117.3 • 23.5 • + 2, 760 +117.3 • ]1,1 ... 3,650 +117,.3 x 36.2 • • ft,25D •112iJ • l8.2 • + 4,485 +117,.] II )6.,!1 c + 4 1 3]5 •117.] • 32.6 .... 3,826 +117.3 • 25.2 •• 2,957 +117.3 • 16.2 • + 1,900 +117,.] Jl 6.5 • • 763 •117,.3 x 2,9 e. ... litO -117,). 10.5 • - 1,2J2
~ 'l'i ~"'" ... >i"T,:at=•=l=";lrr.;,"-..so.;:...:.•OJ~Z~lnch.;:.....;_..;__.,. _____________________ _
)paint (glj
I
radial ~
12 _,.,, • ..., ... 2,1l0 11 -484 x 14,.0 • .. 6, 78! 10 -527 • 21.6 .... u,r.oo
9 +570 X 26,.1e • +15 1060 8 +614 • 28.0 • +17,220
.. "·""~
.. ~~ ,,S" Total M
9 • +49,9)6 tncn pounde
-•6.9 • .5 • ... 'tilt .... ·46,.9 x 3,8 • - 178 .. ·46 .. 9 x 10.0 • - t.69 eo._ -46.9 • 18,.0 • - 846 N
:;~:; : ~~:~ : : ~:~=~-· •73.7 X le5.6 a + ) 1 ]55 1, •7l. 7 • 52,.0 • + 3,8JQ Cb
=~~: ~ : :~:~ : : ::= ~' =~~: ~ : :~:: : : ~:~~ ,.
a!£!!!!!! •117.3 • lt .. 9 • + 564 +117,.] X 13,.8 • + 1 1620 +117.) • 21,.6 •• 2,536 +117 .. ) • 26.6 - + ),120 +117.3 • 28.,7 • + 1,370 +117,.3 x 27 .. 3 • + l,2DD •117.] • 22.9 •• 2,687 +117.3 • 15 .. 6 "' + 1,8JO +117.] • 6.6 • + 775 -117.) • l.2 • • l76 -117.) • 12 •••• 1 •• 56 ·117.J • 20,0 • • 2,JU + f~,Sl."'.,..
c
•
D •
•
•
•
•
A lpalnt (h)l
I!l!!ll 11 _,..., • "·' • - 2,)75 10 ·527 • 14,.0 • - '1,JB5
9 +510 .. 21.6 • +12,)20 8 +614 X 26,.ft • +16,220
of'f'l,~~·
ahea:r
-4&.9 ll .5. - =• .. ,... ::::: 1~:~:: ~=t -46.9 " 18.0 - - ~ +?l, 7 • 26.0 • + 1.915 +7l.7 • l7.S • + 2,76Dc,. +7l. 7 • c.s.& • + l,l~5 > +?l. 7 " !2.0 • + l,8l0 c: +7),. 7 M 55,.) • + 4,065..., +7).7 X 55,.) a+ 4,065: +7l.7. 51.0 • + l,?55
reaction +117.) • ...) • + 505 +117,.) X 12.0 • + l,ftlO +117.) X 17.,2 a+ 21020 +117.l 1111 19.2 • + 2,25S +117.l. 17,8. + 2,090 +117.) • l:J.l •• 1,562 +117.) .. 6.0 • + 70ft •117.1 • l .. O • - l52 •117.) • 12.1 • - 1,50) -117.J • 22.0 • - 2,580 •117.] • 29.6 - - J,•75
+<~,'-'""" Total 1\ • •"l,6'64 lm:n paunda
10 -527 • ..., .... 2,582 9 +5?0 X 14,.0 a + 7,980 e •&lit • 21.6 • +lJ,zao
-t •l.~ ··~
Joa1nt (JJJ radial
9 +5?0- ... 9 • + 2,792 8 +&14 111 1&..,.0 • + 8,61l0
.. ,,,,q,
l!l!!E ..... ,_, • .5 • .. 2ft;. •lo6,9 • J,8 • - 178 • .... ,., JC 10.0 • - 46t,.. +9).7 X li.Q • + 1,)2'7 +7). 7 • 2& .. 0 •• 1,915 +7l. 7 X l?.S • + 2,7&0,..... +7),. 7 X 45,.6 a + J,J55 ;;;; +7l. 7 x 52.0 • + l,B)Q _ .. +7),. 7 X ~5.) • + &.,06" "" +73,7 X 55,) • + &.,065 ?"
IE!!!£ N
-46.9 Ill .s • ... 2&.:
=~:;: l~:g : : ~~}! +7l. 7 X 18.,0 • + 1,327 ... .·u .. 7. H.D ... 1,915 • +7l.7 Ill l7.5 •• 2,760 .... •''· 7 )( 1!1.& 0 + l,l55 ~ ..
:~~=~: ~~:~ :: !:~:,.
.£!!!£!.&!!!! +117.) • l.& .. + 1.11 +U7.l x a.a •• l,Oll +117.,) X 10,9 • + 1,280 +117.J X 9,6 • + 1,128 •117.l x s..o • • 586 •ll?.J X 2,2 • • 258 -117,) X U.l • - l,l2& •117,) X 21,0 • • 2,ft65 -117,) X XJ,.2 • • J,51t2 -117.) Ill 37 .. 9 • - 4,450 -~r.o~ ,
.EI!!Sll9!l +117,3 X 2,0 • + 2)4 +117.) X 4.2 • + &.9) +117.J X 2,6 • + J05 -ll7.J. 1.9.- 22J -117.,)" 9.2 • - 1,080 -117,) " 18 .. 2 • - 2,ll& ·117,3 • 28.0 • - J,28S •117.,) X 3&.,2 • • 4,250 •ll'J..,) X 4r..,8 • - 5,260
-1 s,to:r...-
Total "J .. •ll,977 inch paunda Dt:.
(j,atnt !k) I l!!!!!1
8 +&14 x 4,9 • + l 1D10
I pa1nt (m) I
-.... 6.9 • .s - - 2\,.. +73.,7 II l.8 • + 280 +7l. 7 • 10.0 - + 7]7 +7). 7 .. 11.0 • + 1,327 )>
+7), 7 • 26.0 • + 1,915 • +7),7 X 37,5 • + 2,760 AI
+7).,7. lt5,6 • + '·'"'l; .. +7l. 7 x 52,0 • + l,8l0 1'
!!!!!!! l!l!!E +7l .. 7 Jl .s • + l7
=~~:~: l~:g :: ~~~ ~ +7), 7 • 18,0 • + 1,)27: +7),7 • 2&.0. + 1,915.,. +7),7. l7.5. + 2,760
Total Mm • •11,135 inCh p.ounde ,ur
lpa1nt (n)l
.E!!!!!l
Total M • •I,B£J Pit
+7l. 7 • .5 • + l7 ~ +7l.7. l.& • + 280 00: +7J,7 • 10.0 • • 7l7 ~ +7),? Jic 18,0 • + l,l27 :t' +7),7. 2&.0. + 1,915 ...
.EI!!Sll9!l •117,) • ·' • • ,, -ll7.J. 1.5- - 176 •117.) • s ••• - ,, .. -117.,.) • 12.8 • - l,SD2 •117.3 x U.l • • ~,!llill •117.3 x Jl.S • • 1,700 •1171 l x WI.? • ... lt1 785 -117.3 " •8.J • - s,&&s ., ... , .. ,~
.EI!!Sll9!l -117.] • 1.0 - - 117 -117.] " 5.5 - - 6~6 -117.) • 12.8 • - 1,502 -117.] • 21.8 - - 2,560 -u?,l • n.& • - J,no •117.l. ItO.& • - 1t,76D •117.) • lt8.2 ... 5,6&0
·t&,'U'S"
.EI!!Sll9!l •117.] • .., - - 528 •117.] • 11.8 - - 1,J85 •117.J • 21.0 - - 2,.6J •117.) • lO, 7 • - J,600 •117 .. ) • )9,8 • - 4,&65 •117.J • ~7.2 - - 51550 -,,,,q,
.EI!!Sll9!l -117,3 a 4.2 • • 49l •117.J • 13.2 • - 1,550 •ll7.l X 23.0 .... 2,7Dd -117.] • J2,0 - - l,756 •117.1 • "· 7 ..... ,&60
- ,,, 1$'1
B
. 27.
fpotn& (a) I DIU!1 l!l!!E
+7J. 7 a .5 • + )7 _ +7l.7 x l.8 • + 210•
=~~=~: ~~:::: l,j~~= TaHl M • -6,1Sl lncb paunda ""
lpa1nc !ell D!l&!l one !!IW
+7l,7. .s. + +7), 7 II J.8 • + +?l.7 x lO.D • +
potnt.
Total M • •1,655 ...
ii4!biil
+7l.7. .5. + +7l.7 X J.8 a+
l!l!!E
... )7~
zao,
+7l.7. .s - + l7
+I"JZ,SZf
1::.: .· L: .. 1 .........• ,.
: :·!:·:: • t• •
. . . ..:..l :.:.:.... -.
: .. ! '!:
·-~-· ..•. : !' .;
···-·~ ... .,. . ' • I <:· ·!·
: . . :. i.
.E!!IS.Usll •ll7,J X •• 7 o • 552 •ll7,J. "·7 •. • 1,562 •ll7.l Ill 2l.5.- 2,760 •117,) • ll,2 ... l,660
• i,t1~
.E!!IS.Usll •ll7.l a 5.0 ., ... 585 -117,) • 14.2 • - 1,667 •117.] X 21., • • 2,560
·'i,U1
.E!!IS.Usll •ll7.J X 4,& • • 5.40 •117.J. 11.8 .... 1,4)2
-1'1,"1
.E!!IS.Usll -117.l • J.a • .. 446
.. ao 1, SZ../0
...
u
"\":. l \·,. I
c
D
"'""" -•• an - ouUcollv -• ring (.,..\ riiiQ) ... """"" In tno flgun Oft page 11. Since ,,. •• ...,.,. an ftDIII gal.ng to tr8 cant~SII•ru aa a lad A
an u.. maJ.aeau• alu.t, 1 t will hi IIDH ccarrqnl•c to nsrl~~e~~ tnn .. 1 en corrcant:l'eUd V8luu. Thla can be dane by aal.UplylRQ tha val-.e by tne ere langtn ar - _, ar 10,1 tnBa. Tho naulCIIIQ ... n.:onua\od •ol- an .- In - talllllollng r~g,...,
1\
/ 'I
-
8
/ / ..
--~26
/ -
. 28.
I
I /
/
y
• •15,190 b +17,800
" +156,410 d +l22, .. 20
• ..... 0,)'10 , +SOO,:J20 g ... 99,350 h ....... 3, .. 80 I +317,210 j +139,770 k ·17,730 1 -85,1t4D .. •111,)50
• -aa,6lD a -61,5lD
" -37,590 q •1&,550
• ... ,090 Total·~
bDS!!!s !ii!l!!1 .!1!!1!!1 i!=!!l !.!!! i! !!!!1.siliU S!l!!!l
c d
• ~ g
" I J k 1 .. n a p q
•
• b c d
• , g h I J k 1 II
a p q
•
• 15,190 ,. (+28 .. 0) • - 425,JOO + 17,800 • (+2&.3) • + •&B,l5D +156,'-lD • (+21 ... ) • •),l .. 7,DDQ +l22, .. 2D 1111 (+1 ... 0) • +4,51 .. ,000 .41tD,l7D 1111 (",B&) • +2 1 1 .. 0,000 +510,)20 M (-t..,Bii) • -2, .. ll,SOO ..... 99,350 (Ml ... Q) • --619911000 +lt4ll,.ltl0 (-21 ... , ... ,, .. ,1,000 +31'7,210 (-26.3) • -8,)4.3,000 +1J9, 770 (-28,0) • •3,913,500 - 17,730 t-26,3) •• •&&,JDD • 85, •• 0 t-21 •• ) • +l,B83,DDD -111,350 c-t•.o> • •1,559,000 • 88,630 t-•.a6l • + U0,15fl - 61,530 , ... ,86) • - 299,030 • 37,590 (+14.D) • - S26,lDD - 16,550 t.Zl •• ) • • 35.,110 ... 4,090 (+ft.3) • - 107,560
- 15,190 ( 0 ) - 0 • 17,8CO (-9.57) .... 17D,lldJ +156,410 (-11 .. 0) • -1,815,200 •322,420 c-z•.2> • -7,883,000 ..... 0,370 (-2'7.6) • -12,153,000 +!IDD,l2D t-27.6) • •U,B09,DDD ••99,350 c-z•.z> • -12,aa3,ooo +.ltlt3,.8D (-18,.0) • ... 7198)1 000 +317,210 (-9.57) • - 3,0J5,'JOD +1J9,77D ( 0 ) • 0 - 17,730 (+9,51) • - 169,680 - as,••o t+U,Ol • - 1,5JB,DDD •111,350 (+2~.2) • - 2,69~,8DD - 18,&30 (+27 .. &) .... 2,1t46.2DD - 61,5)0 (+21,6) • - 1,6511,200 • 31,590 (+2 •• 2) • - 909,100 • 16,550 x (+18.0) • .. Z97,9£JO • lt,D9D 111 '(+9,.57) • .. H,lltO
c
•
D •
•
•
•
•
Tne reaul Ung •atreaaaa• an the analogous column tlecorq th8 carrecUng 11011111nta, :ln other woJ"da Cf'lange thel r etQna and add dlhi:Ur ta tha 1n1 tiel mamanta of the CUI' ring.
c "'·· -r. c:. 111y• • try • .Z8,0 • ?,JIG ln lil 0 0 b +26.3 + 6,900 .,,, ~ 9,6&0 • +21 ... + 5,&10 •18,0 •18,170 d •t~.a + l,&ID -2~.2 ·24,420 • .... 86 + 1,270 ·27.6 -27,850 , -~.86 ... 1,1711 •27,6 -27,850 g ·14.0 - ),6111 -2~.2 •24,UO It -21.~ • lti1D •18,0 ·11,170 1 -26.3 • I,IGD -9,57 - 1,660 J -za.o •7,DD 0 0 k •26,3 ... 6,900 .,.5, + 9,660 1 -21 •• - 5,6111 •18.0 +18,110 .. -14,0 - 3,680 +24.2 +24 1 C.2D n -•.86 ... 1,270 +27.6 +21,850 a +4 .. 86 + 1,210 •''·' +27,850 p +14.0 • ),680 +24,2 +21t,UD q +21 ... • 1,110 +18.0 +11,1'70
+26,] + 6,1DD +9.57 • 9,6MI
A
OWB 20'1 Tl'te L1ncall"' Electric ~any Omar bJ Bladgett Nav,8,1%8
B
c d • "• •1l,&2D •ll,620 •13,620 ·ll,61!11 ·U,&ZO ·U,620 M
X • 7,)50 .. &,900 .. 5.&10 ... 3,689 • 1,270 - 1,270
"v 0 ... 9,660 -18,170. -2~, .. 20 -27,850 -27,850
"1 .. 1,519 + 1,780 +15.61tl +32,242 +41t 1 0l7 +5D,OJI
"r - 7,789 •llt,IDD •1D,Il8 •IUN • J,ll7 • 7,292.
' h
"'• -13,61!11 •ll,620 -13,620 ·13,620 •ll,620 •ll,62D
"· - 3,680 ... 5,&10 - 6,900 ... 7,350 - &,900 - 5,610 M -14~420 -18,170 - 9,&60 0 + 9,660 +18,170 y
Ml +419,935 ..... ,148 +ll ''J2l +1),977 ... 1, 77) • I,S44
"r + 8,215 .. 6,9r.e + 1,51t1 - 6,993 -12,533 - ,,604
" a p M • •ll,620 •ll,61!11 •ll,61!11 •ll,&ZO -ll,620 -11,&20 M . • 3 0 680 ... 1,210 .. 1,270 + :S,680 + 5,610 + &,900 M >2~.420 +2?,850 +2"1,,850 .z~.~211 +18,170 + 9,&00 v M1 •ll,U5 - 8,863 - 6,153 - ), 759 - 1,655 ~D'J
"r ---- ~.Dlt + ... .., + ,,,., +10,721 + 8,505 • 2,5Jl •atr-•
ldharet "• • ._..., r~ the laia1 laed d the .alopua column II• • IRQIIII1nt rram tha bendlng •etl"aae• about b-x) orthe enelagaua ~:aluM.
"v • mamant from the bancUng •a:treaa• about <v-v> ar tha analCJQOLI.a colUIIUI. Mi • inlt1al moment or tne at.aUcally d•terminant (cut) rlng,
"r • final moment ar tha atatlcallv ltN:Ietermlnant rtng.
MB•im~o~~~ IIDII.nt an rtng- M• - 1¥,6~ ,;, lk (1'~111.)'" . 2" ~;," Section Udulue or 1• wide l"ing s~ =
Bending atre•a in ring
tr= ~~ ~ ... oZ.4 o{.. z.oo ps 1
t:."'mpres:u#n ~n &J~"t5Jd6' t etr:Jtdn 11111 ln'Sir:ie
-29.
~ ~-!-!-: . ,, ··••t•·l i . . : ; ~ :::; !
c
D
A
Ac\ually ,.,. .... u .... - 1• lly 1.7!1• aurr ... 1ag ~lnp, on 1~· ...,ttou. Til• tnuUing bonding """"" an U.la 1~• Ofilia _,_ la ~- a1ow•
r- 2.0 3,, in ...
fu thtl 1~0 •lila ...,uon, Uola HcaNa UB,91DlC1~) • 1SO,DDD ln lila
The bllndlnQ a&rnsea ua-
-io,:&. tr= Me JlfAIJIXi'btl"t) ., _ 1, '9b pJ;
-y- »S$1'
tM/cie \ I?"= ~Jip.aro'trfi!J • + 5', ,70 p-si :r. :I03.'t
Tile ... '-- ttqaUva IIGUn& 11ft the 1• 1111lda ucU.an af &lla rl.ng le 11,&110 ln lba.
For &N 11,• wlda IAUan, Utle be~ UI,UII)(l4) • 101,000 1n lH
Tna blinding e&ranu are•
TMI auUlda eurrace ar the lft811 hb • tang..,Ual ltl'au _,.1ah varlae fi'GII a tene1an ar 2 1180 pel to a CIDIIPI" .. 1Dn ar 1,~ pel.
Tha lnalR edge ar &he atlft'enlng rlng hila • etnlla wblc:n verlea rru a tanalon ar 1,170 Pill "' o --lan af 1,110 Pill•
Now ... will c::onat.ur the 14• wlfti Hctlan or tN 111'11111 with ltll aurr.nlng rlng H a curve be• .nd 111 lf thla lncr•-- V.. bending a\naBD to any IJI'IIt extent .. Baa O.aign af IRlc:rm.rtte, IICtlan 1.1
~ \ \
\ \
I I
I
I
B
Ha&-llanhl Clangl\udlne1) lhoar atJ.doan Uoo onall and ,.,. aUffonlng ring.
} !:-a::-=::, --::d ':n:!~;• .!:!:a:a;::,.!• 8 ~":!:-~'=• ~.:;-~:r::,~:r!n":. ~=11 1 tna .,.._ lld'llcl'l ia t.r~~n.teerlld \hnugh t.ne lfltlde.
TD Qllt the ... a.. ahur, we laak t'ar two pairrte 411ftlch llaue t.l'la tp'eetee\ ci'W'lga ln &landing _,.,_ FI'IUI llhlld: 19 U.le 8PCIBBI"I m bB palnte (c) and (d) , 10.1 lncnaa ·-··
""·.f. 7. '18"4 q, lk yl'(,,;) - -1()'1, 200 ,;, ,~. .M,.• {+ 2,n1 ni lkY 1¥ml • ... 'D, ~~)() in 16s
_ JI'IC: (-JDUIK>TI.,7) = - 89'1 fl$/ 0,.-y ZDJ,'t
f.·(- B'l'lf>tiXJtl'\t'l,? • - /S,H'o AS,
~ (•ltilti'IOYI.6?) tr,.= y• z.oi+ "'
F;. • fz'IOpt.IXN""IAt'j"
+Z.'IOp-a,"
.... !r,oe o 1~'5
Ttta dlffH811ca ln \haea twa bending farcn auat &renefer out ea ehear wlthln a 10.1 lneh lenoth•
r .. -16i";fo-(!6ioeo) ., Z07t::J ~hnch (t~<Jt> wetrls} l"o /P•/
or 103() lb;,;, per C,'l/et we.lcl
~----- zz.·· _____ ...,
A y M~AY T.•Jt\Y Ia ZZ'\< .!?it 1!.1~ D 0 0
..i"'tLS':t.-7/i( 3.'1'1 -tZ-bi~S /1.08125 31./l.l.
c
D
\/ c•nte.r e~F -f:.-c..---.,..,,..,..t-u.re
•. , ... !Itt' MS t 5,4JZ" l.!i/t.a
~D1~~ /IB.bS'-total 21.'1~0 ~z.l'l$"0 /j'f.798
radt~ or . Z S, 7 0 7 1
;, ...-csntar of ,,. .. t'l Y·~· ~ ~ I. s-oo m• A at"4'IO •
r.,.' T.•J:i~ ... T.'X, -{'l'f~)~ II,<{, '7'1[3- {t.!itJof.33.1'/S)•/f.!l.'7'/&- '18.'-FJS• J/{,.513ti{~-
bendoil<j -sire-s<; mSiae M( r:- r;.) 111 (zs-.1ss--18.) _ • o'l'l'- ft-1
g; = A Us"- r~) rt" z,.n(tr.?o7-ZS:S6"s:X~-bendtn'l stre .. ,. ,. .. :to/Jt>
M(r.-rn) /1'1[?..8.-U.3H) ,. .o;oz M tr, • A {r~- r.) r.: 21..UC U,7"7-2S".iiij'211)
.Tn tlu"s PKRmple-
~ • . 0'1'12 .111 = {.O<J'I2.){2o'I.OOcJtn//;) • 'f,OOO.p-s./
~= .o,oz ..,_ = (.rHoa){zo'i.ooo,;,/6) • .Z,oao. post'
m-;u It ant .. nit ;orce
Fr:i.J.~-~ (,)'+ r: ·/~o/tl.t.7·n8S)+("'s,:.~j ~ i!'-/':l9.? tL,.;
lr'l -:;,;., £70 weld rrei::z ·• "e;,. 11."~'"·-'~'"s Z~'l.q,t tty,;, n
r.o; {~I.OfJo,... 1)~'''7} ~. 11>3¢>" a,.. bea:l:J"t' ::Jf !1;7l, use~
. 30.
•
•
•
A
• F
L--iot~
• B
• . 31.
Moment In dtic at"@ /14 Q Ms +- M., + M,
---------------e.rt• lri.L Ft' .., !1.!1'. !!.• (Lt' +'1\
Fd=}(-t-M,•~..,."'Ot""""~+fif"'"'.''~YXGI. I{ rof}
'I FJ. M,= ~+'{
~o~e. nee. J M.,
M _ B.Et1
And .a. M.L ,. ""' " ""' 'IFI
M~ • 14? + Ms
Lt' FJ "'N" £.., :t:ol +-?
{ Lt' ) 'IFd " M. t M,"'fo\.: M-{1+ ~)~ Mr y;:t'l
(~)a. 1 L-t '"1 t -rrr--&H ~
= '1 Fd # /1'1 (Lt> )) x;;; t- 'I
we need .M,,
~~~:,t we mu~t f,~d M,.
c
0
~>r M."
f1()W uns/der the 1imer dtic a"t CGJ
M11• M,_ +Mn + MNJ
1 Z.Fd ~ S Fd tt' ~~
56 /1, =jl.tl )L l{LJ. • {L t' + I( )L Lx;. +'I xa.
--------------·----------vve nef'd M,11
A
B
. 32-
Example.:
-+-L ---Jj
F• 2 2,000 /b d· zs'J¥u. I .. ~\ '!!.f/2•. 2ol in,
r; = 'f ,;., r • 14 in
F-.. • /'!.,()()0 lb wt -atu.l • 2.'1,178 I~
wt Lva:ter • q,'tO?S lb ., ,0 ~~
o~ -a-z,ooo 1\. em Qt:at:-h beo.r-1'11'3
J:. = 1'/ • 3 • .sr. If Deso<ln C)~ 'We/dments ?.'l-B
C!CIU 17 erlrje SIA('PIN"ted
Cll = .s"( = 2.06
c
•
D •
•
•
•
IJufr!r
beno1n9 <otre~-s in•drsc. o.t h•b, pomt@ radtill ten":>i /e stret>S
'l,ZOO. p-o 1
,%111 iF we were te~ a:>nsti:ler tlte ~ILter ecl9"'s of f.",. dt's c to be st'mp/y '1>1Appt>t"ted, {ht~ l.ck:JUid cbt:~rqe tc. ffle fo 1/f) IAIIn"f -
li...3• (l"s-Yts>' = .s1 :r.... (2&>/)(,S'f
M. .(zz,ODoXls';y){.st){l+ .L t-L t- .. •) .. 79.'100 ,~ IJ. 4 ('lSI) ('Mi/) 1 f'l.stJI
Th~ ac..t"ttal edqe C!dndt't;ptrS of. tl;e drs.'c w,'/1 he SIJme wh.sre be'tu;een t1;ed and s(mp/4 S1A.pf>ort9J, fience ,the f'Q.dJa.l 'tenstle stress r th• :r:·~-· .::r: ~fe hu. 1:. wr II bE> ~ome wherC' 1h betl{)e{'n th("'.;e two sets of ~Jetf«e'3. ..
A
B 71le ciratm Fert?lltlal hl!et weld befltlecn tAe outer cliic an'lr the 5/vJft at' t»hf @ must be aJ/Je to trr~nsFer tl!ri mtJment {1<4) ffl)m the sktft llito the d~ •
5,.,~ ~d'& 'ft'~B/m sa. 3 in..,
r ./01.... 1/Z,?OO _ z, z u,., /~'/':.. ro • --s;- • S'O. '3 - -.c.; "'
qfso 11111st rmnsfer a torque af
T- 1f3,ooo HP • 63,ooo{oroo). Yi>Z.x>o 1n /Js • RP.., Z.'7
a c:lo u biC' sc t of we Ids
rc>~ht-.r/r:l 'J..•11'~-s.'fl':>'· LfOZ.m-,
f+• {~v {'fr,if~:'D"I) = z, H-5'". lb,,/,
t 27.,0il>O If>
t ,F( <ll'l>C
fo {ir,,S) • ZZ,OOO ( '12, ?S)
t.· 21.ooof"t2.~~): sr..'I(:O lb1 A..,, 1td .. 'Ita· zs-,2. ,;,
(. l: S"f.,'IOO .. 1.,1 30, 11>;,,; Is 'l A.., c. ( z s)
-33-
,;tnce t ht vert AI shec:u- CU1d bendtnq. are -su/Jfec't to. q et:Jmp/e.te rever-saf1 we CtJu.ld use tim Far tne fct t '<i uE' a.llo tNQ ble et"' d. ir:to'n -
Z7 RP~
or ~'ttl6){ '1so){2o) = 15!> x./IP6 e9cle.s
"!>0 1./.Jt! w:/1 u.se oulllr Z~a,aoo cqc/O''S
't,_• 1~k .. ~~-o • '/,ooo ps,
1.21,;, or 1?f" ~
partt4.f pe.ae trn.fta·a '/fPD!Je weld
1::::. 3 'f zo llwi ,. • 85s- 1;, 0 ,_ .?§" deep . o/MO p$l
-...,-- .. . . I
~
Welded
Allllllllllllllffih: -~~~::;~~~ bead ,.;9 stress
f:eao.i/e Me _(7.1SO.;,"'•X3t~,;,). '1.05 "'";
~·r- ~s.sr>t. t.•
COII"DreS$t•e ltfc .e/1/SO .. ";P){2.o\~.,. 2 [gl Mi
D;"r· ss.sst.l~ •
c
D
~::a: :n-: 1::r;:.:1!~ ::U::r!::r:::~:f =~: ,.:W"• :r ~ ·::1:!~..:1~r::::::!~ axle plu. any vertlcal portlon ar t"- weld, ... below.
Total lltllgth or alngla wld aaaU~&U to ba erractlve 111 tranarenlng the vertical ah .. r ..
L~2.(21'H~\").,. 701-'ftP Unl t ehaar rarca DR wela.
L • ..Y... 3'1"Z"'" ~ • r, L • ~ ~ 1/,;8 y,,. Lag alza or ru1at weld (£70 we-ld 118tal) ateadv lolld
!..) 'f. HI "fln ZCfS" • =(.7D7X'-' "'~ ~ • ""
but bacau&e or the 1 1/2 lnch thiCk plata, mlnl•um weld elza 11 5/16 lnch.
Ir 11111 .. uaa t"- rauawlftG retlgUII load condltlana: z,onotooo cyclea atraaa range K • mtnJ•u • o, thle bec:amae AISC Fatigue catega.rv (F) and
'i""' =- ..::!i!:._: II 1t.1i = Ill<'-' but not to exc:aed ataady value or 21 kal • 1-K 1-D
B
!:rrt!.~":; ~~..:·~~~ ... a:, til.: ~~."!;-:. ::.. 101~!...""::" .. -;;:.~ Thta Mlll produce • horizontal rarce or lll 111,... Jr we • .._. bn&lel ar ttt. natuft ar the burlAp or the ahll.ve ahairt, that thla rarce le eurlad aqually bv the outal' alde pl-'- end the lrtnBI' aldll plate, thla 1111111 ndu.n tne eppll.ad ron:a tia aiiCh Plata to 56.5 111,..
F•&SO" Treattno Chs outer atde plate 1111 a circular pJ.ete* wlth IINI wltftaut e arrtnl hOle, almpla iiUPPDrte or rbad at tha autar adQe, w get a aallect1.Dn or valuee uelng ronuJ.u rram Aoartt•a FaNUlaa rar Straaa I Streln, ltth Edltlan.
Dut-er ~J~e~ s/mplot •"P~r eJ
@ o;= '" 8 /(s; t;;xmtMI ot
traf hilt
A :dJ, 37 melle:~ . ciro./4r P!"tl' 1
Rt center .. lth -ttt/11 f»(fo
G tJ:: 32.$"/<Si
',.4t&& w ~ent:fAI .tt -~ter r;
4,. o. :1. :l /fteMs eir&A{ar pMtt' _.t: t!mtter
solid
Df~":j t>"'feS
8;• 3"1.6 (<.,; ~f-'IH1:
a-,• Iii, {t 1<si ::.1J:r~e
c.,:' 1!), 1'3 ~ .at center
a:,. ~o.q ~t~i 1 ""'"' or :!-fent.i.t •f cBIIt4r r,
(f..• li,'J K';i
='fr•:t. .. IT.• l.fn~,; ot ~.~ ..
A,• ~'f.::t"i:
711ts wo~l< follows on 5/Jee6®<111ti®
• 34-
Route 4th £d. PIIQII 220, CBU lit
_ 3F(m'!.t) [r"'-t'-1- zmr.'lr:-r."l-Bmr;r,•~ft+'fr.'r.Yifltl){l"'kft-f"] .(); 'ftrlti'Ft' • ' r: {m-1) + r.'" (m tt)
r 1C~.f")~).._1] [ "'-s' ~ 2 !~'(11~s'l- Bt\Ji'6'{s}~J.,. 'f +'1Wfsffkl'{i>te'ftJ" o. I ?I ~le 6' Y'ltf.;'i)'fiGoJD'b'l.l' ll1)'(;\-1) + (s)'t~ .. l) &t<6tlfer) ·
Roan ~&h Ed, ·PBu• 218~ """" 1
0, 2 Z /1/C/tt!S
(•t <e11ter)
c
•
D •
•
•
•
•
Traa fgllacdlng aaclr:et and &hlll'lk for a large ~:oupJ.er 1a to ba 1nvaat1gatad ln ragard to weld &118 and
A stresses an the unit.
] 811C8UBU Of t.na lGDBIII f 1 t 1 we will aaeuma that the shank cantaeta the &aekat at just tw oppaa1te pglnta •
The socket ra~lll be traat.ed sa a at.ruct.urel frame. It 1e etatically lndatermlnant. Th• •calU!Uft analooy• msthod utill be ueurd. Thh nthod la c.av•r.S ln Rmra d111taU in the book •oeaign ar Welded Struct.una•, Section 6.1.
The calUIIll"' enalagy method involves finding t.ha propartlaa af the •aeaUon•. Tnat the fra11a H the c~mtla section of a column. The dlmwneiana of t.ha •aacuan• are the same as tha soCket, BJICapt that the wldt.h af· th& •section• bacamaa l/£1 of th8 socket.. The fallowing three prapert.in of t.he section 81'8 found-
a) area b) 1110ment of inertia about the <•·•> neutrllll ada c) RIGIII80t of inertia about the (y-y) neutral elllla
The fnN ie then cut at aoma paint, thh •ekes u atatically determinant, Md the IDDRtanta are found using tne appUad loads,.
B
Tha resul Ung aoment.s an than t.reated as s lDad on tna •analvQG&e column• aecUan~ These •1oade• will causa-
d) an axial laed (P) e) e bantling moment about pia (x-x) (M ) f) a .bendl_ng l'lloment about ads (y-y) (foJ:)
Using t.hua •load&• and •ma!Mnte• with tha propartlal!l af the •analogous column• aactlan, the resultlrtQ •etrasaas 111 on thie uection ar• found,.
g) BJiiel strne p
"•. i M c
h) banding streaa • .-;;-M C
l) banding stress (J =+ y y
-35.
These •atreeeae• . .aceme carrrctlvB momenta whlel'l must be •ddaa tD the ar1g1n•l mamente of the st•Ucflly determlnent frame. Since they ere corrective, their algna IWet be changed.
c
The reaultlng moment.a tnan became t.he final mamente an the statlcelly :lndeteJ'rdnent. frame. ·
Tnere lo one ='::. do the roaleUng shear farcaa occur only ln twa oojocent aldea, figure h), el' ua t.hey 1n ell faur alGae, figure (b) 1
21,'1{,8 .. -a._, ..
The resulting banding mamants era shm.~n bdaw-
... +6o,fil7r~lJl;, JIILIIII!miiii[J]]IllJIIII
--· ... c.u. t
"---~,v--f -r; -stmph'f~ the wDr I<- the f.,/,4,.,,,.;., wlll be u.sed-
A~tt.;,l Ea~ne on &:~nt:l/d'!OU'S aolttmn
P• ;a(taX~j." YJ,.,'I) + (!tl;,_~:¥9~ .:: ~,.f<M-o
13end 1~ moment a~~u t I'X-J<) QJU"J
l Jl.l?'tlGta't"'i·$:1S)-tl6.(31,1'1'1l'l.s'2!}i-3.tliU'/)ti(-31,J'I'tt'l.r6~- ~. IJ<II'I) ,_ M... EX rx £1:
I~ .!IO,,ooo E"I .
Bendrry moment abo~t.t IY~Y) axt'S
f!1y=-O
= .Att.c ., {1_73D.'@/af'l.5"~'- 5) .:: /S", rBB Oi .:z:;, . OCt; d)/ e-..r
''~A>o 14,c ,t2'139+0<) l~..r'(3.o'1!'1) ~ / 1,8'.3 d;.... .r;. stJ,, s In:
tlyz zero
A
,.._ -1!{11(; O
·I!J,?I.> f(ll~
B
. 36.
' ,. -B,?Iii ilf".588
(IJQ) (/TyJ
......
~rom th1~, """ 9et the f1;.21 rvl'!!=fl?i'-: :.~- ,J ;,.:
-;tgtlcall'f li?deter,'Tl/,'nate frame
\Jue v,',tl eomider t~ 10 mch /e.J19th 0~ StJC/<e'f io earrtt the two ~86.1 000 lb ~orces,
~ i:;;;;J
"i"'.U81b
.... (,,871 c ./If,? PI')
I.J I, 200 J"··
c
•
0 •
•
•
•
•
A
lt m1ght be erguad that the torque 119 tronsferrsa tr•rouqh t~-11 fDLir plorte!l liB fallCIIolll"'
'·-·l \!.1r ····· Za6Q::>6
/~88'1 11>
ln thb CIIISB we cen trem·fer the two outside farces in tna 1st ~:notvels tc tnesu ·four farces Dy ad~1no the rall['b•lng ta the prPsent Bl'li:llysls-
Ll&.int. the colwtn ~alagy matttad. we CL.rt one leg of"ll:' calcuh.te tne ll:m.tnt~ or tr.ie aht1cdlly aetern.lnent fr-BILs •
+ 9~.330
rr:,I:?••J '' 1>acl' e,, a .,e.tc1.~!,"" ·""r '~~ "'"
a)l. t'al had'
- ~9.330
p~ 2·~( 9'03o)'91ta)~ 9o~ 380 In
''/'l<:"ilt .P~6Uf /.Y· /)
B
11.- M'1'1,33oJ9%/1'f,S6jj)1 Ye('19,33tl)''17sY+ /.n 1)= +2,?S,,BOC) /f;J
m"mud t?!oiit l'r-Y) , ' ;111 , fz/9''l310,l'9tef·'I.S$:.S)-t~(91,31o}9iaY-t.s::u) .. -~1S'-B.oa. !r.L
• 37-
resij,ftr~') •o;tte:us" or correcir'ue /lloment'S
co,ecl tr:L:: qo.e, ?JBO e -t 2'1d 320 A 3.l.S' . I
_Pl. c. _6;:, ?~,Boo F'IS":Js). r2 vd, 32CJ o;, - .:r. · so.l. s-
·r:.cse roncr·' •; •ts 41C llo<•.· 4/.-t·.'·i- .J. t~ t ht' /716f!l€'rrf: of !i,.. ~,lafrr:>llr1 :1,...-/.',./mrrbnt ·frame ((-ut frQmP} o~ <:.hr:-e( 'I /e. tJ · C'
c
D
A
Notloo oo oheet (3) tbot tbo Jan lloJol .,.... HCtl.cm of tbe rtaa t.o1lda t.o -alodarl.llo, !bLII will c111111e •- portl.ooo of tbo l'lDa -tlaa t.o -· radia~ l.mrard; placiD& tbeo Ulldor ol.rcaatereatlol c_...,.l.oD, eed ot.bor portl.ano Hdia~ Ollt'IIUd, placiD& -. ODder ~ormtlal toael..,
B
Ql oboot <•>• tlfe l'edlt.l.q c._orootllll otnooeo tbrout~J>oot tho HOtlca ora detoft11De4, At tho bcttoa of tbla oboot I.e 111 _.leu tor tbo I.DterDal potootl.lll energ oboorbad bjr tbLII atraoeed oocu ... , !be -1 nhloo 01'0 ""- em oboot (S), oooumi.Da tbot tbe mu ooctl.cm (1 !.Deb thlck) rototeo -ab m BD8lo of 1°, !bLII I.Dtonuol _., la oot ~ to tbe -mal BDV/11 of tbo oppllod. torque rotot!JI& tbi~ tba oamo ana10 .of 1 , Prom tbla lt 1e f011Dd tbet tbo mu t.orquo far o ...-... or 1 1.11 )201,7 !.nab ll1pa - !.Doh of looatb of rtaa, -·• tbo ootaol lllllt t.arqae oppll,S bjr tho rp 1.11 602,1 lllcb ll1pa por Inch; tblo - tbot tllo octaol roto\1.<11 u ~ot.oe! !~1:!,;4 ~~~~:-~ !~5 :::.:::1 aUOCWitertmtUl atrease.a are .188 of
U1ln1 tbeee nw •aluu• tbe nerap olrcumfenntlal teDIIUe et.ra•• 1n t.ba bo\t.om plate ot tbo •IDa 1lo fOOIIIII to bo 11,17 bl. em ahaot (6) ood an obeot(7) tbLII u r-.1 to...,.. o radial fcru of U26,J. tipo, Tbl.a foroo 1.11 n...sad to ot.roao tbLII - ploto to bbo e._onDtLIIl toael101 olroe4v f-d, !be o.,..oopood!JI& Talno for tbo top plato of tbo rtaa 1e fOUIId to be 829.9 kt.po on ·- (8),
Shoof; (9) ot tbo top, oanol.dora 1 al.aUor raollltonoo otfarod bjr tbo l lCI>al.todi.Dal web platoo, All of tbl.a l.o .,._~d ot tbo l011v portion of obeot (9) and 1t 1.11 Dotl.cod tbat- U.aa fGN:u balance oa.t Vff17 QU.
the vertlc•l •'-ar 'Lran1111fer ehCMJ at t.be top of ebee\ (10) ..... to be t.abn 081'11 of tol.rq nU. At tho bottom of ohoot (10) l.t •- tbot tbo .....,.t \nnofor lll.pt 01111110 o problalll, •-u~ at tllo bott.oo plato of tho liq, !be top f"-- of ohoot (11) bettor Ulliatratoo tbe problell boo- of the loci< of -t.tnc oold1l to tbo -pbto of tbo ri.Dc 011d tho tnnnoroo web plotoo, fie leoor fl .... 1.8 a -tl.cm vMeb 1tOilld prool.de o bettor t.ronator of foroo,
-38-
T y
L· /(
.. AX• .-...- )( moHment raJiiltl'l mi...rd
CQ. •ses co tn preu tOn or "'"ll'lt•ve rtM•n (-f:}
:t~;,(tHo<) e ,;, ees ot t eos !!> s,;,.., ll,.
:ui. (sM)• cr
set e&v.a.l
·- (• :t.. . ~ ) - .L!_ -)· d coso~. + d smo~.- sr . £ ~-r~•~ ..t
cl
o-= e: E
b t lf •. ?J'3 c -1/,,.719 d -1( •• 1111
.s\1" ;...""'~ _..tn.er ·~··11 ... ----------- ,..,.,2 .. 11
""'"""~'" rtr-..• """'' .~,ft .~ pate~
ll,.
JL).[s•nte•«L} ll--x sms ~
sin8'.:
eo~B·f x(ech<-J) 1 '( sirr<JI.
r-}(.
t!M"'f~ ,,n~ fo.- pcsiitof' :rl r•u;, """' pt'f;~.p st~/km.ln)
no,., + !IIJ'l '" t enSflilt1
t:lrtd- Stqn 11 a.mptft11Dtl
c
•
D •
•
pto.te..
.!J c'f.:r~~'.r> k+11/i'l}. +(1:1.'1"1 x: .,'" ,, )+(""' ?.l}i ~ "/. 711.8
® . Ct.~%~;~{~9 [(-"12.J~j\~q"'''-,t..33,,1)t(• m~j ~
© '·'~n:!!\P [~u,.flt+C-:'"'"~·"'·06Jt(.,., . .,,~. f'i\\ C'IB~Yj,.f83) f~m.l'f-:tf-13?,1'fvif2,8l)t{iOJ.Bif~. ,fb M3D•Io') L 1 J.." J
S"'t the'~ t~J" eQoAQ( to eacb otltt'r
.B~/1
j.86l
A
{t)/, ~ .. ,.;t tDr•rAeJ ,,~h ~~P~ of torQ\lO per {nch o( ctrCL\mfercnce or lerqtb of rinq
t· -l ('-?.9'1o) =- ·"~'ls'1{27.'11fo)" 3'().t,7'l ~ (t...ced kyon" ~tQioon of "','•) (tor"'-"')
!lowc•llr Mt •c.i UAI "nit Ur&ue ,, •.
l = 6t'I.S'"'~ X'43..l'8 irl) • a S"/.3'{ in
i'KQIA.f 4Ntt '" 'fl, '65 ,;·, 10 ,...,.tNt•) •f"'C•cl sl.3'1m •p<~rt
"oz. I' ~~"~ ~<•p
tAere rore thF oc~··e>l t:~f19ular {7;)t,;;trt>ni'.J) t!I'Jd the eorre-::.pondr.n<"1 :;tre-~"''S wit/ 1-e
3~/."~ ~r ./BBD'/&>f tho~e va/u~'S alread4 used,
fto~o now 011 ~,,. o,_;/1 ~•., tht: actual vq/11.e of th~ :streo:>I!''S B
'"1 ITI"Ii ,[>lopirt:t the vreVIDlt~ value'S bl.j U"'o; foetor .1880'1
,, ' ....... ............
8.'110~ . ·,',,~~ ...... '~~~~ ~<.'....: -~'\. '· -loo, ~-. >, ~/3.t.Z'r"''
fl.,r·.:>~e at~41 mrmol -stre:.s ,;, fJ•.'·""' ('J"<JI!' iJI~ic ~~
tT rul!'f;auo ~ //. u,'fiiSJ
Now i/?e fRVt:'"J~Itin ,; ,; wfwt rod·.:i.l fore~ {t>dh~r un;te>rm or concenirafecl) t$ relflLIIrecl to str~s'S tlus ruiq !o the alxne Pircqm(ererd/a.t (l{oop) stress !
/111~ Foru m,~t be tranJnred throv9n the circum fer entta f welds t!onnect thq t hts ~tt"f71 phde to the rtnCJ.
. 39·
c
(each cJrcum Fe rerrtta I weld) ., • £?D w~ld meta I
or ~ D... -:.tead'l /oad
Fi, li;
7anfcl'lfl,f.t (emile fence ,;, rtt~
at ..,..p/t'c.at,~n of f.:>r::<>
T~ /.539 F
F.' /12.~.'/J /flf~ •
PIJ.?~'
f'/•10 forces
?P!f l""'l ~tweer> force<;
(IIUSt b~ frQnT ferred D« t b~ ~ .. itat.le weLd'l.
The hon~nta I ra.duil [
~orce (F.) ,r, th( •·~to'f' piA'te. of the rin9 rna~ abo be fz>u nd b'l the fDUo wn1'1 Mel !?~a .
t!"n1ider the top p~te ;n a -s/mi/tu m.:>•mer
The auerl'l'le eircto(mfercflf ,;,f eompressive stress ,., the t"p prate ,,:
~?./3Si/8.2_1/,. :t~./0?~ XSI
A
The ~ t.veb jlfQtes r.uitl also d>(fer -:.ome ff";,•:t::tnC'e to mo11e rneh t".
f ll ....
+ ~~·
~"" port,on :J e. I 'l.(rms'fn.unY.•·IDZ)sin•a•• ~(01.DM(n.tf3t,e3)•mt8'+Mu. 7'1ifl7,f81t.. 18'1)~mtd'J • Jo'f't'l"
boffonr pt:>ttuin _, zf'h('·"""YPl'/.1.1tTJ.)$ir,lfJ'+ M~.l11BX"V){.'-')SiniB''f- f.('f.m 'f"i''/..98'1)r,,lf'l' 'l!.oa~
tntsttnq momeqt M..(B)9.21.~,.,.7'C{u~)<l<'-"'l:t'~.ll>?)+(ll2f.H")(",'2o) <~ppl1eJ mo1116flt M• fll't,!>'ftt3.~l>8)
I
• t I I
I
r I •
1 :~ I
ll·~·~.f~ 1 ~ ""11'l.Sil 1 I I
t,aJ I I I I
F•1t'I.S~ I I
L __:_.:_--:._-
'II '--
'31,~:t'll 111111p ... 3o,96'"1ft JtP
I I ·------------· h'l"'-' e 1
' . :J
L I
l - I . I . . ' : ... I .
I . I I I
j I I I
I I . I I I
loaJ I : I
L ___
II 1 I .
'TransFer .,f {,acJ as moment. 7lte llfper /lprtiDntal mclt.;_l eom~nent pus/res the -t11p plate .r;F tfte rtt1f tit~ o ~1174/lert!irde. The ~wer honiorrtllt rar/ta/ tompon~nr. ent~ tlte
b"ttom plate-:. oF tht: rin9 qnd p<t.!h th~m thtut lorferct~le·
B
. 40.
These are the ferce~ 4ffllecJ tt:J s~tton d I the n;,9.
'II'IS"
fbere 1.o o reoe-blo voaotor ot taroo (Ia!? .L klpa) hom \he IIPP01' tlonp ot the rea bnokot tlorWp tbo 3 tro-.... web ploioo l.oto Ulo Ujl- plot.e ot tile rill&. ol111o tho web ploko oro ,.ldod dlftctlT to Ulo l'llla plato. I dCilt belieVe tbt8 Ia troo In* oeee ot tllo 1o1m' ploto ot tile rlq. It tlooo DO\ oppoor tbat the 3 web plot.eo oro nldod to tllo -- plot.e, I - - boo t11o rodlal ,_, ot 1126,S kl.po J'ell'llzed to poll * -- l'llla 011\wonl ooa bo devolapod bT tbo n• brookot throulh tblo orlUC81 comer,
g...f.....-4 ... bt
i
l waulcl 11Uq08•t eome a~ethad of W8ld1r'lg the 3 trii!1Mv_..e W~lb platu tD tne bQUDG plate of the ring rnu:Uon ae wdl as to tha tap plate. Parhapa tnla caula be done before the central and 1nward wllll plat .. are put tn plac:•l The central c.reb plllte could tie welde£1 by uetng • single bavll groove IUI!IIld.
·----·:-:--' . I'
'. I' . ' '' '' '' '' .. ,_._: __
·- ---
--,.-~~= I I I I I I I __ l_~~=
msK U 11110Uld nelo to add same harhantd briiCk.ta lnllde the rtng secUan to help ln transferrinG the horbontal r11d1ll farce dF C.2?., k lps from the flanglt of ttle nm bracket into the trBI'averae r11eb pletl!la, both tnp and bntt.am •
c
D
cros.s sectr"n of. rin'l
4A~ ~eded a.:. iheJ.e IS M reslstt~ 0 .S -tor~ue, ,/u::;t rett3t'"1 ~17'(
~ M, • t ({i:-) also = f. e
Pr or ~. • 2.JZ
A
B
• 41 •
Tht's .re-s;~tinq moment- ez"t 0 re.prneqtecl bq h,r-ce-s (~~ ac.ttnq o:t a di•t.qrrce (e), wilt CO~<H' ~fie- f.,p_,.,, !':.·1 moment at t:l.'l'f 9;,., f"'t'i7't ®
Pr cos 6 .. M., • F., e." z.]Z:e -. 11. Pr cos S .,·- 2.{1:
The SQme re~u·stin9 mtJment < (}) ""ill co<~~o<se the FoJ/~twing t•r•ILe 4i!' point @
' ' \ \ a
~
- --_A_ _L_
Prs/ns T,;1 " t., e. .. -a /2. e. e
Pr sine f., • ~b ">in 6• · 2. ~ e
~ c.o«~~ter-t::./ocJcwtse ~ ) (+) torQ~.<e
-.- Pr sinS or t 111 •+ Z.{Z
c
- -- D
The same "l>u.pport reacttDn at (j) will cause tl>e tDI/Dwins torQu.e at pDtnt @
Up to the point. ® o'" the Jrrst lo• d
e - o -t#} '(,s•
From po•nt® of. the fr.:St load to P"'ht ®
e = '1~· to 9.? 0
.M8~~[(1-i}}sinc9. +htt- 4-)cos~ + 'fJ sin 9
orjM ... ?f(2.-./2.)sJn9 +{is,;,(;) I To "'~ [tlf- :lf)51;,h ~- ~)12»e]t .r;C~J&e~ P,f~-li)cosQ t .fl ~a
or\ 7;. ~(.?. --Ia) el5 D ~ !'j ro~ B-1
A
8
. 42.
8• 0 it. '($"0
,-v •• t-[d s~ns+r(,mB-W)] 8 • 415'·~ fa•
M.·-ls•ne( d +,21lZ9or)
T.•!-[d CDS9+r(~tcM-t)] T.•l ccse(d+ • .zllZ'1or)
• "• rt> • l&SJ!"OIP --1192 -----
j_
j_ . 7
+ +
5 + +
l • • . • • • .
To
+ 1811./UP
429.
••z.
? 0
v. ]0111
lfle•O"" .. ''~in, KtP
mrnrJeJ'lt dta9/12m fJ f rlnfJ
-:. heo.~ d rQ.'I tQJn
on rtnq
c
I
D
A
••lllc.a banding amnent ...... Ui5J. ln. kl.pa
'• .... ln. klp \• lO kip
"'mer:zn dimen:w®s DF- se~t;t<.n
, I •.!·
:::
E70 weld met-a/
i~ the amverler IS charyed ever'! h.t~IF h,u.r
2x 2.'1 h4u~ • 3'-o dars • 30 ~n szs;''OO c.~ or U$t! ..V~ S'C4 ooo"" t» 2.~01 0t:Jtt:)"""
Pari11:i/ per>e~ra,tt,;n ~ove weld in siJeqrFati9Ut> cDn d r t16n @ CJr o::d:e9or'( ®
1" ~ = 1/,"oo,.,; /e'l! ~ ... '!/::,~ ~~~ =: 0
!""rita I pcrrtt r.f,,·,, 9n'"' e wrtd
'll' I 'I 37u f: i/,000 • ' 7 'I
lienee 141!!
7"= '"()()()psi
*when -the rinq is tlite~- 90: "the CrDs:s ~ec tu/n l!n<~f711P5
from -B- ~o -[E]-
B
h:J.~ r.~t /f~S 't/,;,'7
;~ :If". 35'1 and there ,;. 11" lr~fl?it.'!:'1'1'ql shear Dn Hie weld ff"'m ,..,r:un.,, hence use
beco"se of W ~ hence u::.e ~· + Ye' Dr
f.'2." de-ep 9roove
J<· ~·~ = 0
.. ,., ___________ _.__ __________ _ IJ.n &~nal'l<.i!S :shot.t!d te 1114de wr'th the rm9 ;n other /'0:;/ttdn-s, for e.xQrnf>le t/lt'~<>' over to pour.
-43-
Oft abeet fZ) , I have considered the foraes to be traneferl'ed tbl'cu.gh tbe two cil'aamferential fillet welds. If we aasume t.he flanges to
~~0~1~1~1~0 n:!..!:f!."i!i = !"S.:sett!"i":~o~~o~..:::1:o!:"' ~:;.,. appear to be relatively low. ~hls work. should be checked.
Bowever, when. ve t.reat the flange as we abould, in that: it deflects somewhat and 1nUoduoea momut int.o the ad of the shell, tbeD the
. atreaaea ill the shell and, of aourse, tbe connecting welds could be IIIQCb blghar. On sheets Ill and It I, l have used fomulas from Roark •a 11 Fozmulas for Stress au4 Strain• Fourth Edition, page 307, aaae 32. This would indicate a l<mgUudinal bending st:resa ln the shell adjacent to the fillet weld of 11,310. pal. On sheet lSI, I have used similar fonaulas fl'om Harvey • a 11 PI'eaaure Vessel De&itJn", page 14& and arX"ived at: a bandiDg st.resa of 18,400 psi, 1110 there is naaoft&ble atJI'eemeftt.
GoiAg' back to sheet: (!) , t.here is an axial stress in the shell of i50 pal. Consl.derlng that the unit luis an applied l<>&d of 4000 lbs. - 11,500 lba., this would indicate a range in cambined·longitud1nal stress ())end.intJ and axial) of +18,720 psi t:o -9,055 psi, or a range of 27,755 pal.
If t:heae fiCJUres are correct, I believe this would inclicat:e the .possibility of fatiCJUe ~l'acking 1n tbe shell just: adjacent to the circumferential fillet weld.
'l'he.ae calculations are on the basis that the ahell, with it:s axial load of 4000 lbs. :t 11,500 lba., is 11upported only by the flange.
IUIOthe.- Jmpoztant question ill fatigue loading is the proper stress allowable to use. If rc!JU were to use AISC fatique allovablea as a igU1de, the allowable fOX' the &bell (center tu.be) plate because of t:he attached fillet weld would oome under condition 30 1 catagory (B) , and. fOI' 2,000,000 cycles, t:he alloWable stress wou.ld be -
o- a 7~~:
where K• ruqe of stress := • ; :!: In t:bis example applied P max • 4,000 + 11,500 • +15,500 lbs.
J' min .. 4,000 - 11,500 • -7500 lbs.
and X - ;U~3oo a -.484
eo the allcWable fat:ique stress would be -
U' • i~1~.484l • 4720 pal however, ve found the maximum oalculated atzess t:o be 18,720 pal.
Sheet Ull sbowa """"' possible methods of BUPPMt of the bolts to t:he shell wbicb will qrea.Uy decrease t:he bending stress in the shell.
"7'hts ass~mes ~ n.9/d fla119.e 1 170 d;llecf.-~n,..., hence ;«s't an tfUtqf 'elnc/ ~pqq/ ,..~rce.
flpwe~er flam.;f! d61M del!t?ct' and places ·&I behd//19 HffJil!lfn't on rne ede;e tPf t-he she//.
tm flte /1f'J(f 5/teefS /(;e ~vi// C'"n-;/der- (he 'Sfrf!,~IPS on 1/le shell eke to the ·mpvement ~F file f!e~n9e -
c
D
Use ~ • F"rmu.la1
T~-n l~li
r· P = Jc~(:£~) .. 3
a~ at.'' b = 3'1~· d • 'IZW," t. t,•· II~ ~z.·
p=o P = ;s;soolk
t~t3a'+s-d·) .. ,..,)' r ~,,).+6"('1Zt.)•J., T, .. h '(d.·- a .. ) (te).. [('fz~) "- ( ·")'] 3. '" 9
• ' h' ( 11• T,<~-te& f. t )V. +hTtP ·A lit 1'(f -It 'Ti)
~*= ;. a r. 11 - 1.'ft.¥t c
ta.)(1./i,9)-tt•sr.(if~)](-/t/,2.) 1- ';..{.tJt.?o) (ls;SDD)- zero M,.. M' ?J,fhf) (k)- '3,'1, IV)
1<1. • + 18 '1· ~ lh /l>;,;,ch
a; ... ..!._ t /$.~00 • A . .,- 3,(11/j • S'SO ps.1
+18,"1~0~~· +----· 1~/bs
•/7,(,U1 '
:on the reve>rse qte/e +'~-//.SOO • 7S"CJo/6,
~= + IBI70{-J,'f:6)= ; 6'li:J0pa/
Or
I. .:? ra119e ,.;, '5tren .,f
D1d'S/Je Of Site//
tns/cie of <t.he/1
"t 1817ZO psi t-. -f,O!SY ps/
-17,1.2opa/ t-. -t'2525""ps/
A
B
-44-
j 91. 5" ;n /Psj !ltfe«r Inch
bend u?9 ~ires~ (# M • • ~(t"fl.~)
tr-= h,'t. (t.,)~
lf thl• 1a breaking beciiUH at the lndlcatltd bandlnQ et.HeBIIa ln thtl ahell acJjacent H t.ha flUe\ wald• parh.- eaN af thll fallowing ldne might tla helpful.
8rac1Cate cauld b8 plKBd bet.an the nanga and shall an aacn aida at the bDlt.a.
A t.hnldad round atack, wlt.h an offaat. could b8 1118lded dlractly tia the ahall and t.ha flange. lt-la ldOUld t.n:nafar the ulal forca aon dlrect.ly t.a the shall wlt.hDut aa rauc:h banding acuan.
A at.ralQt-t thrallded I'DUJ1d atock could be walc18d dll'tlctly t.a t.l'te shall and thll tlenga. Trtle also would tiranafar the a:aclal foi'D8 mara dlNcUy to t.hll ehllll wlt.haut u CDUCh btlndlng act.lon.
A thicker shell aecUan adjacent to the flange, and tna ahllll could ba uaad. Trtle would grntly reduce tihl banding atraaaea in \lila raglan. Far PUtPle, wl tn 1 112• thldc aact1Dn next. to t.fta 1/2• flange,_ tne bandlng at.nas &J&OUlq reduce to about lt760 pel (calc...lat.lld). Thlt!l 11 lllhV moat rlangea uaad ln PliPlftQ and pnaaun vnaala have a hpand aacUan.
1 r! 11 r
c
•
D •
'I
"..!!!!' '!!!!!!!!! !I! -~!l!£1!.~-~
r..· W(r,'-r.'l-~t!ll~f~] :r...· c-1 eo. in lb ~·""
'!1!:!!l!!= ~rnarsv !! ~ fllitz!l!eda•
"_ :r.. 1.()2_ {z•t.3BoX:t~.,l' _
--~- 7- 2.. -
If 'the crusher ia a\opp8CII ln one n\lal1.1Uan or e etrak• af 1 1/lt j.nch, end we ... "" thia la tne IIDIDUnt of 1110veant of the pitman where lt atrllcea the na1at1ng flarce af a atnl objact accidently di'OtJtJI!Id inta the crusher, th.na
Work • F d
Crank le S/8 inch off center ..
Mu:lmum t.hrcw of Cl'llf'dl: 1a 2 • 5/8 inch "' 1 1/lt tnch.,
F(l~irj =- :v~~o,'1~0 ;, fh
F = 3• 'St..o, '? 2 0 :: ~)088, 7 ?>&. 1'11., lf't
!be lup n.n-... ~pt- .... "" ... - ........ -b--·b -"' la ~ oapporlburlDp ot .. ·-· tiWo -- ..... ~ ~ _, ot .. pl'tMa .. tbe •batt .rot;eta. ... left, blad. ttcure.
'rbo toaJ.o plno - u • lllllt Uld olao ...... • ll1liii&SIII -- ot tbo pitaoDo
!be rtibt lwul f~ roP*- \be ooo- ...., vl\b • eo.....,__. ...... -· rod! .... lolq\b 1o (r), Tbl.o - boo- a f- bU' 1I.Dialpp ......._ !be -. (I') 11Jlpl1o4 ....... 1 to lbo ~ ot ~ pt- ...,... nao\10118 ot (P~) _,_ to \be
- Ollila ot "'" pi-
fie \OQle plot.e 1o - ,.... ._...1011, \btl -. 017 bo - - la\0 ""' .._-, - • ...,........ 1o - raoo\1011-1 to \bo pt- (I'~)- ~ -· ) --' 1o 1 ,_u. toroo ooUas Ia 1tao vl\b lbo me ot \be pt- ( z. ~ iJ
'fbeoo ""' ·-'" olao -·' n lbo ap- u4 ot \be pt- u4 vl\b \be - oq1e (If} u ot \bo l..cnror ODd, !be raoalt.aDt ot tbtllo two • ...,......... { ~)
oov oo t.bo - ob.ott wld.Ch •- 1o \bo -• ODd 1o o\Vahod to \be l1;rwoo1.
'l'b1o renlt.aDl toreo 1o aoo -- 4WD laH tbo ""' ....,......... -.b oot ao tbo Hllll obott, - oov Wipe\ \o tbo n.ft u4 ~ 0\bor oov aona1 R' ...U..l \0 ~ outt. 'rho v..,-tal toree ._..,- ..J.t1plled -.r ta ...... lolq\b (r) - t.bo \Oiqq wld.ah 1o aappltod 'V lbo oatt, \b.o ndiol force "-' - DOt. ottoo\ \a '-• boa\ will wappl;r \be _.,... 011 lbo boulaao
X, ~r CoS G
)( ~ l(,+llz. • 2. X -~ a- &.
o{~ t!JttBO"-:ujJ-M
F. F ~in ol ,.· Tilii1
x .. •- t SIIIM Y~· r ct~1M-Q a·;. a {+J nllm/)er
a= 73 ;, t. 31 ,.,.
pe88 ito ,... fa t(,
A
B
• 45-
I z
I I
c
D
A
,.,.ItA/ rodoctl
¢ f r "' ol.. f9:i 'SU,«.
e K, Y, ~ 1//t &iiiii 0 •. r.zsd" 0 .. I71CO~m ~-~~'lffl 108. m<~' ·-~~~~ ~~ .li~ .JW. .1~flf
20 •• s8'13 ,tl38 119-'lll.l n.t150 JOII.:IWI ""'' l/dl:tt>l'f - ~1'1, ,t.18h ·.IH6 'ID +.'17811 .'101 11'tb3, 52.5588 117.8'1'1¥ •. ~73'7 110'1-ll'lf'/ .·~ ~oMS ~8 4.0 •. ?>Ia$ .'S'II'6 I '1\5'11'1 S2.81'1& o?.S'I'I'I t.'l~~ 't7. 3020 2'/.0'11'1 • NB't .:l$3
eo •.tfl8$ ,f.IS! '"''~ 52.'1115 1821851 t.DI'IWI 111.~ 'IUSI33 _qJ<tl .'IS6(~
/0() -.1()8, .r..ISS n•w• S211'1DS' lf'/.3852 ·.oB'f'I'T P?.~ltlt'l •"".$11'1~ +,2'188 51'18 tllo ·''25 .5'11' 'IU~l't 52.81'18 1~1.5'1$'1 - ,.y,r /I?,'JS<fll ~Jt!O o,o$'111 ·""'" 1'10 -.'178& .'IDI? n'IDJS 52.5:188 1118'11'1 .·m? 1011. 2'-¥i JD6.6$'12 ,IMS •. ,03'3 /liD -.5813 .. ,.~ ,,.,_,,, S2-l150 l/JB 'M.Ifl ,'15"'- III.'IU. .,;.~ .~m I~ 181) .uso 0 13.tlo:IIJ sn'[qO l!f&m'l ,'I'IDf !...~·U'!'I •l'l'j.2186 -.m.L, r'""" "zoo -.S8'11 -,2.138 171.7886> 51.1)61 lii~l .,.,,,'3 ~-~~ :;-.,iitil -.h25':1. .Wl<l 220 -.'1'188 .'101'( u.s'I'IS ist'J.'l"'IJ'f lfll-t."S ., H7'f liO, DCfl'l 181J.(JI)9$ .M'11 .,ogqu, 2'10 -,'li)S ,!i'IIJ 12.'W'I'I . SO.'TI'I8 ,,,,~'Jl ,')'111 IIDJ.I'I'I'i ~37~ ,5'1.8'/ 3D'1o zr.o -,1085' -,&.ISS' ~,,, ·!IUh?b JIIJ.IIhl -,ll8S'II 1/D.'l.ll~ ·~ .... ·"~'' .YB(,.I 280 .IIJ85 -,ltrSS 71.38'16 SO.Sltfl.
'116, ''' t.l>i5'11 10.(!'02 ~\1l83'16 ,'l'W1 ,,os7
JOO 'Wl5 -,S'II' U~S'l'l S0.71~8 ·1/!lll'f'l, +,?.'I'll /t/1.?~0.2. 418.8'/IJ~ .()12!1~ .r.'l5'1 120 .. ., .. • '1011 ~5'1'16 SIA'lllll'l Jdf.t.'IS *· 111'l lt>'l.1oS3'1 ~.?bStJ .~D1() "{,l)'f' no ~. 581l -,ll'f& I ~'18Sf. 51.%1)4 ,~, •.'IU1
1118. """ ~sw> .'i'W! -~
3t.fJ • ·".so (> I7Mil1o 51.'11'10 111f.'!_~ .. .,~~ fl8.'-'11l> ·~u..o ,'$1{/)'f .3'WL
( co'ci. ) ""'·- wolau '""the -....u-1 t-,- ill - or 2 'lin; are pl.MtM optao\ the -11• -- or Ule erut ( &) oa \he ~ """"'-
1~-
"
!.
I ·I -t "! It
l'.r ... ""''"'.;
B
... ~+-'-ftt!±t f Q
·i ~:+rirl±t •. ~
.o;f
M!mtt.= ~--,...__·~-'-1-!+t:lf a -~p.~+;-s
·-~EthillillJI ~ 'i~ -: , ;.~ ·- ....... /~/fl.. I " . 't
I
.. r
. 46-
""'- bow.,..-- w. -•- -Uplled. by the fone appl.l.e4 -1 w w. 111.1po1M at "-o pl.- (J') """by""' 1oDc'b at tbo ona ... (r) ftPNOoa\a "--- ill -t.et~a~ ~ t- (F) oa W. pl-., !loa-.-"'-- (I.&Wpna) lA t.o dl..U. l\ lAW JJ? .._. """-""' ....... -..1 ... ~ at ..... 161•Vo ol- ..... -. -\l.pl;r·\hl.a naby W.uplutl.a\eMeSa __ at_lO .._...
e
30
'U> }'!.Q. ';'I() ,5'0
()
J1L zo 30 'ffl
0 ~ '()
511 0
tDO /10 IZ.O
l!eil!lt\.
.DI/.
.:1.0
.llfl
.~ ,!1_1/ 5'1
.5'6
.•1 ·'' .1...3 t.2
.5'8
.5'3 ·'f'l 'S'i 30
·'-,()'f
·~
IP • -se'ftnerlt ~ .n'f~ rttJrans I": f$ IRch
W.,rK= 7.~3 F(~'f.ms)•.JJtJ3 F tit·lbs
Eneryy 1n i~<M ~fy wheels • .f.,.: .J;,w ~. z(U8o.Y.JCU.)
2. z. .Q_: 3, 8 60, '12.0. lit·l'"
S ... t eG!WLI
, t1o 1 F"' a,st.o,qz.o
F 3,86~'fZO
"' • 'ill) 'J
We wUl- calal&W""' paol""" ot W. llldpOtJd ot tllo pl-~ tllo aubl.q ._.u .. .,, flH'Uo .au--'-'!l··l p mao
9 J(, y, x. y, . ~~ 'lr. {II
o• •. t.'l$0" O" '*f,.~ i-ll&'IIJIIO l·l'f.~_H' ~ 20 •.fS'I t,?-1'118 -~.'U'I58 1-BL'f'I'IS 1-1'1.'16~ I-'!LHJ8 ~0 •.'1'18 ,"101'1 ·2'151.'11 -ea. 3D'!' 1::1'1-5"10 ~'i5l8 (.0 +. ,,,. t>S'II?. I-~IR'I2. -81. ?.1<1'\ ·l'l.lt'f~ .... sm eo •• 1()8 •-~>ISS ~S'I,, b&,~I'IO -19.'1'111 -'10o8DI8 /DO • /08S •·415'5 1-~rMJ.
~ ~~~ 7e>.W~'I2
IZ.O -.~1:1.5 •.fi~l1 141.517.!1 lo'IIS'l 1"1!.'16'1'1 ,o,,I'JZ I 'I() .'1'188 'fl>l'l ~~ --~~ -'!1._1'1!.1 '10.'181'1 lhO .. ;s" . ,,a -11f,J.S'fl lll.<t'l')ll "''f..~215' ~'1'1
180 •,t.,60 .D... -:&~ -8S)0'8 -lf,qq&J -'f.I>Ol'l zoo • 581} .0.1~8 ~· -8L'!m -1¥.68'11 . ., .. , .. ,., 112/) -.1/'IBB .'lol'l -2f,l'l8"f ·8UIJ?'/ I-Jt.8Dl1 I "G.<>~ Z'f() -.~1,.5 ·.S'II~ ~1!'1'13 A~ l-19.'/fJ~'I -1/2.1:1.11 26.0 •.tDBS .wtS!i 2!1.b'I:R ~'lM,i -f1,J,IJf/J_ ~ 2.8" ./D8~ .415'5 1-%1. 11'1'1 f-111"180 -1'1.6Dfn. ·'11.111.8 7o.rt1a )00 '· 3125 .5'113 f-tf,/H'6 •'1501 -IY-'116' "-11..9987 'ID·'fia. szo .'1'188 ··'!PI'l 1!1-211111 f-1111=-S -1'!.3'f&'l -'11.8110 7D·2li'l~ 1'10 •SOt!> .~~~~ .,.iSS, ~ oll,~8'10 _.,_ll'IJII'I
..3Ml ·~ 0 ~.'#'n() fll.'IIJ'/0 -l'f·'ffi8S ::'/!,~
thea Yolau 1ft plottM GD U. am olloft. I.UC. U. ---- :,of "'" plt~ua lll ·- o.a -.
11av rworldJtll """"' (1), uolllc tid. dl.otame ot o.a - .. ...- - tbo 1 lA t.aohN vUlllft ...
c
•
D •
t
. : :r.--'":;~-. r ·-:
...
.... . ..
_,.,,. f .41At
..... ~ _,,._ _,,, ....
I ·•"' .... 1,,,"7- / j.'ll.t+-,.,,,'!- I .-a·~ I ~'IJ..~ I _lfQ., ... .• u.~
- -- ..w boo .. ..-.. u.o IJpaloe ow1U4 ...... ~boela ,_ -,_ (r) •-pi-_,-"' ltda •- o1>up ta aplar- et the ~111.
.j
v. 1Jill p1ft - yoJMo et (:.C:.;) llpl.llot \bo (t), 'hta I.e - .... - - -"
v. vlll e1loe - - '--' 111'11 - •'-1 ... ,..,, ..... - ·~ -· (W) .. ..,.... et ......u. (111'11) vlll-• Uaarll" 111"' \bo -u ....., 1.e ....-...
r "'J.!A':[ ,,
:ztt; T iTTmr1"1"1TnmTmm"--{w)
-6• 6 f1m8 at. t!tstiVI( Df /Jrl~et tf • l:tme '"hen pitmon --. to ,. .. t
averi:l'fe 40fWetr ~loc:,i!'l cJ,.r,nq tlu' ftme tr:
:l.u, ~ o zlf." i 0 , ~ rAciJ., w.,. = --z-- = --r- • '"'· ~ '5e
.ftlne t.D C~;me t:t> rest
t daitetnce 'It FT4d f• Velocity c 12.1~ .l~~'f Set:OPdS
A
at tMtmt •f hnpae. t""'-
atr~t: ----
B
. 47.
c
,. /GRIM! *
rc~t t:~me (. CO$t/o.) 8 t..., zmfl BOOU 'J.., -.D/27'1
"'' o• 0 ()
'3'-0 I .OI381J t 'J.t:/10 ~'10 3" .D2'!33. t il't88
UOorO s o'l5'/'l +.s<lb't :to '1 .06'10! ·""0 '10 9 .08'103 t 62'15' '0 II _,/OU.1 lt.S"~q BO 13'1 .!'WI~ L'f'1'll
/fJ 0 /09 ./68CFI +.?.'156 /ZO 17'f ·'"'"'-7 t 03711 IZZ 181 lS'S"3 0
D
1M ....... ..------""~ IIJIP1W"'"" ~-pi-....... •..s-n u.- ~"' , ..... - nla .. u.s.--... .-1~ .. -- "' - ,_. (r) 11114 "'" laatb "' .. - - (r).
A
,. ----u.s. - ... papldel1 -- wl.l1... ..... .,... - - wl.l1 .,. UYI.M4 tate --'"• - llft"'C 1 llue liDo-~~ fll 0.01 ......._ 'llle nvop -""11111SP' lor---' II -. 11114 -· to~ llol.'lplftaa U.S. ~ .. tllo O.Gl ....... - wl.l1 i!lft u. -' !me '" 02.
lo1 :o'l
·"'". cbs. .1'./l_
.0.8 l.nCJ .ID .11 12 11
:J, .II Ll5 :...20_
:at ~~
112') U.l'f li'Jfr !L~$'1
Ef!1) 12'1 ~l
."'I c5'J 58
',I.: ., .. l'«: ~ml: .5'1 '18
·" . • 1 a
,lS ar ;n .. n ,JD· ,07 .0'1 .u~
0
Cltanfe P1 1111111entum of tire two U'f 141heels =In,(~-tc.>) ~ ..:r,.(lc>.·%el'l))
• z("'37<tZ){2'f,,)• 3/~8sf7
rmpa.lse .. Chanf1e ;, "'mentum
.o~'tC. F • 31'3,8S7
F.,SI'3,8S'.1.~ .OS'((,.~
,j,~Js.oaact tine carve
/"'• X • X..,, '/n(f.-t-) Arett•.t: ot • x_ fjtf.~) d{ • ~[?tt~) d~~t-)
1 •.••
Arect •-~ eo-s{'tt) ,. - ft )(,.4'(cos1/'-l!o3 o) 1r ,.. 11" " ~ r----------. -1 H
I A rea. • + 2:• X,... I h4re t "'.2$S'f ~ec r• ~ md,
. . Km•.l.!> F A c a(.:tt>rt\C.43F) e,/OZ.UF
r<tQ. 'b" -.
.I'mp•he =(AreaX'r) •(to:J.'IF,X~.) ·.()~'{ F
.Tmp .. lse ... Cha'!fe 1n al!tJt.dar 111PPU!'ntam
• tJ&.'f F = ~ 1 ~.as?
F= '~!::7 ., @~'if:ott;. ~
8
• 48-
.._. - 'IOlaoo .Of - S.DDD,OOO ~ II 1 - ~- o ololl R3on ..... lmo Use oru-, - om wo dD --' Uf
1. 11a4~ - - .-u ... IIOal4 GOlF ...... 3oft • I• ,_, .._.. waal4
~ ..::.:-.::=:. ':".& .~ .. :':.;":!:::.• ~-= =-~=l>la -· -u-. -· wo f11f1 •• "'" r1a11. •-.ua fll t11o •torill le \Ill ollwPle.
I, Fono fll t1uo .......... , lt11t ~· \llo pl-. \Oull ploto, Ulllll obon, OJUIIorl-. oto waal4 dof1oat. .- - --1nA oo * oo-.1 olil~ w - of ""-~~~~~~~ - tr> .. t11o - ~~~,~oat. ....u ... -""' """ llldlooW. - wl.l1 ·-... ...,, - lllr "'" .... -~~ ..., Of tllo - ~. u.s.·neal\ 111 o 1aow r .... (r).
J, I llolilft ...- \11111 Ill""'"' loOd _,l.cllw aftJ4 •- o --wit!UI fll 11114 p.-1 t.o noll\ - lood. Pwtlopol on - no ... plato ooald .,. .-. tbl.e waal4 ooko o ·- oeo\l.cll .,, of "" 01111 ~ U \be wob plo""• .,._ 11114 llmor plotoo .,.... 3 lllollu tllt.ot. ODd - ODd poDol
..Utll ot tile - ioereuod t.o 18 ~ o\ tllo -· U.S. ...U i!lM u o -Ofla-.41
I • 26,892 lah
-.. ... lllu.no w --~ -· t11o nu M\11 onA.io111o11 'IIIJ 1.67 , Ia __,...,... -. ,.. M\11 ODd- ... _ .. - --~ ......
""w .. &4, 160 ll>tm I.,, . .. l (.'1D'IXZ1~)006'1) • .v,, I ",.. I ~
u porU.Il _.,._ -· ..uo- "'Ill .... (witll ....... 1.67 _,
lit • .. ;u, 160 111All ~ l ~ {'.I,«Dp'II)CWI) ' ;7~ or ~r 1ttt-
--,...·-· V"' 'J..f•lo•tM A..,• 2.("3,n" 18m) .. /08 1;,"' V Z,J"ll/D•Ik Z'~ LY> •
'T= A;" IPS th'L , ,,.,.., "'' 0
jf. we anclud,. the f!Antt• t/ltcl:n'i5 fo,.. tlted .. ptlr tJf tiP UJe.b A ... ~ 2( }on ""'~•;,)= '"" ,;, .. "'- .Y. as alit lin , . '-~: 1'1'/thL " 1,, .,,Op\1
"S/IIt4('' AIIDWt116te. 'T''"·'Ic?by .. ,'10("-«<Ipsi)= /'(,I(()Op'SI.
*'rf. we m'erea~e b'f M/'1 je!.(,'14'ii,l(~;)r 2t',tJSO p~," Jltbaap tllo .._.. •-• II ~ I dGD\ IMilleoo tile - wU1 buk1o .- U.S. oboeUl.lll-- lood.
c
•
D •
•
T T ~ ,..J::=+====::::::=:::=,===:::L,r T~------------~ >I
Tbo les ol.oe ot tho !Wet wold u """ - 117 dlvl.diq t111o N811ltont ..,l\ f- ot b,67 lr:lpa ,P81' lbloor lllcll 117 tile wold aU-ble,
Far ataaciJ loadbls aDd 170 •ld metll1 tbo au-llle u (,30)(70 kal) • n kal
ar 'f.&7"t.td._ ~15' o/i • tu•(.101){11k~l)'' cr "'
but bocaU8o at tho 2 lllcb tblok tlanp plato, """' uo @ FOr tatliue load&• uaa tbB "'al.UII prod.d&4 "1 the AISC.
•••- 1000000 oreleo, tlllot wold aOlldiUOII (JS) parallel oboar, oatoFJ7 (F) llld • fWot veld conditlan (37) tooolan tnnavene, oet1FJ7 (0) wW oGDVel. 1 1;,.• 15'~1
Ct...t not tD e~J Z.l "'I)
or U5e@
.. baaed - "" averaae ot 3 eyoleo pv hoar, 8 boDzoo, 200 dQU, ODd 20 roora.
8
A y
20 .. ~ '1().0 -~o ~·54 na 0 "-0 ,.z 1/().0 t.29.t)
M•AY
ro fbld tho _, ot blertlo of tblo eombtaed aeetl-., ve ehall. ue u 1 Nfennoo ado (.....,) o llarlaoot.ol llllc """"'ah tho -• ot tho web plato.
I,· MY r...l. -11,0. •3'H,'to. 11·
0 () 1~9?~ 1411~0, IH~.,qo. "· 17t"' ... il 17.17 +3.2.'¥8 .. ,.,5',3 +lfl.~·n. ?/ .
r.tcr 13'1.1'1 +S4S. 3 + 'U.,'/9$.
I.onsitwllna1 - Ill !Wet Velda1 porallel to tile azlo of tho welda
f.~ v~~·•a,v.). t'7o•('IO•Z'I.~'/tl'l.l~·ze,'ll) c 2. I2.S' r1,,., • n 'l'l,f.'I8(Zwof4c)
'fblo - oroJ oUFtl¥ Ill.,... ••leo tar the la>aitladblal olloor oo tba nllot wold lA \bl.o _le, 1ll.ll oot obmp tllo ronltont lllllt toroo •817 lllDb. rile lea ol.oe ot tllo tlllet veld. wCillld not ln01'88H.
T h'l'f'
1
I
I'""''-". a= ..,,.1..-
. 49.
@ veld on oolli:ID vi tbbl beam oaaneotlm
~ aM!,{U2"}'&~'1\.Io) e o'f k,. a rn. {,.,.,. ..... • . .,Ill
to tbu .,., be .-blod tba -· ... u tor-
A pDI'tlcu at tho - tleop tone ....t be trmofOJTocl -all t;b1o wold wltbbl tile dUtoooo d ............ q,., Tba •-bldor of thlo rarao u --dlroot!J' Into tbe bartaGDt.ll atWeaere. f. • F ~ dfo• li&.!.'l•z\ ..,~(p ""' A...,• ..... H
0
"" (1849 ...Z.)fZflO ... J) • l 'I I
t.bt8 1a a ual t. 1'oroe Cll tbe veld. of
Jm Z~'l• ' " ~~· .... ~·~~(, ..... II'
tho roolll\orlt Wilt tone on tho Weld lo
~.·)f:+ ~:. Jr..o''+ r..C.l1
• 10.'1{, "'1,;.
tho les aloe ot tho nllet wld lo
c
D
b .. d A z Jlf•AZ I•MZ I .r, ~.rid f'l"pert,es of ,;ect,;m If If( 1./)0 c. 0 0 I .J'{()i. , :17,. s.oo J~ B.IZSO /3.:1031 ~~0112.
~U..I S.oo tl.lZSO. /$"."1'17'1
c,• 1.011..~ lfl• /,?>"'I •n
Co' '.ZS-1.~'11' l.iS"f in
~dlf1 f /lever 6e.a, {oi.d mo.qrnrun Jo,d M# PL t.r"' ~ ,. 1¥-- "r p: r:; en beam
e:~//e>w&~.6te ost~-s ASI'I Steel (f!Jenciii!CIK ftmpereJ) d;•totJ!rSI
,-=.ti.' ~r· [.r,,){toox~l)" tJ.(, xsi
P .. .a_. ~ Kst)(~<.'1tO Jiif) " '1.55'" .Ale> V· lf.ss" J.. G. "6.0 in)(/. 8~ i~
Alloo.u ... ble -sheQr orr J~in ch4nrett'r p/a9 weld l/!0 WFiri l!'e!o:~' F = {l~"qV1r po•IIOO<'Oi): 2"1. 2S' I<•P~
B
I,..= 'lfJOO, in'~-
At ceMe1"llaao tbON · -t. he ........ vel,d to t.r ... fer 72,67 kip, there u a vold at. tho top •• v.U •• at tile bottom at t11a bozo, h811Ce ... h veld baa )6,]4 kip.
Aoouoll! • leacth at s lnchea or veld,
34.l4 olp • r ~ (·707){11 ~1)". y e<r II'/• e>r
At. -b 811111 tho reaoUon u hoU or ti!U, or 18,17 ldp on oaob veld, tcp md bot.t.cm, md oOilld uoe
• 50-
I
A Y <llst.u.:e
Wllo•"'~ 18.9 /'1. 3 S' WT8•32. '/.Ill 0
"TDtttJ Z.8 .Z I
W II.•"" A r 18. 8 /p 2
I,~ 83!.. ln4
WT 8•3'- k= 9.41 inz :I;"' 'I 8. 3ln4 y=- 1.13 ill
M•.AY I..Z:.•i'IY l.:t< Z4"l."76 3B1l31j 83(,.
0 I 0 1,..~ U'l-7 .. I '1'15'£!."/
f Vo.Y ll'o"X"·'IIIo'l'I.S4in) 6 ~<.' hortaqnf:-a{ smr . rn. l'-'':s·~""'•)li-1 .... )" s. '1 '"/liMtr tnelt
lot!f SIZ, ,.f ~Wet weld w ·~.!;}17!c)· .2.~'i or 'At Inch
Bot. hooao .. or tho , 71$ !Deb t.bl.clr tlaop, aoat - @
c
D
Clleck bend triq :!tre s ~ in bea lfJ •
M" (~o in'f.7S t<i11' = "'SOO tneh l<•pr
- M c _('15'00 in ~tX s1Et ... ~ <> • r- ""':- 36'1.~ tnor " "'·
0 "''
Thti t'.l Above the yietJ 5iren1 th () f A 'II.( I steo~l, hence · ac.counts Ft:ir the hell!ltn f'tt'lti? a/ermcment /Jend
occa<;;/on.:rllr. Thtr wou.ld no h&~ppen /f the beam were marie o" t () F A S/1/ -:,tee I lif_u.enc/111d and tempered) since tlu"s ht.l:t a /(){) ;<SI ttield stren'jtQ •
•
•
•
Treat 1t?9 tilts sectton crs a t?;e IJ,.,)..~1d (t)
a .. 3 t bm y-:f(.&.603)b,:: .S'J7'JS L.'t1 T:;;- r!,SD t b;
f.b= Vra.2
Y,.. (.8660~) V _ • 3 lf~ll 1 Y 2.6"bm - bm
Tlle unit -sheor foi"C.e 1.. it: where t{b..-b,).~o3
or
cou.ld trea.t .
the sec.t:/6n a.s a c ...... d on .. he- flcow) /me-
1--b,.--!f where A = area t.ui thn1
med1on = z.sqa ~ ,--- ---, , \
,' \ I '
I \ ·, ) T \ , \ ,'
/ . , ~-----J
8
-51 •
t!!D~tld also treo:t as a ltne
't= ~ ~
~-'f"t .. ¥ where C. • Dm J= 2. r • f).O r 6!.,
li>t
l Check. colu.mn 1n bencla~
.J>Jf'{.&,a3}'~-~')•Ji(,U603.XIZ.z<t!.//,7/~" ~,I?Z. in+
M·(~«<I 1~3~n)• I,~OO.~m 11-
tr= .t!Lc,.fJ.BOt::!.oooYtz.29). /o, zoo pru' I 2,172.
chec.J IPnr/tudtital sheor from !Jend/;,_, -
~ _ 8(. B~)V(b!-b,') • B(.8,(,03'f.Str~:~'f1Z.Z't!ll.11') b- 15 ( 1>:- b;•) I!J ( ll.Z'f"-1/.11")
ch~c/t hnp/t-udrnal ';fht!!4r fmm t~rS/i:Jn-
r • 'f 'T • 't(~DOO., 60) ~ lj, .. b~ + b," " n.ztt'+J/.11'
rep~"t, trecdl;.,fj sec'tton as a ;,;,e
'" l..fio t:b:.· z..so(ft)~t)'"" 21'-D
~= (!.sea. ""o :(tz.zq) = /P, ?oops,· :1 16C)
hn9;t'11o'tn¢1 shtu2r from Jt!!/Kitt?<;-
,;, ...
f. • lB'~ 3) Y. CF%o3)(.rooo) " l'l 0 lA;,;, b l.fi 2.~( IZ.)
IDnf/~~tdtnal ,h_r ff'l:Jrn tof:s,;,n-
L T Sl>OIJ• 60 : jf Ol li • s: 1 q' II! • (1.191. )( rz-)"
'b;,;,
c
D
A
a" Z.'II'IO (b:.-h.') .. (b~-~'")
y = • S"/DZ, ( b;-1!')
(d,stance between C6 t:~f tll!'s (l~U and Mil. of w/,p/e sec ttlfJn)
:C= /.B602 (b:-b.') !TII)ment of
1nertiR D{ whofe sec:tl(;n
V = shet:tr df'plterJ to member
~ !Drce D.!J. welt!- fn:~m benrhrlty
I~ per hnear inch of weh' (each wefci)
Tre4 t ~~ this sec. tto'n as a hne (bm) ami (t)
a., 'It A, yc. ?BBSJ b, I= 6.11./8 b~ t
• 25'5"<;7 v f.b· ..__ __ _ b.,.
L.emyita d11ia/ ~
where
~ 7ira ... ea c ·.H"3" O .. t b.)
t• I.Z.t:J71 (6.-P.) J= s.?~"'~" ox-b.')
Treed ,,;9 f/le -s,u "tt~n 111s 1ft ltne -
f • 'T'"t = If..! where c c 1. so,s? b, i J
f T 1.'30€.5"? b, t ~"' "· 31 3"' b! t
( : • /lfJ60 T" l"t b·.,
er bcase d upon shear- ~low
B
. 52.
Cl-= tr(r .. '- r,·) ~rea held !J'{ we/Js)
~~~~ ;-r;') _ tt{r,. .. +r,r. tr.•) _ /Y =-,'IT(r ... ·-r.· - 31T(r.:r,) ~ {d,\Uince betiAJeen c.c:; ,( t!lr., an1:1 "'"- and A/.A. of. LVht:~le sect1~n)
I= ;rcr .. ~-r."~). ( /lii)ITietrl- o~ lll~rita o( ~·;!,,k, :·1';·l.~) V• shear appluid tl> member-
/pnep"tttdtOal shear force on .Weld .------, dt.te "to bendto/,
I F = V 'l Y I Jl,.s pjr lm'enr tnch of we lei r 2.. (2 welds)
..1....------'-
T Uar.)
The u.nit ~hEttr f-orce ,., T "t where t· r..-r; c. T(r-..t-r.)t v T(r;1-r,)l"-r.) 't 1r(~;.4-re"') 1t Zr.;•- r.¥ or
where c.• r.,
. Tt-ft #1'" 1:" 2:tv r:,
or ., ... -£--t-.-~-T-r-:r--.
•.• /dl 'let the '5a.me result U.'i111'l
c
•
•
or
A
lA + .... -----"\ \ ~~--~ tl.ltS
"=:: .. ,._-: __
Ths banding atraaa at env polnt (r) tn a sacUon af a curvad memttar ta:
center o~ 1...3rv4tull!'
---ol
T.i b I .
.C==~~-r,..D l r.-
r, • radluB to inner f'aea Df IDBIIIbBr (and GU'tBI' fibBJ' Df inner plata) ® .10 • radlua tg outer face af member
·r..._ ... radius to tnnar fiber af inner plata <!) r8 • radius to neutral BJtla
r9
.. radius Ul center af gravity c • distance fi'OII nautral &Jt1a ta point 1n quaatlon
c 1 ... dlatam::a from neutral uta ta inner fiber af 1nnar plata (!) c;L • CI1Btence frcua neutral ax1a ta outer fiber uf inner plate (!} b .. width of the lnner plate
I B
I lcmterol .~
4 I
1-r---l r·r01il--l
Tna radius <r,) of the central effect af thia force (f) 11-
Z(arb dr) r rF· :E .r~b c:lr
The Clanaminator is the total forr:a (F) SJtd h88 bean celc:ulatad above, BD 1 t ls anlv necusary to calculata 'the nuaaret.ar, and 1t la-
~P~ fi~~ r~
• _f:!1k_ {_n.-r) dt r • ...!::!..!_) (r,.-r) dr .~ (r.r--2ra\
A{ I;- ra) r r A£r,- rn A!!i•rn) /r•rt ~n ~~
... ~ [r.( r~- r;)- r"';z.-r,J A(r;-rn)
so r,' r;,(r ... -ri)·(¥/ r. lo1 *- {r,..- n)
- 63.
Z.A r.· ~(1. locj.li)·~ r;
ax/a/ stress
center "~ Clir~at.irE' -..1
F ANMJ00/1. / d.ii=- A= .2'/.tr,;, .. = + 3,;j,90 pt•.t-fensmn}
benduiq 5tre:;:.o;:, an bac.k 'S ,.cl e
c
D
o; .. M(t;-r..) ~ {MtwJo•Pf.'i8s'JI'I•'IS'- 3-4/.L - /Z,S'70ps•(t!1Jmprl:3SIM) ll(f3·rn} r. ('.9,2.!lJ.'-'·3.(,1Y.IV.1S) -
Tot-41:: t 3:190- n .. !i?O • - 9,'J.BO ps/ fcomprPSsron)
Force 1n inner flo.n9e diA.e io bend inq
F= A7r,"-r•} ~ ltt~,e ~: - (r,;r.)J
F ... {t'frt, ~00 x. 71Z)"' /t/)~1 zoo lb
center of 9rtll'l.t'l oj: tl11's force
r..(r ... -n)J~i ,.. .. ) ( ) (2.2f"'-J..rL) ... ' \ 1,,, ~.2S'•I.S • --e.-- ~ /, 30/
'"'G r, 1.,.5l..cr.~~-n) ·?lz. -:vz:. /.827" rt
or
Y • r., c:os e
F =- P( 4 + r;. rl)ss) z d F• PZ (- S/n t9) c:/!)
lu.t n• r;, e ar~d dn= !;dB
c = hnF ~ dF c PZf- Stn!J) d6 _ .fZ... . B 18 a a r,.dD r,. de = t; '5111
F
-then p,.. ..:.F...;.A.:..(~r..J..,-"r.;;.=)'---=-----=-(<t +rn)b rn '·~e ~- (r.llt- rt~
sub si:itu ti!: tlu$ Into the Formula tor (f"s)
~,. F Sth8 s {at r,) r.
$/nee mqximum (f,) occur:!> when this hec.ome<5-
(b<~ th welda)
Thla unit ahaar farce ta figured along the axta ar the cantral afhct or the farce (r, ). It rtq:JI'IIB&nta the dlfferanca ·tn the rtanga ron:a (F) whiCh awat t:Gia8 out as anaar (" ). tr the conn-.ct1ng WBld 1a nat located exactly an tnla axle Cr, ), than tn1a value nwat be adjusted because of the difference 1n the length or the weld. If (r•) rapreaanta tha l'Blu• af tna connecting wld, than thla un1 t anaar farca IW&t be lrlUl t1pl1ad by t;. ) r., •
and (both wslds)
This value wound tnan ba divided bY the n~r or welda.
£"&1.111p/e~ F • 106,2.00 lb. r;.•z.u• {~ld a.t ( oF Flo.nge)
f. _ _E_.. /0&,,2.00 /b"S ,. tt2(oO ~· (l.oth welds) .-£cttl'h)r., (l()'t'at3.,t)z.2& -. • "'
or f~,. 1,630. ll>n;, ea.ch weld
A
B
. 54.
Moment •r•• diatanca l:l•tw••n nautrel •d• end appUcat1an of laad
-''II."- r. e.:o,,g .. H 14 ·-9.1,3'~:i5'f• .. fi!/,'B6<.t" Bending IMHnlftt ~~pplhd to thla ~::rau a.cttan, uaumlng • 9 k.l.~ loM
M .. q~(n8'~in) .. ?so,7e inch t<iP'
r,• r. (r,-fi)- ~(r;!-r.'). '1£3{4\-,t..)- ~ t~'-("'1.), =
ra IDfc ~- (r.t.-li) 't"3'"-k- (c.~-~~) lnw.rd radial untt rer.:a an walda (2 flllat wdds)
f. .L.13.00t 'l'f'l"'' • r. '·'-'-'llu ~ • nn ----·-··- ------------
Thia unt t r1dhl farca would CIIUae tha fall;~wtng a Una an 'lha throat ar these flll•t waldl'
;(8.:1.~ liSt JB.fj(,
l'i.l'i II. '32
lfow check tha longltudinel shear on th ... fillat welda.
c
•
D •
•
Tho -- longl\udlnol ollou Dn tho OIOldo W1ll DC- 0' 6 o 'llfi' olnco tho ... .,., aa \ha £1'1111 uc\lan chana•• ura l'arl1dlv t'lua.
.F,·. ~0 •r..(tJ) .. '1.2.0 .. /ill tn11 111111 lncn ... VII pnutc.,. atran•• by zr.s.
The tallawlno la..,. uw appll.c! an ttl• given era•• ucUan:. F t • 5.29 kltl8 fiiS'DI tl'8n8VII' .. ta UCtlan
F1 • 1.28 tlp '••co PVOllol to oocUon N ... 250.8 ln k lpa _.nt ebaut n.utr11 u11 ar uctlan
Aalal litr••• an MC-t.ilm-
_. 0 Ft- _ 6",z<'ll< I..C ~a 1' ""' Jr" - '1.5"1111•" .. ... ~~
-t ~--m~q-~tr,rtl"T-~
I' \.,.1.:.. L~Lw-·1~4l
~ett• of cu.rwd'"'rl!
~~ 'moment" di<><tram
A
8
-55-
111 figure Ill , ,.. -.t.ce ~~ tile applied -ill!l -~ 1111 aau ... a U..olle fane IPI l.D ""' lowu' f1U19e •
Beoauoe ~ flange 1e ouzved ltlle - -ioo 1e cuzved), tbio U..oile fOJtce ...,.... an 1mlud J:adlel 11J1U f- If.,) dine~
· -ud tile -~ of """"tva ·m be ~ed m any oecUoD of tile fleDge,. He figareo 121 and IJ).
'l'hh 11J1U redial fOJtoe applied m a DDi~ width of tile fl8119• 11• vide), figure 141, .. ,.... U to defleol: deOIDwud lndiaUy l.D-l ao a be... 111 oo doiii!J, iu rodiua to tile oeo~u of can>a~uu will cbaoge al01>11 tile width of tile flU19e -.l1II!J to tile deflectloo """"".
'l'lle canual pc>J:t:ioo -111!1 - ll.Dwudl will ... ,... tile ndlu ·~ tbla pol.D. ~ to decnopa by tile -~ of tile deflacUoo. IU radial oual.D will be E • ;r-. IU oual.D ill the auaa.f- OJ: UDge~~Ual dluotlOR will aloo be ~ to thla -~. By ll\llUpli,.iii!J tbla valu by tile ~ ....
:~!:·~~. 1:1.!;!.·~~,.:: :t': .~ ~~!:i~ :-"'..!!!"u ... cbaDgo iD oUaoo 1-reUiOD) will CIOCJUJ tllenfou, tile l.Dl~ial uoalle ·~·· iD tile fleDge iD tbio h!lioD will daoru-. to tbla ..,uple, tile oot;ar edge of tile fleDge dofleol:o _...s loa-), and iu J:..U.ae g tile aeabJ: of OIIZ9&mu wUl l.DOitaOH, pJ:odocio9 • paaUhe auaio eod a paaUiYO ~·• cbeDga l~ile). 'l'lleufOJ:a, tile ioiUal UDelle ~- l.D ~be fleDge •~ tblo h!lioD will 11110raa ...
Ae a renlt of thia auip of ~ fleoge beadiDg ae a beea, then will be a uaa-ae ~-11• ouaao 1-111!11 ac:roaa the faeo of the fleDge, being -~.oua •~· the - of the fleDge ju~ aa l.D a olaileJ: -· Aloo, tble ouip of fleo9e acUOil u a - wUl J:OUb ltll a~ ""' pol.D~ of euppoJ:t:, tile fille~ wold m tile web. It 1o tblo J:OUU011 nleb - u - tile wold.
'l'be followlDg will belpa
Ill If tile fleDge could be made thloku, tlleoe ~·-• eod
-~wuld-. 121 n -ld be po .. il>le to .. ~ tile web plebe iD oli9bUr to
• paiD~ -"• thb _.al.u rouUoa •~ tile tl8ld VD\1ld be ouo.
, We/Jed 2. '"Tiin Prets F~me
lfoOO Jb<.
2~ ®-------------2...,
chect v~rtte41 seetmn (i-i)
r, • .,, ~" £A Z~t 'A/'• 3~'' r.· .:r(I>J..r.#-)"' z·:..·~ 'Hf=
benda01 ntm- IDMr ~ at" M(r.,-r.) • 2000 lb"Zllt'):''I.Z,!.z,n1
A 0;- r,) re '·'~ ~s--~z&) z.1s
c
D
A
r,· ?.$"
£A .;!ll.t.,n~ li - '· 37" 1"""£11(~~)" z,.,..ZfO ~ -
&Jil U!:!.u F ZCJoo lh
DO.& A= .,,7f;- /p'L " .Y~o. P'/
ehecl<. buck/1~9 aF back. Stdf'~ 'fdresa-
- /S'-/0 ps/ $mp) + '120 . /
0
"!Dial - 1/:J.Opsi(t'tJmP)
~.,\w'n ~I.3{.. , ~1
&.~mprnsum ~a·?"~ CJ>mp/'Y!IJS,;,n
ol..= 'Yb" .%ra= z.
. .ac. ,. $t11Ce IT = tr,. we 90 -to step (l)
B
® ~nsert 11alue CJf. ff /nt-o Formulct ®
.. Dj. (f!f-r- • r~3·,o'X3.3z,.,.,4t ,., 33 aoq ; tr~ ./8% ayz. t(ff}'- .1836(s.3'Vo~)~+('-3Z.wto")z. ' ps
and cr/tJC.a/ 6uckl1i9 'S'trc!'S3 r.,: &cr- ,.. try
Fr-om f/11~ 1 we wou..ld e.xpect no
anws ua./ 6uci hn9 proi$/em-s Since
tlct"~<~al aompnesston 1~ a/Jout s;8"8'0.ps,'
a/sCJ the tank w/11 st,f{eo thr; t-e9/on.
. 56.
i '-i I<-
"
Shear dt'octrom
c
D •
•
A
® I ru ~""'
1 '·l~
'h ~.~r
~~" encl pfo.tt> l" iMid<!' plo.te
... nit ~=e en weld uno't force on welcl ( • '13'/,l ~ c " 'I Kt . r '1•1?in • m
leq st3e o~ f<"U..t weld (E10)
w= t:..'?>t •tw. .. • •ns.~ .7o?{:lt~<~o)
or ... :~e Y~' ~
F • ~:\~: = I.'Jfl«tin
leq s,-2 e of frlld weld
/.75 "lm c . • W = .70'1{:1.1 K~l) • II B on
bu.t becQu.~e of l" 1 1.1~e $)r.,' 1:1,
B
v_. 1&6".'1!' I
-------L, ..,.,
! F,• ,3'1.2" F•.2S't.2" f t v·t:.?sk ~ n '(. .. .t; ::: ;:: . ~ ~ •
t ~ ~ .... ...
Yli'
1 web plAt~
I " """' a SJ!I9~ ;:a po.nef .., "' ... ~
'1- " • i ~ ::}
~«--• a·va· ____,., t T T -v. 18( ..
"'"'t hom.potAI shear ferce on {.,'1/et we/J heiMu::en flaage A wep , v, 186: G• • . r,•-r = ~· 1.~0 ftro
l£9 .,.,;.e of fitfd ,.,,.JrJ
?.20 "'in L18f!i' IV= .101 (2.1 ••I) "" .-, ~r U)e Yz" 1:::..
c.h<!'c../( ?heo.r ,t-r~s ,;., web + :b. 180.'1" .. . ' = A .. = ll,'•l:l"te". I ··'-0 K'\1
+ ... II" N ... • ~
d WO';Lid be we(/ t~ keep flu$ w.•'tlu~ '1'•,'10G, -.'lo{'!t~)· l"f,'-/K1i <>tlrt:rw,.e i{le reo.oltlll? oil•?"',../ cDMptrn_, mtVbf <»ucr t-./ti""'DF- ..,..f>.
a I" tluC.!< we6 pfa.te w~ ... td d" thts V. J8tio'i~ '
"i"=~= ~· 1~,<(0 1<!>1
. 57.
~·
'l'be vvt1aal -"' force ot 417,1 kipo "" the left, eater a tile web -1 41recUy f,_ tile 3-1/2" tllld: - plate tllrough tile pair ot l/2' verUaal fillet -ua.
'l'be 2" l:biclo: :Lnll14e plate appl1ee a vertical alleer foroe of 129.1
:!f:.~ = :=J:-!t ~~ ~!.Cirtoo~':f;ll~~:f. f~!!:!.. already 11110 a verttaal Oau of 337.5 kipa (oae-Mlf of 675 k:Lpel. 7.'beae boc! va1uea a44 to 417.1 kipo.
TT ----- ..... -
,. ... ...;
A
'""'' 3~<.' G.3.00 ,~1·· )'Ill,' 'ILl .. ,
?.•:~.'f•11'4' 5"'1,5"0 /'jS,OO
y fiii•AY 815" SS'.I1S"
~o.~?> ,.,.,'J,qi.! 4o..:lS" :t31'f.~'lS"
3867. <I !fl M _ '!S67.'1l6 1 .. .. ~,
Nfi•A"'- /"ffi,OO r r••-
r._•MY ra 'IS.ll't /& • ..0'18 30~,,.'t8 Ul'f.'i S' •nrnsct '.IA."\'18
~~~'I~0."-8
J;.A• l:t:r"i-(rVA)M• n~;J'IO.:l8-~'f.'i'&.(3f387.'138)" ss;'J."'/,~7 in+
Hor;:.ontal shegr pf fitlst "'"14 befwetll tti!l (/sOfe t11nJ we6
f: 'Y:r .. y J~3~.l•Y:l•?.lo.'•n""'J'ao.'!J') • .,,"' '3~ lltm (No..,woool>) {n, 'l.'ll,ldt'J.'I .,etch)
/~"' ~tie w= "·"' 3 "of., • .ll'J.0
7 ,1D1(11KS1}.
b~<t bec:,.u,;e ~~ :l~" t m~<st u.se Jz' ~
c
D
I ,,.
~o---- 3. o• .~· le-I I I I I I I I
1.-- ""'~
L center o~ ro.duis of ao.rvot11.re
A
8
. 58.
oendJn9 stress (Jh ~nner s~rhtce -
/~6GOps/ I
/f. thts were a st-rru91Jt hee~m
.,.. = _,111_ ,. N>t:i I( 96 = z 2 .n::> -,. S /,J2.7 rw
The. re~d~1is IJf. the ~nt/ffl/ ef.fect of fh1s force ,S-
t; = r;,(r.,t-lj·)-~(,_.~-li'): /,033fS"Z-,'IIJ)-~{.5"Z\Y•) ","lot." F t;, lo'/a ~ -( r.~e·Ji) ./$'}
trl d1a/ fore e on t-he two Sl'cle:J. -F H'/0. 73 u 1J • (; • ) F .. • r., m ~ • 7~ '!117 t,.,o stde"
or f = 3'70 ~'1,;, {1Jpe :uCie) r
t'Ats res~.~tts ;n 11
..... ~~~ .. I "' "t- '• .IZ
17!1dllil shet:~r st-,_3 of!?1¥11~
30, 6oo ps/ ~ fvce
chec:; l~n'fltud/nal s/tf!!4,..
ass um~ r.; • ,.d,/is t~F ~ oF mner fla'19e •. Y''"
r _ F ,. 33'f0 ,.. 7S. J~· (1:.- de) r-,.- (a+t;,) r.. (9'1"/.~nY,•i') WI s1 :s
or I,=- 37.s- lbJin (one s,.'de)
this res11lfs Iii 11 late~~:~/ skt:lr sfms of -
it. a?,S" 3/0 p•,. ..,.. = -t = --:;z:: ,. ..
c
•
TORSIONAL MEMBERS
7:= ll a L T.· D!. b L
4,.-l;a+~'td)+ !jet
T. _-T, a -{latb) - ia+b4Cl d- L
e-T•bH..a e ,E ,.- E,R ' £.R
·A • ena enclosed. vlt.h.lD. MaD di_..lCII \ 8 • tbi- ot oectlCII at ·poW (a)
~ • shear 1tzoe .. at potnt. (a)
a • t.orelcwael rui.lltuaa, sJI 1• • = • ~:-=~':.~ aheer e • ....,wr llrlot, n4lua L •lon&Q or-..
A
8
T ·d· d R=~ l. b+d
-59-
{jf .s Dl'f ~~ ... J a "o"-.J ~~S" ; o .... ·E-J.-~ J.i ..r·-1 ... :!r ~o__,
-~ ~ ~
rJ oil
c
D
n...& n,.• PIJ.IIlbcr o~ ltnq,h:dialll a ttant..erte mem••ra
.~r~l:,.(T.<I,!R,)+.ji J;,(ml,+R.)l or A" ~ ~[.:!!._+ ~1 A, !DE,J;[ ~r,t.+JII,I>,U,+il<) ] 4,- 1,SJl E, I, Jd
~·>or, f ~ l~.sz, + R,) 1 l u:,(n:r,.a..)+~ild(I01.~i;lj
._ If nBQlact d8fbct1on due ta bending af elda end end memb•r•• ::t'• cD «-.tr naglect. at.lrtn••• dYe t.o \.Qnlonal nelatllf'ce ar aide and end Ulllbar•• 1.,•0
This is the tall g~~te of a trtJck. Aa the 1111terial is dumpeo into the tall and or the truCk, this oate ls pulled forward by No hydraulic cyUndan and forc:n the material into the truck under pre a Sure. Occaaianall y a solid DbJsct b8CD111118 Janned into the f'rllllll 1 8118 left hand elde, Blld holds thia end of the frame fi"'OA I!Dving further while the other end conUntJas ta be pulled forward. The h""raulic cvUndera are capable or exerting a force or about lO,DOO pound&. This subjects the frame to a twisting action. The rnme la rather fluible ln regard to toraion because of 1t 1 a open J tleam .sections and flat plate, hDWJver 1t does have Iii 6 inch diameter tube llllong it's length &nd thl& contributes almost entirely to \he torsional resistance of the friiiDa. Thls torque therefore will be reeiated almos\ entirely by this tube, vet 1t alone doea not have aufflclent atren;th to do this.
Po1nte (a) end (tl) •r• rallara mounted on the end mambar of tha frama llftD rids in tracka flhown aa daehad lines in flDIJI"I 1,
A force (F) is applied to \ha lower IIO:rtUn of' \he and ll:aaba~ u roller (b).
!::la~=r;~~=·~:a:i~BCI!~!i:~ ~r:!u~:r:; ~~i) t:!~::!l t::.~!!:~;. !: :::::.. ~~ ~=::::;.a~~!~: ~~) d:,::.,rats!!!::'~h!n..!, d!~::!o~n::a:!::'.:'i~' \a =!::~ i:n~~!edroti.!:. the left, \here 1B an axial tensile farce (F' 2 • F ")
~~= ::a~O::~r!:.:.=!:1 o;r t=~::.;.:a;::r~~!i~ ;:;!:•~r t~ ai:~s r:!~~:r (~.a
dirac\ ion a\ righ\ angles \a \he mSIDbar and 1n \he appalua dirac\ ion of (F 3
;),.
AMlal fOf'ce 1n end aulbar ( t.analan) la the aame •' 00\h enda-
F,=-F'y (!) ~t roller (a) -
Fr sin B = - ~ • F1
F.s- cos $ = - F. Fs ,..,.. thio we gat tan 6) ~ g
® ®·
At tollal' (b) .. taking \he summatlan at forcaa in lina of \tte u.ia of the and m~r to be zara -
F~ + Fa. eos ¢> - F C!O$ o(, e 0 0 taking the ~H~~~~~Btlan of for1:11a a\ fight angles to the &Mia of \he and ~~~HJ~bar \a bl!l zero ...
- F, - Fs/nol. + ~ sin ~ eo @
A
B
. 60.
SullaUtutllog t•> into fai'IIIUla (6) we get
- F; ian B- F sin cc: + F2 sin (/) •o G)
Taka foi'IIUlae (5) and (7). solva for (F2) and sat these tlllll equal to aach other -
Fit sin tP " r3 tQn I!)
Fa= ~tan 61 'Sin~
F L"OS o(.
cos;
+ F'>ino<
t~ sln¢
®
®
-F-. + F t!.OS b( :::: F, tan& f F sind-(!05 tfJ cos ¢ sin¢ sin¢
h{- c~¢> - ~'f: $)
F,• _J~: Leost;
o•
F { l'osrA. tan~- s;no(] tan tP + tan t9 /j
F,
~
Fs-
and
f3 tan&
F coosa(- F3 ~OS rp F,
s/n I!)
E)t.arnple d=60" !- = 30. 00-:J s 'S
9 :; in a.. • . S"4? CO'i.r).• , 8660
0 ::>tn ¢. , . ~IWd t!os¢• .t736 icw~· S.6713
/tJ.
';_l•t:;'l • /'/;)6 tafl6 • 19'1'/
(.SM,O•S.'-'113- ,S()OO) 30,()00 !.'!!1:22,${>.)/1
fi" 30,000 .1'1'1'1+ S:t;713 • • ........
® :.2 2, "so lb
® ·~~.&SO • ./Cf'{l{=
fr\ 30,000• '8,60 - l ,,,so I(!:) • '17 3~
'-f,O/& ./908
-i J,o~ o.ib
Sin~:a \he 6 inch plQ& cantribu'ties the graatas\ 'ta the torsional reeia\enca of \hll frBM, lt will wUhtl\and moat or thia torque. Ita polar moment or lna.rtta la -
J"' 2.r= 2.(2a.JII,;,~) .. 6,.:2a ,:r." and will raaul' in a al'lur a\raaa of •
't- Tc _(I, 35'3,,ooX3.3~) - J'" - j"G, !!8
ao,ooops.i
Thla would 8CE:OUnt far \ha plpa tearing au\ of \he wllba of \he friiiD8.
c
•
•
/,,')it. ·(3
<------'
CljJ .. .30
~I ifll > 0.6
1.0 ~
ifll " 0.6
1.0 Of = 1.22 - 0.5U ~ ~
allowable punching shear stress
CD I rp = ___!!_y__all Of I' ; 0.9 ,0.7 ;
but not to exceed 0.40oy
K .. 1 + sin 8 a 2 sin 8 ·
Kb=1+3sin8 4 sin2 8
, .. tb [a a sin 8 + !!t] ~;~n of plane bending tc Ka Kb · ab = J a by + ab.z
actual punching shear stress
Stepped box Punching Shear
10.5.1 10.8
OjJ= .25 1.0
0(1 - (J)
iTO>"Q.5 ~ ifll c;; 0.5
Ot = 1.22- 0.5U 1.0 ~....--.
____..,__. if u > 0.44 if u .;;; 0.44
allowable punching shear stress
@ ,, P r a$ a;of] but not to exceed 0.40 ay
K = a + b sin 8 K = a + 3b sin 8 a (a + bl sin 8 b (a + 3b) sin' o
® r =...!Q_sin2 11 (~ 40b ]
1 .. ..!2 [a a sin ° + ..'!..b...] if out of plane bending tc Ka Kb use· ~----,--
• Ob = V Oby + ObZ
tc · 1 + sin 8 + l + 3 sin 8
For circular sections in which JL> 3600 local actual punching shear stress tc ay
buckling at IIXial compressive stresses less than yield strength shall be investigated 10.3.1.
a-. 1
_ lb . , fla + b) a a (a + 3b) Ob] o,:v - tc sm 9 La + b sin tJ + a + 3b sin e
If sufficient thickness (tel of main member is
used a distance of % beyond each weld, general
collapse need not be checked 10.5.2.2.
fillet welds limited to jJ .;; .8 1 0.13.1.3
The use of fillet welds limited to ll c;; ~ 10.13.1.3.
Optional Yield Line Analysis Box Section 10.5.1.4
!11 < .s 1
allowable shear stress
(from Commentary) Table C1 0.5.1.4b
axial load in plane bending
@ r = SKF OIJ.-!L_ OjJ = shape factor . 0.5T a .1. . f
_!!__ +--2-1 -II v'1=j
II> 0.625 Ojl = 4111 +/ir-
'---------1 1 = ut1 IZatlon actor
~for suggested values)
K = reserve strength factor see commentary SF = sef~ty factor Table C1 0.5.1.4&
.!L + ..!1....:!.1.. a 0625 n. 2 1 -ll .. < . -, = 4111 + JJ)
U = rat1o actual to allowable stress - main member
.brace member of yie/o' stren~th
' , , , ' 1111 '· ,',' 1,'
----!.,·1 J..L--------- ---- ------(lnif rorce on weld ,!rom /JrQC8 111~m1Jer of yteld stren,ptll
F, = Uy tb ( in. ~j weld) (14a)
vltlmafe shear 0/'1 Me moill mem/Ju shear area , / at f'qillll"e , ' ,.,
,, ,' 9 _____ _L:~ ... ~J_j ___ T -----~--r----t .R
I
tz = 1.8 Ta i: lb.jin. t: _fa_
~;sine weld_
--4 1"1-~ 1111/1 kf1.9llt ,{weN
fs., I.e Tat sine
(14b)
- 61 -
( lb. )
in. of weld
ultimate .strength or welded COIInectlon ,' , , , , , , , ~ ,
• ----~~---- n fw • Z.il7 (.7o7w){.so exx) ~
(fillet weld) __.61.1-
~w = *z.,7 (twH.3o Exx) _ll (partial joint penetration ) ~t,)
. groove weld (14c)
Stepped box- 10.5.1.3
If I (J > .81 or I (J > 11 I or both a < b sin 6
O(J = 1.25 (1 + 11) = ~·
if T/ < 1.0
1.22 - 0.5U = ~
if u > 0.44 allowable capacity
2.5 ~
if T/ ;;> 1.0
1.0 ~
if u ~ 0.44
I r a fJtc Op a, J I @ F = 0.8 tc ay LS'iil8 + 0.12
2
(J = ~ D
D 'Y =~
n=aox= a D sin 8
FATIGUE STRESS ALLOWABLES
X ~~~~
f'_l I I'
......: ,.._ E' o' " .... , ....
c•-- D 5..'-E
~
""' F ... ......_6 ~
~ ~':.l-:: ~ ~ iiiii;;
:"...,;:! ~:-.... ...... K ~ :""!.. , ... ....
' """ I" ::'Iii:. .... _
~ .... .... -.. ~ T ..... r-.. l ~ -t-.
:::::: ~ ... t;;:: !'ooi"'!o;;;: 8;
s,.,. - ~ -... T
104 105 101
N- CYCLES OF LOAD
. 62-
Matched Box 10.5.1.1
I (J = 1.o I O(J and Of as in Fig. 11
allowable capacity
(j) F = 1.2 tc Oy ay [ins + ~]
10.5.1.2 Full static load capacity of branch allowed if:
Complete joint penetration groove weld and matching weld metal.
2 ~ < 22 or 'Y < 11
3 av of main not less than that of branch.
tb 4 "t; ~ 0.72 or
!~ -- 1.0 d "" an U .s;;; 0.44 (main ·member)
5 11 > 1.0
--------:
14-1- : -·-1-- -c-;; t- I -
if' X-II:
lr ~~ ~ i-'I; ! =
r..:..
'!;: t:= K-I--
5000 4000
30005 z
zooo' Ill
~ u
&i 600 ~ 500 Ill
4oo I 300 ~
z ::iii
200 ~ Ill
..I
:! 100 ~
I Q: ....
Ill
•
•
•
<D ~ ® j Unwelded l TCBR
® ~ { Butt weld -complete joint-reinforcement off
® radiographic or ultrasonic inspected TCBR
® ~ { Butt weld- complete joint@ reinforcement off
no radiographic nor ultrasonic
@ ctb inspection TCBR
{
Butt weld -complete joint -
© ~~~~rcement on ·
®
®
Pipe with longitudinal weld TCBR
Mernbers with continuously welded longitudinally otiffeners TCB R
~@ Members with transverse or short attachmerm -TCBR
TCBR
Here the attechrnent is long enough so It will load up. Hence a force rnust transfer out of the end, through the notch or change in section, causing a stress raiser in the 111e111ber at this point. Welds checked by @ (unlforrnlv loaded)
At termination of double wrap
TCBR
At termination of cover plate
At termination of longitudinal stiffeners or gusset
(does not apply at simple tubular connectoons)
ALLOWABLE FATIGUE RANGE OF STRESS
For Tubular Structures AWS 01.1-Rav. 1-73- Section 10
T = tension
C = compression
B = bending
R = r~rsal
K-~ max stress
•but not to exceed steady stress allowable
Stiffened connection - bela- joint
Force is transferred through joint by additional -tarial
Stress distribution in lnnch -is essurned to be unlforrn
Complete joint penetration groove weld
Partial joint penetration groove weld or fillet weld
TCBR Welds checked bV @ (uniformly loaded)
Slrnple T, Y, or K connections - no additional stiffening
Stress distribution in branch rnemiJer is not uniform
Check main member by ®or ®
® @
Cornplete joint penetration groove weld
TCBR
Partial joint penetration groove weld or fillet weld.
In branch member
Welds checked by @> lit @@@ (nono<Jniformly loaded)
Lap joint
@ ®' Shear in weld
Tee joint in tenaion·or bending
Simple T, Y, or K connections with fillet or partial penetration groove weld
@@ @@ Shear in weld Shear ·in weld
Uniform load Nono<Jniform load on weld on weld
FatigUe Stress Allowable Categories
10• 1a• N • CYCLE& OF LOAD
CompleK tubular connections where load is transferred by:
eccentricity Stiffening rings Gusset plates
traduction in fatigue strength is caused by uneven distribution of stress in lnnch -.I Main member checked by @or® welds checked by @') Also check punching shear in overlapped portion of branch member
Simple K connection
TCBR
® SlmpleY conneCtion
in branch member
~..;;24 I
Simple T connection
Allowable punching lhaar otrass on shear eree of main -bar. Por R/t > 24, raduce allowable stress in proportion to
Allowable fatigue stress =( 24)0•7
Stressfromcurve ®or® R/t
Where actual stresa concentration factors or hot spot strains are known* use curve ®
CURVES FOR DETERMINING DIHEDRAL ANGLE
....
+ t:JG- • ---.--• ...,f-f-Y-/4-/'V''-V"'J.<Q
t .... 0
uo ..
!: __ : 10-
~ 70:·-
110---
'ii-1'H ·.. rHO·•
OUIG
j 10-·--· ...
'" Ci 10 --···
. ..
no-···- ---- ----- ----··
1uo----·
1•00·----· ;;,. ______ _ •
. l
9=40"
9=6fJ
-64-
9·35"
.. ... ---------k./-l-?/-J/-,4~~~ .. r'o "--~~----~--- ... ·······-------t>• .... '-/-'/-/~/-v--/-1
-;too- ~ , . -·······-·---Jl)!f..r.'/__,~V-,L
~ta'6
~,. -----W#'~~ ID-·-·--·
. , I i i j ------4---1 -1-i..lW
10--"
tao 1W t40 tsa 110 t70 110
9=55"
110---- -·- --- ----+/-b4--!-,---4:~~ .. .... ~ 140--.. ·--~----- ··--·--J-r-/·t-/'1-c.b-+-'.. r,., ___ _ j.lO---------J-1-'f-,/,_• -;,<--_;-<;-;._..=.,_.. :~~~~=t 1ino-----· • £'0•------i- 1-i'-V'-/f'AY~""--
j u-- ------ ----'--/fi~A/-vi;A,/--1-.
1t0---
tTO-••
1==~-:110 ___ ----·-r:;; Juo ___ , ........ t-IDO~
90-----l 0
! , 1 : ' ; l i j I. L.L .. , ...... . l.
tOO no 110 ~~ uoo no '10 t10 110
•
•
•
bend '~'1 ~tress in branch member /11 !)00 ,;., •
Pbr S ..- 39B,Z ln' = /, 25 /CSI
bra ne h mcrn ~~ t oo· z<1.o,;, Il}• 2 "l,t)Jnt.• /.!),', A • ?Z. Z' ;,• I • '178~00i•4 "' • 3 '18.'1:1 iP3
f>OO ro<h ~·P•
F• +1000 l<•i>s
8
A•Z1rr-f•211'Cus;.)Cu, )• t2,2,,.•
S• l'll'r"-,•(/ .. }ll(u..f•~IS..S·' X• ~1rr' -o(IJ¥1rlu.G),'"'II4.'
s· !· '!:!:J!f.·· '~e.z ;.,t
If), s. I
3b r<si ~ ~. 3/ J<S/
o. 9 ( "/.() '")"'7 IY>tn
'T'~ iL{.£ + ...ei).. to,;, (r:J.s'f• 51 + ~··) .. .s: so xsi "' )(,. Kb tft ,;, t.?s t,re I
V<ilkt"> o' J(.•/.75 tmJ rb•I.S8 Qrt Foon d horr c IIQr 1
s.ao < ~. 3 I IJI'r>:e. or<
. 65-
&n$ider us""l a fl!ld weld
tlte "1<1Yi!J1'.1171 Mnit [,rce on tile t"dnnf'ct'~ tfJe!d frettt:trdff"::J'3 .,f t'fpe. of vJe!d ) fll4'1 be 'o .. '1d by mult,iJ/tfiPJ fhe p<•nc l1·~"l o;kar :trp-;1. ;orm~la (T) b'f the fhtcl<n~s e.( /he ma'f1 mo'1 b,.r {t), To ~"ha"''e (rom '! hP nl.lrmQ( ~orce '"ompo••ent ta llr Pctil.al 1/fJ/uf!, we mq;t t/lctr <In•,(/(' thtTJt-Ujh P'f ('Sin8)
II . ~{¥,; + i;J I fmct. L"<l'K'f <I 'h'.'QI"' -;frC~) {tnoa. j,l.nlt fore~ on weJ:d.)
f'IO weto· mefQ/
A/5o checf< r. - ,,.o,;,. 57 -x- - ' 1.~ ;,, •
11i71:-e t t,,s raf:o 0 r tt:>::lii t'"•ceed ~ J'& fhP /;ranrh merne.-n,e• 'll·t:t ~,.. tl'veiJri al~n9 tl,f' s1de p:ut1on of -!~r r:;rJ"er:'•of7 -seF.-'It.tJS Fi'f~.t9.1.'3
Un euen p,·s tri bt< t1i:m d L(J(J,J "n Connect r~t} Weld:. 10.5'.1
Bntt:e member "" vielrl stt~tlf(/7
U(t!inate 5/iearDfl main member 5h_earqr«t qt fqil~<rf'
f., /.B.t"~l· 68('-31KSoYJ~.;,) = jl.f,O"f Kiln '> 'S1n 5in 'tS"
()Jtimate strell!fth of weldecl c.qanection
~ .. : z.~~>'1/.•Y2.t KlOI) = Mo'(,'lff•-IIP){:~.I 11~) ~ 3'Uo t( "'ltn
If" eoJip/stf> pen,tn~t!M <JnJtJ~I! wdJ were used, /t wou.ld not be JH!C~11t:lr'f to e/lec.l. the ab:JtJe unell41l d•stributtDn of /QQ.d .:>n the connect1nq weld
c
D
Lamellae (ettr m /0. s-. 't -rn~ ,...;fiKIII 11Jdra/ ()£ frtlnSVt!""' /8t"'k 'IJttns "fPili"~ to flu surk.a• 6f tM IIIDin member '~»V be fo~~J 6v /110/tlplvmq tilt! form• r.,; !foe llltl,;,..,.. jl<ln<htilq shear .tren (1") b~ the thtckness of the ITIIJth flle111 l>er [t> ancl clivlclrivf b't tlte It:~~ srie <If the fillet weld lkl) ar tlri'Otl.t "~ the 'i f'!'Ove w elcl {t.,).
a(io=~(~+~\"Y' t..(§...tA.\ w t:,., "'•) t;; K., K, )
in thic er<ttm pit tr='if. eo "'''t II'. In) "' a. 70 ""'; < z o ,..~; t,om
hu/Ce 01(
,V.,.., consider the ':lame CCJr~nectttin 1<nder the fotiDIAIWrq fotl</~f'~ofldrJ A N=number ~~ er<te<. •1•106
~nqe K• -1lli; • +/It
aJti4/ ~' itl 6rttneh member F. s~• · ·
11&• A. 7~.2.& In\ = &,qa, Kll
~endin'i st~' tn bmncl! member 0.• ~ = ZSO ••t ., &. 2. IC-, 1• • .. J98.Z. •
t()tal tr: &,92 +.&."-.~ ?,S'( ICSi
A/lowo.bl;..., .,hear in mai~J,...mcmbcr (fatt{Jile 164d) . IA'l ~.·'l~e~ C«t&ttO"''W N~ , .. ,o• ofc/e$ K·~· +lit
h·om ~•1u.re to,?. '"I reAd st~ess mnlfe T,.. • 2,S' n•'
'l>o 1':: • .-!it_. 2•!;t = '3. S ~ KS• {tn.t n.t fo e•ue<J 5'1-;Jv 1114
• t-1<. 1
af/•waiJit l>f '·" ~~•)
Cafc .. !ated puncht'n'f 'SheAr :rtrn'5 tJfl main member
_ .!t(r. ~., ~Din ("•z. + ·1>2),. z."'o ,,,. < J,,; h~r~ce ()/< '1' - f K., t 1:~ .J I fr it> T.'ff t.S8
8
• 66-
t=idt~u.e af/l.wable in branch !l£mbe.r fi'l Q9 ad egor'( l.9
From ~oqu.re. /1), 7. 'f read stres<> mn9e
c!l;r z.s~s, 3
_73
,.,.; ,o o-._.• t-K • 1- ?v =
(assufllr (illel LOe/ds<lr pt/Jfll pMTetndttlfr '/(DOlle
welds 'tzteto beiAsec/)
OOr• z.B "~;
B .. t act Wlf -5trr..s ,5 ~ )'/ xsi ~ 3.'13 xsi hence f.ill~t we !ti-s or padtaf icnetrw.ttdtt 9rt»V€' welds ~ Pe use<~,
Tn~re{ore use t>tJmplcfc penefttJtiM :;re-ove wefd-s <4nd ~~ io;
f·'<j~ cat e9ory ® (Cbmplefe ~netro:t.,Dr, 'jrtJO•e we(ds)
( ronr f i~~tr~ to.'{, 'I read ~trt!'SS ranqe b",. • ? ""
u-.,. 'I ~s,· so o-... -•• ~. ~, -r.a 3 "''.
t:<ctuo.l ~tress ts ?.3'11<'>1 < ~3Jx~t' hef/Ce OJ<
'3,nce CDmplete f!:''et r~ (,o·n rrOt:Jv 'i! welcJ~ are (o l>e uo;ed 1 it. wi II flot bt" nra-;.:;ar<f to c!1('c 1: the uneven d~tribu.t•o'n of loacl on the connec.td19 LUetcl<; as In /Q,S. 3 /h1s only QpjJ/Jf>s to ft~fet wefclf; Ql,c:/ par-tialrperyetrott<'fl tr"oue wetd-:..
lamt'//qr I ear~'?<] /tJ. s; lf
y
tr".!! .~ •••XJ%tn). lf.lo~" < zo J<S• tw (IIi>) ht!nC.~ OIC.
The followill<j wou.ld be one of o;ev~rul method"> uled to oHa•n suitable jol'nt details around th~ l>l"'och mem""r- for the welded CDnnection
3o'io 50' so· t. B''
n'l' to IJS"
Y· t
o·
qo•
'37' u, '15'
anf{le art>utK! ao\r< of bn>n<h wemkr, weo-.ure& from the /1«'{ dihedrAl an'lle t::~nf/e removed frDm S.Or.to.re edqe remttin1nq antj{e ()f edqe of branch mem/H'r ind~<decJ an9te ()~ joint
rp., ~ +w • ~ +'10-c(
c
•
•
SHOCK LOADING
@ ~L 2
d,es /t l11t ft'll (rom ou.'t D( nowhere when 'li!JtJ
dt;,n-1. e, piF'ct it
,. t/1tJdlfht ,,. llle-rt> • nsr"" ft>r '" 1 b.rtf mtr.sC'I
F"ffl'l
hlghar fore:• from applied 1 aad
aame atrangth
From the abava, lt 1e aeen Ln &hoek loadlng, that. the fDJ'CB rasulting from the
load Ia greater than lf lt ware appllad in e steady manner. Tha atrenoth of
the material (member and welds) f'or all p:ractlc:al purposes la the aama aa when
undel' steady laacUng.
FoJ'mulas are avallabla for cllllculating tha raaul tlng a trees and daflectlon far
shaCk loadtng, but tbay a:r11 nat alwaya varv sccurate, thera Ill'S too many
r'Bctara whlch wlll change the rasul t, Haa.a\1&1' 1 tnaae eua farmulu cen ba uaad
ta batter understand tt'!a problem and •• 1n what dlnctlan one waulel go ta
lmprove the problem. Far example, ccneldar a almply auppDrtad beam wl\lc.h muet
A
B
support a shoCk load aL mlda•an, case (1) of Table l.
far the energy absorbed-
We could Lake tne foJ'IIIUla
E~."Z and cnange 1 t around ta g lve the ~:saul tlng streaa-
• .jr..H..sz Although thls formula may nat glve a vary eccurat!' value far the stress (a) 1
nev.ertheleas lt daea shaw us that the atreas c&n be nduced by lncreaelng tne
lenQth (L). In regard t.a Lha Prapartv of' tna crass sBCtlan of the millibar, the
atnaa can be rKiucad by l~reaalng tha value af (1/~. Notlce that we~ cannot
separate the moment of lnertla (I) from tha dhtence Co the outer flbar td, Lhasa IDUSt be consldar•d together.
- 67-
W • .atlflllcar vcloc.d.yJ rddlliii'S/:Sec..qd
F • fr•" ... """• ~~ln/ssund Ril'l• re .. lv.toontmtiuoJe V • veloc.it't, tiKk•!•ec...nd t • rQd ,,. .. , tnc.lle~ m =ma-n. • '-1. IS W.• u.e19hf, pou.od'l 5. !J~C.t"/er•t,O,, olqnawof~' ~&&.. itlf•ec. .. F. • centrifu'f"'l forc.e, f"'"-Rd ">
c
r • d.;.t, bet""'~"'""t""'..r 'l"'"i"f ~rotattoir,1hch.,, h • h""!ht ol k~>uid , ioc ~es
~~ndi< enl'rQu £.·¥ Q'" .5•den-.lf~oll•v•'d ,!V./i~ 1 ---...,.,--_;;-=:..Y.__ p • umt ~rnwr# tJt LDtl•"" 1 p>t
-~:te:.t·o! ~- ,..0"" x~--F _ _". t• ttme,H:<ond'S ~ T F•f.,rc•·P"':'nd'S
i.,· k,h E,•fa.FO• W • wor!l tnc.h-1{1~ -------"'----------- 6 • .dclld.t ,.;, . mD•• ment, inche5
w = ... d '""''" ...... nd, K. ':.f'r•n~ CD/I'> tR"'t r "k..' lb. per inc.h P• power, on-lbf•ec.
P• Yf- • FV 1 HP• ~50 ft·l!yt«• ~~JDOft·l~l,.i•• i>6tJOJi>·l6/>«"l'"·:JDOdlllrmin •'l'fl• watts
V.Jo~ · ooot' on D t.odl:f ~~ IPtOIA.41 to: A) <haqqe /n />{netic ""'r:$<1 w. m(v:-v,')
2-
In-pufte
Mom en tum ~ m V
ld1th thh almpla •thad, ona ahrta with ttte farmula far the mavuant af thl
11181Dbar, .. elano•11ian far tanslh ar CDIDPr.a&lva load1ng 1nd dafllt;Uan hr
b8tld1ng.
&..lvlda the applhd farce by thh mavam~nt (A) ta abtaln tha aprlng canaunt (K).
The patantlal anargy atared h then-
.,,..
pt.J 1).:: 'IBeX
F '18FI I<=?;; ,.. -rr-
D
m. A v -"·
F,. ••• v,.{Ki
SoM Y•lue• ot IPI'IDs coartanW are lbted belw.
__..., L. ~
LU n• munber ol t~<ru d • diameter if rod D• IJle<~n dr4met<'r ol cod
I £,• rmd•l•:; tli- eiD-:.t.Crl:~ (~~ .... ~)
1-ro---d-
r :X:. ~~;.,P'"' ~u.pports
I
l
~d
T b I
l
- -- \118 - ol ""' - !lo,) I.e evenl¥ distl'tbuted.
T l
/ ~ • .ied ends
'!lie laltl.al fOI'CO ol I.Dpot (1'1) 1lill Dot be U creat, bea&UH tl8 I008a ol tile -(Joe) I.e Dot --~reel aU at ..,.., but.l.a epraad aut .,.., • perl.o4 ot u..o. - ... , (Pz) vi.U ........,. baoa- 1ua - I.e aboorbed Ill -sac .... (llz~l -jiGJ'ti.JOiol (liz) ottl8o_.,rto-not .....
!bl.a prai>loll- bo ...... ldencii>J' """" .. 0 oquival-· ..... <-.> ~"" tile - (liz) 4apaDil1aa liP'"' bw U I.e ._w aDd bw lt u loacled, for ezilopl.o-
-[ -I
A
8
-68-
c
·~k L.. J: 7[ ~
~instAnt
b~fore tinpq.ci "f i " '
-- ""''1~!'f'=:.:..\ mometrtu.rn ---~1
hotn thl~ I.Ue 'let v ... v.(m,!'~) Kine~i
. e.tlu<f
L
£.· ¥-
~
J(tfteTW:: enet<f'
-Pufttoi/41 ener1'f
(bod~ ,:. _,ins)
-1M sum oF kitlmc .1. PotutMI t!l1er'f'es is undtl.t-+ V."lll' ~ -r~er~-,l r.~ x:_
z l111 • .,;.•l + 2ii, = ""'2T. + ~u .. From tho's w~ 'l"t
F._=m,v,~ or f.."'rJ,V,~
(•1 ol \118 -1dll bo -~ "'• T
h
r@:;llvir1 r*MJ;Jl!J;l ... 1. ~--~;;-d"~ t
.Not loehorc ornpoct • ., llntut ~~~ ..... :;:..~ .... T -· -~ct
171, "· + me D 'I (m,+me) "· ~ COIIS<r1:!ti"" .. f-'fl"I!Jflftfu.•
hom tho's ~><e~ lv~·v.6n.rma} I c,..·~ c.·~v· IC 2. \
""'""'- .. ~~tilt. •r-~ ~ .. ~ . ~
or and
tp • m.!!Jh Ep• -6. :a. • L£ Ejo• fr. + 2. a -/11, 'a 6
r.• F.' F. or ell;+ ~-Pt.9jt 2. I lK, 'L
--71o~ suar .f IUMioU Pt::ft:'J...ff'""'"- is um'btnt ~
. ~--~~~.... +-lf:- l F. ... +JL. -m.!J .!i. ~ . I 'iir.- 2.1(, K ..
' \S ~m.;:, =-cr J; - 'm•'l F,.- 111,1- " o
Dr
I
I
•
,. f"c m,[~tN+~J F~1•i•~sfw!~~~
•
®
® ~11M' .... of--
.l!t..[ ... F=v.Jif
® _ ... _ • .;.l\1.::,_, f
F·W.~/w.•+-~a.
@ Y~Opllao MH of..-
k-j<--ld"----.1
H-4 T 5"
l ~ 1'--Ji' ~ 1--}lz·
w-..•I'IS'.IS" 16 r. • 1~8,1 io4
F•W,~ --"'- N{• ':l(W,~Wo)
F= '!>:l,I3Z.Ih F=~~ 2 n.u.~ F • :>.~. 0 l 3. lb• F • ~~.1 'l. 3. ll.s
f7""' z1,1en~i fP 2'f, 87~. !"•' t.r• ~ •• '"'· p•l r• z 1, 'I 's, p•i
6• (J./'1'1 '" a• (),/fiO in 4•0.to7,;, 4• o./0?#1
a 11000 pGOII4 o~Uo -•llllc "' S ldlell - .._. IJI to be otappod Ia • .u.u..,. at S laabu - ~ l.lnO o wU. !be '-"' IJI to be oluUoolll" m....- lor • opria ..
llhat tono ... , tbe -tiDe 1111ldo be doolpo4 tor7
'm K
~ :'::""""
~ E!.J-' F/J. «' F'" 2 ·:~.11:
trlnet/c, enllf9'f p11tentl•l .,..,.,'I set eQIA.a/ ~. m
2v,'
IF~¥'1 1'-,oso. lbs
Dr A(JUJSO)• '80 :l.S lbs on e41!1t '"PPDrt
/his t'O .. fd pe tlarr-/eJ b't :l~l;w,IS Df ~'1 4 r,Uef wtl<l
~Ia,;..) (~ ln){.'1o?)(~I.OOOp-..j"" ...J1S 90 • .IJ,s . J
£?()1\oual:i metal
B
-69·
Iron Dn dropa fram a Cl'lute 1ncl1ned at lt5° with 'the varUcel at an 1nlt1al
c
velac.Uy af v1
= lDO lncnea par aecana .. The raUlng are etrlkea a bUIRPIIr .,.:a.ta, l.2&l 1nchea belaw. whl~h h inclined at
lfl'' with tn.1 WBI'ticel.
Find th• raacUan an the plate ®• to tna
veloc.it"t (i)
c:l,',tc:tnce /z) fc.l!en t:
From (I) we 'let
cr {~)
or ('1)
.Tr. th•5 n am p le
v_, = 9t + v" 9t ..
'Y'"-r+V~t
t " v.~- v., -9-
fal:.lng an.
plate
v .. ~ V, CO :I lfS" ~ (/tJO y. 70710'/) "' '/0. 1/0'1 Rr/:~ec
f'i) Vv .. = Jz. 9 Y + '1,. z. = j z.{3~.t/tY.IZOln) d'IO.'ltfJ'I)'" = 'o'(. 'lOS~
(•' V..gV., _ 30Y.'IDS- '10.'1107 : • id:H>3. se.CJ:>nc/S '.j t~ - 3a&.o't
horriootAI d,:,tance X" t ~ V,= V, sin 'tS 0 •1DD(.70?II/J) :::-7~7107 ~ ..
Jl.~{~os3Y71.),7/0'I) = 'l:l.go ,;;~bn
D
\
\ \ \ \ \ \ I I \ I I I \ \ \ \ \ \ \ I \ \
Xn.wwiq ""~.-1 Un we / t!An qet 8_,.nd V,
\1." Jll,G/0 10hc
• /!.07"
rna valacity J!I!I!!ll.el. to the bl,..mper pla1.~~r h
V,•v,a .. ~(I1.0.,i30)"31,.Sl41S'13,1J'/• ":l-:!.5.:1~ ,;,n,.c Tne valocUy .22£!!1. to the bumper Plate 1a
Yn·U...~'n{I).O?t3o)=312.S/ smY3.47'- 313.'1/ "Yser:
A
8
-70·
Tllo .. locUy •' &110 Uti I!!E.!l1!! &o tho -,.. lll•~o (V') will no& _,PlW any '•rca unleu tn.re le .... nii~.~C:Uen ln val .. tty lllwt te fri.ctt.n lllltd.,.
tne 111111ng are _,.. t"- plata. Jr than ahaulct lr• 8\lf ra~n tn thill .. 11'KU1m, U: would ba parellal ta the plat. .. ., woullf nat c:auu u u Dend.
The valaclty af the are !!S£!!1 to tha bumper plata 1a raducael to ••ra bac•u.• the an atrtkaa tha plata ~d anaota aut P•nllll t.a the plata.
(f.) Tnis change in the narmal velocity of tha are caua.a • forcatta ba applied
!!!B!!!lta tha platat and in the a~~Qaalte directian t.a the appUIId valocit'l vect.ar. Tnia farce may ba faunell in the fallawin~ ftUIRitar.
.l!!f!&U. 18 the applhd fare:• (F 0 ) 11Ult1p11all by l.ha tncrnant af time (AT)
fUr1nQ whiCh the fan:• acta ..
CH!NGf li'C MOMENTUM il the lilna ar tNI Ntutal invalvd aurtng t.ha tlmo ~T) DW11:illl1111 by ib cl'l.nga in velocity (Vn • D) ..
Th.tl naw. of 11'1 will bl CDnltant 1:hrDUQhau1. it.& mtln fllll, tnat h thl flaw
in IHM'Idl par minute will ba canatant.. Jr the m1tarlal bahevld •• a liquid,
tlla erne aactlanal araa would vary lnvanaly 1111th 11:1 valacity, Tho fa•t•r
11: travel•, the .malllr would be ito craaa aacUonal area.. S1nca thll ara
canaiata ar 11111111 aolid Jt.arttc:laa, there cttuld be ai:JIDII aproading aut during the
fall, with air vl1da praaant 1n tn. intariar, a that ito craaa aactianal .rae
ay app.~~ar to ba greater then it octuolly 1&. We ciiN\Cit mo1a~o~r1 tne craaa aacUanal ar•• af the ar• flaw juat •• 11:i atrlkaa tna plata, and if we could, it
prabllbly would nat bl • true walua bae.uaa ar tna air voida. Sine• tha rna
ar flaw at tho plata. ia tna auo 11 tha nu of flaw fram tho cnuta, we w1ll
uu thl latter linea U can ba muaurad.
The 10111 of t.h1 ara in.,alv.U during tn. u ... interval at (4T) ia
rnQ.n (m) = A V, .5 tAT)
9
c
•
D •
•
A
FlAT) = m (v.-o) IIIPULSE I:HANGE IN 104£NTIM
F::::
Suppaaa • 111 pound piec:a ar ll'an ar• ahaW.II DC.Ceaionall y fall out or tha chub and •tr1k• tha pl ta. whai. wa.uld be tha :naul Ung banding atr ... on tha
plata aaaMbly 1
~·zo• pl...te
~W 1.• zS" t.-ms ~~ Ao7-~5",n'
I• S3.5" in"~ d • ,,S1on Lr ItO in W,•z.~q., Jb,
B
eQ w.•\}(wt")~IH.B lb.,
Proper t'( of bumper pla.fe - IL..e rekren<e •••;, £z.-z)
A y lfi•AY r•~t~Y .:rs t.·~l!O· zo.oo ,26' z.s ,,zs 2ll.t'Jt()'f
t ... W6•2S' .1'1.'10 T.·fl!l5" S'f,II>'IS 19'1.1!.11(, 10 'f,() 2'1.'70 $"(..(, '1 ,O'l,-1'1
N.-1 ...... r·~ ~~!" z.a't ,;,
t I=-l;-t.r,-f'=J;i'.:xHy){/>4) • Jo7.'f'[email protected]'lX6C..6'1 }..- /77.,7 fr,4-
. 71 -
If we wue to ne'll~t. tlte dfeet DF tilt ii..tA ol fit• hmper pl11te 4.5Semlll'f
mv' a
c
. D 'i1 we consider the effect of t/Jt! mert1a of tht' hu.mper p/fA..te assembly
n•t.Ce tire r-ed~~.c.t/im ,;, ~rce w-ht~n Me Jnertti:t DF the bumper plate assem611.1 1~ ~~ns/d•retl
d.e.flec.tro'n
A• t "' IV I,WiD • • 0 8 f) Jnt:.hes " lf.O lf71> 6
~,'/let welds b ... tween 6" p/a..te and ~ea.m
IAnit ~orce 00 wetJ v~ %. = ?01 730. ~'
'l....:.l'~~=:..,.;:;:.A..:~.u. =- .:1.0 ~b. t~.y;nc.'!.,
- ~ ·~ \ f.
\
canal"er naw tnat. thl! trallar t.a atuck in tns earul., The t:ruck i& backe" up allghtly unUl U ill. tight: agalnat: tl'le hUcn, figure (b) irld tnen maiU!IB 8 run far U, aU.empt:lng. to jal'k thl trailer aack ont:a thl!l roadway, flgura (c)~
Tna truck atart:lnQ st nat wlll eceoalarata to a velaclty ar (U2
) wUhln the
111et:.-n.:a (S).. ale rlllll •••ume tb8 traUar ln thla CBill doltlil nat mava lllld tha
ttnaU.:. anargy of tha n·uCIC k.!lll be abR:rb:ed by the c.ongue af tne t:rall~ar ..
·F tr•A
Ct-ud pulls a/Jcad hq c:
/"'preunt t I!IDVIi.c, irw;J:.
~
.,__ __ :... ----··~ FL £A
A
B
. 72.
kriletic eneuty of moving frudc
E. tn..v~z WL'41. /('f:. z. 29
Pot.entttif ener9'1 abst:Jrbetd b., ffJn9ue.
Ep• Y11 Ftl Fa.
er set these
"'""" etr~~a.l
_Fl = m, v, ' I F = v.JK m. ar ZK -y-
h!J 1.1.•euer
NM~ wa auat .gat en BKIWeaalan for the velocUv af t.M truck at the t.n&tant ar
'"""u cv2l.
A •vlnt tlady atart:lnQ •t rnt: and aut.jact to a conetant ~~ecel•rat1an (a), hence Iii eoaat.n' fare• (f)Jwlll prgduce the fallawlng vllac;ltle& F': ~
~·a·~ Q)v a.t-
Ft m.
®<J " !!La FtL z. 2m.
hence® y~ .. 24':l 2 FS --,;r;-
lila wlll •••..,.. • c:arhtn pawer •v•U•bla at thta f1nel ·v•lacl ty Just befof'a lmpocl (P).
® P"FV Sull1t.lt.utlng ttlla lntD (!} lid gat
c
•
•
A c Sl.H or rw.t. nl4. to ••1'17 u:ota obaot -
~~ co: II lo-'1"-1
Slaee ve bo .. -...011 Ula -.,.. Ia tbio ooaldu\ol obaot lGid, --lldl-
t.o U1e 7lel4 Rnllo ('f)1 ""v1U laorouo U.. veld . .U..ble 1Q' Uae ._ t..-
Unit to- ... tWet. veld
F=-LF = 1/1,8,3 1!.~ 9322• lb;,,;
IZ. 1h "
las ol.H or tul8t nl4 , 1'10 ... u - -
'13ZZ 3" w::{U.?Xzt.ooo)(.7o?) "' o. J?G, e~r 7e b..
B D E•IIDPll: The truck walgha ~tODD 11111&, thete ie 1/2 1nc.n 11 play 11 ln the hitch,
we will aaaume thet the pewer af the truCk buUda up to 25 HP at thl lnat•nt "'
impact when tha maximum.. valaclty at (V2 ) ta relehelll. The tgngua ia mGe af
twa Chlll\nela, hav1ng • tatal craaa aacUanal area af 3 .. 18 1n2 11rut a length at 50 tnchBI.
P=ZSHP" n 17SD r.t-~., /.t,fiJ</0~m-l%oc: Wa <(OOO II.
m~-= T = 3&-o'~ .. 0:, "' k. 1~c.fr
A= ~.18 in ...
t:= SO /n
Z.( /,(,~A./()r)( fa.)
if""'o;;~..,~
Th.i.'" ia abaut tha vtela strength af ttw BiBel.
-73-
tt. _.... ..- af tlae \HUor - Ia tlae H04 0114 OD 1~\ap\ la •de t.o 3uk "
_ ...... --.. -Ia....__ ...
m,• mau of trU:ek-V,. ve.loc.it'i .,f tt"-~" be~ore . im P.act m.• mo.ss .of trailer =DO (stw.c.k in E!<1~tll) ~· v. • 0 (eo.rth d .. es n.ot move)
To avotct the Pl'Db!em cf mulUplylng t.~nrtnUy by zera squared 1n \he case ar
<mz><u2 f and ('"2)(Ul)e, u wUl be boUu to do the roliawlng-
SiiJce V ..... V,• 0
F-j K ( m, v.~ t- r¢...'l- m, v:- ry/;) a I I< m. (V.'-v;)
orl F= v,{K:J here
f= z.fi,Jt..jdqoaoxto'Y.'!JfS:t) " JJI,Br..3. lbs
.L F 111.8'-~ lh_ -:or-177 . / t . td) 5>~'SS tr= A.. 3• 18 fn... - .,,,, P'" c.or a y1e
TM tl"'ltler langue muet tnn~~rer Ute rorcae stu. ta the deld laM blaldllr) an ~· tnUer. Hawavar, thue farcu ere not v•J'V gnat etnce it ,..., ill paaelille fol"
ana ..,.. to pick up th• taneua lll1d CDMact it ta hta truck. lf ~·•• war• t1ta
rmly fal'cee involved, then wuld be 1t0 pralll• 1n daelgning 1 aut\Ule \Piller
t.angw. The prabl• li11 1n ahack laedll encauntered ·in pulling tbll tr1ller
•lang the. ned. Thaae fare•• 1r1 rattler hiQh be.ceuee any bUIIP ln the roed will
nave an e•tr ... ly .nart u .. lntervel, pruduclng hlgh accelnattone and thereran
la.rp ro.raee. Foll..awing •r• aau typo of attack laede lmpoeiHI upan the treller
tangua.
Jn flfJura (e) 111111 •••wu the center or ntetlan ar thtl unit ie the hitch. Any up and dawn 1111tlan ar the nH a.Ul apply 1 \lerttc:el force an the treller through
it 'e whll1l1. If the wheeh an located at 1 point known •• the S!!!l!£ !! .I!!J:S!!II!.!!• tUn will be no varttcd eccalentian at point (a) ( tn. hi tDh) lnd
th11nfon na vertlcel fare. would be applied ta the hit.dt or the tengua Coute1ct.
or thaee c:eueed by th1 deH lpad).
CG . ,___T"" __ ....._ __ --:0 (p)
f F l"'int oF po•nt of. rot o.t/Dn p~ld,lon
Tha point or percueeian wlll lie allgnUy b•yand the c~~nter ar gravltv ar the
trailer Un ~il figure, to tha left) ..
Sim:e the whe1l1 an ueuallv placed alightlv ~M-van&t th8 e-nter or gravity Un thlil figun, ta the lett) 10 that thtl taneue would ard1nerUv rest on the ground, I
would ...... tnat tn practiCe, thl lllheele en verv cloaa to the canter of
pen:uaa1an (altnaugh ther• was no 1ntentlon of •otnv th1al. Far th1a r•••an 1
dan•t baliava thara will ba much up and dawn •at1an ar th• hitch dUll to the
.1E!!1!£ itself 110ving avar a rough ron. I don't belteve thla will pne~Mtt cnuch or • problp. Th1a 1a 1llustrat:ad ln figure (a).
Hawever. then 1tl • prabl• with the truck mavlng up and dawn, flgura (b). in
thia cue a rapid vartic•l 11111vU~ant or tM hitch due ta the trUCk gaing av•r 8
bump 1dll cauee a twiating action ta \ha trailer and w•ldu. B•c::•u•• ar the
!1!!1 !!1!121 .a! ..l!ll.!:1!! af thia unit nalaUng t:hia rotation, there will 1M' 11at: up a ra•i•Ung tarqua equal ta
T=-IC( (For tor.oo.e)
F= m a. (for 1-Qrce)
s dista.n~~ t = v . Vei'i<7lii
so
h Q z.,t.ches S ~ IIJ ~3 d • 7 feet V .. 30 mph
"'·"7fee't •, illl Feet
A,
8
. 74.
®
liar ..,. nee• tM .... -•nt ar lnartla ar th• w.ldar and t:raller. Th• actual
value ia rather •itricul t ta find, but lll8 ahell ••• .... that the wa1ght ia unifU8l.y •tetrlbutall avar • langth ef 60 lncnaa (5 flat).
lOa I[]
T= Fd
A I
IJ~ 181() "" "7 J6(al' m•3• ~·· ,, --,;,-"'
c
•
•
Mam.nt an tangu• af treUer
M= Fe:: ~lzo 16XY~m) • 'io/, 8tJO;i, /6
or :12,'1~0 tn lh ~n eacb '1/de
2!t'•ZI'z'•~· an9/e' .r,. •• 981( in"" A~ I.'J':Iin'
17, 3oO psl compressHJn
Of caure• tn•B• atrUeaa •r• calCiulated on the bi!IBh af the truak (ar hitch)
gain; over a certain aiza bi.Dp ( · i.nct., ''lut',) at 30 •Uaa ptlr huur. ate don't knN wMt apeer:la and ain af bumpa shauld be uaad. Never the leu, U a 11•
5.,1t lb cha•nal .,." uead, the aPia driving conditione would reSult 1n a
r.OUC:ad b11ndlng atnaa af 11 1600 pal. And thia tong..,. wuuld nDt hav• anv cut awaV ucUan whllfh wauld we~en it.
--- ---------
------
---
------
----[ I.· 3,8E>m"
A ~ 1. set irF
Thle brlnga out thll advantega af tha four wt'teal traUar, Jn thil cue till
tangua 1a hinglld and anY vertical movement at the hitch will Jua.t move U up and down wlthaut introducing anv moment ar banding atreaa.
A
8
ln rtgura (c) tha uial farce 1a epplhd to the trai••r by m:.calaraUng and braking the truck. These farces could be cauaed bv the truck ar trailer hitting
chuck halaa in the ~ad. figure (d) lllustrataa the tranaverae force ceuead bv
aide matla11 af either the truck ar traller etriking ruta in thll raad.
The ring tvpe tratlar hitch hils a loaaa fit and 111ill praduce mor• of·a jerking action 1n caaae (b) 1 (c). and (d). A batter fitting hitch, fo.r I)I.B~SJPll a ball
and aockat typs ad:OUld reduce t:ha P88lr:l an thne loada.
The tangua lllUat have aama tlorizantal atltfnaaa and atrangth ta prevent tt tram
binding if the tralln ehould •jack knife• IMhtle backt.ng 1f the rear whaala or the
truck ahauld be PIJ'Bhed inta the tongue, see ftgu.re (a).
. 75.
1 believe tna ;rntaat: rar-cn 1n the tengVI' emf tNllar- en "' ... ca..- 11¥ "'
hitch (truck) moving var, rapidly up 1111• Uwn •v• te &I~ 1ft the ..... , Ill flgura (b). lha valuaa af thaae ·rar-cn era •itflcult H .. tanlnl IIKeYII •'
the uncertainUu ar-
1) actual aiza or tr. bump ar hale in the ~"•••• 2) .BIIlDUnt af 'an.rgy ebul'bld by tha Uraa and aprlnp af tna trucJc,
3) velocity af the ti'U:IOir., It) NBI IIID!IIef1t of inartle af the welder and trailer •
Hawavar, I ballave t:ttaaa are real forcn, tNt they caulll be vary high uftCier
unusual road candi Uana and therefan 1 batter ta"9U1 ahttuld be uan. far
IK&mpla, that·mada af tRI 11• Channel.
l bdiave no patnta af weakneaa enauld be allawuf, far .... ple,. c:ut auta, II'
carnera 1 cut, bllllt, and then welded, with poor quality welda, the quality 111hict'l
may vary wl'daly from ana tangua ta the na.t.
It aha bat.hara ID8 that 1111 muat rely uPlift ~~Mae cuatalllr t:a llllkl thll iq~~~rt.,t
carvt.ctlng welda ta tn. trailer, aaM \n ttte avarhaad paaUlan. Thil .. Y be tha f1rat aut af paaUian 1111lding thl cuetomar 111a ever mellla in hh life.
What }or.ld (P) can tlte'iie ws.ld'S
trfJIIS fer ?
p
rrelcl a - ~- P
~-- ~·~ f--2.'1Z"4
c
D
••r.h .:emn~tlln t.
S.,· Y+J'{,,.t~.a~¥· 'M•?in'"
~or two ~nnf!d'ums
...., .. F,;.n,;, .,. Nllllffr
d.t:-Wtlf'
'S.,.,. • .,,r.'? = 't.3¥in'
F,;· Pees a •· 'IBS" P F.• PtinB •,1'1'/P (o-me 8 • 10:)
M".ifB5PC88•n)-t.!7'1P(2.~11o) ~ 1.2s~ P(inJ
.41 f. .t1 1.288 P{lll) f .L. r--;- <~>r b • S... • .,,,., ,.,, or 6' ·l'i?'t m
Rr, .. lt4'1t ,.,;,t r.., .. btl weld f,..=/(~ ... f.)'+ f.' ~r -j(.mt-l;+.ot.~f,)'i-{.ot'J.If,;)" "'. z.o~ <; 16,
b.._-t ~.· .707 W '-I,ODO Jt .. , lO''t-#;" .'/O?w '-1,0()0 ~U."
p..(.?o7Y&X~·ot)o) 10 ' .~6
th•s ,~ for st~dct /d4d 4/le e?D we lcl tneta.f
'Set et~~U.O.I "to . ZDcS'r ~,;
a • '70?{ II, m) 2.j,(J()0 ~,;,•
or P= n.ooo lbs
y I
«r.(Uitn'c wei 'ht '~" 2. lbs
r.,•r1(~+·~)· L$'~•Mt¥-·~~~{] 1 ..... -~ S"-----1 IK" tlf'l .,. ;.'
A~z.r(J • 2£z.7rXI.I)~'Ib)o 4.2'10 in
rt&>\6 (z.'fS)(.90U1) 2 '1? • e~-r"' u'""~' , .1 111
r 1 ... t1~-liaf!)•(z".1,)(,.JJ~'II.-·¥}·1S.fi 28 itt
A y M•AY ~·l'.'f_ r._ s• r.oo +LOO • S.Dtll) +S,DOO 0
a•ZI'el' •u.s -.Dt.25 .. 2" 07 ,,,0() '-2'10" u.~ .,1'17 ·13.?6'1 1--·"" j,ljljq
to;fr.l IS.'t'l -8.'11$' 1&.180
HA•~• ~· -,S?'9ito ','"· (;~;7{/ . ., J;..·r.•J;·.f• 38.180- =- '~'fBO m
ts>' · .. • " Iy•tr t ll{Zlfs){z,S)+ /S.,28 • 6'::t.,07 m
J..• r., t r,· '2.~80 .._ s2."o 7 • B s: s-6? in'
Aw• l!i.'i<f in (le"'ltb .~ welcl)
Frm:es. en wel4 centrlf~<y<tl forc.e v., v T<Pflo)a. •
F• W. ir'-rlii.P~,. 'fU. u,, .._zltoiriJliOOD : Z.B 71/J..J/n,• l8.11 l<1f1'S § "J(JD '"" • '100 •
b&or&i>'l reA<'ttt;n {alSIJ s.lrear lfn welcl} !t•V·~ .. (:eB.7f)• 14.3' 1c1p•
bend,n.; 111•ment t>n w41J !'Is&'{,)" kip){'l~ip)• ,S,J'f 1irk1p
A
B
. 76-
bend•"'=t '1.'1~ ''hr.
- t11a booo 1.8 troo to _., \ID ... trlpotal tano h<D t11a l'Ot<lt.lDc 'bclq oa\IDI ca \be 'b••• vll1 var,. .
u 'bclq (a,)-•1-, -., 1.8 OD lm<ud rodlolacaolon~lml ot (o,), fb1ll vaal.d oa .. o • t01'08 ot r, • •••• w ""' ca t11a _.n~.q booo <•.>· :ra CAl, llol>b torvoo ot acooloroUca ot t11a - bOd1lo on em tho - ODd - to -. l\ ~ o.,..ID11\ to aocoloro\o 11J1Vud (o1.), :r. (B), - torvoo at occolordlca ot \ID - bodiu aa\
:... T.J!" =~· t!W, ·=..e:, dou.:" ,.;.:" ,:_~ot :;. ~= "' "" -•lor•- ot t11a to<o 'bodl.ao vW bo oll.ahtll' lou, or ~ \o ••· oL ,
!be 1'00111\Jac ~ toroe h<D tho bCid;r vUl bo
('bclq) r • •• (o,• .._)
aad tbl.o _, bo -1 \o t11a tano vlll.ab •- t11a boao \o occolon\o
(booo) r • ... l S1Doe t.beJoe are two bodiu• u.z.e an two tonu. haae
.2m1(Q,·¢a) • ~a .. (a•••• o) ( 1 buo)
al-.o a,• w"r- $1> w'r-al = ml:;,•
lh {!:;t•) = w .. r and a .. • w"r(~m,"!: m .. )
!be 1'00111~ -1tllpl tone oo\l.q ca t11a 'bclq 1ll t11a •muol -- u
~ F,•m.(a.-a~) • 2.m,+llla
fb1ll 1.8 looo -tho ... trl.fllpl t..._o oo\l.q ca tlla 'bclq ID tho borlson\ol 41rac\loa
f'b= m,a. • w ... rm, !be ronp ID t- oo\IDc ca t11a 'bclq 1.8
k .. S. ... !!.("'~rm.tn. \/_1_\ ... --.!!!!__ F,... r., uvm• ]\i..,~rm.J a m,-t-mz.
bodot bos,.
Ill,• "~"2. lhfj m, • $l'DD ILJ_,
~·.oaela.,.trolto of Y"'"~~ 32. z ~~ .... 38G. .. ,_.
Po\!IU o~lo ca vo14 USC - ..... tulo\ 101ldl1 oon41.\1CIII ()7)1 ooi.ocao7 (0) o .. r t,ooo,ooo 07"108, aa11 1;.• a bi
..:st. .. e. l<li :r ""0 . .,.._ •• 1-11 /=:iii " 1<~/
bo\ - w - o\oo<lr ou-blo at t1 bl (1170 vol4 _,_)
.... u. ot tulo\ vol4
<~.s-<t "'';, ~ , • ~ .... Lu"' C.1D7"t'-1 iiSI) ~ '.,,., m Dr 71(, b.
1m ~~- of tho S IDob tbt.ak nilb\o tlla mn1am tUlo\ w14 oloo 1.8 @
c
•
•
PJogparUn af Craaa sacuan - Glrl:l•r
Thla work. would lndicata tn.t tha ada 1.1111uld mava har1zantall\f to the right about :J lnchaa. lt waul 1:1 be batter in thh parUoular example, ta weld tha twa Tea aactiona, each n a ••parata aubaaaelllbly. 1t 1a aatl.oatad t.hay will each bDIII about 7 lnchea, haw8VI1' thaaa aa&.~Jd be etnlghhned .in a bull-dazer, ar thay could ba weldad 1n • pra•bent paa1t1an 10 11 to be atraight •ftar w.ld1ng. The atra1ght TN ncUonil would than ba aa&amblad lnta tha final glrdal'. flllat1ca tMt; thh nnal waldlng wlll not ba lDcatad on tha wttb, alanv Uta neutral Pia or tne lllhDh aacUan. Th1a llnould aauaa no ~aawlng aaUan and wlll raaul t ln an .J.mnt; atra1Qht glrdar.
'deal ~ !! .! 1!!1! !! ! !!!!!!! I! !.lll!!l .._,
•
KA~o Tha 11111ld along with ••• lldjacant plpe t~ r•:llal rurca (f r) along VIa clrcumt'ertme:a ar =~• •:~!:';t :!• ~:::u .. 1nwarll
The clrcumferantlal t ... alh raaldual etrna ln tfte wld 1
B
F "" A K rl ..... I eQUal ta• • v A
111 • craaa aactlanal un ·ar t;ha ldld
K • ralatl¥a ••wnt at •Jaaent ,..,. -inglna lllong wUn ... ld
•v • rnldual ~tnn in waJ.ct .uaa
!~1~:·;~~!' 1~0;~: :~:•:n-: !;:•rd radial fore• Bltl'llU U the GirGUafarana•
r •! • •
where
Puttlng thla tagatnar, wa gat--· "V•·' (Pooi-~ nat-•o)
Ar• ~If; /.Z81>
Thle biCOmtiS•
ualng: K .. lQ O'y • 70 kil
r-----------_;1 • JD • 10' kol
Ad =3.0></0L A..,J1i l(r..r "'''~-steel) !!!!!f!! r • U 5/8 ln t • 1 1/2 lft A" • 1.n 1n2
..--....... --~-A, ... lOA/O'A..}!; • lO•If{" (1.1'~) Jlttii or At- a • 0 'f <:~;.:.~)" know tha v•lua or K, lf lt war• luger, tn• Miirl"lllftl!!ll"l::::':i'::"'"
. 77.
tan .20
Vertti:al Up '-' pa.s.'!>sS
~e
Vert/cat Down 39 ptuses
tan l- j
act uRI = II"
actual /,
~4/c"/t!lted = /3D
..La(
T
c
D
.20 tan e ,.,
actll.4/ "" '/0
ct~/cula:f.eci = 11.3 °
~tuai 12•
calcu.latec/ = /1.3•
ruo 1/1' t.hlak btn1 80 te 90 teat l•a •n liJI veld&4 t~ vUk S/W tlll.et. welda. !be t•brioa\or tlada ibQ" briDd aboat the strorlf: nb (I..X) eMI:Qt I to L teet.• bat; ....-u, do an baed abatlli tile vuk a:l.a CT·T),
X
.!... ff-1 'It' y-·- ~ ~ -y .l.. .,.
I ,.,.
I T , ---·---------------------
x,-
Ptopertt<is abaut (Jl-J<) :r"'!'l';.~:,","').,"f: ~~~
= ...... +:<L-t-=-:-1-'::7.;';;;.-t :I: • ..,y -t-7!'...-1
r•-1• -Hi{,;;;; z.o'f~'l in
r,.. r-(ttM)• !rB-'1~6 -(-z_.,X-IhU) • + as; 'f8 in"
~ b A,. • Z. " l'z(lif6)' • .O"t 8 /n2
\fj'!.. A,.• Z • .., l\111' • ./'f I ina
L\m .oo~A,d 1.•. .oos(.o<t&'J.2.oCf!r)l94o)". rss.¥8)
'-=eo' • 'lr.t>' dr ~.()4(.5''
Properttc!l
'(_ 't'.&lllrillmzllliilfj.JIL~i!!hi' .. " _y_~[A' +.uW
abt>ut IY-Y)
'·
Y· ~ • ··~~~ • .nu.·· I.: I{vt,.t)•.'f58}}-(,11"X.•'s) • • J'f~'7 in oJ
. "' ) .. A.·""~ A.d L• .oosGo,sX.II.,.J.'U.t> • · t!r ?J. • '? ~? '-' J: • . ,~~,
~,t.M tabl'ieatm' aald the _..... dld aot. bell.- ill th1a directlca,
In tbb aue Lhe ~~~DWn' or lner\.la (.U.lttDese) ot the Ulllber t.a YU7 lCN (t•.3la4S s.nl&> tnd altltwah t.he def"'1.Mt1Cin ronula doel I.DdicaM • larp cletlact1tz, the valght. at the lll8l'lber t~OIIld w4ou,b\clllll' keep 1t 1¥tDs flat. Cl1 tbe fiOCO' ot t.be tabrlcetlns: sbcl:p.
It Use 111911ber lhD"8 to at.ut. 1\Rlng \IP off at the tl00:1'1 lt VOQ14 reqnlre " bend\a& aVeaa or:
_;;:-. "/,' ..
' /
7"' . ; ...
"'"it ..,~i~ht of member w• (S.i' HIX'hn (,ze 1 ~~ .. )~ i.S!? n.A;; = M..· ~ .tMnr"ot, m '''·'" '"' < ..., ~ (m.>'WrJi> lbi'{.l>13&io) v 31 '1 'li'€. ... ; = tY: r ,. c~~., ;.•) ' ... .
0810.17 Printed Sept. '85 5M
A
B
$htJrtemn9 ol ~ D ... e ~ k"'f/tqdtlW .~ (- ..t .;.w. wU.k"''• eHct <>I tr .... u••• ofiff-.)
•
A.. • ..,.. .. ud""'" llrd# "f """ f/lkt .,.td (ill') ~.1' • <1/PSS sect_!_._ cl 91ider (tit?
1'\ • relo.trtie GIDSS ... ~t,iJnill Qf't!!;f;f tt~f
9,ra., aJj•c,,.r t~ ""'lei W~tc/1 s6nnts tl{""f ..,,til wetd.
IT • eo.ucr"'f" rllst'dual fl!lrst{t' sfress ,,,; .... ld and acl;aeePt ..,...
(i • '-"'"fre9'Sttie ~tra ,_;, "'"'?'1 til~ /Mp t/1 of ~ 91rder ( liV'1
/emile shait&,qr b!!r« F• fA..IC (}" {tbs)
lhti 4'""'er ts onl'f as 'i"'>d as fhe '""""'""' 114111•1 o ~ ®and®.
!k-h~ beHer va.l~~.es "~ ®ano® c.. ... td be abt4tne& I>~ ~eci<!Mf bad on preurO...,. 'l'~rs whtch wer-e welded.
Ex,.tnple; L • le11'1th .,f 'lirdcr = liO 1
Aa. z(t"•IO")t(.la"•lli) r 'lfi,(; m'
A,.• ~(~,·· i.1)" • .o6. irl
~ /0 (.,r;. .,f adjacent pW« shn'ntmq al6n<l,.'with weld ti 10 t/IR!O:s: fhe weld area}
~ >~ooo fKi {r-Hr'du.af t en,t'lt" st-res:~)
an'( '1'"9" p<>1;,t ® ..,.-11 '""ve Ji, ~war-d the cente-r hrie o d,Hance ~6/ 1 wheu Q) ,S th~ ,;,itu:i{ dtstance of the pomt {D the cent.er-ltne.
&~v-era)/ /enqt-17 tJ~ the 9irder will de«eA'f!.e ""~ (L.€)
here
~ ®a..!~ ...-e ~ uafu.~ 1 at present w• t!Mt haul! 41111 9~»d V"-f"'"'·:r l>eh'~ve ""~ c!O .. Id ~·imte thew u4la.e! if we I!Du.td ge-t slmitl(oqe uoliLe'l. f,.,. .... actual p/Qft' ftTders welded m the pA_'f.1:.
THE JAMES E UNCOLN ARC WELDING FOUNDATION CLEVELAND, OHIO
Litho in U.S.A.
c
D
••
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