Blodgett lincoln-solutions-to-design-of-weldments

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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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I

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 prob-
lems 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 .................. 77A
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 I1 )(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
Tension normal to effective throat. (41 .30 x Nominal Tensile strength of weld metal
lksil except stress on base metal shall not
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.
• 1 •

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
71e teDaion COOipOAeftt would
require matahlD9 ""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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prggnrt;y gt H''ded qonpogym - trutfn• - weld .. a line
1 1.• 2r(}
·-~--r· •zt~
,.,_i. _.ltr_ ~ _•· :z;,= r'(tH ~}
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TR@
•
detallsattaahedby
lilletorfiRICM!welds
a<2" c7'<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
0
TR@)
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)•
•
lilii1J~jlA 60 36 24 24
NJ~B 46 27.5 18 16
~~.c 32 19 13 Stnm
0 27 16 10 7
rE 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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A
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 &qY:res or the
d1atances to t.he (x•x) and (;y-7) axea1 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,... r7
y
I
z : m I • J
,I
1r
/; -!
: dp •
B
:· t'L___....,...---; ' X
'I
I ---~
•
@)
1 :
I ' 'I ,_,
I .._
---
.- -
y

'z
...i----1
K l 1
I
' I
~- I
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•
- 5-

',
z
' -
4 ]'.: {de) e•
y
··-0':·/a..ts) 1( .,.__~ Y,
X
e"= Y'+~t a/$t> y: r Sin.I.
So e'&= y .....sinLib1
¥
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)
c
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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
RPfo Zoo ' '
1
" $
'ltd• 'It 'I ~
propert'( 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)
I 2
"' 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
•

A
•
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
11101181t& on tbe eo~~plar.
•
•
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 additiQI81 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::.~:.:::af!:"~!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>oweIE'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~/ hd 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----bc s'""'----~:JI
f
I l I I 1 1, ' ) I ~ 'A•1f·"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 ~nZe>.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 IT~ /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 tta ~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 • e1T ( 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.
Tw
l
r
c
1-.ho.Hct_
: 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:jl1-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 l131 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-rK• ~ K•.L..
' r. ,. r.
To tor~ue
l~t1" • weld sbe:rr allowable
OSSIUII~ 'If' thtrJQt ~ t~qx
_., r 1>- --lw 1'-
T [i ' tH: ] 'IT;;r: = (1+ 1<, tKJ- lrl(, +K, 6.{aT.. 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
Li
t
tr
~""'
"l
1.1); <r.
:::jl")
"1.::)
Lt..
'"!I
~
<::
"! q.. '1 "! ~
f·.; D
I• ·•·.
I '
0
~
·.;::
eell
~§
~~Q:
'- 1J1.1)
""'
~
";
~
'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
or3..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
1ISC: <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
rtr;t.
lmtpUdlllal · - 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 plae 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 war tRill of tho torlr,
th1a vbole 11Dl tends to pbo abcN' tbe lonr ooraer vbere 1' been liP apW
lui 1- """" bor, Tho •-1batl horloODWl r_. <rb) •• tho R_. tRill of t1u1
tori< lo takeD b"T be top - · - · Tho .,... - le 11ildo4 to tile vonloal
- ot tiJa ll.fbatl al-t.
T Fj, Us·)· P(3d')
/5° fn• 2 p• Z.(LI ~oj>)• 6,0 Kp
l
In th1e case tbe bgriscmt.al toroe (rhl la applled e tbe Up ot tbe bar at 808111
ec:oenrlott¥ (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
BI :·.~·
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 aa'
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"'aa.•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""lleI 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 ~<;,;,
(,. If•• +f; . I6.00'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 /WId..
b d.Jd.:tO: .. db/t!:td:

A
1RANSFER OF MOMENT f1tlm OA!c ,MEMBE-li W ,4.":;ru~ I<
F,
~ e ~ I
ldi
D 1II 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"
TL.
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 loqitu.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.encb 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': TI 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~ ••'pJ('io)'+ (4)' ~ I 'f.'5"' lq ps
f c £c..• 11:1.4,1; J<tP• r ;o.'17 K1/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, addltlooal valcla 111117 bo neee....,.
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. jL'-+ 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,.• ~ jL'-+ 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 ~
1f,~ ta-b
~~n·~l
A
8
tr= ..&...,. 'P eo.e
t . f:"
11ormal sifrj$ {tensile)
p
____.,..
i - ...£:._- E..Ji.!!.i_
- t - ~
'iJiur stren
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_ jcos•e +'I si/1"6
2T"" t- l Zt- -
ai.P
• 'f..,.
co>& +&'eHSJn'ee 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 vithln tba all<orabla,
t
l
The tact.ore 11se4 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;~ ( ~0
0~~~) " • 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 euoq11, 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
akel 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
!!._j2_~
z
c.blf&•Z1DO."'...;,
if,•'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
tllil8rd, 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 curlut.~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 hale 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
'/'------------.(~we4 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 DOob
(""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~ereU'"' ..-. 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 ~ ereaa 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 lno 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!Cb
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 o n - (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 of1!. 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
eompf1(!'5S(Di7
&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'ioitecl 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 mem6er 1i
'SIA.I> jec.ted io bendttlCf
~ 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'1 76S"(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" j2. ~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 'If0 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 kl .. 'It<~ i 'b•:t n.t t• .o.ce•"' Z-t ....)
.... ~~ 1-.o ~
c
•
D
•
•

•
I
I
A pulley ta very .:aplp and cflff1cult 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~:.'::~.(fr) 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:.~==~~.!~=d1~·~=-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 G
8
b) bending stress a~t b•d a;•
c) bandln9 atresa about <v-v> §Y
nDIII Dacoma ttut corrective mamanta wtieh -.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 • + 11 667
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 • • 41 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
Tatill 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 + 41 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 • +151060
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 • + 11620
+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
Ipa1nt (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, 1t will hi IIDH ccarrqnl•c to nsrl~~e~~ tnn ..1en
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.:onuaod •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) • ... 71 98)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 reaulUng •atreaaaa• an the analogous column tlecorq th8 carrecUng 11011111nta,
:ln other woJ"da Cf'lange thel r etQna and add dlhi:Ur ta tha 1n1tiel 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 +241 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 +41t1 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 +18,170y
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
. • 30 680 ... 1,210 .. 1,270 + :S,680 + 5,610 + &,900
M >2~.420 +2?,850 +2"1,,850 .z~.~211 +18,170 + 9,&00v
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 ps1
t:."'mpres:u#n ~n &J~"t5Jd6'
t etr:Jtdn 11111 ln'Sir:ie
-29.
~ ~-!-!-: .,, ··••t•·l
i . . : ; ~ :::;
!
c
D

A
Acually ,.,. ....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 21180 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 anaBD to any IJI'IIt extent..
Baa O.aign af IRlc:rm.rtte, IICtlan 1.1
~

I
I
I
I
B
Ha&-llanhl Clangludlne1) 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, lkyl'(,,;) - -1()'1, 200 ,;, ,~.
.M,.• {+ 2,n1 ni lkY1¥ml • ... 'D, ~~)() in 16s
_ JI'IC: (-JDUIK>TI.,7) = - 89'1 fl$/
0,.-y ZDJ,'t
f.·(- B'l'lf>tiXJtl't'l,? • - /S,H'o AS,
~ (•ltilti'IOYI.6?)
tr,.= y• z.oi+ "'
F;. • fz'IOpt.IXN""IAt'j"
+Z.'IOp-a,"
....!r,oeo 1~'5
Ttta dlffH811ca ln haea twa bending farcn auat &renefer out ea ehear wlthln a
10.1 lneh lenoth•
r .. -16i";fo-(!6ioeo) ., Z07t::J ~hnch (t~<Jt> wetrls}
l"o /P•/
or 103() lb;,;, per C,'l/et we.lcl
~----- zz.·· _____...,
A y M~AY T.•JtY Ia
ZZ'<.!?it 1!.1~ D 0 0
..i"'tLS':t.-7/i( 3.'1'1 -tZ-bi~S /1.08125 31./l.l.
c
D
/ c•nte.r e~F
-f:.-c..---.,..,,..,..t-u.re
•. , ... !Itt' MS t 5,4JZ"
l.!i/t.a
~D1~~ /IB.bS'-
total 21.'1~0 ~z.l'l$"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-;uItant ..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,;, nr.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.Et
1
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•.s-
r. 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-o1
,%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 ciratmFert?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,,/,
t27.,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. ( zs)
-33-
,;tnce t ht vertAI shec:u- CU1d bendtnq. are -su/Jfec't to. q
et:Jmp/e.te rever-saf1 we CtJu.ld use tim Far tne fctt '<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
Unlt 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.
1
i = 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-BtJi'6'{s}~J.,.'f+'1Wfsffkl'{i>te'ftJ" o. I?I ~le6
' 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 1t 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 •etrasaas111 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![It<o,,...8'1/
T"!fs''-
l '--
.L
"r
+ll.'l5'd'"'
T= /, 184 ZOO
11
tr
....=I= J,9",ZOQ,. 28'-~N.
r; d, ,,.,.,~
Zl?, '80. 1£
CPc>lurnn
On a I" th.CI<. -r.I!Ce ol th•'s fn:ane,
t~ for<:•~ ,!>~me -
D
The ero~?. secfti:>n 1$ treated as .::~ Fr-4me{ ,
Tf t"s now t:""t so it become'S -statlcclfy cle ermmate
0
~%
· ..-c:c..o.t here
~ 1.'14& IIUr

--·... 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 ~86.1000 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 1
1>
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 roto1.<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 bot.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-
Ty
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CQ. •ses cotn preutOn or
"'"ll'lt•ve rtM•n (-f:}
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:ui. (sM)• cr
set e&v.a.l
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cl
o-= e: E
b t lf•.?J'3
c -1/,,.719
d -1(••1111
.s1" ;...""'~ _..tn.er
·~··11... ----------- ,..,.,2..11
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no,., + !IIJ'l '" t enSflilt1
t:lrtd- Stqn 11 a.mptft11Dtl
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