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FEDERATION EUROPEENNE DE LA MANUTENTION Section IX
FEM
SERIES LIFTING EQUIPMENT
9.341 '1 st edition
Local Girder Stresses
1 Local girder stresses The flange bending stresses UFx and UFz arise as secondary stresses in the vicinity of the place of load application in a girder, regardless of its supporting structure (figure 1.1 and 1.2).
(E)·
'10. 1983
The variables R, t1, j and A necessary for the stress computation have the following meanings: R represents the maximum wheel load ascertained upon consideration of the dynamic coefficients. tl is the theoretical thickness of the flange at the load position j (without tolerances and wear). is the distance from the girder edge to the point of load application. A is calculated as the quotient from j
A
=
b
s
2
2
2 Determination of the coefficients c x '
Figure 1.1 Parallel flange track section
Cz
The coefficients established here are based on numerous test results 1). Theoretical investigations of certain test results with the method of finite elements have proved largely concurrent 1). 'he equations listed below, which are the product of test results, are valid for the ascertainment of the coefficients cx, C z . Positive values of cx/ z mean tensile stress on the bottom of the flange.
2.1 Parallel flange track section according to figure 1.1 Transition =005-058.A+0148.e3,015.A (1) Cz O , , , . web/flange
l----
b _.- .... -,10
Figure 1.2 Girder with inclined flanges The stresses are calculated with the help of the equations
R
UFx =
Cx ~
u Fz =
Cz
tl
R
2
tl
" The factors Cx and c/usedin the equations can be determined separately according to the type of girder (figure 1.1 and 1.2) and the load position j or A for the specially marked points (0), (1), (2) on the flange.
Load application point Edge of the flange Transition web/flange Load application point Edge of the flange
czl= 2,23 -1,49· A+ 1,390·e -18,33 . A (2) c z2
= O.73-1,58.A+2,910.e-6.O' A
(3)
CxO = -2,11 + 1,977. A+0,0076 .e 6 ,53· A (4) cxl = 10,108 -7,408 'A-l0,108 .e-1,364(~ Cx 2
= 0
(6)
2.2 Girder with inclined flanges according to figure 1.2 Transition web/flange Load application point
CzO = -0,981"':"1,479· A+ 1,120· e1,322 . Am czl = 1.810-1.150.A+l,060.e-7.7OO .A(8)
Edge of the flange
c z2 = 1,990-2,810.A+0,840.e-4,690 .A(9)
Transition web/flange
cxo= -1,096+1,095',A+0:192.e- 6 •O 'A(tO)
1) Hannover, H.-a. und Reichwald, R.: Lokale Biegebeanspruchung von Triiger-Unterflanschen (Local flexural stressing of girder lower flanges),f+h-fordern und heben 32 (1982) Nr. 6 (Teil 1) und Nr. 8 (Teil 2)
Copyright by FEM Sektion IX . Also available in French and. German
.
!
Sources of supply see back page
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Page 2
FEM 9.341
Load application point Edge of the flange
The equations in paragraphs 3.1 and 3.2 apply to cranes. Corresponding equations, to be taken from the respective national regulations, apply to crane runways or other steel structures.
Cxl = 3.965 - 4.835· A-3.965· e -2.675 . A
(11 )
Cx 2
=0
(121
2.3 Lower chord of box type girder The lower chord o'f a box type girder is to be calculated as a parallel flange track section. Figure 2 represents an analogous depiction.
4 Explanation of the design rules Design rules are given for local flange bending stresses on rolled sections with inclined and parallel flanges. The design rules are based on the results of tests 1). Measurements on the following sections were evaluated: 1200, I 300 as in DIN 1025 part 1 and IPE 200. 300, 360 as in DIN 1025 part 5. The load was distributed symmetrically along the longitudinal axes of the girders. The lower chord of box girders with an underrunning trolly should also be calculated using geometric characteristics with the equations for the parallel-flange girder.
R ~i-
I I
.~
•
2
(~
b* _!. 2
~tf-.!.---,
-t- rr Figure 2. Lower chord of a box type girder
3 Ascertainment of stresses The flange bending stresses aFz are to be superimposed on the main stresses O'Hz resulting from vertical and lateral forces. The flange bending stresses are diminished by the factor e = 0.75. This also holds true for the flange bending stresses to be considered for the proof of service strength.
3.1 General proof of stress In the case of composite plane stresses, the following must be proven with consideration of the signs in structural parts:
cp
-
O'x . O'z + 2',Txz2
<
O'aw
- Taking into account local flange bending stresses increases the accuracy of the carculation. This prevents uncertainties. which would allow a lower safety factor v. O'yield point
32 Proo'f of service strength ( O'xmax O'xa
r
+ (~zmax )2_ O'x~ax . a zmax + (T xzmax )2 ~ 1,0*) O'za
laxal· 100za l
When determining stresses, flange bending stresses should be superimposed with the main stresses from vertical and lateral forces both in the general stress proof and in the service strength proof (e. g. in a box girder lower chord). Thus for O'penn it should be borne in mind that in crane girders there is a principal load picture with vertical load and lateral force. In superimposing flange bending stresses on principal stresses. the former are reduced by a factor e. This reduction may be accounted for by two basic facts: Flange bending stress produces a local stress peak only. The flange bending stress is very rapidly attenuated in the longitudinal direction of the girder. At a distance of 10 mm from the point of the maximum, the flange bending stress is approximately only a half of the maximum.
in welding seams: az °' - JO' x2+ 2
The wheel load is ideally assumed to be a load point in the middle of the Hertzian surface. Tolerances in the thickness of the flange are not taken into account. Generally, no reduction in the flange thickness as a result of wear is to be taken into account. Results of tests on four overhead travelling cranes with underrunning trolleys after 14 years of operation have shown wear of less than 1 mm. Only on heavily stressed suspension tracks is it possibly necessary to increase the thickness of the section on account of wear (e. g. by 5 mm for a flange thickness of 30 mm).
Tx:za
v
=
O'penn '
Definitions: O'xmax O'zmax
calculated normal stress in the x and z directions
T xzmax
calculated shear stress
'a xa O'za laxal (Uza I T xza
The value € was arrived at by comparing the results of calculations for numerous single-girder overhead travelling cranes on the basis of both the traditional and the F EM methods. Consideration was given to craneS-which' had not been damaged by flange bending stresses even after many years of operation. The flange bending stresses which accur are proved using a calculation example and the superimposition of flange bending stresses,on main stresses demonstrated.
admissible normal stress corresponding to O'xmax and O'zmltli stresses sum total ofa xa and a za admissible shear stress corresponding to the stress,
T x z max
.) This inequality represents an unfavourable condition. allowing values slightly above 1. If this is so, the following inequality is used for the calculation:' / 2 2 2 (aX max) + (aZ max) _ a x max . a z max + (xz max ) ~ 1.05
J
a xa
a za
Iaxal . Iazal
Tx
za
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FEM9.341
Page 3
5.0 Calculation example
5.3 Values incross section of main girdersection:IPBl360
The application of the calculation formulae shown for flange bending stresses in the x and z directions is demonstrated in the following calculation example. The stresses in the middle of the main girder (see fig.5.1, intersection b) of a single·girder overhead travelling crane with parallel flange section girder are.to be·calculated. The design rules used are: FEM Rules for the Design of Hoisting Appliances, Section I (2nd edition) ..
The variables are labelled according to fig.5.2 to fig.5.4.
5.1 Technical data of overhead travelling crane Single-girder overhead travelling crane 3,2 t x 11,0 m SWL Span Approach dimension Main girder IPB 1360 (DIN 1025 Part 3) End carriage
3200 kg lKr = 11,0 m lan = 0,57 m Material: St 37 GH
h b
350 mm 300 mm 10mm 17,5 mm 33090 cm 4 7890 cm 4
s
t Ix Iy
5.4
eKT = 2,00 m Electric hoist trolley vKr 31,5 m/min vKa 14,0 m/min VH 6,0 m/min
5.4.1 Calculation of A 2 . i b-s
0,0966
5.2.2 Max. wheel force R • 1JJ) . g
cz2
Czo =
0,05 - 0,58·0,0966+0,148. e 3 ,015' 0,0966
czo =
0,192 (web/flange)
Cz 1=
2,23 - 1,49 . 0,0966 + 1,390 . e- 18 ,33 . 0,0966
= 2,323
cz l
Cz 2 = =
2,207 (edge of flange)
cxo = -
(3)
Cx 2
2,110 + 1,977 . 0,0966 + 0,0076 . e 6 •53 . 0.0966 1,905 (web/flange) (4)
cxl
10,108 - 7,408·0,0966 - 10,108. e-1,364. 0,0966 = 0,532 (load application point) (5)
Cx 2
= 0,0
=
(edge of flange)
(6)
g= 9,81 m/s 2
5.4.4 Flange bending stresses ·R
R
(2)
0,73 - 1,58 . 0,0966 + 2,910 . e -6,0 . 0,0966
=-
Cxo
(1 )
(load attachment point)
5.4.3 Factors Cxo, Cxl, (equations 4 to 6)
cx )
5.2.1 Oscillation coefficient Osci llation coefficient 1JJ = 1,15
G4H
2 . 14 300 - 10
5.4.2 Factors czo, cZl< .(equations 1 to 3)
f: z 2
5.2 Calculation of the forces and moments in the middle of the main girder (intersection b) The proof of stress in the middle of the main girder is carried out with the load case I. Components consisting of the deadweight of the main girder and that of the trolley and the load lifted are taken into account in the ver· tical direction (y direction, see Fig. 5.4) and the inertia forces from long travel in the horizontal direction (x direction).
+
i
( 490 + 3200 . 1 15) .' 9 81 4 4 ' ,
UF!(z)
and
uF!(x)
The quotient, occurring in all the equations
10227 N
has the value
5.2.3 Bending moments in the x and y directions 5.2.3.1 x direction Main girder deadweight component Trolley deadweight component min Load lifted component
= 1890 cm 3
Calculation of the flange bending stresses using equations 1 to 6 (parallel flange section)
=
GKa 490 kg Trolley deadweight Trolley wheel base eKa = 0,420 m d Ka = 0,140 m Trolley travel wheel dia The overhead travelling crane is classified as FEM Group 2.
R = (G:
WXl = Wx2 2100 cm 3 15780 cm 3 580 cm 3 526 cm 3 14mm
d KT = 0,16 m
Travel wheel dia. Wheel base
Trolley . max. long travel speed . max. cross travel speed - max. lifting speed
a
Wxo Wxow Wyo Wyl Wy2
R
10227 - 175 , 2
t.2 1
Mx(HT) Mx(GKa) Mx(GKa) Mx(GH)
Mx(GH) .1JJ
16614 Nm 12719 Nm 1370 Nm 83063 Nm 95522 Nm
5.2.3.2 y direction Inertia forces from long travel component: MY(Kr)
Thus the flange bending stresses are calculated: 0,192 33,4 = = 2,323 . 33,4 = = 2,207 . 33,4 = =-1,905 33,4 = = 0,532 33,4 =
uF! (zO) = uF! (zl) UF) (z2)
uF! (xO) UF! (x l)
1320 Nm
33,4N/mm 2
UF) (x2) =
0,0
6,4 77,6 73,7 63,6 17,8
N/mm 2 N/mm 2 N/mm2 N/mm2 N/mm2
Licenced P,age to SCHOSS SA 9.341 4 FEM r,
5.5 General proof of. stress in middle of main girder (underside of flange)
5.5.4 Proof of stress point 0 (transition web/flange)
5.5.1
z direction:
Bendirig moments
M xges
(Mx(HT) + Mx(GKa) + Mx(GH) .
1/1) . M
az(O)
=
withM= 1,0 (increased coefficient Table T - 1,34) M xges
(16614 + 12 719 + 95 522) . 1,0
M xges
124855 Nm
M yges
My(Kr) . M
M yges
1320 Nm
direction: Mxges .
a Z (2)
=
2,5
€
Wyo . + +
1320 15780
+
. 0,75 . 6,4
az(O)
66,0
az(O)
70,9 N/mm2 ~ 160,0 N/mm 2
+
0,1
€ • aFl(zO)
+
4,8
. aFl(z2)
a z (2)
66,0
a Z (2)
123,8 N/mm 2 ~ 160,0 N/mm 2
+
~
x direction:
My
-- + -- + Wx2 Wy2
+
+
7,7 N/mm 2 ~ 92,0 N/mm 2
124855 1320 1 890 + 526 + 0,75 . 73,7
az (2)
Wxo
124855 1 890
5.5.2 Proof of stress point 2 (edge of flange) Z
M xges
--
ax(O)
€. aFl(xO)
ax(O)
0,75 . (-63,6)
-47,7 N/mm 2
I ax(o)1 ~ 160,0 N/mm 2
55,3
Reference stress:
J
acp(O)
x direction:
a X (2) = 0,0
a:(O) +
a~(O) -
az(O) . ax(O) +
3 . T to)
aep(O)
acp(O) =
104,2 N/mm2 ~ 160,0 N/mm 2
5.5.3 Proof of stress point 1 (load application point) 5.6 Welded web plate / flange design When there is a welded connection between the web plate and flange (fillet welds, see fig. 5.3), the general proof of stress and a proof of service strength is carried out for flange point 0 (top side of flange),
z direction: az(l)
Mxges
= -Wxl
124855 +1-320 - + 0,75 . 17,6 1890 580
aZ(l)
az(l)
My Wyl
+ - - + € . aFl(zl)
=
az(l) . =
66,0
+
2,3
+
5.6.1 General proof of stress for the weld seam point 0 z direction (
58,2
Normal stress, longitudinal loading of the weld point 0 54,8 N/mm 2 ~ 160,0 N/mm 2
126,5 N/mm 2 ~ 160,0 N/mm 2
az(O)w =
Shearing stress, transverse loading of the weld seam
x dii'ection: aX(l)
(including the stresses resulting from the longitudinel distribution of the wheel loads)
€ . aFl(xl) T(O)w
ax(l)
0,75 ' 17,8
aX(l)
13,4 N/mm2~ 160,0 N/mm 2
= 26,7 N/mm
2 ~ 113,0 N/mm 2
x direction: Normal stress, transverse loading to the weld seam 2 ~ 113,0 N/mm 2 ax(O)w= 47,7 N/mm
Reference stress: 2
acp(l)
~h26,52 + 13,42 - 126,5·13,4
with T(l)
~
a'cp(l) =
Reference; stress :
T(l)
acp(l)
0,0
120,4 N/mm 2 ~ 160,0 N/mm 2
acp(O)w=
..J 54,82 + 47,7 2 - . 54,8 . 47,7 + 2,26,7 2
Ucp(O)w=
64,0 N/mm2 ~ 160,0 N/mm 2
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Licenced to SCHOSS SA
FEM 9.341
5.6.2 Proof of service strength for weld seam point 0 The weld seams are classified -in the K4 case of notch toughness. 5.6.2.1 Limiting stress ratio for normal stress z direction: min Uz(O)w =
MXlHTl + minMxlGKal W xOw
min Uz(O)w =
16614 + 1 370 2100
t
/~
:$
=:1'"' wL: ,.'' 11 -
i_
f::J
,
1ii'tf=leL1='= = = = = 1--
---:.j ~
...M. 54,8 --
KzlO)
I
bolted connection d-d
~
b
min Uz(O)w = 8,6 N/mm 2 maxuz(O)w = 54,8 N/mm
Page 5
drive
2
(tension)
016 ,
wheel 11
wheel 21
Figure 5.1
Single-girder overhead travelling crane
Figure 5.2
Main girder section, intersection f
x direction: min uX(O)w = 0,0 maxuxlO)w= 47,7 N/mm 2 (tension) Kx(O) = 0,0
5.6.2.2 Permissible maximum for normal stress perm UOz(K z) = 160,0 N/mm 2
~
54,8 N/mm 2
permUOz(Kx) = 160,0 N/mm 2 ~ 47,7 N/mm 2
5.6.2.3 Limiting stress ratio for shear stress min T(O)w ==' 0,0
r
26,7 N/mm 2
maXT(O)w
0,0
5
x--
--x
5.6.2.4 Permissible maximum for shear stress perm TO(KT)
= 92,4 N/mm 2 ~ 26,7 N/mm 2
Y11
,f'----- b ---(
@
5.6.2.5 Proof of the combined stress (UZ(O)w )2 + (1x(O)w )2 _ uz(O)w . (1xlO)w permCTOz(z) permuOz(x) Ipermuoz1·/permUozI TlO)W )2 + ( perm TO
Figure 5.3
Main girder section, intersection b welded- design
~ 1,0
5
--x
x ---
0,1173 + 0,0889 - 0,1021 -+ 0,0835 0,1876
~
1,0
o Figure 5.4
Main girder section, intersection b
durchSA den Technischen AusschuB der Sektion IX der Federation Europeenne de la Manutention (FEM) Licenced .Erstellt to SCHOSS Prepared by the Technical Committee of Section IX of the Federation Europeenne de la Manutention (FEM) Etabli par le Comite Technique de la section IX de la Federation Europeenne de la Manutention (FEM)
Sekretariat: Secretariat: Secretariat:
Sekretariat der FEM Sektlon IX . cJoVDMA Fachgemelnschaft Ftirdertechnlk Postfach 710864 D-60498 Frankfurt
Zu beziehen durch das oben angegebene Sekretarlat oder durch die folgenden Nationalkomltees der FEM Available from the above secretariat or from the following committees of the FEM En vente aupres du secretariat ou des comites nationaux suivants de la FEM
Belgique
Italia
Comite National Beige de la FEM Fabrlmetal Rue des Drapiers 21 B-1 050 Bruxelles
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Deutschland
Luxembourg
Deutsches Nationalkomitee der FEM VDMA Fachgemelnschaft FOrdertechnik Postfach 71 0864 D-60498 Frankfurt Lyoner Str. 18 D-60528 Frankfurt
Comite National Luxembourgeois de la FEM Federation des Industriels Luxembourgeols Groupement des Constructeurs et Fondeurs du Grande-Duche de Luxembourg Bone Postale 1304 Rue Alclde de Gasperl 7 L-1013 Luxembourg
Espafta
Nederland
Comite Nacional Espanol de la FEM Asociacl6n Nacional de Manutencl6n (AEM) ETSEIB-PABELLON F Diagonal, 647 E-Q8028 Barcelona
Nederlands Natlonaal Comite bij de FEM Vereniging FME Postbus 190, Bredewater 20 NL-2700 AD Zoetermeer
Finland
Norge
Finnish National Committee of FEM Federation of Finnish Metal, Eng. and Electratechn. Industries (FIMET) Etelaranta 10 SF-Q0130 Helsinki
Norwegian FEM Groups Norsk Verkstedsindustris Standardiseringssentral NVS Box 7072/ Oscars Gate 20 N-Q306 Oslo
France
Portugal
Comite National Fran~is de la FEM Syndicat des Industries de materiels de manutention (SIMMA) 39/41 rue Louis Blanc - F-92400 Coumevoie cedex 72 - F-92038 Paris la Defense
Comlssao Nacional Portuguesa da FEM Federayao Nacional do Metal FENAME Rua do Quelhas, 22-3 P-1200 Usboa
Great Britain
Schweiz I Suisse I Svizzera
British National Committee of FEM British Materials Handling Federation Bridge House, 8th Floor Queensway; Smallbrook GB-Birmingham B5 4JP
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