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DIN 18800-02 - Structural Steelwork Design Construction - DIN (1990) | Buckling | Bending
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Analysis of safety against buckling of linear members and frames
1 General ....................................... 2 1.1 Scope and field of application . . . . . . . . . . . . . . . . . . . 2 2 1.2 Concepts ..................................... 2 1.3 Common notation ............................. 3 1.4 Ultimate limit state analysis ..................... 3 1.4.1 General ..................................... 1.4.2 Ultimate limit state analysis by elastic theory .... 4 1.4.3 Ultimatelimit state analysis by plastic hinge theory 5 .2 imperfections.. ................................ 5 5 2.1 General ...................................... 5 2.2 Bow imperfections. ............................ 6 2.3 Sway imperfections ............................ 2.4 Assumption of initial bow and coexistent initial ........................ 7 sway imperfections . 3 Solid members ..... ........................ 7 7 3.1 General ...................................... 8 3.2 Design axial compression ...................... 8 3.2.1 Lateral buckling ............................. 3.2.2 Lateral torsional buckling*) ................... 8 3.3 Bendingabout oneaxiswithoutcoexistentaxial force 8 8 3.3.1 General ..................................... 3.3.2 Lateral and torsional restraint ................. 1O 3.3.3 Analysis of compression flange ................ 12 12 3.3.4 Lateral torsional buckling ..................... 3.4 Bending about one axis with coexistent axial force 13 3.4.1 Members subjected to minor axial forces ....... 13 13 3.4.2 Lateral buckling ............................. 14 3.4.3 Lateral torsional buckling ..................... 3.5 Biaxialbendingwith or coexistent axialforce 15 3.5.1 Lateral buckling .... ................... 15 16 3.5.2 Lateral torsional buckling ..................... 4 Single-span built-up members .................. 16 16 4.1 General ...................................... 17 4.2 Common notation ............................. 4.3 Buckling perpendicular to void axis .............. 17 17 4.3.1 Analysis of member .......................... 4.3.2 Analysis of member components .............. 17 4.3.3 Analysis of panels of battened members ........ 18 4.4 Closely spaced built-up battened members ....... 19 20 4.5 Structural detailing ............................ 5 Frames.. ...................................... 20 20 5.1 Triangulated frames ...........................
General.. ................................... 20 Effective lengths of frame members designed to resist compression. . . . . . . . . . . . . . . .20 5.2 Framesand laterallyrestrainedcontinuous beams . 22 5.2.1 Negligible deformations due to axial force ...... 22 23 5.2.2 Non-sway frames ............................ 23 5.2.3 Design of bracing systems .................... 5.2.4 Analysis of frames and continuous beams. ...... 23 5.3 Sway frames and continuous beams subject to 23 lateral displacement ........................... 5.3.1 Negligible deformations due to axial force . . . . . . 23 5.3.2 Plane sway frames ........................... 23 5.3.3 Non-rigidly connected continuous beams ....... 27 6 Arches ........................................ 27 27 6.1 Axial compression ............................. 27 6.1.1 In-planebuckling ............................ 6.1.2 Buckling in perpendicular plane. . . . . . . . . . . . . . . . 30 6.2 In-plane bending about one axis with coexistent axial force ............ 6.2.1 In-plane buckling .............. 6.2.2 Out-of-plane buckling ........................ 33 6.3 Design loading of arches ........ ....... 34 7 Straight linear members with plan thin-wailed parts of cross section . . . . . . . . . . . . . . 34 7.1 General ...................................... 34 7.2 General rules relating to calculations . . 7.3 Effective width in elastic-elastic method 7.4 Effective width in elastic-plastic method 38 7.5 Lateral buckling ............................... 38 7.5.1 Elastic-elasticanalysis ........................ 7.5.2 Analyses by approximate methods . . . . . . . . . . . . . 38 39 7.6 Lateral torsional buckling ....................... 39 7.6.1 Analysis .................................... 7.6.2 Axial compression ........................... 39 7.6.3 Bending about one axis without coexistent 39 axial force .................................. 7.6.4 Bending about one axis with coexistent axial force .......................... ... 39 7.6.5 Biaxial bending with or without coexistent 39 axial force .................................. Standards and other documents referred t o ........ 40 Literature.. ....................................... 40 5.1.1 5.1.2
Copyright Deutsches Institut Fur Normung E.V. 04.93 Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`,,,`-`-`,,`,,`,`,,`---
*) Term as used in Eurocode 3. In design analysis literature also referred to as flexural-torsional buckling.
Continued on pages 2 to 41
ufh Verlag GmbH. Berlin, has the exclusive right of sale for German Standards @IN-Normen).
DIN 18800 Part 2 Engl. Price group 7
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Page 2 DIN 18800 Pari 2
(101) Ultimate limit state analysis This standard specifies rules relating to ultimate limit state analysis of the buckling resistance of steel linear members and frames susceptible to loss of stability. It is to be used in conjunction with DIN 18800 Part 1.
(102) Serviceability limit state analysis Aserviceability limit state analysis need only be carried out if specifically required in the relevant standards. Note. Cf. subclause 7 . 2 . 3of DIN 1 8 800 Part 1.
(103) Buckling Buckling is a phenomenon in which displacement,v orw,of a member occurs, or rotation, 9,occurs about its major axis, or both occur in combination. A distinction is conventionally made between lateral buckling and lateral torsional buckling.
(104) Lateral buckling
Figure 1. Coordinates, displacement parameters and internal forces and moments
(109) Section parameters cross-sectional area second order moment of area
Lateral buckling is a phenomenon in which displacement,v or w, of a member occurs,or both occur in combination,any rotation, 9, about its major axis being neglected. (105) Lateral torsional buckling Lateral torsional buckling is a phenomenon in which displacements, u and w ,of a member occur in combination with rotation, 4, about its major axis, consideration of the latter being obligatory. Note. Torsional buckling, in which virtually no displacements occur, is a special form of lateral torsional buckling.
1.3 Common notation
(106) Coordinates, displacement parameters, internal forces and moments, stresses and imperfections axis along the member (major axis) axis of cross section (In solid members, I, shall be not less than Iz.) displacement along axes x, y and z rotation about the x-axis initial bow imperfections in unloaded state initial sway imperfection of member or frame in unloaded state axial force (positive when compression) bending moments shear forces (107) Subscripts and prefixes characteristic value of a parameter k design value of a parameter d grenz prefix to a parameter identifying it as being a limiting (¡.e. maximum permissible) value vorh actual red reduced Note. The terms ‘characteristicvalue’and‘designvalue’are defined in subclause 3 . 1of DIN 18800 Part I.
Physical parameters E elastic modulus G shear modulus f y yield strength Note. See table 1 of DIN 18800 Pari 1 for values of E , G and f y , k.
radius of gyration torsion constant warping constant elastic section modulus axial force in perfectly plastic state bending moment in perfectly plastic state , reaches bending moment at which stress u yield strength in the most critical part of cross section Mel
apl= MP1 plastic shape coefficient
Poisson’s ratio moment ratio Note. The term ‘perfectly plastic state’ applies when the plastic capacity is fully utilized, although in certain cases (e.g. angles and channels), pockets of elasticity may still be present. Where cross sections are non-uniform or internal forces and moments variable, Npl,Mpl and Mel at the critical point shall be calculated.
(110) Structural parameters system length (of member)
7 ~ *
axial force at the smallest bifurcation load, according to elastic theory
(E * I )
s K = i T ; y ,
effective length *) of a linear member associated with N K ~ slenderness ratio reference slenderness ratio
&=n/-&
aK - =AK = ( 3 non-dimensional slenderness in comNKi
pression reductionfactor according to the standard buckling curves as used in Europe member characteristic
NKi,d 7
distribution factor of system
*) Translator’s note. Common term as used in design analysis. In Eurocode 3 termed ‘buckling length’.
DIN 18800 Part 2 Page 3
MKi,y
design buckling resistance moment according to elastic theory from My without coexistent axial force non-dimensional slenderness in bending
Table 1. Methods of analysis
Calculation of internal forces and moments
Note 1. Where cross sections are non-uniform or axial forces variable, (E. I ) , NKiand SK shall be determined for the point in the member for which the ultimate limit analysis is to be carried out. In case of doubt, an analysis shall be performed for more than one point (cf. item 3 1 6 ) . Note 2. The reference slenderness ratio, ila, for steel of thickness 40mm and less shall be as follows: 92,9 for ~t 37 where fy,k = 240 N/mm2, and 75,9for St 52 where fy,k = 360 N/mm2. Note 3 . Calculations of in-plane slenderness ratios shall be made using as the values O f f y , ( E . 1).NKi and MKi asspecifiedinitems116and117eithertheircharacteristic values or their design values throughout. Note4. V K ~ shall beof thesame magnitudefor all members making up a non-sway frame. Note 5. Where cross sections are non-uniform or internal forces and moments variable, M Kshall ~ be calculated for the point for which the ultimate limit state analysis is carried out. In cases of doubt, an analysis shall be performed for more than one point.
(111) Partial safety factors YF partial safety factor for actions YM partial safety factor for resistance parameters Note. The values of YF and YM shall be taken from clause 7 of DIN 18800 Fart 1. Thus, the ultimate limit state analysis shall be carried out taking YM to be equal to 1,l both for the yield strength and for stiffnesses (e.g. E T , E - A , G - A Sand S).
Elastic theory Elastic
Elastic theory Plastic
plastic plastic theory theory
Note 1. Details relating to elasto-plastic analysis are not provided in this standard (cf. [i]), though this is permitted in principle. Note 2. In table 11 of DIN 18800 Part 1, the generic term ‘stresses’ is used instead of ‘internal forces and moments due to actions’. Note 3. The conditions of restraint assumed when individual members are notionally singled out of the structural system shall be taken into account when verifying lateral torsional buckling. Note 4. Simplified methods substituting those set out in clauses 3 and 4 are listed in table 2.
(113) Material requirements The materials used shall be of sufficient plastic capacity. Calculations may be based on assumptions of linear elastic-perfectly plastic stress-strain behaviour instead of actual behaviour. Note. The steel grades stated in sections 1 and 2 of item 401 of DIN 18800 Part 1 are of sufficient plastic capacity.
(114) Imperfections
1.4.1 General (112) Methods of analysis The analysis shall be take the form of one of the methods given in table 1, taking into account the following factors: - plastic capacity of materials (cf. item 113); - imperfections (cf. item 114 and clause 2 ) ; - internal forces and moments (cf. items 115 and 116); - the effects of deformations (cf. item 1 1 6); - slip (cf. item 118); - the structural contribution of cross sections (cf. item 1 1 9); - deductions in cross-sectional area for holes (ci. item
Reasonable assumptions (e.g. as outlined in clause 2)shall be made in order to take into account the effects of geometrical and structural imperfections. Note. Typical geometrical imperfections are accidental load eccentricity and deviations from design geometry. Typical structural imperfections would be residual stresses.
(115) Internal forces and moments The internal forces and moments occurring at significant points in the members shall be calculated on the basis of the design actions. As a simplification, the index d has been omitted in the notation of internal forces and moments. . 2 . 1and 7.2.2of DIN 18800Part 1 specNote. Subclauses 7 ify rules for calculating design values of actions. (116) Effects of structural deformations Calculations of internal forces and moments usually make allowance for deformation effects on equilibrium (according to second order theory), using as the design stiffness values the characteristic stiffnesses obtained by dividing the nominal characteristics of cross section and the characteristic elastic and shear moduli by a partial safety factor YM equal to 1,l. The effect of deformations resulting from stresses due to shear forces may normally be ignored.
1 2 0 ) .
As a simplification, lateral buckling and lateral torsional buckling may be checked separately, first carrying out the analysis for lateral buckling and then that for lateral torsional buckling whereby, in the latter case, members shall be notionally singled out of the structural system and subjected t o the internal forces and moments acting at the member ends (when considering the system as a whole) and to those acting on the member considered in isolation. Details on whether first or second order theory is to be applied are given together with the relevant method of analysis. The analyses described in clauses 3 to 7 may be used as an alternative to those listed in table 1.
Page 4 DIN 18800 Part 2 Table 2. Simplified ultimate limit state analyses Internal forces and moments Simplified analyses as in
Solid members Lateral buckling Lateral torsional buckling Lateral torsional buckling 3.2.1 3.2.2 3.3.2, 3.3.3, 3.3.4 3 7, 8, 12, 14, 16, 21
Lateral buckling Lateral buckling Lateral torsional buckling Lateral buckling
3.4.2 3.4.2 3.4.3 3.5.1
24 24 27 28.29
(E* I)d.
Lateral torsional buckling Built-uprmbers Lateral buckling
3.5.2 4.3 4.3
30 31 to 38
Note 1. In calculations of internal forces and moments according to second order theory, for example, the member characteristic,s,and the distribution factor, ~ j - ~shall i. be determined using the design stiffness, Note 2. Reference shall be made to the criteria set out in item 739 of DIN 18800 Part 1when deciding whether to base calculations on second order theory. Note 3. Deformations also occur as a result of joint ductility. Note 4. Deformations resulting from stresses due to shear forces shall be taken into account as specified in clause 4 for built-up compression members.
(117) Analysis on the basis of design actions multiplied by YM As a departure from the specifications of items 115 and 116, internal forces and moments and deformations may also be calculated using the designvalues of actions multiplied bya partial safetyfactoryM of l,l,in which case the ultimate limit state analysis shall be carried out using the characteristic strengths and stiffnesses, substituting these (denoted by subscript k) for the design resistances (denoted by subscript d) in the equations in clauses 3 to 7 .
i be made, for Note 1. Calculations of e and v ~ shall example, using the characteristic stiffness, (E. I)k.
(118) Slip Account shall be taken of slip in shear bolt or preloaded shear bolt connections in members and frames susceptible to loss of stability, using the values specified in item 813 of DIN 18800 Pari 1. Note. Due account shall be taken of slip if this greatly increases the risk of loss of stability. (119) Effective cross section If the full cross section of parts in compression is taken into consideration, their geometry shall be such that the grenz (blt)and grenz (dit)values specified in DIN 18 800 Part 1are complied with. If,for thin-walled members,these values are not complied with, the analyses shall be of lateral buckling with coexistent plate buckling of individual members, or of lateral torsional buckling with coexistent plate buckling, as specified in clause 7 of DIN 18800 Part 3 or Part 4. Note 1. The grenz(blt) values differ according to the method of analysis selected (see table 1).The grenz (blt) values for individual parts of plane cross sectionsare given in tables12,13,15and 18of DIN 18800 Part 1. Note 2. The grenz (dlt) values for circular hollow sections are given in tables 14,15and 18 of DIN 18800 Pari 1. Methods of analyses of circular hollow sections the geometry of cross section of which does not comply with these limits are not covered in this standard. (120) Deductions for holes Deductions for holes need not be made when determining internal forces and moments and deformations if it can be ruled out that premature local failure occurs as a result. 1.4.2 Ultimate limit state analysis by elastic theory (121) Analysis The loadbearing capacity may be deemed adequate if an analysis of the internal forces and moments according to elastic theory shows the structure to be in equilibrium and either one of the following applies.
Note2. The alternative procedure set out in this item is especiallysuitable forthe global analyses described in clauses 5,6 and 7 but may also be used by analogy in clauses 3 and 4, giving the same results as would be obtained if yM were assigned to the resistance.To preclude the risk of confusion, it shall be stated explicitly in the analysis that this alternative procedure has been used. Note 3. See subclause 7.3.1 of DIN 18800 Part 1 for resistance parameters.
calculation of E for the total axial force due to all actions is necessary in both cases.y is greater than 1. the failure criterion may be 10% higher than design yield strength (cf. The analyses set out in subclause 4.`.`-`-`. Note 1. only two-thirds the values specified forthe equivalent imperfections in subclauses2. Imperfections relating to special applications are not covered in clauses 3 to 7.5 DO (cf. but not that of the structure.3 shall. The aim is to achieve on average the same mean ultimate loads when applying both the elastic-elastic and the elastic-plastic methods.1
(201) Allowance for imperfections
Allowance shall be made for the effects of geometrical and structural member frame imperfections if these result in higher stresses. equivalent imperfections need only be assumed for the direction in which buckling will occur with the member in axial compression. shall generally be assumed to have the initial bow imperfections given in figure 2 and table 3.
Note 2. Note.apl. (203) Imperfections in special applications Where provisions for special applications are made in other relevant standards. bow imperfections need only be assumed with DO or W O in each direction in which buckling will occur.3 Ultimate limit state analysis by plastic hinge theory (124) The loadbearing capacitymay be deemed adequate if an analysis according to plastic hinge theory shows internal forces and moments (taking into account interaction) to be within the limits specified for the perfectly plastic state (plastic-plastic method). Interaction equations are given in tables 16 and 17 of DIN 18 800 Part 1. Ultimate limit state analyses of built-up members as specified in subclause 4. however.V.3). Item 123 gives information on limiting the plastic shape coefficient.3 need be assumed.
(204) Individual members..`---
. Where lateral buckling occurs as a result of bending about only one axis with coexistent axial force. the internal transverse forces and moments occurring may be determined by superimposing those internal forces due to actions which result in moments M yand transverse forces V. frame corners and foundations.
(122) Internal forces and moments in bi-axial bending Where bi-axial bending occurs with or without co-existent axial force but without torsion. d (elastic-elastic method). in turn. a bow imperfection equal to 0. In the case of lateral torsional buckling. Instead of reducing the resistance moment. Other possible factors which may affect the ultimate load. Note 1. Where lateral buckling occurs as a result of biaxial bending with coexistent axial force. f y .DIN 18800 Part 2 Page 5 The failure criterion is not higher than the design yield strength. The elastic-plastic method allows for plastification in cross sections with the possibility of plastic hinges with full torsional restraint at one or more pointS.members making up non-sway frames and members as specified in item 207.`.
Initial bow imperfections of member in the form of a quadratic parabola or sine half wave
Copyright Deutsches Institut Fur Normung E.the resistance moment occurring as a result of Co-existent normal and transverse forces in a perfectly plastic member cross section shall be reduced bya factor equal to 1. In the elastic-elastic method. Equivalent geometrical imperfections may. The equivalent imperfections are already included in the simplified analyses described in clauses 3 and 7. welding and straightening procedures.25. a distinction being made between initial bow (see subclause 2. As well as geometrical imperfections. Note.This permits the plastic capacityof the cross sections to be fully utilized.. For this purpose. item 749 of DIN 18800 Part 1). A reduction by one-third takes account of the fact that the plastic capacity of the cross section is not fully utilized. d .
L Y J 2
1. always be made using the full bow imperfection stated in line 5 of table 3. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`. Note 1. or shear deformations are not covered. shall be such that they are optimally suited to the deformation mode associated with the lowest eigenvalue. equivalent geometrical imperfections shall be assumed. Note. At isolated points.. table 3) may be assumed.`.z is greater than 1. See item 746 of DIN 18800 Part 1 for f y . and those resulting in moments M. equivalent geometrical imperfections also cover the effect on the mean ultimate load of residual stresses as a result of rolling.25. assumed to occur in the least favourable direction.. the actual moment may be increased by a factor equal to api/1. such as ductility of fasteners..25/aPl. which also justify the value of bow imperfection stated in line 5 of table 3 (cf.4. The analysis shall be made using interaction equations (cf. such specifications shall form the basis of the global analysis.with specifications deviating from those given in this standard.2 and 2.2
Bow imperfections
2. This only applies if the structure is in equilibrium.Thesame principle shall be applied to each of the two moments in biaxial bending if apl.associated with an axis of bending is greater than 1.25or apl. be accounted for by assuming the corresponding equivalent loads. Note 3. material inhomogeneities and the spread of plastic zones.
Limiting the plastic shape coefficient In cases where the plastic shape coefficient. The equivalent imperfections need not be compatible with the conditions of restraint of the structure. However. Note 2. the specifications of item 117 being applied by analogy.
(202) Equivalent imperfections The equivalent geometrical imperfections. The internal forces and moments (taking due consideration of interaction) are within the limits specified for the perfectly plastic state (elastic-plastic method). tables 16 and 17 of DIN 18 800 Part l). and transverse forces V. Note 2.2) and sway imperfections (see subclause 2.25 and the principles of first ordertheorycannot be applied.. Note under item 402).3 are based on comparisons of ultimate loads obtained empirically or by calculation.
Table 3. Since. where 1. and p p o or ~ 0 .
r2=1(í+t) 2
Figure 4. WO?u0
11300 11250 11200 11150
In the above figure. with less than 25Oío of the axial force acting in the column submitted to maximum load in the same storey and plane. Not included are columns subjected to minor axial forces. shall be substituted for the length of the column in that storey for calculation of Il. ¡.L. Ideal member or frame (chain thin line) and member or frame with initial sway imperfection (continuous thick line)
Initial sway imperfections shall generally be calculated as follows (cf.`.3
Sway imperfections
Note 2. r2 400 where
Figure 3.. the storey height. See table 23 for bow imperfections for arch beams.. the total length of columns.. Note 1.`. is the length of the member or frame.
Calculations of 12 for frames may generally assume n to be the number of columns per storey in the plane under consideration. In the other storeys.`---
Assumptions Sway imperfections as in figure 5 shall be assumed t o occur in members or frames which may be liable to torsion after deformation and which are in compression.V. item 730 of DIN 18800 Part 1 ) : a) solid members:
Note. is greater than 5 m. Assumptions for bow imperfections (examples)
imperfection. the height of the structure. the length of the member.. in calculations of shear in multictorey frames. of cross section with following buckling curve
3 1 4 1 Built-up members. with analysis as in subclause 4.`. the ~.e. is a reduction factor allowing for IZ independent causes of sway imperfection of members or frames. Figure 5.
po = -r1
b) built-up members as in figures 20 and 21 and subclause 4. or frame..e.Page 6 DIN 18800 Part 2 Bow imperfections need not be assumed if members satisfy the criteria specified in item 739 of DIN 18800 Part 1. initial sway imperfections are assumed to have the most adverse effect in the storey under consideration. sway imperfection of the member or frame. having the most adverse effect on the stress under consideration. ¡.L. L or L. figure 6). L. Equivalent stabilizing force for bow imperfections as shown in figure 2 (assuming equilibrium)
is a reduction factor applied to members or frames.
Solid member. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`. may be substituted for I (cf.
Copyright Deutsches Institut Fur Normung E.`-`-`.. reductions in the sway imperfections may be assumed. L. Bow imperfections If the criteria for first order theory set out in item 739 of DIN 1 8 800 Part 1 are met. Allowance for sway imperfections may also be made by assuming equivalent horizontal forces.3: 1 (2) po = -r l ..
The reduction factorr2 may be used byanalogyfor roof bracing providing extra stability to beams.1 100.~ = r 2 -with
f T f l
--`. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
. The same applies for any suspended columns connected to.`-`-`. the bracing system. shall be assumed with both initial sway and bow imperfections in the most unfavourable direction.`.2 to 3. item 118). &. of more than 1.
Sway imperfections for analysis of bracing systems The initial sway imperfections assumed for the columns of bracing systems shall be as those for the columns of sway beam-and-column type frames. Initial sway imperfections in frames (examples)
2. and thus given extra stability by..`---
Copyright Deutsches Institut Fur Normung E.5 apply for individual members and frame memberswhich are notionally singled out of the system and considered in isolation forthe purposes of the analysis.. Assumption of initial bow and coexistent initial Figure 8 sway imperfections (examples)
.`.2
P o .1 General (301) Scope
The analyses specified in subclauses 3.2
Variant P0..
Note 4.6. 1
(P0.`.2 = r 2 -r l
POSI = r2
Figure 6 ..4
Assumption of initial bow and coexistent initial sway imperfections
(207) Members in frames.
Figure 7. If members are notionally singled out.2 = r p -with 200
n =2 n =4
4 -I!!
DIN 18800 Part 2 Page 7
= r1Zö
970=r1Töö
po.V. Lateral buckling and lateral torsional buckling are dealt with separately.
3 Solid members
3. Sway imperfections due to slip of screws may also Note 3 require consideration (cf.. allowance shall be made of the actual conditions of restraint relating to the particular member.
Equivalent horizontal forces substituting initial sway imperfection 100 (assuming equilibrium)
970?2
970. which may exhibit sway imperfections after deformation and have a member characteristic. Note.
0.taken from table 5.3.hollow sections: .e. 1 Lateral buckling (304) Analysis
The ultimate limit state analysis shall be made forthe direction in which buckling will take place. (303) Lateral torsional buckling
Members notionally singled out of the system and considered in isolation shall be analysed for lateral torsional buckling.2 Design axial compression 3 .3. the analysis shall be made using equation (3) for all relevant cross sections with the appropriate internal forces and moments. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
. I sections (including rolled sections) do not require ultimate limit state analysis with respect to lateral torsional buckling.3
0 . Subclauses 3. .
(305) Further provisions for non-uniform cross sections
and variable axial forces Where equation (3)is applied to members of non-uniform cross section andlor variable axial forces.5
Figure 9.5[I
+ a (XK .and in addition the following conditions shall be met:
3. Parameters a for calculation of reduction factor x Buckling curve a b
3. See subclause 3. the initial forces and momentsfromfirst ordertheoryshall betaken asa basisfor calculations.Page 8 DIN 18800 Part 2
(302) Lateral buckling Since the analysis of lateral buckling specified in subclauses 3.1 and 5 .0
2.`. 3 . Torsional buckling is treated here as a special type of lateral torsional buckling..
Bending about one axis without coexistent axial force 3 .`.5. Effective lengths of single members of uniform cross section (examples) Note 2. providedthat their non-dimensional slenderness in bending. Reference shall be made to the literature (e.l
0. 2 Lateral torsional buckling (306) Members of uniform cross section with anytype of
end support not permitting horizontal displacement. N 51 (3) x Np1. the load on the member changes direction when this moves laterally. in certain cases. 3 .5already includes both types of imperfection and second order effects. Note. (28) and (29) is referred to as first order elastic analysis with sway-mode effective length (equivalent member method.4.2 : x =
k = 0.with the reduction factor x being determined for buckling about the z-axis.`---
Copyright Deutsches Institut Fur Normung E.2: x = 1
>0. Note 1. subject to constant -¡al force shall be analysed as specified in subclause 3 .4. 2 .4for bending about one axis. (241.2. cross section properties and axial forces. conditions outlined in subclause 3.2) + nK]
> 3. 3 shall be taken into consideration when applying the equivalent member method to members notionally singled out of the frame. In the literature.2to 3. 2 .il
0. 2 .g. except in cases where bending is about the z-axis or the .2or 3
5 0. is not more than 0. Note. 2 . If. 1 .49
Note 1.12 0.`.2. Note 2. and figures 27 and 29 may provide assistance in other cases..34
0.this factor shall be taken into consideration when determining the effective length (e. 1 shall ~ be calculated substituting for N K i the axial force occurring under the smallest bifurcation load for lateral torsional buckling. [2]) for the use of equations (4a) to (4c).d The reduction factor x (¡. AM.and the buckling curve for the particular cross section.
i" I" i" IN
ß=SK
1. using equation (3).2 for verification of sufficient restraint.76
--`.) shall be obtained by means of equations (4a) to (4 c) as a function of the nondimensional slenderness in compression. 3 .3..NKi..g.`-`-`.The moments in the span may then be calculated by first order theory using these end moments.3.members designed to be in bending.
Table 4 . 3are met.O
D. xy or x.V. the combination of equations (3).AK.O:
as a simplification. for short).with the aid of figures 36 to 38). An analysis of lateral torsional buckling is not required for the following: . 1 General (307) Ultimate limit state analysis shall be carried out as specified in subclause 3..05man M.Their end moments may require to be determined by second order theory.
min M.members with sufficient lateral or torsional restraint. The effective length required for calculating 3~ is given in the literature. in cases where AK
í& + a) a being taken from table 4. Four simple cases are given in figure 9.
2.`-`-`. taking into consideration the likely residual stresses and plate thicknesses. Note. t
s 40 mrn
hlb > 1.. which is not less than min t.
t580mm
t>80mrn
Welded I sections
Channels.2.`.`---
.. Thick welds are deemed to have an actual throat thickness... Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`. a. T and solid sections
plus built-up members to subclause 4.V.4 Sections not included here shall be classified by analogy.`.lty < 30
Rolled I sections
hlb > 1.2.`.DIN 18800 Part 2 Page 9 Table 5. 40 e t 5 80 rnm hlb 5 1.
Copyright Deutsches Institut Fur Normung E. L..
Welded box sections
eN@i
Thick welds and
2 Lateral and torsional restraint (308) Lateral restraint
Members with masonry bracing permanently connected to the compression flange may be considered to have sufficient lateral restraint if the thickness of the masonry is not less than 0.8
I Figure 10. Note 1. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.35 for the elastic-elastic method. If sheeting is connected at every second rib only. Equation (8) is a simpler check which makes use of the characteristic values.Pagel0 DIN 18800 Part 2 Lateral torsional buckling
(309) Torsional restraint I beams of doubly symmetrical cross section with dimensions as for rolled sections complying with the DIN 1025 standards series shall be considered as being torsionally restrained (¡.
+ GIT + EI. C and d) and obtained by equation (18) with n equal to 2. is to be taken from column 2 of table 6 if the beam is free to move laterally..
is equal to unity for the elastic-plastic and plasticplastic methods or 0. Reduction factors x for lateral buckling (buckling curves a. 0. due to their axes of rotation being restrained) if the condition expressed by equation (8) is met. Note. 0... Lateral restraint (masonry bracing) If trapezoidal sheeting to DIN 18 807is connected to beams and the condition expressed by equation (7) is met.e.. Masonry.2.5
for lateral torsional buckling.`-`-`.3 times the height of cross section of the member.
3 .`..orfrom column 3of table 6 if the beam is laterally restrained at its top flange.`. Coefficients ko
Compression flange Figure 11.`.V. Equation (7) may also be used to determine the lateral stability of beam flanges used in combination with types of cladding other than trapezoidal sheeting.`---
k. provided that the connections are of suitable design. S shall be substituted for S.25 12
S being the shear stiffness provided by the sheeting for beams connected to the sheeting at each rib. b. 3 . the beam at the point of connection may be regarded as being laterally restrained in the plane of the sheeting.
Copyright Deutsches Institut Fur Normung E.
vorh b
vorh b is the actual flange width of the
b.k. with a vulcanized neoprene backing.V.')
Washer diameter. ~ .k
with 1.')
I Sheeting subjected to suction
b.cb.. any deformations at the point of connection between the supported beam and the supporting member shall be taken into consideration.3mm in diameter.k. CfiA.
Table Z Characteristic torsional restraint values for trapezoidal steel sheetins connections.k
--`. not less than 0.
-C@.
Copyright Deutsches Institut Fur Normung E.k is the torsional restraint due to deformation of the supported beam section (cf.k
C8M.k.k is the torsional restraint due to deformationof the connection. [3]for further details on the use of C@A.
is equal to 2 in the case of singlespan or two-span beams or 4 in the case of continuous beams with three or more spans: ( E .4.`.`---
with is the actual effective torsional restraint. assuming a rigid connection:
I 1.rib spacing. C@.`-`-`. Note 3.3.
3) bt .
The values stated apply to bolts not less than 6. Instead of applying equation (81. check then being carried out as specified in subclause 3. substituting ?@&k from table 7.251
CbM. assuming a flange width. bolt head to be concealed using a steel cap.k7 kNmim
max bt3).25 where
I 2. may also be considered when determining the ideal design buckling resistance moment.g.
2 . r a ) k is the bending stiffness of the supporting member. When determining the actual effective torsional restraint. Cbp.
Ka ..`.k
COA.k
where cg. inmm
in C'A. in mm. is the theoretical torsional restraint obtained by means of equation (10) from the bending stiffness of the supporting member (a)..`. M K ~ the .75mm in wall thickness.DIN 18800 Part 2 Page 11 Note 2. a is the span of the supporting member. [4]). by means of equation (9). Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
.. Cf. e. used with steel washers not less than 1. arranged as shown in figure 13. Bolting to top flange bottom flange
Position of profile Line
C@P. the actual effective torsional restraint.washer diameter irrelevant. that of trapezoidal sheeting being obtained by means of equation (11 a) or (11 b).flange width of sheeting.Omm thick.
5.`.`. . is a reduction factor applied to moments as a function of AM. Where there are moments My with a moment ratio. 3 . Calculations may be simplified bysubstituting fori. Arrangement of screws in connections between beams and trapezoidal sheeting (example)
3.`.buckling curve d being selected for beams otherthan the rolled beams in line 1 oftableg.shall be multiplied by a factor k ..
Buckling curve c may be used in all other cases.. chan-
*Figure 14. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS Not for Resale
--`.Page 12 DIN 18800 Part 2
Asimplified method using equation (14) may be used where equation (12) is not met:
Figure 13. for A. from figure 14.V. W. Torsional restraint (example)
0. i .n. Beam coefficient and associated factor k .`-`-`.y.4
(311) The ultimate limit state analysis of I beams. do not require a detailed analysis for lateral torsional buckling if
nels and C sections not designed for torsion shall be by means of equation (16):
is the maximum moment as specified in item 303. Equation (15) shall also be met by beams coming under this category: 5 4 4 t
h being the maximum beam depth. Note. isareductionfactorasafunctionofbucklingc_urvec or d. from equation (13).
t being the thickness of the compression flange. greaterthan 0. with a
compression flange which is laterally restrained at a number of points spaced a distance c apart.`---
where II is the beam coefficient from table 9.d
is the maximum moment.843 M~
Mpl.the beam coefficient. obtained by means of equation (4).. which are subject to in-plane lateral bending on their top flange.g the radius of gyration of the whole section. 3 Analysis of compression flange (310) I beams symmetrical about the web axis.3.
n Type of section Rolled
2. n. M K ~ .5
Welded 2. as specified in subclause 3... 8 min h
min h 2 0.d
MKi. Calculation of äM is only possible where the ideal design buckling resistance moment. from table 10
(312) Members subjected to only minor axial forces and meeting the condition expressed by equation (22) may be analysed for bending without coexistent axial force.`. Izll'..77
.DIN 18800 Part 2 Page 13 Table 9.
Note 1.2.k
f y ..
pmaxM maxM -1cp1
1*h2
240 fy. X M may be assumed to be equal to unityfor beams not more than 60cm in depth (see figure 1 5 )and of uniform cross section provided that they satisfy equation (21):
0.039 1 ' * IT
Npl.1
Bending about one axis with coexistent axial force
MK~. k being expressed in N/mm2. Beam coefficient.
Note 4.. X M may also be taken from figure 10 if the beam coefficient.`.`-`-`.25 max h
Haunched*)
Figure 15.4.7
+1 .4.3.`.
NK~.is equal to 2 5 Note 3.5 zP)
Members subjected t o minor axial forces
is the moment factor applicable to fork restraint at the ends.
3..2 Lateral buckling 3.E .25 Z. Beam dimensions qualifying for simplified analysis using equation (20) or (21) Note 2.
<0 .32 b * t ( E * I .4.y).. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
Calculations of beams not more than 60cm in height may be simplified by substituting equation (20) for equation (19). l
Io + 0. n shall be further multiplied by a factor of 0. or (20) may be known (cf. ( 1 1 .`---
Copyright Deutsches Institut Fur Normung E. + 0. is the distance of the point of transmission of the in-plane lateral load from the centroid (positive in tension). ~ is.
15 When flanges are connected to webs by welding. [5] and [6]).0. Equation (19) applied for beams of doubly symmetrical uniform cross section.. = C * NK~. is equal to n2. Coefficient n allows for the effect of residual stresses and initial deformations on the service load but not the effect of the support conditions (these being allowed for by MKi.V.1 Simplified method of analysis
(313) The analysis for lateral buckling of members pinjointed on both sidesand subject to in-plane lateral loading
--`.4
is ~ the moment factor associated with lateral torsional buckling. For doublysymmetrical cross sections with a web comprising at least 18Yo of the'total area of cross section. ~ with a maximum of 0. while substituting in equation (4 b) k from equation (23). and I sections of monosymmetric or doubly symmetrical cross section.according to first order theory. Np1.
xz * N p l .. -O. The torsional bending load plays a major role.
--`. as ) .d.2 Equivalent member method (314) Analysis The ultimate limit state analysis shall be made applying equation (24) and using the buckling curves specified in subclause 3. If a more detailed analysis is required.
ky=l
ay. Due regard shall be taken. isequal toN
x'Npi. Note. Note 2.0.d
+-I D '
Mpl.2.`-`-`. where & z is equal to -the non-dimensional slenderness
associated with axial force. B M .l if the following applies:
.25 x 2 .
3.3.d.1. exhibiting uniform axial force and not designed for torsion.z for buckling perpendicular to the z-axis.%. taking intoaccount moment diagram My. may be analysed by means of equation (3). but not more than unity.`. Where the maximum moment is zero.equation (3) Note 1 shall be applied instead of equation (24) for the ultimate limit state.3 Lateral torsional buckling (320) Channels and C sections.the design of connections shall be based on the basis of the bending moment according to second order theory. is the uniform equivalent moment factor for lateral buckling taken from column 2 of table 11.shall be analysed for ultimate limit state by means of equation (27):
and the appropriate buckling curve (see table 5). set out in tables 16 and 17 of DIN 18800 Part 1
xM ' Mpl.
+ a (&
.V.4. NK~. d in equation(24) may be multiplied by a factor of 1. for displacement in the moment plane. imperfections being neglected. 3. is a coefficient taking into account moment diagram My and a K .
Item 305 shall be taken into consideration.. M p l . Note 1. Note.
where ay = 0. equations (5) and (6) in item 305 shall be met. Note 2.2) + 3.4.9 where & M .. Note. for example. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
x 2 * 36. Note 4. substituting AK.d
+ An <1
1 . Mp1. assumed as acting at these points.A$ or 0. from column 3 of table 11.
(317) Rigid connections
In the absence of a more rigorous treatment. the moment in the perfectly plastic state.z. Moment factors less than 1 are only to be used for members of uniform cross section whose end support conditions do not permit lateral displacement and which are subjected to constant compression without in-plane lateral loading. with all relevant internal forces and moments and cross section properties and the axial force.`. M . a function of
with V K ~> 1 . rigid connections shall be calculated substituting forthe actual moment. The yield strength of cross sections not in compression shall not be less than that of those in compression.l. A portion of a member not in compression could bea beam connected to columns in compression. is the maximum moment according to first order elastic theory. In addition.
(315) Effect of transverse forces Due account shall be taken of the effect of transverse forces on the design capacity of a cross section. Further information shall be taken from the literature k g . taking into account equivalent imperfections. It shall be calculated as follows:
(319) Movement of supports and temperature effects Any effects of deformations as a result of movement of the supports or variations in temperature shall be taken into consideration when calculating moment M .
x-Npl. 1 5
E a reduction factor from equation (4). of the fact that this analysis does not take account of design torsion. 1 5 Note. VI). This may be achieved by reducing the internal forces and moments in the perfectly plastic state (e. d
ky< 1
.4. z . with relative dimensionsas for those of rolled sections.2.1.. value of unity gives a conservative approximation. the analysis shall be made applying equation (24) to all key cross sections. M ..`. Note 3. particularly in the case of channels and C sections. Calculations mayde simplified by substituting for A n either 0. in members subject to torsional restraint.y. A k.
(318) Portions of members not subjected t o compression The analysis of portions of members which are not themselves subject to compression but which are required to resist moments due to being connected to members in compression shall be by means of equation (26).g.d
but not more than 0.Page 14 DIN 18800 Part 2 in the form of a concentrated or line load and with a maximum moment. d
(316) Non-uniform cross section and
variable axial forces Where cross sections are non-uniform or axial forces variable.
N K ~ is the axial force underthe smallest bifurcation load
associated with buckling perpendicularto the z-axis or with the torsional buckling load. d The following notation applies in addition to that given in subclause 3.d)
Item 123 shall be taken into account when calculating Mpl.`---
Copyright Deutsches Institut Fur Normung E.15jK. xz is a reduction factor from equation (4). Tsections are not covered by the specifications of this subclause.
ky + k..and ßM. ..1
Biaxial bending with or without coexistent axial force
k. .d
M. Moments from in-plane ateral loading
Moments from in-plane lateral loading with end moments
MQ = 1 max M
1 from in-plane lateral
Imax MI
where no alternating moments OCCUI
Imax M I
+ Imin Ml
where alternating moments OCCUI
...V.`.
<. . from equation (4). apl. MY
ßMs
Moment factors.
..y. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.: .DIN 18800 Part 2 Page 15
3...y and ctPl.
for lateral buckling
for lateral torsional buckling
& .. With a ( 2 ß ~. 4) ~ + maximum of 0.44 y
y.5. 8 0. Moment diagram 3 d moments
ßm. are the maximum moments in first order theory (disregarding imperfections).)
Table 11. taking into account moment diagrams My and M. x ) .. . .d
where x = min (xy... . ... . .5
ay = & y
(321) Method of analysis 1
The ultimate limit state analysis shall be made applying equation (28):
N x *Npl.. d
is a reduction factor for the relevant buckling curve.7y
Copyright Deutsches Institut Fur Normung E.=1" Y
ay.66+ 0.8 where ßM. = 0.5
3.:s ..
..44. with a maximum of 1. (Item 123 is not applicable here..`.:.`---
with a minimum of 0. Moment factors
3 Moment factors... . . I 1
MpL z.1)..`-`-`. .
but not below 1
-VKi'
=1 . is a coefficient taking -into account moment diagram My and AK.y It shall be calculated as follows:
Myand M . from column 3 of table 1 1 .z are the moment factors ßM associated with lateral torsional buckling. are plastic shape coefficients associated with moment M y or M .`.
3.subject to axial force shall be analysed for the ultimate limit state by means of equation (30):
Figure 17. k. If there is only one moment. In this method.
N ß m .
is a factor taking into account moment diagram M . k.1 General (401) Buckling perpendicular t o the material axis*) Built-up members having cross sections with one material axis shall be dealt with as solid members as specified in clause 3 when calculating lateral displacement perpendicular to the material axis. and k . Analysis by the equivalent member method assuming solid members is specified for battened members with two chords..z.
Item 314shall be referred to fOrAn. with xy= x .2 and 4. This analysis does not take account of design torsion.`---
k.5 give a conservative approximation.d ky + Mpl.3. . k.2applying by analogy. in the perfectly plastic state. Note 2 .4. the other items of subclause 3. equation (24) shall be substituted for equation (29) where the reduction factor in the plane of bending under consideration is substituted for x . The actual increase in the internal forces and moments in second order theory is accounted for 'by calcuLating the non-dimensional slendernesses AK.
and fim.1). =CY
Myand M .3.
with a maximum of 1. + A n j l (29) x . = c . + ßm. z * M.
3 . x shall be the reduction factor for the plane of bending under consideration.. Built-up member with a cross section having two void axes (y. . being taken from item 320 and item 321
respectively.d where x = r n i n (xy. M y k . with xy < x. equal to unity.3). disregarding item 123. c xy. shall be equal to cy and k .=1 xz
a .3 and 3. Tsections are not covered bythe specifications of this subclause.and z-axes) (example)
*) Axis intersecting with components. (2ßM.. xJ is the reduction factor for the relevant buckling curve. are the moment factors for lateral buckling.`-`-`.. My.. Note. d Mpl.4. shall be equal to unity and k. with x.with both deformations due to moments and those occurring as a result of transverse forces being taken into consideration. the design of each component shall be based on the global analysisofthetotal internal forces and moments present (see subclauses 4.2.
ky and k . Note 2.`.Npi.5. Note 1. shall be equal to unity. and a K .1. Built-up members with cross sections having one material axis (y-axis) (examples)
(403) Cross sections with two void axes The following information applies by analogy to both axes for cross sections with two void axes.overtheeffective lengthsforthe whole structure (cf. [8]).in which built-up members of uniform cross section are dealt with as solid members. 5 . A k. **) Axis between components. Frames may also be analysed on the basis of all of their components.. from line 2 of table 11. 2 Lateral torsional buckling (323) Monosymmetric or doubly symmetrical I sections with relative dimensions as for those of rolled sections. . Note.4.y. .
1 c .4) + (spi.. taking into account moment diagram M yor M .. Note 1...
fim.3.`..
(402) Buckling perpendicular t o the void axis **) Calculation of lateral displacement perpendicular to the void axis may be bythe equivalent method. value of 1. Note 3. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
where a . obtained using equation (4). For compression and design bendthis only applies when there is no design ing moment.z.
Copyright Deutsches Institut Fur Normung E. If equation (28) is applied for bending about one axis and coexistent axial force.
(322) Method of analysis 2 The ultimate limit state analysis by method 2 shall be made using the following equation:
4.V. p It shall be calculated as follows:
k.`.Page 16 DIN 18800 Part 2
--`.z. bending moment M .
are the maximum moments in first order theory (disregarding imperfections).. value taken to be equal to unity and a k .
is design moment M. The literature shall be referred to for information on members with more than two chords [91.8
Other notation is explained in subclauses 3. =
Mpl.yandaK. with a
maximum of 0.
Figure 16. .d
Single-span built-up members
Item 305 shall be taken into consideration.SUbStitUting~KaSSOCiated with x .
The effective length of parts of laced members consisting of four angles shall be taken from table 1 3 .
Copyright Deutsches Institut Fur Normung E. correction for battened members (cf.slenderness ratio of the equivalent member
Note 1.V. with its ends nominally pinned t o prevent lateral displacement will be as follows:
2 ) .`---
order moment of area of the gross cross section about the z-axis (assuming rigid connection of components.Z
4. distance between centroidal axes of chords.1
is the effective length of the part of a chord under maximum stress.I L
Sz*. ) design second order moment of area of the gross cross section of laced members. AG gross area of cross section of chord. providing shear resistance).2 Analysis of member components
4. effective length of equivalent member. Laced and battened members (examples)
Note. disregarding any deformation due to transverse forces.
v.z = .3
Buckling perpendicularto void axis
AK.y. aK.y.d
section modulus of the gross cross section. = AG .
+ 17. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
. relative to the centroidal axis of the outermost chord. [IO]) shall be consulted f o r internal compression and design bending.d
NKi. and h.`..2.`. = -
n-Mz 1
--`. for battened members (disregarding deformations due to transverse forces). 1. = 2 (AG . a length of chord between two nodes. Note 3. shall be obtained as follows:
SK.3. h.`. 4for laced members as shown in columns 4 and 5 of table 1 3 where a is subject to transverse loading.=. in the chord undermaximum stressequal to the following:
NG shall be used for analysis of the part of a chord as specified in subclause 3.
4. Correction. for battened members
N K i . y . equal to unity..
AG ..)d
1 +-s. z.
+ I z .
Figure 18. ~ design ) second order moment of
w. I z .1 Analysis of member (405) Analysis of a member shall be made taking into consideration the conditions of restraint.
I .2.3. AD gross area of cross section of a strut..d
at member end: max V. usuallytaken to be the same as the length of the chord.g.NG.1 Chords of laced and battened members (406) The global analysis of internal forces and moments acting throughout the member not resistant to shear gives an axial force. The internal forces and moments in a member designed to be in axial compression. assuming pin-jointing on both sides. The shear stiffness corresponds to the transverse force resulting in an angle of shear. Examples of shear stiffness of laced and battened members are given in table 1 3 . table 1
at member mid-point:
M z=
Table 1 2 . between nodeS.DIN 18800 Part 2 Page 17
4.. ~ )second
4. The literature (e. The shear stiffness of battened members has been multiplied by the factor n2/12in order to exclude failure of single panels solely due to shear.G second order moment of area of a chord cross section about the centroidal axis parallel to the z-axis.
system length (of built-up member).
sK. d =
( E I. The analysis may be made as specified in subclause 3 .
The slenderness ratio.1. design shear stiffness of the equivalent member.z. Note 2. a.y .
area of the gross cross section of battened members. 4 smallest radius of gyration of one chord.. 1 .`-`-`. number of chords. A = AG gross area of cross section of built-up member.3. Ys distance of the centroid o f each component cross section from the z-axis.
which generally makes use of highly ductile fasteners which must be taken into account.Page 18 DIN 18800 Part 2
4. The total transverse force required when considering a member in axial compression.
In the case of monosymmetric chord cross sections. 1
1. i l .d does not apply to scaffolding. Effectwe lengths sK.3. The moments of resistance.2.*. VG.
m a r Vy a MG = r 2
rnax Vy
4. Vy. The plastic design capacity of the chord cross section as obtained from the interaction equations may be utilized (cf.!.in columns 1and 2 onlyapply to angle-sectioned chords. rnax Vv. Note. Note 2. Further information on ductilityand slip of fasteners and on eccentricityat the connections between web members in laced members is given in the literature (e. the resistance moment. sin2a (m = number of braces normal to void axis)
Lacing systems (38) where
(407) The axial forces of web members making up lacing
systems shall be obtained from the total transverse forces.1 and equivalent shear stiffnesses..occurring in the chords at their connections with battens are of different magnitude owing to their different directions. being calculatI d on the basis of the smallest radius of gyration.3.. Failure of a panel does not occur until all M p ~ .`.NG derived from interaction equation (38). [ 9 ] ) .The effective length shall be taken from subclause 5. values ~ G have been fully utilized (cf.d.sK. [ 9 ] ) .l. Note 1..`. Note 3. M . obtained from the global calculation shall be analysed by verifying the ultimate limit state of a chord subject to the following internal forces and moments:
end moment.3 Analysis of panels of battened members
is the position of the batten on the chord.2.. s.
The effective lengths. in special cases.28 a
Sz. the slenderness ratio.1. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
. Note.`-`-`.
--`.`.9.
Copyright Deutsches Institut Fur Normung E. d = m ( E A& cos a . M. If. at the ends of the part of the chord shall be obtained from the mean of the moments f Mpl.52 a
1. shall be obtained from equation (33). The information relating to Sg. normally being neglected..`---
(408) Panels between two battens The panel between two battens resisting the maximum transverse force. [9] and [lo]). this may be accounted for by increasing the equivalent geometrical imperfections accordingly. transverse force.N~. The moment axes shall also be taken to be parallel to the void axis in the case of angle chords. of laced and battened members 1
Battened members
SK. fasteners are used which are likely to slip.acting in the laced member.ili.the transverse force.V.
DIN 18800 Part 2 Page 19
(409) Battens Battens and their connections shall be designed for shear and the design moments (cf. (412) Cross sections with two void axes Where built-up members as shown in figure 21 consist of main components with a clear spacing not or only slightly greater than the thickness of the gusset. depending on whether lateral displacement in or perpendicular to the plane of the frame is being considered. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.The moments in the centroids of batten connections shall be taken into account.in the connection This also applies for closely spaced built-up battened members as shown in figures 19.V. this only applies when the packing is adequately connected to the gusset.which are connected at intervals equal to 15 il or less apart..20and 21..
Figure 19. apart.A. T
Shear. When determining the area of cross section. consisting of two star-battened angle members need only be checked for lateral displacement perpendicular to the.`. (411) Star-battened angle members Built-up members. same. According to item 503. connections or packing may be calculated fora transverse force equalling 2.`. the radius of gyration. table 14). If packing plates are used to connect the main components in built-up battened members as shown in figures 1 9 and 2 1 .5 are not more than 15 i. of the gross cross section relating to the centroidal axis parallel to the longer leg:
. b) continuous packing plates are used. io. provided that either of the following conditions is satisfied: a) battens or packing plates positioned as specified in subclause 4.5% of the compressive force in the battened member.15
Moment diagram in the connection due to shear.material axis (figure 20) by the following equation:
Table 14. the mean o Angles with a cross section as shown in figure 20 b) may be verified by the following equation. T..
Continuity of packing may be taken into consideration when calculating the second order moment of area..`-`-`.
a) r = 2
b) r = 2
Figure 20.the specifications applying to the built-up members in figure 19 shall be applied by analogy to the two void axes. Star-battened angle members Consecutive battens may be in corresponding or mutually opposed order.4 Closely spaced built-up battened members
(410) Cross sections with one void axis Built-up members with cross sections as shown in figure 19 may also be treated as solid members as set out in clause 3 when calculating lateral displacement normal to the void axis. Note. it is sufficient to design the connection for resistance to the actual shear. Closely-spaced built-up member with two void axes
.`.`---
If the effective lengths of the two members are not the f the two effective lengths shall be used.. Shear may be determined as specified in item 410. the effective lengths of diagonals or verticals in triangulated frames differ.
io =1. Built-up memebers with a void axis and a clear spacing of main components not oronlyslightly greater than the thickness of the gusset Figure 21.
4. Distribution of forces and moments in the battens of battened members 1 Cross section of built-up battened members
Copyright Deutsches Institut Fur Normung E. The shear in the battens.
Non-rigidly connected triangulated frame members for out-of-plane buckling
Effective lengths of frame members designed to resist cornpression 5.5 70 (41)
. of frame members which are rigidly connected using at least two bolts or by welding shall be 0 .
Vertical member held horizontally.1.This also applies to laced members unless cross bracing is used instead.Page 20 DIN 18800 Part 2
4. (502) Analysis of compression members Analysis of compression members shall be as specified in clause 3. if both members are continuous.1. non-rigidly connected at one side
Noie. the analysis for the sway mode of vertical and diagonal members held horizontally by cross beams or transverse members providing non-rigid connection. The effective length can be determined with the aid of figures 36 to 38.1. SK.2.
5.`. The number of panels shall be not less than three. the effective length.due account shall be taken of the fact that the gusset will also function as an end batten or end packing plate.plates or frames. Note 1.. (505) Members with one end allowing lateral dlsplacement and one or two non-rigidly connected ends Where verticals and diagonals in main triangulated frames also act as the columns of sway portal frames.
Vertical member held horizontally.V..`---
(414) Arrangement of battens and packing plates Battened members shall be connected at the ends by battens. the connection between them shall be designed to withstand a force acting in the perpondicu!ar plane equal to 10% of the greater compressive force.4 or 7 . Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.
(507) In-plane effective length The effective length for the sway mode in the plane of the triangulated member shall be assumed to be the system length to the node of the intersecting members.any load eccentricity in individual members may be disregarded if the mean centroidal axis of each cross section coincides with the centroidal axis of the compression chord.and thsirbot-
Copyright Deutsches Institut Fur Normung E. and equation (41) shall be satisfied: a . the rectangular cross-sectional shape shall be retained by means of cross-stiffening.2.5
Structural detailing (413) Retention of cross-sectional shape Where member cross sections have two void axes.. for example.2
Triangulated frame members supported by another triangulated frame member
(506) Connection at intersection At intersections. the use of packing plates being permitted instead for the members shown in figures 19 and 21. Note 2.`-`-`.`.
(508) Out-of-plane effective length The effective length forthe sway mode in the perpendicular plane appropriate to the structural detailing involved may be taken from table 15.1. 9 I for inplane buckling (42) and equal to unity for out-of-plane buckling (43). The other battens shall be spaced as equally apart as possible. Note. The effective length.of triangulated frame members as shown in figure 22 for the sway mode in the perpendicular plane may be determined by means of the diagrams in figure 27. Chords may be held in the perpendicular plane by a road deck. is a function of the structural detailing involved. the effective length in that plane may be determined as for compressive forces which do not always act in the same direction. If built-up members are connected at the same gusset.2 (504) Non-rigidly connected members In the absence of a more rigorous treatment.. S K .Secondary stresses as a result of nodes may be disregarded. ~ . members shall be connected directly or
via a gusset.
5.`.1 General (503) Rigidly connected members In the absence of a more rigorous treatment. non-rigidly connected at both sides Figure 22.1 Triangulated frames
5. Cross-stiffening may take the form of bracing. Where the cross sections of compression chords are nonuniform over their length.
tom chords are in the perpendicular plane.1 General (501) Calculation of forces in triangulated frame members The forces acting in the members making up a triangulated frame may be calculated assuming nominally pinned member ends.
5 Z Continuous compression member
but not less than 0.DIN 18800 Part 2 Page 21 Table 1 5 .5 I
N .5 1
--`._
N-1.. Il vhere -
ir where the following applies:
Dut not less than 0.V. Out-of plane effective lengths of triangulated frame members of uniform cross section in the perpendicular plane
I . 1:
but not less than 0.`.`---
Copyright Deutsches Institut Fur Normung E.`.5 Z
I . Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
..5 1 Nominally pinned compression member
but not less than 0. 1:
but not less than 0.`.
1.. 13 1 + I ..`-`-`..
Note I .50+ 0. equation (47) need only be applied to the lowest storey if the stiffness conditions there are not considerably different from those of the other storeys. Non-dimensional slenderness in bending.2. from table 16.2 Non-sway frames (512) Non-sway braced frames In cases where the frame and the bracing components cooperate to resist in-plane horizontal loads.I
is the bending stiffness.
5.646 AK
. Rigidly connected angles (examples) If one of the two angle legs is rigidly connected at the node. is the frame stiffness with respect to lateral displacement of the points of connection of solid members and of columns forming part of the subframe in the perpendicularplane.5 S.this being the case when equation (45) is met:
members with elastic support at mid-length for the sway mode may be obtained by means of equation (44): (44) where
E * I > 2.1 respectively. Equationsfor calculation of the stiffness of bracing systems and of multistorey frames are given in table 17 and subclause 5.2.`-`-`.`..2
Frames and laterally restrained continuous beams
(509) The out-of-plane effective length of solid truss
5.<3..3
Solid truss members with elastic support at mid-length
5...1 carried o3t using the non-dimensional slenderness in bending.4
Angles used as solid members in triangulated frames
(510) Where angle ends are nominally pinned (e. the effects of eccentricity may be disregarded and the analysis of lateral buckling as specified in subclause 3. Ak.2# = 0.2.2. L is the overall height (see figure 25). If E -1or S varies over a number of storeys.0
n# = 0. Solid member and frame stiffness
5.`. is the storey stiffness.
I may be approximated using equation (46):
Ali Are the width. the lateral displacement at the free end asa result of transverse force is at least ten times that resulting from the bending moment. the effects of eccentricity shall be taken into consideration.this being equal to not less than 4 N I L
E . ¡.Page 22 DIN 18800 Part 2
5.2 may be deemed applicable if the deformations due to axial force of the columns of frames and bracing systems are negligible.L2
where is the system length.
SAusst
Figure 24.their mean may be used. Examples of stiffening elements are wall panels and bracing.V.
O<A. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.`. Table 16. of the bracing system or multistorey frame.`---
fi<3.
Copyright Deutsches Institut Fur Normung E.isat least five times that of the frame.35 + 0.2. Equation (45) ensures that in a cantilever member whose low bending stiffness and storey stiffness remain constant under an evenly distributed load.e. Criteria for calculation of I by means of equation (46) It shall be presumed throughout that for the column of frames the member characteristic is not greater than unity.1.
Figure 25. Note 2.<112
.3.in the storey under consideration. by means of a single bolt).g. is the maximum compressive force acting in the member ( N I or N2).. Sb.SAusst.2. Note.753 AK
aK=il
non-dimensional slenderness of solid
2 5 SRa
system length minimum radius of gyration of angle cross section
By a simplified method.Their stiffness may be taken from table 17.1 Negligible deformations due to axial force
(511) The specifications of subclause 5. and cross-sectional areas Ali and Are of the columns being as shown in figure 25. B. the frame shall be regarded as non-sway provided that the stiffness of the bracing system.1.
1 Calculation by first order elastic theory (519) Global analysis of beam-and-column type frames (regardless of the number of storeys or panels) which are pinned or rigidly connected at their base.e.2 Plane sway frames Note. When analysing beams by means of equation (26).
Bracing system Wall panel (e. The effective lengths required for the above check are given in figure 27.with SAusst equal to zero.1
Sway frames and continuous beams subject to lateral displacement
Negligible deformations due to axial force
(516) Item 5 1 1 shall apply in the cases where the deformations due to axial force are negligible. In the analysis of lateral buckling of non-sway frames as the moment factor. the stiffness S.
NKi. In the above. A simpler method may also be used.3. qo. provided that each storey meets equation ( 5 1 ) .for latspecified in subclause 3. may be designed by first order theory.. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`. eral buckling. shall be obtained by means of equations (52)to (54).g. S may be calculated as specified As a simplified method. Stiffness of bracing systems. The use of bolts or welding for unstiffened beam-tocolumn connections requires due consideration of their structural behaviour and susceptibility to deformations. is the total vertical load transmitted in the storey under consideration.first ordertheory may be applied provided that each storey meets equation (49):
SAusst.`..8/q~i) provided there are no (or virtually no) compressive forces acting in them.d = SAusst.4 Analysis of frames and continuous beams (517) The ultimate limit state analysis of frames and continuous beams may be effected by analysing their main components as specified in clause 3 .. S.`.
E .3.2. shall be as follows.2. d
N.2. Note. d
5.`---
5.3 Design of bracing systems (514) Principle Bracing systems shall be designed by second order theory assuming all horizontal loads and uplift due to imperfections for both stiffening system and frame. In the first storey (where r =l). depending on the conditions of restraint at the column bases: rigidly connected:
SAusst.3
Diagonals (one diagonal effective)
5. is defined by:
If equation (49) is not met. as specified in subclause 2.&. The following general case applies to bracing systems: Figure 26..3 shall be assumed forall columns of frames and the bracing system. (516) Calculation by first order theory In the global analysis by elastic theory.taken from column 2 of table 11 may be used to calculate the moment components from transverse loads on beams.4.
.`-`-`. N -PO) is multiplied by the factor a obtained by means of equation (50).3. Table 1 7 . using the notation and values given in figure 28.`. in item 519. 5.in which the transverse force according to first order theory (including any uplift. ¡. with columns of equal length within a storey and nodes permitting only lateral displacement.DIN 18800 Pari 2 Page 23
(513) Stiffness of beam-and-column type frames The stiffness of beam-and-column type frames.. Stiffness of beam-and-column type frames.2.S .d is the total stiffness of all frame bracing systems in
the storey under consideration. their plastic design capacity combined with their rotation capacityand theirdeformations under service loads.
S=VJp
Note. the maximum bending moment may be reduced by multiplying by the factor ( 1-0. Practical examples are given in [ l l ] .2.
5. the bracing system design shall be based on the transverse force calculated by second order theory. masonry)
G-t-1
5. A sin a * cos'a
Value doubled where bracing sufficiently preloaded
Copyright Deutsches Institut Fur Normung E. being the sum of all vertical loads transmitted in the
rth storey. (515) Imperfections Initial sway imperfections.V.
or c..`.`-`-`.Page 24 DIN 18800 Part 2 Special design situations
Figure 27.`. =
2 11 1s +3 Is 4
c.`---
$--Cu=
c O ..V. =
Rigid c. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.`. (whichever greater)
2 12 15 I+
3 1s 12
Rigid Nominally pinned
qKi=
Division of non-sway frame into subframes with only one column...3
Copyright Deutsches Institut Fur Normung E. SK. for columns of non-sway frames where seam is not greater than 0. q ~ iand . effective length.c o
c .. for application of diagram below
K i + Kë
K6 K s ' i K:"
(Resolution of K3 and K 6 may be freely selected. Diagram to determine the distribution factor..)
(whicheber greater)-
~ ~ \ z E I s
N...for columns of sway frames where . as follows:
l+Storey under consideration
Ca KO
KS. Notation and values for calculation of Special design situations
In all six cases (disregarding a ~ ) :
1+2SK = ß J ! S
c. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`. or c.`---
0. and c .`-`-`...
Figure 28. 3 is not greater than 0
Copyright Deutsches Institut Fur Normung E.2
Beam r 1
er= .V..s
q K i = N =
ißk.C l5
kI-l = .DIN 18800 Part 2 Page 25
Cr+l = .`.`. and effective length.ô
0.. Diagram to determine distribution factor.IK~.6
0. sK.3
For multistorey frames.`. calculate c ..
2. giving a decrease in the principal diagonal terms.2pr N .
--`. to be obtained by means of equation (56).
If an analysis of external horizontal forces by first order theory is already provided. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
. Systems including nominally pinned columns: additional transverse force in a storey. also be obtained by means of equation (55).
Approximate calculation of transverse force in beam-and-column type frames If equation (57) is met by all storeys.. and po N . is the associated angle of rotation in the r t h storey.`. V O(obtained by means of equation (59) and illustrated in figure 30).4 Analysis applying first order plastic hinge theory (526) Beam-and-column type frames Beam-and-column type frames as specified in subclauses 5.
prsloN. (524) Cross sections not in compression Analysis by means of equation (26) for cross sections not in compression need only be made for beams in sway frames where Mpl of ihe beam is less than the total Mpl of the columns meeting the beams.6. E. is the total vertical load transmitted within the r t h storey.q K i .
V.as specified in clause 3.
(521) Transverse force in beam-and-column type frames Where the member characteristic. r may be determined with the aid of figure 29.`. may be analysed according to first order plastic hinge theory provided that initial sway imperfections from subclause 2..
5.3. = v.3. V. the additional term 1. The initial sway imperfections as specified in items 729 and 730 of DIN 18800 Part 1 need not be assumed in addition to VO.
is the transverse force from external horizontal loads in the r t h storey.r = -
pr * Nr
VF p.Ausst.
qKi.. or using figures 36 to 38 in cases where compressive forces are liable to change direction. higher transverse forces in the storey. Where.r
Sr. In first order theory. . equation (58) may be substituted for (56) to obtain V. but using the effective length of the system as a whole. obtained by first order theory. When applying initial sway imperfections at the base or top of columns.3. in certain cases. may . (59) V O= 1(Pi .3 are assumed and the columns in each storey satisfy equation (60). the angles of rotation. examples are given in [ll].d
is the stiffness of any stiffening elements in the r t h storey. N r + 1.2gives a conservative estimation of the design bifurcation load.i) where p0. Note.
Figure 30.2. being unknown.2 Simplified method applying second order theory (520) Method Calculations shall be as in first order theory but assuming an increased transverse force in the storeys as set out in item 521 or 522.p0.
5.H + 90 .
=(VT
+ Co * N I )
vKi.V. by approximation. VO Note.2.r. = V. an increase in the load terms. Note.1. the compressive forces acting on the frame are liable to change direction during buckling.H + 80.d/1.`---
Copyright Deutsches Institut Fur Normung E. Thus calculations are onlyslightly more complex than by first ordertheory.i is as specified in item 205. (525) Systems with nominally pinned columns In global analysis by first order theory.Page 26 DIN 18800 Part 2 nominally pinned:
In the other storeys:
v.. Effective lengths may be determined using figure 29.. N .`... sway systems including nominally pinned columns shall be calculated with an additional equivalent load. the reduced initial sway imperfections p~ specified in items 729 and 730 of DIN 18800 Part 1 shall be taken into account.3.
(60) (611
v. in order to take into account initial sway imperfections. the simplified second order method gives an only slightly different result than the first order method. q ~ i . (see figure 30).29. Note 2. of beam-and-column type frames is less than 1.
Note 1. pr is theangleofrotation ofthecolumnsintherth storey (calculated by the simplified second order theory method).shall be used.2.`-`-`.3.
90from figure 5.with columns having no or virtually no plastic hinge action at their ends. N .d
assumed as being equal to S.N I
where VF is the transverse force in the storey due to external horizontal loads only. this shall be taken into account when calculating the effective lengths of members. of the equilibrium equations.3 Analysis by equivalent member method (523) Global method The ultimate limit state analysis for sway frames may be carried out byanalysing each member separately. 00 is the initial sway imperfection as specified in subclause 2. Alternatively.
N K ~under ..
6 Arches 6.5
Figure 32.The angle of rotation of the column according to the present simplified second order plastic hinge method shall be substituted for qr in equation (56)..3.DIN 18800 Part 2 Page 27 where V r is the transverse force in the storey due to external horizontal loads only. the axial force of the compression chord positioned between two subframes may be averaged to give a constant value. Figure 33 shows buckling coefficients obtained by means of equation (63) for various types of symmetrical arch systems.2 assuming transverse forces in the storey as obtained by means of equation (56). Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
(531) Averaging of compressive force For solid web beams.1 In-plane buckling 6. may be adopted as it stands in plastic hinge theory provided that there are no (or virtually no) hinges at columns.3. Formula for calculating pr for single-storey frames are given in the literature (cf. pr is the angle of rotation of the columns in a storey(ca1culated according to first order plastic hinge theory). elastic support is usually provided by subframes (cf. h. Examples of spring stiffness. Arch axes Note. 5.1 Axial compression
6.1 General (529) Analysis of non-rigidly connected continuous beams may be on the lines of subclause 3. same as the height of the frame columns. Notation used in equation (62)
Z is not the If the height of nominally pinned columns. all of which assume that deformations due to axial forces can be disregarded.
(527) Single-storey frames First order plastic hinge theory may be applied for the frames shown in figure 31 provided that there are no (or virtually no) plastic hinges at their ends and equation (62) is satisfied:
subject to axial compression when considering out-ofplane buckling. Note. Note. N .
5.4.2.3. the vertical loads on the nominally pinned columns shall be multiplied by the factor hll. table for spring stiffness of such frames).
5 . Cd.. 1121). the chord cross section being taken to include the chords plus one fifth of the web.
Simplified calculation according to second order plastic hinge theory (528) The simplified method according to second order elastic theory as specified in subclause 5.
Figure 31.2. In the case of bridges. is the total vertical load transmitted within the r t h storey. 3 Non-rigidly connected continuous beams
5.`.`.1 Arches of uniform cross section (601) Analysis The ultimate limit state analysis shall be made by applying equation ( 3 ) .`. .1. /? is used to calculate the axial force at the springing. of a subframe in trough bridges Trusses and solid web beams with subframes in perpendicular plane & + 1 i -
+-I R * h
where a is equal to 3 or 6 for nominally pinned or rigidly connected bases respectively. N is the total vertical load..3.2. 3 .
Table 18.`---
where sK is the effective length and s half of the beam length.1.V. for calculation of N .3.2 Compression chords with elastic lateral support (530) Trusses and solid web beams The compression chords of trusses or solid web beams may be dealt with as non-rigidly connected continuous beams
--`. the smallest bifurcation load (see equation 64):
I * \2
Copyright Deutsches Institut Fur Normung E.1.`-`-`. This specification may give very conservative results since it covers the whole range of possible plastic hinge configurations.3. N being the value at the springing.. Note.
a. figure 18)
System on which analysis based. d. reduced spring stiffness shall be assumed by calculating the second order moments of area. u and b. I. are second order moments of area of the diagonals and bottom chord with respect to bending perpendicular to the main beam..u
Any areas resistant to bending at member ends shall be deducted from dl. Bottom chord of centre panel only resistant to bending. b .
--`. are second order moments of area of the cross beams at the left and right of the panel with respect to bending of the deck.. Z..1.`. rn. of all inner cross members with only half their values.
Spring stiffness: C d
A+B-2D
Idl. from u1 and u . .`.
I.. Z T ~and ITr are the torsion constants of the adjacent bottom chord members. Spring stiffness of triangulated structures without verticals 1
Typical Warren truss bridges
Subframes in Warren truss bridges
*) Hinge allowing for torsion
Through bridge design on which analysis based (cf..
1u)d ~
h2 .of the bending curve due to buckling of the top chord is less than a half the number of panels. Idr and
If the half-wave coefficient. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
.`-`-`.`---
Copyright Deutsches Institut Fur Normung E. adjacent bottom chords only resistant to torsion.
D =-a. b.l and I..
d 3 .`.V..Page 28 DIN 18800 Part 2 Table 19. and those resistant to torsion. I..
/3. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`... Figure 33. for in-plane buckling of arches loaded in their thrust line (deformations due to axial forces being neglected)
Copyright Deutsches Institut Fur Normung E. for in-plane buckling of arch
Antimetric buckling
Symmetric buckling
Pa: parabola..g. Ke: catenary. hydrostatic pressure) shall be assumed to correspond to the arch form in the case of arches of the parabolic or catenary type but to act linearly in the case of one-centred arches.`. Kr: circle
Loads (e.`-`-`. Buckling coefficients. ß...`.DIN 18800 Part 2
Buckling coefficients.V.`---
taking AK from equation (69). covering the change in direction of the load in lateral buckling. is the in-plane bending stiffness.1. For parabolic arches.`---
Copyright Deutsches Institut Fur Normung E. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
. k is an auxiliary value taken from table 20.. Snap-through buckling loads cannot be determined for arches using this standard. Further details are given in the literature (e.
For one-centred arches. is the angle of the one-centred arch. subject to constant radial loading corresponding to the arch form. is the buckling coefficient taken from table 22.`. for in-plane buckling of parabolic arches with m hangers (relative to the axial force at the springing ( K ) )
(602) Tied arches In the case of tied arches where the ties are connected to the arch by means of hangers. is the radius of gyration of the z-axis at the crown.Page 30 DIN 18800 Part 2
6.and shall be calculated applying the non-linear theory using large deformations.1.2. AK. The ultimate limit state analysis for the columns o f portal frames may be by means of equation (3). Note.2.`. ß.1. [13] and [141).
NK~..g.V. under a uniform vertical load distribution.K is ~ the axial force under the smallest bifurcation
load of a one-centred arch of constant doubly symmetrical cross section with fork restraint.2.`-`-`.
is the buckling coeffcient taken from table 2 1 (assuming loading to correspond to the arch form).greaterthan O but less than n.
--`.2
6.since it is not usuallysufficient to check the section of arch between two hangers. obtained as follows.1.2 Arches with wind bracing and end portal frames (606) The sway mode normal to the arch plane may be calculated by approximation.
E ..1.. using the in-plane slenderness ratio. A is the longitudinal stiffness.
6. it only being necessary to take into account buckling of the portal frames.the ultimate limit state analysis shall be carried out using the full effective length of the arch. Buckling coefficient.. E .1. I .1
6. (603) Snap-through buckling of arches Snap-through buckling will not occur in flat arches provided that equation (65) is satisfied. with both ends of the arch laterally restrained in the perpendicular plane.
Buckling in perpendicular plane Arch beams without lateral restraint between springings (605) The ultimate limit state analysis of arch beams without lateral restraint between springings may be carried out applying equation (3).`.
Note. is the radius of the one-centred arch.2 Non-uniform cross sections (604) The ultimate limit state analysis of arches of nonuniform cross section shall be by second order theory assuming equivalent geometrical imperfections as specified in subclause 6.
q =total load
q H = load component. a k being the angle between the sloping columns of the frame and the beam. by multiplying the averaged hanger length.. Buckling coefficient. Buckling coefficients may be taken from the literature (cf..`-`-`. h.`.`---
0. constant
0. Note 2.`.075
Two-hinged arch Rigidly connected arch
Table 21.50
0. h.59
1. transmitted by hangers
Via columns')
9% + 0. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
. is the radius of gyration of the z-axis of the portal i. shall be assumed to be negative where the deck is on supports.45 9
qst = load component..DIN 18800 Part 2 Page 31 Any transverse loads (such as wind load) shall be checked separatelytaking into account bending moments as set out in item 314. [15]) and figures 36 to 38 which cover loading corresponding to the arch form.s
0..`. as featured in figures 36 to 38 shall be obtained . k
Loading Corresponding to arch form Via hangers
1 1 . Auxiliary value. not just in portai frames of arches. frame column.0... ß.
Deck Figure 35. Braced arches with end portal frames and suspended deck
Copyright Deutsches Institut Fur Normung E.. Buckling coefficient. h is the in-plane height of the column of the portal frame.t -I_ f
J z * *a
Note 1. (at crown)
where ß is the buckling coefficient. h ~by the factor llsin Czk. Table 20. transmitted by columns
deck is fixed t o the arch crown.65
/z.V.
I.2 0.
Figure 38.Page 32 DIN 18800 Part 2
hlh.V..`. Buckling coefficients for portal frames with rigidly connected column bases
hlh. Buckling coefficients for portal frames with columns connected by two beams of equal stiffness
.`-`-`... Buckling coefficients for portal frames with nominally pinned column bases
Figure 37..`.
WO for
cross sections with buckling curve (cf. table 5) b
Form of equivalent geometrical imperfection (sinusoidal or parabolic) a
Three-hinged arch in symmetrical buckling
Two-hinged arch. AK. Note 2..2.a2)2 n2 + a2 ..obtained from equation (75) to determine K .2.(0. to determine K. .2.
is the buckling coefficient.. Static system for laterally restrained arches Table 23. The effective length of arches of uniform cross section with in-plane buckling.
i. SK may be derived from equation (63) in conjunction with figure 33. In-plane equivalent geometrical imperfections in arches
E . l a
6.1 In-plane buckling (607) The in-plane buckling of the arch shall be analysed for ultimate limit state using one of the methods listed in table 1. ß. a is the angle of the arch equal to 2 slr but not less than O or more than TE.47 .`-`-`. with fork restraint
(6103 An approximate ultimate limit state analysis of onecentred arch sections of uniform I cross section may be carried out usingequation (27) and employing the in-plane slenderness ratio.
In figure 39.V.equal to 2 sir but not less than O
or more than TE.13. may be calculated by first order theory without taking into account equivalent imperfections.
G*1 . .
The following applies for arches in compression:
Kt = 2.`. = L G ' IT
One-centred arch sections of uniform
One-centred arches of uniform rectangular or I cross section.2 Out-of-plane buckling 6. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`. assuming equivalent geometrical imperfections from table 23 occurring in the most unfavourabledirection. k
(TE2
where Figure 39.08 k2)' ) o : 1 (
The following applies for arches in tension: 9 58 7/58
.2.1 General (608) The ultimate limit state analysis for out-of-plane buckling of arches may be carried out as specified in subclause 6 .(3+ 0 .2
i cross section. satisfying equation (io).I. Cf. 2 1k ) -
Copyright Deutsches Institut Fur Normung E.. 2 . s
a is the angle of the arch.`.2 In-plane bending about one axis with coexistent axial force
6.iK.6 k + 0.`.4
1. item 201 when applying the elastic-elastic method. I..036+ +10+ k
6. s & =(71) i.
6.`---
+ (700 . equal to where
. three-hinged arch.
+ k)2
.0.2.2. obtained by means of equation (71).3
E . with their chord in tension or compression (609) Laterally restrained arches with the static system as shown in figure 39 may be given a simplified treatment using equation (3)and employing the in-plane slenderness ratio.
ß.2.226. fixed-ended arch in antimetric buckling
.2.DIN 18800 Part 2 Page 33
for calcuJation of the reduction factor
from equation (18) usingAMfrom item ll0.2 to7.`. 3 Design loading of arches
(611) The ultimate limit state analysis shall normally be made by the elastic-elastic method. The resulting effective cross section is taken as the basisforcalculations.. The grenz (blt)values shall be taken from tables 12. Design loading plays a significant role in arches exposed to outdoor conditions due to the possible effect of wind acting transverse to the arch plane.the effect of buckling ofthe individual parts of cross section on member buckling as a whole is taken into account. In the absence of lateral restraint of arches between springings. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`. the loading conditions set out in subclauses 6. Note.6.to be determined as specified in DIN 18800 Part 3 .. shear stresses when analysing plate buckling of thin-walled parts of cross section are so minor that they can be disregarded.
(702) Analysis The ultimate limit state analysis shall be by the elasticelastic or elastic-plastic method. Where there is transfer of loads via hangers or columns.2 to 7.
7 Straight linear members with plane thin-walled parts of cross section
7.TC~
E*I. Plate buckling of individual parts of a cross section usually affects the buckling behaviour of the member
Note.. Out-of-plane equivalent geometrical imperfections o f the arch Form of equivalent geometrical imperfections in horizontal direction (sinusoidal or parabolic) Two-hinged arch. either in or perpendicular to the plane of the arch.2 to 7.an effective width. ¡.`.
7. Hollow sections are considered rectangular where blr is not less than 5 (cf.figure 40)orb'. table 5) a b
I ''-r6'
MK~.`-`-`.d
is the ideal buckling stress in plates due solely to edge stresses t.`.e. Note 2. assuming feasible equivalent geometrical imperfections in addition to the design loads.`---
General rules relating to calculations
Effective cross section (model) In a model of the effective cross section. allowance for the additional effect of shear stresses may be made as set out in DIN 18 800 Part 3... In this case. In subclauses7. b'(cf. The application of plastic hinge theorywill not be possible until its viability is given sufficient practical backing. Note 1. there shall be a plus sign before the root if My results in tension on the inside of the arch. channels.6 are applied.k is sufficient to assume imperfections acting in a single (i. the equivalent imperfections may be taken from table 23 or 24. if they meet the following conditions:
'pi. Equation (78) assumes fork restraint perpendicular to the plane of the arch. Note 1. a2
In equation (78). figure 40). fixed-ended arch
for cross sections with buckling 'curve (cf. which then requires the effect of plate buckling of such parts on the buckling behaviour of the member as a whole to be taken into account when calculating both internal forces and moments and resistances. C sections. Note. three-hinged arch.b.Circular cross sections and T sections are not dealt with. The analysis may take the form of the approximate methods set out in subclauses 7.of the thin-walled part of the cross section.the most unfavourable) direction.
as a whole by causing a reduction in its stiffness and a redistribution of stresses within a cross section to parts exhibiting greater stiffness or less subject to stress.
6 .6.
Copyright Deutsches Institut Fur Normung E.1 General
(701) Field of application This clause shall apply in cases where the grenz (bit)values for individual parts of a cross section are exceeded.2 to 7.Zsections and trapezoidal hollow ribs.6 shall only apply to members of uniform cross section taking the following forms: hollow rectangular sections. it shall be assumed that these retain their design direction in the state of deformation.
If equations (79)and (80) are not met. Note 2.shall be obtained by means of equation (78). doubly symmetric or monosymmetric I sections.
(703) Effect of shear stresses In cases where subclauses 7..Page 34 DIN 18800 Part 2 Table 24.V. 13 and 15 of DIN 18800 Part 1 .
(704) Permitted sections The provisions of subclauses 7. This does not affect the necessity of also taking into account the overall reduction in stiffness of the member.1 and 6. issubstitutedfortheactualwidth.2 are not met. required ~.e.
OD.=M. For convenience.6.4 (elastic-plastic method).. this shall be increased by AWO from table 25. Figure 40 b) shows a reduced cross section in elastic-elastic analysis.e.etc.l6].
(706) Approximate methods The effective cross section is obtained by reducing the zone of tensile bending. For a cross section symmetrical about the axis of bending. A W O
e. y. due to the positive moment and the negative moment are of equal magnitude.
dueto+M
Note 2. and e may also be taken to be equal.
Centroidal shift (examples)
(710) Increase in initial sway imperfections Where members are assumed with an initial swayimperfection PO.
Note.V.k/YM. and assuming that a compressive stress. actual) to the effective cross section shall be taken into account.
M. The diagrams shown in table 25 are onlyexamples of moments. the governing bending moment shall be that resulting in the smaller effective second order moment of area. UD. Note 1.this may be done as specified in items 709 and 710. even though compressive stresses may occur. wo. may be conservatively approximated to fy. Of significance is the occurrence of positive and negative moments... Increase in bow imperfection.2 Note 3 to 3. If the cross section is not symmetrical about the bending axis and both positive and negative bending moments occur. the bending moment as a result of bow imperfections shall be used. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.`. It may prove necessary to examine both directions in the case of monosymmetric cross sections. This approximate method is elaborated in the literature [cf. I’.
a) Gross cross section
(709) Increase in bow imperfection Where members are to be assumed with an initial bow imperfection. ep.This moment shall be assumed to be constant over the length of the member. Accordingly.DIN 18 800 Part 2 Page 35 Table 25. the compressive stress.e. this applying by analogy for elastic-plastic analysis.with the inclusion of practical examples. Effective cross section (example) Note 1.
Figure 41. Provisionsfor the calculation of b’ orb” are made in subclauses 7. Note 2.5 and 7. The zone of tensile bending is not reduced using this approximate method. If the reduced zone of tensile bending is used.I“ to b”. The methods of analysis set out in subclauses 3. cross section properties A’.)íZ if both
Copyright Deutsches Institut Fur Normung E. In the absence of a design bending moment..3 (elastic-elastic method) and 7.`. of the centroid in the transition from the gross (¡.`---
. + e.`-`-`. Iteration may be avoided ’ by also making a conservative approximation of the edge stress ratio. = centroidal shift due to positive moment en= centroidal shifi due to negative moment
(707) Analysis of cross section The analyses shall be of the effective cross section. Thus. subject to the modifications specified in subclauses 7.`.+Ne
b) Reduced effective cross section as a result of buckling of upper flange
Note.5 also apply in principle to members with effective cross sections. all cross section properties of the effective cross section require to be determined. .
(708) Centroidal shift as a result of reduction in cross section The effect of a shift. The reduction in cross section shall be in correlation with the direction of the actual bending moment in the bending compression zone of the member after deformation. and A”.this shall be increased by Apo = (e. e.. are assigned to b’.
?#=O
O>W>-l
0.34 1.8
ends are restrained and moments with different signs are liable to occur here.
= 189800
is the thickness of the thin-walled part of the cross section. 8 1.43
0.578 + 0.7
Note.0.. This is an assumption only.07W2
82 + 1.`.`-`-`.3
Effective width in elastic-elastic method
(711) Stress distribution In the elastic-elastic method.`.`---
7 . Buckling factors.5 I +
0. ep or e .57 . The assumption of support on both sides presupposes that the supporting construction is of adequate stiffness. (see item 709) is equal to zero at this end..`.
=: b.. obtained by means of equation (83):
.0.s
23. but not exceeding b
0.57 ..Page 36 DIN 18800 Part 2 Table 26. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
.22/äp0)
for npo > 0.85
23.21 q + 0.78W 2
0. Note. k
1>q>o
0.6.673
.V. is the non-dimensional slendernessrelating to plate buckling.05 7 .07@ 0.673
7.70.and is not based on actual fact since the actual stress distribution is non-linear.
(712) Determining the effective width The effective width shall be determined by means of equation (81) for cases in which plates (web or flange) are supported on both sides with constant compression and equation (82) for support on only one side.70 1. If one of the ends is nominally pinned. in N/mm2.
is the width of the thin-walled part of the cross section from table 26.21 ?# f 0..
for Apo g 0.57
--`. calculations shall be on the basis of a linear stress distribution in the effective cross section.29 + 9. An additional imperfection is to be assumed as a result of this increase in sway imperfection when the equivalent member method is applied.0.
.1. b > = Q +b .
Effective cross section Figure 42.b . Note 3.04 @ .u is assumed to be less than fy. Where plates are supported on both sides.u
Effective web width with u and y =
. k .`.
<?pio
Effective flange width with u and VI=
. equal to 0. y. in equation (83). but with b 2 b (84) i being between unity and 3.0
-1 < * < l
(Y2. u is the maximum compressive stress according t o second order theory acting at the long edge of the thin-walled part of the cross section.2.
Copyright Deutsches Institut Fur Normung E.3.Coefficients k . if. thin-walled sections) for suitable stiffness of the supporting constructions for plate edges. t2
12 b2 (1 .. Determination of effective cross section of an I section with bending about one axis
7. = Q . The stress distribution shall be calculated on the basis of all internal forces and moments. . can be determined as specified in item 712.The long edge is taken to be an edge of the gross part of the cross section. calculated on the basis of the effective cross section.. and in line with provisions at national and international level. Iteration is usually required for calculation of the effective width.10.DIN 18800 Part 2 Page 37 is the buckling factor from table 26.
bi = kl * t
(713) Resolution of effective width
Resolution of the effective width.subclause 3.shall be as in table 2 7 .being a function of the stress distribution in the effective cross section. shall be obtained thus:
Table 27.1 to 7. the procedure described here has been modified somewhat in (87) Note. Calculation of the e. u.97 + 0.04 q2+ OJ2 I#+ 0. b'. k . and expressed in N/mm2.58
u.. =
5~' *
E . Where u is equal to fy.0. Note 2.2 of the DASt-Richtlinie(DASt Code of practice) 016 Bemessung und konstruktive Gestaltung von Tragwerken aus dünnwandigen kaltgeformten Bauteilen (Design and construction of structures with cold formed. and k2 and resolution of the effective width shall be as in table 28. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.`-`-`.d.. ensuring that ZN¡=N and b = Z b i . y may be calculated on the basis of the gross cross section of the part under consideration. u shall be substituted for fy.`. As a simplification.. Note 1.`.. U ) '
inserting a Poisson's ration. Note 2.u. Reference may be made to.3. kl and k2 values is such that the buckling factor.4
Effective width in elastic-plastic method
(T14) The effective width shall be calculated using one of
equations (85) to (87).03W ) .
-0. the edge stress ratio.d in the analyses specified in subclauses 7.2.k .(OJ6 + 0.12 I# + 0.d. Resolution of effective width
O Q 3
-1 5 * 5 1
= &o
[(0.5.`---
comparison with line 3 of table 1of DIN 18 800 Part 3 and table 12 of DIN 18 800 Part 1in that the factorc is not applied for y equal to O but not greater than 1.42 +0. Note 1.V.06tp)/IpJ
F a>
O CL J WI
0 . npo is equal to Xp from table 1 of DIN 18 800 Part 3.forexample.
5.fy. allowance for the effect of Awo is made by substituting a supplementary term in equation (91). i is the radius of gyration of the gross cross section. to be calculated as set out in item 709.`-`-`. the stress distribution in the web being estimated. I ' .
..2 Analyses by approximate methods 7. . r D and fDare the distance of the compression edge in bending from the centroidal axis of the gross or effective cross section (cf.. Subclause 7 of analysis.2. calculated on the basis of the effective cross section.1 Elastic-elastic analysis (715) The ultimate limit state analysis shall be made taking UD as equal to or less than fy.I ? I j ~O~
2 ?)& 2 -1
k.The long edge is taken to be one of the edges of the gross part of the cross section.`. The method of analysis specified here corresponds in principle to that set out in item 304. is the eccentricity as a result of a reduction in cross-sectional area.d
k. In cases where this alternative method is used.
X'*A'.Page 38 DIN 18800 Pari 2
. determined assuming constant compressive stress over the whole of the effective cross section.V.`. 5 .
7. in some cases.. where UD is the maximum compressive stress at the long edge of the thinwalled part of the cross section. In a manner similar to item 313.1 Axial compression (716) The effective cross section obtained by assuming effective widths in bending for the compression flange and.5
Table 28.. figure 40). The provisions of item 706 may be applied. Note 1. The ultimate limit state analysis shall be made applying equation (89). an analysis shall be made using equation (95) on the basis of another effective area. the term featuring AWOshall be deleted.5.`.5
k2 = 11
H Ea=yc. A'.
7. 2specifies an alternative method Note 2. SK is the effective length.`---
Copyright Deutsches Institut Fur Normung E. I
k ' +'i
but not exceeding unity (90)
(93) (Compression) (94)
I' and A' are the second moment of area and the area of
the effective cross section respectively.56
(717) In addition to the analysis specified in item 716. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
.d (88). for the web shall be taken as a basis. a is a parameter taken from table 4..5. 2 .Ej
12?)&20
kl={
4.No reduction in cross section of the tension flange is to be made. allowance for the effect of AWO being made by inclusion of a bending moment My equal to N e Awo. calculated taking into account the effective second moment of area.
Magnitude and resolution of effective width b"
(CornDression)
for Mpl. [17] and [18]).`-`-`.2 Global analysis (725) Design buckling resistance moment according t o elastic theory When calculating the design buckling resistance moment.3.1 Analysis (722) The ultimate limit state analysis for lateral torsional buckling may be made as specified in clause 3. (727) Elastic-plastic method When calculating as set out in item 110.2.DIN 18800 Part 2 Page 39
_.6.V.5.d shall be substituted for M p l . If the elastic-plastic method is applied.
equation (13).6. A number of buckling factors of whole sections are .
Copyright Deutsches Institut Fur Normung E. Tí for&. item 719) or I" (cf.4 Bending about one axis with coexistent axial force (728) The ultimate limit state analysis shall be made applying equation (27). with subclause 7. (719) Elastic-elastic method The analysis of bending about one axis with coexistent axial force shall be made applying equation (24) but making the following substitutions:
w p i .d in equation (14). red M K ~ shall be calculated on the basis of plate buckling of the individual parts making up the cross section. I ' (cf.5..obtaining i.y.given in the literature (e.1 Analysis of compression chord (724) Analysis of the compression chord shall be as set out in subclause 3.2 applying by analogy.under the smallest bifurcation load in the analysis of lateral torsional buckling according to elastic theory. d for Npl.y. as set out in item 110. Mblshall be substituted and in the analysis using equation (16). When determining the in-plane slenderness ratio.lK. Note.1..d for Mpl.
A%and Note.. respectively. the effective second moment of area.dfor Mpl.d. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`. by means of equation (98) and substituting MPIJ for Mpl.
IZ.d.2 and as for lateral buckling as specified in subclause 7.d
(720) Elastic-plastic method The analysis of bending about one axis with coexistent axial force shall be made applying equation (24) but making the following substitutions:
for Npl.
M ~ i . AK. obtained from equation (97) shall be substituted for Mpl.4.d =
I' 7 ' fy.3. the moment red M Kobtained ~ by approximation by means of equation (99) shall be substituted for M K ~ . is the gross web area. 7. M P 1shall be substituted for Mpl.
M%l.d.
(726) Elastic-elastic method When ca'culating the non-dimensional slenderness in bending. taken from table 26). is the relevant section modulus of the full cross section. shall be obtained from item 712. calculating the resistance axial force as specified in subclause 7.6.d shall be substituted for IL.
Npi. M$shall be obtained by analogy from equation (97) for the effective cross section having the width b . Note.6. 7.g
Nb1.2. equal to unity in
7. M$. x" for x ..2. is the buckling factor (e..3. but with the modifications set out in items 723 to 727.2 Bending about one axis with coexistent axial force (7l8) Analysis The ultimate limit state analysis shall be made applying equation (24).y.6. AM.d. If a more rigorous treatment is preferred.5.on the basis of the cross section with an effective width b". A.5.5
7. applying by analogy provisions of subclause 7. 1191) for an alternative method of analysis.6
7. T K foräK. NKi. ~
for x . Note 2. the properties of the reduced cross section shall be taken into account for calculation of the axial force.3..5.
Note 1.2.6. is the reduced area of the compression chord..d.3
Biaxial bending with or without coexistent axial force (721) The ultimate limit state analysis for biaxial bending with or without coexistent axial force may be made as specified in subclause 3.= p k * Ue *
Biaxial bending with or without coexistent axial force (729) The ultimate limit state analysis may be made using equation (30).
is the reduced second moment of area of the compression chord about the z-axis.! and Mgl. .5.d
w (100) this being the ideal moment relative to plate buckling of the cross section or the relevant part of the cross section. Reference may be made to the literature (cf.`---
.`. Mpl.`. MP1.
7.1 and the resistance bending moment as specified in item 726 (when using the elastic-elastic method) or item 727 (when using the elasticplastic method).2.d
(96) (971
Mpi.d =
A'*fy.d Mpi. When calc!lating the nondimensional slenderness in compression.g.6. but assuming k . These values shall be obtained by analogy with equations (96) and (97) and item 716.g.6.
Bending about one axis without coexistent axial force 7.`..d. Examples of b" are given in table 28. item 720) shall be taken into account.2 Axial compression (723) The calculation of lateral torsional buckling shall be in analogywith subclause 3. x' and & being taken from item 716. d .y In the analysis using equation (16).
Stahlbau. Näherungsweise Bestimmung der Knicklängen und Knicklasten von Rahmen nach ?-DIN 18800 Teil 2 (Approximate determination of effective lengths and buckling loads of frames to draft Standard DIN 18800 Part Z). trapezoidal steel sheeting. J. 1989:58. Palkowski. safety against buckling. dimensions. Düsseldorf: Ernst & Sohn. H. A supplementary design proposition). Statik und Stabilität der Baukonstrukrionen(Static and stability of structures). analysis of safety buckling of shells DIN 18807 Part 1 Trapezoidal sheeting in building. U.. limit deviations and static values DIN 1025 Part 3 Steel sections. Dabrowski. dimensions. Roik. Palkowski. Stahlbau.. trapezoidal steel sheeting. 1984.169-172. 1960:35.`-`-`. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
--`.. overturning and bulging. Rubin. D-5000 Köln 1. hot rolled medium flange I beams (IPE series). 1972. overturning and bulging.Page 40 DIN 18800 Part 2
Steel sections. Ordnung (The method using initial sway imperfections for simplified calculation of non-sway beamand-column type frames by first and second order theory). 2nd ed. mass. construction DIN 18800 Part 1 Structural steelwork. Kindmann. design and construction DIN 18800 Part 3 Structural steelwork. I.. Stahlbau. Part 2.ein ergänzenderBemessungsvorschlag(Biaxial bending and coexistent axial force. Stahlbau. S.173-179.. mass. 1985:54. 265-271.161-172. Stahlbau. S. analysis of safety against buckling of plates DIN 18800 Part 4 Structural steelwork. 467-475. structural analysis and design DASt-Richtlinie O16 Bemessung und konstruktive Gestaltung von Tragwerken aus dünnwandigenkaltgeformten Bauteilen I) DIN
1025 Part 1
ECCS-CECM-EKS. 246-250. dimensions. Petersen. Gietzelt. 1987:56.
Copyright Deutsches Institut Fur Normung E.. Das Ersatzstabverfahren Tragsicherheitsnachweisefür Stabwerke beieinachsiger Biegung und Normalkraft (The equivalent member method: ultimate safety analyses of frames subjected to bending about one axis and coexistent axial force). K.
178-182. symbols and units used in civil engineering. limit deviations and static values DIN 1025 Part 2 Steel sections. limit deviations and DIN 1025Part5 static values Quantities. Zur Anpassung des Stabilitätsnachweises für mehrteilige Druckstäbe an das europäische Nachweiskonzept (Bringing into line stability analyses of built-up compression members with the European concept). Stahlbau. 33. G. 365-373. mass.`---
.. general requirements and determination of loadbearing capacity by calculation DIN 18807 Part 2 Trapezoidal sheeting in building.Ultimate limit state calculation of sway frames with rigid joints. H. 1982:51. 1986. Lindner..`.. J. Gregull. 137-145. limit deviations and static values Steel sections.103-109. Uhlrnann. dimensions. 1982. J. Ebertplatz i . Brussels. 1982. determination of loadbearing capacity by testing DIN 18807 Part 3 Trapezoidal sheeting in building. Rubin. J. J. Lindner. R. W. dimensions. 1989:58. hot rolled wide flange I beams (IPBI series).
Obtainable from Deutscher AusschuB für Stahlbau. Rubin. Stahl im Hochbau (Steel construction). principles DIN 1080Part 1 Structural steelwork. Berlin. R.Zweiachsige Biegung und Längskraft. Roik. Bauingenieur. Biegetorsionsprobleme gerader dünnwandiger Stäbe (Problems with flexural torsion of straight thin-walled linear members). München. Lindner. K. Publication No... limit deviations and static values DIN 1025 Part 4 Steel sections. 1.Düsseldorf: Verlag Stahleisen mbH. 1987:56. Carl. Stabilisierung von Biegeträgem durch Drehbettung . W.`. vol. Chr. design principles DIN 4114Part1 DIN 4114 Part 2 Structural steelwork. safety against buckling. H. 1987:56..Statik und Stabilität von Zweigelenkbögen mit schrägen Hängern und Zugband (Statics and stability of two-hinged tied arches with diagonal hangers). Braunschweig. Vieweg und Sohn. mass. Stabilität von Zweigelenkbögen mit Hängern und Zugband (Stability of two-hinged arches with hangers and ties). Baustatik ebener Stabwerke (Statics of plane frames). T. hot rolled wide flange I beams (IPBv series). Köln: StahlbauVerlag. 1984:59. Stahlbau-Handbuch. Das Drehverschiebungsverfahrenzur vereinfachten Berechnung unverschieblicher Stockwerkrahmen nach Theorie I . Knicksicherheit des Portalrahmens (Safety against buckling of portal frames). Ramm.. 1 4 t h ed. Bauingenieur. 1981:50. Vogel. Lindner. hot rolled narrow flange I beams (I series). Stahlbau. Wiesbaden: Friedr. vol. undII. hot rolled wide flange1 beams (I PB and IB series).`.eine Klarstellung (Stabilization of beams by torsional restraint). Drehbettungswerte für Dachdeckungen mit untergelegter Wärmedämmung (Values of torsional restraint for roof coverings with thermal insulation). Stahlbau.V. trapezoidal steel sheeting. mass..
E 04 B 1/19 E 04 B 1124 GO 1 B 21/00 GO 1 N 3/00
--`. 1986: 55. 5 2 ~ ~DIN : 4114 Part 2: 02. Priebe.
The revision of the content of the DIN 18800 standards series has been accompanied by a redesign of their layout in an attempt to improve their clarity and make them more convenient to use. Provided by IHS under license with DIN No reproduction or networking permitted without license from IHS
. 141-148. 1981. R.`. The stability of flat plates. Bed-Knick-Problem eines Stabes unterDruck und Biegung (The problem of plate-bucklinglbuckling of linear members subject to bending and compression). of plates and of shells now being dealt with in different Parts of DIN 18800. bringing it into line with the current state of the art. W.`-`-`.und Stadtentwicklung des Landes Nordrhein-Westfa\en (Research report issued by the Nordrhein-Westfalen Ministry for Urban and Rural Planning).S. Schrade..52~..
DIN 4114 Part 1: 0 7 . c) The standard has been revised.DIN 18800 Part 2 [16] [17]
[18] 1191
Rubin. Zur Methode der wirksamen Querschnitte bei einachsiger Biegung mit Normalkraft (Effective cross section-method for bending about one axis and coexistent axial force). Forschungsbericht des Ministers für Landes.V..`..`---
Copyright Deutsches Institut Fur Normung E. Stahlbau. 79-86. Bulson. H..
The following amendments have been made to the July1952 edition of DIN 4114 Part 1 and February1953 edition of DIN 4114 Part 2. Schardt.the text is subdivided into smaller ‘items’ each of which contains a piece of self-contained information which can be incorporated into other standards. b) The material has been rearranged. The new layout is based on the type employed by the Deutsche Bundesbahn for its regulations covering construction work while keeping to the rulesformulated in DIN 820. J. a) The number and title of the standard have been changed to bring them into line with the reorganized system of standards on structural steelwork. 1970. Grube.. the resistance to buckling of linear members and frames. P. Bemessungvon Dachplatten und Wandriegeln aus Kaltprofilen (Design of roof plates and wall girders with cold-formed sections)..`. London: Chatto and Windus Ltd. Technische Hochschule Darmstadt (Darmstadt Polytechnic). R.As well as the conventional division into clauses and subclauses.. 1990: 59.. Stahlbau.
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