p-9veze

1

VEZE I NASTAVCI

Presenter

Presentation Notes

This lecture gives generalities about the design of structural joints in building frames. In particular, the concept of semi-rigid design which is now included in Eurocode 3 is introduced as an alternative to the traditional simple and continuous framing.

2

Montažni nastavci

3

Radionički nastavci i veze

4

Različiti tipovi veza u konstrukciji

B A A

C

D

A

A

A

D

C

A

D

Presenter

Presentation Notes

The lecture covers all the structural joints which are usually met in a building frame: beam-to-column joints (A) beam splices (B) column splices (C) column bases (D)

5

Deformabilnost veza grede i stuba

jednostrana veza dvostrana veza

M b2 M b1 M b

Presenter

Presentation Notes

First the sources of deformability of a beam-to-column joint in bending are pointed out, for a single-sided and a double-sided joint configuration respectively: Single-sided joint configuration The bending moment Mb in the beam may be reduced to two statically equivalent forces (one in tension, one in compression) acting in the beam flanges. These forces allow to define: a compression zone beam flange and web in compression column web in compression a tension zone beam web in tension endplate in bending bolts in tension column flange in bending column web in tension a shear zone in the joint. column web panel In each of these zones, deformations take place and finally result in the development of an internal rotation PHI between the axes of the connected members. This is why the behaviour of a joint is usually reflected so a so-called M-PHI deformability curve. Double-sided joint configuration Similar deformations take place at the end of the left and right beams, but the shear deformation in the column web panel strongly depends on the values of Mb1 and Mb2. When these two values are equal, the shear deformation vanishes. In the lecture, sources of deformation are also defined for other structural joints.

6

V wp

V wp

V b1 N b1

M b1

Izvori deformabilnosti

V c1

N c1

M c1

V c2

N c2 M c2

V b1

M b1

N b1

V b1

Konfiguracija veze

Smicanje rebra

Savijanje veze

Presenter

Presentation Notes

In a single-sided beam-to-column joint configuration, two main contributions to the deformation of the joint are defined in Eurocode 3: The deformation of the column web panel in shear; The deformation of the connection in bending. These two contributions differ by the type of loading to which they are subjected.

7

veza

spoj

Desna veza

Lijeva veza Desni spoj

Lijevi spoj

«veza» i «spoj»

Presenter

Presentation Notes

In Eurocode 3, the words JOINT, CONNECTION and SHEARED PANEL corresponds to clear definitions and they should be used in a proper way. In a single-sided joint configuration, one joint and one connection may be identified. In a double-sided joint configuration, two joints, two connections and one sheared panel are defined.

8

Krive deformabilnosti veza

spoj smičuće rebro veza

M b,i

Mb

M b,i

Mb

θ ci M b,i

θ c γ

γi

φ

θc + γ

Mb, Mj

Presenter

Presentation Notes

For sake of simplicity, reference is made in Eurocode 3 to JOINTS, and not to CONNECTIONS AND PANELS. This leads to an easier modelling of the joint behaviour in the frame design analysis and design process. More information on this topic is given in the lecture, but it seems not so useful to enter in such details in the present presentation. So we can just say here that the M-PHI curve which caracterises the joint behaviour is obtained by adding the M-PHI deformation curve of the connection to a M-PHI curve reflecting the the behaviour of the web panel. To derive the latter, approximations have to be done (a “shear” behaviour has to be transformed into a “bending” one) and account is taken of the level of shear forces in the panel.

9

Karakteristika moment-rotacija

Rotaciona krutost Moment nosivosti Kapacitet rotacije

ϕ - relativna rotacija između grede i stuba

M

ϕ

Presenter

Presentation Notes

A joint M-PHI curve is characterised by three main mechanical properties: the rotational stiffness the moment resistance the rotation capacity

10

Klasifikacija veza prema rotacionoj krutosti

krute veze zglobne veze popustljive veze

φ

Presenter

Presentation Notes

In a traditional design, the joints are considered as pinned or rigid. Pinned joints transfer no moment between the connected members but possess a large rotation capacity. Rigid joints allow a full transfer of moments between the connected members without any relative rotation between the members. These two assumptions are extreme ones and are rarely met in practice. Most of the actual joints have an intermediate behaviour: they transfer moments but also deform in rotation, leading to the development of a relative rotation PHI between the connected members.

11

kruta veza zglobna veza popustljiva veza

Modeliranje veza (elastična analiza)

M j

φ φ

M j M j

φ

Presenter

Presentation Notes

In an elastic design procedure, these three categories of joints are modelled as represented on the slide.

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Odnos “presjek nosača - veza"

φ /2 φ /2

φ

M j,Rd M b,Rd

φ EI/L

nosač veza

Sj,ini

Presenter

Presentation Notes

A parallel between between “member sections” and “joints” may be identified. The joints therefore become “real” structural elements, as beams and columns, which influence the frame response. This differs from the traditional design approaches. It has to be understood that the joints may still be considered as rigid or pinned, as before; but besides that, Eurocode 3 offers now, in view of a more economical frame anf joint design (see next slide), an alternative where the joints behave in an intermediate way.

13

Veze u analizi okvira

Modeliranje veza

– Kako fizički predstaviti veze pri analizi okvira

Idealizacija veza

– Kako idealizirati krivu moment-rotacija

Presenter

Presentation Notes

the joint modelling: how to physically represent the joint in the frame analysis the joint idealisation: how to idealise the moment -rotation curve for sake of simplicity

14

Klasifikacija veza prema krutosti

S j,ini

φ Zglobne

popustljive

krute M j

Granice krutosti Početna krutost veza

Presenter

Presentation Notes

Let ’s start with the classification. Eurocode 3 identifies three different classification systems: classification by stiffness classification b strength classification by ductility For what concerns the classification by stiffness, three categories are defined: rigid joints semi-rigid joints pinned joints The classification is carried out by comparing the initial stiffness of the joint (Sj,ini) to stiffness boundaries for rigid and pinned joints. As an example, a joint which possess a high initial stiffness will probably classified as rigid and will later be modelled accordingly.

15

Klasifikacija veza prema nosivosti

M j,Rd Djelimično nosive

Potpuno nosive

zglobne φ

M j

(nosivost veze)

Presenter

Presentation Notes

Now the classification by strength. Three classes are defined in Eurocode 3: full-strength joints partial-strength joints pinned joints Full-strength joints posses a design resistance which is higher than that of the connected members. No plastic hinge should form in these joints. The bending resistance of partial-strength joints is lower than that of the connected members. In pinned joints, the design resistance is quite limited and it is therefore neglected.

16

Klasifikacija veza prema duktilnosti

– krte – djelimično duktilne – duktilne

φ

M j

Presenter

Presentation Notes

Finally the classification by ductility. Brittle joints, semi-brittle joints and ductile joints are identified. This classification is of high importance as soon as plastic frame design is concerned. Eurocode 3 provides the user with some information, but rather limited, on how to evaluate the joint ductility. Recommendations are however available which allow to define, in most of the cases, whether the ductility is sufficient or not for a plastic frame design.

17

Nastavci aksijalno opterećenih štapova

•Pomoću zavrtnjeva •Zavareni (ugaonim ili sučeonim šavovima)

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Proračun montažnih nastavaka štapa Prema sili: • zatezanja (Nt,Ed) ili • pritiska (Nc,Ed).

Prema površini presjeka (statički pokriven nastavak)

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Tri faze proračuna: 1. Kontrola nosivosti oslabljenog presjeka i ojačanje

ako je potrebno (kod zavarenih profila);

2. Proračun podvezica;

3. Proračun zavrtnjeva.

20

Raspodjela sile NEd

ff ,Ed Ed

ww ,Ed Ed Ed f ,Ed

AN NAAN N N 2NA

=

= = −

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Nastavak nožice

Određivanje optd0, ts,min ; Kontrola nosivosti neto presjeka:

y uf ,Ed f ,Rd f f ,net

M 0 M 2

f ,net f f f f ,1 0 ,f t

f ,1

f fN N min( A ; 0.9A )

A A A ( b n d ) t

n broj zavrtnjeva u jednom redu

γ γ≤ =

= − ∆ = − ⋅

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Granična nosivost neto presjeka je mjerodavna kada je slabljenje rupama za: • S235 veće od 10% ( )

• S275 veće od 13% ( )

• S355 veće od 3% ( )

Mjerodavnost loma neto presjeka:

y y ynet M 2

M 0 u u u

f f fA 1 1 1.25 1.3889A 0.9 f 0.9 1.0 f f

γγ

≤ = =

netA 0.907; A 0.10AA

= ∆ ≥

netA 0.888; A 0.13AA

= ∆ ≥

netA 0.967; A 0.03AA

= ∆ ≥

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Smaknut raspored

nc-c - broj zavrtnjeva u cik-cak presjeku

25

Ojačanje nožice kod zavarenih profila

Povećanje debljine Povećanje širine

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Proračun podvezica

•Mjerodavan posljednji red zavrtnjeva uz prekid elementa; •Jednostrane za IPN ili obostrane za IPE, HEA, HEB; •Dimenzije se određuju iz uslova: f ,Ed p,f ,RdN N≤

p,f y p,f ,net up,f ,Rd

M 0 M 2

p,f

p,f ,net

A f 0.9A fN min( ; )

A bruto površina presjeka podveziceA neto površina podvezica

γ γ=

−

−

27

Položaj i dimenzije podvezica na nožicama

28

Proračun broja zavrtnjeva na nožicama

FR,d minimalna proračunska nosivost zavrtnja u smičućem spoju

minFb,Rd minimalna nosivost na pritisak po omotaču rupe nožice i podvezica

f ,Edf

Rd

Nn

F≥

Rd v ,Rd b,Rd

f ,Ed ,serRd v ,Rd b,Rd f

s ,Rd ,ser

Rd s ,Rd b,Rd

Kategorija A : F min(F , minF )N

Kategorija B : F min(F , minF ) ali nF

Kategorija C : F min(F , minF )

=

= ≥

=

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Proračun nastavka rebra

• Kontrola neto presjeka na mjestu veze i ojačanje ako je potrebno (kod zavarenih nosača);

• Dimenzioniranje podvezica (obostrane);

• Određivanje potrebnog broja zavrtnjeva.

30

Kontrola oslabljenog neto presjeka i ojačanje

31

Dimenzioniranje podvezica na rebru

32

Nosivost zavrtnjeva na rebru

FR,d minimalna proračunska nosivost zavrtnja na rebru

Nosivost zavrtnjeva na rebru nije ista kao na nožicama

w ,Edw

Rd

Nn

F≥

33

Kontrola nosivosti čitavog presjeka

Kontrola nosivosti oslabljenog presjeka

Kontrola nosivosti podvezica

Kontrola nosivosti zavrtnjeva

Ed t ,Rd f ,Rd w ,Rd

Ed p,Rd p,f ,Rd p,w ,Rd

Ed Rd f ,Rd w ,Rd

N N N NN N N NN N N N

≤ = +

≤ = +

≤ = +

34

Statički pokriveni nastavci

Bez kompenzacije - valjani

yt ,Ed ,max t ,Rd

M 0

AfN N

γ= =

y ut ,Ed ,max t ,Rd net

M 0 M 2

Af fN N min( ; 0.9A )γ γ

= =

Sa kompenzacijom - zavareni

35

Ojačanje poprečnog presjeka kod statički pokrivenih nastavaka sa kompenzacijom

Nosivost neto presjeka na mjestu nastavka treba da bude veća ili jednaka od nosivosti bruto presjeka izvan nastavka (pojedinačno za nožice i rebro i ukupno za cijeli presjek)

f ,net ,Rd f ,RdN N≥

w ,net ,Rd w ,RdN N≥

net ,Rd RdN N≥

36

Proračun montažnih nastavaka prema sili Nc

• Raspodjela sile na nožicu i rebro vrši se kao kod zategnutih štapova;

• Ne vrši se kontrola oslabljenog presjeka niti njegovo ojačanje;

• Proračunavaju se samo podvezice i potreban broj zavrtnjeva;

• Podvezice se dimenzioniraju prema bruto površini presjeka.

37

Montažni nastavci ugaonika

Sila se dijeli na krake ugaonika prema površini, proračun se vrši posebno za svaki krak.

38

Montažni nastavci sandučastih presjeka

39

Nastavak štapa u zavarenoj izvedbi

40

Montažni nastavci nosača

Izvode se: • pomoću zavrtnjeva (običnih ili visokovrijednih); • u zavarenoj izvedbi (ređe).

Proračun se izvodi: • prema presječnim silama MEd, VEd i NEd; • statički pokriveni nastavci. Položaj montažnih nastavaka se locira izvan područja maksimalnih momenata.

41

Raspodjela sila

Ed

f wf ,Ed Ed w ,Ed Ed

Ed

w f

w fw ,Ed Ed Ed f ,Ed Ed

Moment savijanja M

I IM M M MI I

Transverza lna sila VI I

S SV V V V V 0I IS S

= =

= ≈ = ≈

42

Faze proračuna: • Kontrola nosivosti oslabljenog presjeka i po potrebi

ojačanje;

• Proračun zavrtnjeva;

• Proračun podvezica.

43

Oslabljeni presjek na mjestu nastavka Rupe na zategnutoj nožici mogu da se zanemare ako važi:

U suprotnom, moment nosivosti neto poprečnog presjeka Mu,net,Rd treba da se odredi za odgovarajuću klasu presjeka, na osnovu redukovane površine zategnute nožice:

f yf ,net u

M 2 M 0

A f0.9A fγ γ

≥

u M 0f ,red f ,net f

y M 2

fA 0.9 A Aγγ γ

= ≤

44

Kontrola nosivosti na mjestu slabljenja presjeka

Redukovana površina zategnute nožice: f ,red f f ,red

f ,red

A b tt redukovana debljina

=

−

u ,net ,RdMoment nosivosti M određuje se u skladu sa klaso m presjeka

45

Proračun broja zavrtnjeva

´ ww ,Ed w ,Ed e Ed Ed

IM M M M V eI

= + = +

46

Proračun zavrtnjeva na nožici

f ,Edt ,f ,Ed c ,f ,Ed ´

f ,Ed

´

f

t ,ff

Rd

Rd

MN N

hM moment u nožicama

h za jednostrane nožiceh

h t za obostrane nožice

Nn ( broj zavrtnjeva )

FF min ima lna granična nosivost zavrtnja

= − =

−

= −

=

47

Proračun zavrtnjeva na rebru

(smičući spojevi kategorija A, B ilii C) Opterećenje zavrtnjeva: • smičuća sila VEd (i NEd ) • moment savijanja M´w,Ed

Zavrtnji su uvijek dvosječni. Raspodjela VEd i NEd ravnomjerna na sve zavrtnje. Raspodjela momenta M´w,Ed neravnomjerna, (najopterećeniji zavrtnji su najudaljeniji od težišta veze).

48

max max

max max

visoke h / b 2 proračun prema POLARNOM momentu in erciješiroke h / b 2 proračun prema EKVATORIJALNOM mom entu inercije≤

Postupak proračuna zavisi od geometrije veze (visoke i široke veze).

49

Proračun prema polarnom momentu inercije

50

Sile u zavrtnjima

51

Proračun prema ekvatorijalnom momentu inercije

52

Sile u zavrtnjima

53

Proračun podvezica Provodi se za: zategnutu nožicu pritisnutu nožicu rebro

54

Podvezice na zategnutoj nožici:

p,f ,t y p,f ,t ,net uf ,Ed p,f ,t ,net ,Rd

M 0 M 2

A f A fN N min( ; 0.9 )

γ γ≤ =

Podvezice na pritisnutoj nožici:

p,f ,c yf ,Ed p,f ,c ,Rd

M 0

A fN N

γ≤ =

(Iz praktičnih razloga usvajaju se iste debljine podvezica na obje nožice)

55

Podvezice na rebru

Moraju da zadovolje slijedeća dva uslova:

yEd p,w ,Rd p,w p,w

M 0

yw ,Ed p,w ,Rd p,w p,w

M 0

Ed M 0p

p y

f / 3v V A A površina podvezica na rebru

fM M W W otporni moment podvezica na rebru

( zavisi od klase presjeka )Iz uslova smicanja :

V 3t2h f

γ

γ

γ

≤ = −

≤ = −

≥

56

Statički pokriveni nastavci nosača

Moment nosivosti neto presjeka na mjestu nastavka treba biti veći ili jednak od nosivosti presjeka izvan nastavka (po potrebi ojačanje kod zavarenih nosača. Moment nosivosti podvezica treba biti veći ili jednak od momenta nosivosti presjeka izvan nastavka. Moment nosivosti zavrtnjeva treba biti veći ili jednak od momenta nosivosti presjeka nosača izvan nastavka.

57

Proračun nastavaka u zavarenoj izvedbi

p-9veze

Documents

column joint configuration

joint behaviour

words joint

c2 v b1

wp v wp v b1 n b1

c i c mb

column web panelin

singlesided beam