Curs 5 ELEMENTE STRUCTURALE SOLICITATE LA RASUCIRE
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1 Curs 5 ELEENTE STRUCTURALE SOLICITATE LA RASUCIRE Rasucirea (torsiunea), ca stare de solicitare nu apare in mod independent, ci in combinatie cu alte solicitari (ex. incovoiere cu rasucire, compresiune +incovoiere+rasucire). In practica se iau masuri constructive pentru a elimina sau reduce efectul de rasucire, nefavorabil in special in cadrul elementelor cu pereti subtiri cu sectiune deschisa. Rasucire libera (cu deplanare libera) Fibrele longitudinale nu sufera alungiri = > in sectiune apar exclusiv tensiuni tangentiale τ. Rasucire impiedecata (cu deplanare impiedecata), Deplanarea sectiunii este impiedecata (prin rezemari si sau legaturi structurale) = > Apar tensiuni normale σ si tangentiale τ 1
2 Elemente cu sectiuni deschise RASUCIRE LIBERA t τ t = (1) It d d z G It 1 3 h t (3) 3 ϕ t θ = = () It α 3 I z = hi ti (4) 3 In calcul de rezistenta se poate lua acoperitor α = 1. tt (4) - > (1) = > τ = (5) 1 3 hi ti 3 Valoarea maxima a lui τ apare in peretele cel mai gros (tmax). Elemente cu sectiune inchisa
3 = T b + T a (6) z a b T = τ ( t a) T a a a = τ ( t b) j j j τ at a = τ b tb = const (7) t t τ a = ; τ b = (8a,b) abt abt a b Formula generala (Bredt) 4A I z = (9) ds t t τ t = - fluxul de forfecare (constant!!) (10) Am Am - aria delimitate de linia mediana a sectiunii. Pentru a se prelua momentul de rasucire (torsiune) conform formulelor, sectiunea dreptunghiulara trebuie sa ramana nedeformata => se prevad diagragme pline sau cu goluri. 3
4 Rasucirea (cu deplanare) impiedecata (Teoria lui Vlasov) materialul este izotrop, omogen, perfect elastic. tensiunile longitudinale din rasucire variaza liniar pe grosimea peretelui. Sectiunea transversala a barei isi pastreaza forma. (masuri constructive) Bibliografie : C.Dalban, s.a. : Constructii cu structuri metalice EDP 1997, Bucuresti P B σ = I S τ = t I - momentul de incovoiere rasucire B bimomentul S - moment static sectorial coordinate sectoriala. 4
5 Verificarea la rasucire conform EN
6 6
7 VERIFICAREA STABILITATII GENERALE A BARELOR INCOVOIATE (flambaj prin incovoiere rasucire) barele incovoiate in raport cu axa de inertie majora, nefixate lateral, isi pot pierde stabilitatea prin incovoiere laterala in raport cu axa de inertie minima si rasucire flambaj prin incovoiere-rasucire. Clamp at root Buckled posit ion Unloaded position Dead eight load applied vertically L Elevation Section Plan z u x y φ omentul aplicat pentru care bara isi pierde stabilitatea prin incovoiere rasucire(instabilitatea generala) se numeste moment critic elastic. 7
8 Pentru bare solicitate la incovoiere pura: cr cr π EI z π EI = ( GI t + (1a) L L EI z Icr L GIt L I z π EI z π = + (1b) Unde: - It constanta de rasucire (Saint Venant) sau momentul de inertie la rasucire - I constanta de rasucire impiedecata (deformare impiedecata) sau momentul de inertie sectorial. - E Iz - rigiditatea la incovoiere - G It - rigiditatea la rasucire libera - E I - rigiditatea la rasucire impiedecata sectiunile inchise au o rezistenta si stabilitate la rasucire mult mai buna decat cele deschise sectiunile deschise cu talpi dezvoltate (dezvoltate pe ambele directii) se comporta mai bine decat cele dezvoltate preponderent pe o directie Ratio of to cr for box cr section Ratio of length to 8
9 14 cr p Ι- Section H - Section 457x15 UB 60 54x54 UC 89 3 W pl(cm ) y(cm 4 ) Ι z(cm 4) Ι J (cm 4 ) 31,5 97,6 (cm 4 ) Ι 54x54 UC x15 UB 60 L L (m) Ι Pentru reprezentarea comportarii unei bare incovoiate care isi pierde stabilitatea prin incovoiere rasucire se adopta un model similar cu cel utilizat pentru flambajul barelor comprimate centric. N λ λ p l 1,0 0,8 c r p l 0,6 0,4 0, St o c k y In t erm ed iat e Slend er 0 0, 0,4 0,6 0,8 1,0 1, 1,4 Rezultatele experimentale arata ca pentru zvelteti relative mici λ 0.4, bara scurta incovoiata nu-si pierde stabilitatea = > se verifica numai d.p.d.v. a rezistentei in domeniul plastic. λ = p l c r barele de lungimi intermediare 0.4 < λ 1. flambeaza in domeniul elastoplastic (cu plasticizari partiale), fiind sensibile la efectul imperfectiunilor. Barele lungi, λ > 1. flambeaza in domeniul elastic, fiind mai putin influentate de imperfectiuni. Relatia generala de verificare: f y = χ β W (1) γ j, Rd pl, y 1 9
10 χ 1 = φ + [ φ λ ] 0.5 φ = + α λ + λ (3) 0.5[1 ( 0.) ] α - factor de imperfectiune pl λ = ; pl f y Wpl cr β - depinde de clasa sectiunii () = (4) Datorita tensiunilor reziduale induse de sudura, barele incovoiate realizate prin sudare se comporta mai slab decat cele laminate. χ Reduction factor 1,0 1,0 0,6 Rolled sections 0,4 Welded beams 0, 0 0,5 1,0 1,5,0 Influenta incarcarii Stare de solicitare la incovoiere pura cu moment defavorabila, in cazul cand bara nu este fixata lateral = > π π EI = EI GI + (5) L cr z t 1 L GIt 4.4 π EI = EI GI + (6) L cr z t 1 L GIt 4.4/π =1.365 = C1 (7) In general : C π EI = EI GI + (8) L 1 cr z t 1 L GIt Slenderness λ constant este cea mai 10
11 = C cr 1 π L EI GJ 1+ π EI L GJ Beam and loads Bending moment C max 1 1,00 1,879 - F F F F Nivelul la care se aplica forta FL 4 FL 8,75 1,365 1,13 = C cr 1 π L EI GJ 1+ π EI L GJ Beam and loads Bending moment C max 1 1,00 1,879 - F FL 4,75 1,365 F F F FL 8 1,13 Conditiile de rezemare similare cu cele de la compresiune pentru flambajul prin incovoiere rasucire 11
12 Verificarea la flambaj prin incovoiere-rasucire, a barelor incovoiate conform EN
13 13
14 14
15 15
16 16
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