[ ] ( ) ϕ ε ϕ ε ϕ ε ε ε υ ε υ σ ε ε υ ε υ υ υ σ ⋅ ⋅ + ⋅ + ⋅ = ⋅ + ⋅ - = + ⋅ + ⋅ - ⋅ ⋅ - ⋅ + = 2 sin sin cos 2 1 ) ( ) 1 ( ) 2 1 ( ) 1 ( 2 2 yz xy zz yy yy xx nn yy xx yy zz yy xx zz yy xx zz yy xx xx E E GRAÐEVINSKI FAK8/7(7 69(8ý,/,â7$ 8 5,-(&, OTPORNOST MATERIJALA A F = σ l l l l l l Δ = - Δ + = ) ( ε A E l F l t T l ⋅ ⋅ + ⋅ Δ ⋅ = Δ α ε σ = E u p ε ε υ = [ ] = zz yz xz yz yy xy xz xy xx ij σ τ τ τ σ τ τ τ σ σ [ ] n ij n r r ⋅ = σ ρ [ ] ⋅ = ) , cos( ) , cos( ) , cos( n z n y n x ij nz ny nx σ ρ ρ ρ 2 2 2 nz ny nx n ρ ρ ρ ρ + + = 2 2 n n n n n n σ ρ τ ρ σ - = ⋅ = r r zz yz xz yz yy xy xz xy xx σ τ τ τ σ τ τ τ σ + - - - = s s s z z yz xz yz s y xy xz xy s x σ σ σ σ σ τ τ τ σ σ τ τ τ σ σ 0 0 0 0 0 0 ) ( 3 1 z y x s σ σ σ σ + + ⋅ = ( ) ( ) 2 2 2 1 2 1 2 , 1 4 xy yy xx yy xx τ σ σ σ σ σ ⋅ + - ⋅ ± + ⋅ = yy i yx oi σ σ τ ϕ - = tg ° = + 90 02 01 ϕ ϕ ( ) yy xx xy o σ σ τ ϕ - ⋅ = ⋅ 2 2 tg 3 2 1 σ σ σ σ σ σ + + = + + zz yy xx 3 2 1 σ σ σ ≥ ≥ 4 0 1 ˭ + = ϕ ϕ ( ) ( ) ( ) ( ) ( ) ϕ τ ϕ σ σ σ σ ϕ τ ϕ σ ϕ σ σ ⋅ ⋅ + ⋅ ⋅ - ⋅ + + ⋅ = ⋅ ⋅ + ⋅ + ⋅ = 2 sin 2 cos 2 sin sin cos 2 1 2 1 2 2 xy yy xx yy xx xy yy xx nn ( ) ( ) ( ) ϕ τ ϕ σ σ τ ⋅ ⋅ + ⋅ ⋅ - ⋅ = 2 cos 2 sin 2 1 xy xx yy nt ( ) ) ( 5 . 0 4 2 1 2 2 2 1 12 σ σ τ σ σ τ - ⋅ ± = ⋅ + - ⋅ ± = xy yy xx ) ( 5 . 0 ) ( ) ( 5 . 0 2 1 1 2 1 σ σ ϕ σ σ σ τ + ⋅ = - ⋅ = MAX ( ) ( ) zz yy xx OKT σ σ σ σ σ σ σ + + ⋅ = + + ⋅ = 3 1 3 2 1 3 1 ( ) ( ) ( ) 2 1 3 2 3 2 2 2 1 3 1 σ σ σ σ σ σ τ - + - + - ⋅ = OKT 2 2 OKT OKT OKT τ σ ρ + = t T yy xx zz xx zz yy zz yy xx E zz yy xx Δ ⋅ + + ⋅ - = α σ σ υ σ ε ) ( 1 2 1 2 xy xy xy E G xy γ υ τ τ ε = ⋅ = = + ⋅ zx yz xy G zx yz xy τ ε ⋅ = ⋅ 2 1 ) cos cos cos ( 2 2 2 γ ε β ε α ε ε ⋅ + ⋅ + ⋅ = z y x d ) 1 ( 2 υ + ⋅ = E G V V t z y x T E V Δ = + + = Δ ⋅ ⋅ + + + ⋅ ⋅ - ⋅ = + + = ) ( ) 3 ( ) ( ) 2 1 ( ) ( 3 2 1 1 3 2 1 ε ε ε α σ σ σ υ ε ε ε ε ZAKOVICE i i M ni F n F F n H F V H ρ ρ ⋅ ∑ = = = 2 2 2 y x F F R + = DOP DOP t d R d x R σ σ τ τ ≤ ⋅ = ≤ Π ⋅ ⋅ = 4 2 n = BROJ ZAKOVICA X= REZNOST ZAKOVICA ZAVAR t a l a x F t b F DOP ⋅ = ≤ ⋅ ⋅ = ⋅ = 7 . 0 τ τ σ x=BROJ VAROVA TORZIJA p t p T W M I M MAX r = ⋅ = τ 32 4 D I P ⋅ Π = r I W p p = 16 3 D W p ⋅ Π = l I G M P t ⋅ ⋅ = ϕ ) 1 ( 32 4 4 4 D d D I P - ⋅ Π = ) 1 ( 4 4 3 16 D d D P W - ⋅ = ⋅ Π ρ τ ⋅ = p t I M