RC uckling elastic uckling of initiall ent memer full-plastic ultimate elasto-plastic uckling model cover concrete initial imperfection 1 Fixed-fixed Hinged-hinged x x M M 1
3 1 a π = 1 cos x πx = a sin 1 3. M x = + M = ( + 1) + M ( M x = = + 1 ) ( x) a ( ) π a = 1 cos x ( ) π x = 1 sin 1 cr x 1 / cr 3 a 1 M = 4 1 cr a 1 cr δ ( ) = 5 v Euler s load cr π = λ EI cr πr,σ cr = E 6 A λ 1 λ = λ =.5 3.6 cr 4π EI π EI = cr = u u 1 v 1 v x
ε < ε = φ max ε σ = Eε = Eφ M = σda = Eφ da = EIφ A 7 A εmax ε ε = φ ( h ) φ = ε h 8 ε max = ε ( ε h) = f I( h) = f W M EIφ = EI 9 section modulus ield ending moment φ > φ elasto-plastic stress state 8 ε = φ ( < h ) φ = ε 1 σ = Eε ( ε ε ), σ = ± f ( ) ε > ε 11 φ > φ { } h h σd + f = d f 4 3 M = σ da = A 1 = full plastic stress state plastic section modulus M p = f h 4 f Z 13 < < M p < M < M p f (, M, V ) = σ 14 = da = m f A h M = A σ da = ± f 15 M M p f (, M ) = + 1 = 16 = σda = A d m ( θ + sinθ cosθ ) 17 3
1 M 3 cos 3 A σ da = ± d θ f 6 = 18 17 18 ψ ζ ψ M ζ f (, M ) = + 1 = 19 M p ζ1. ψ.13 M Mp M 3 =, = ± cos θ π Mp f (, M ) = + 1 = m ( θ + sinθ cosθ ) M = δ + M = M σ v M M δ v + M σ max = + = + 1 A W A W σ max = f 5 1 δ f = ep epa + A W 1 cr 3 4 {( 1+ β ) + } {( 1+ β ) + } 3 1 = ep cr cr 4 cr 1 σ {( 1+ β) σ + f } {( 1+ β) σ + f } σ f 4 ep = cr cr 4 cr 4π EI β = aa W cr = π EI β = aa W cr = β = cr < ep = cr cr > ep = M = δ v + M δ 5 6 λz δ v A 1 ( ).13 λ = λ =1 5.13 M = Mp 1 6 4
f f h f f h d W h 6 d 3 3 3 Z h 4 d 6 d f f h f f 5
load-deflection curve of initiall ent memer 5 full-plastic curve 5 a v 1 cr 4π EI π EI δ cr = cr = 5 λz δ v A 1 ( ).13 λ = λ =1 5 4 5 5 6 a a 1 ap 1 Mv = v 1 cr 1 cr 1 cr M δ + M = = ( = M ) 7.13.13.13 Z = δ ( = M) 8 ( ) v v + M = 1 Mp 1 = M p 1 A convex side c c d = 1 M M 9 6
cr ep a v u u u x a x v x v x v = cr crs ep -M relation -M v relation M p M M M p M 7
d dδ u, axial = ε dx AE 1 dδ v dδ u,def = dx dx d δ u, rot d δ u = dδ u,axial + dδ u, def d δu = dδu,axial + dδu,def + dδu, rot δ 1 dδ v σ π dδu = ε + dx δu = v dx dδ u = + δ 3 E 3 31 3 σ π u 1 a δ = + E cr.13 σ π λz u 1 δ = + E A( ) 4π EI π EI cr = cr = 31 λ = λ =1 3 σ average axial stress ε average axial strain 33 34 s σ A 33 s 1 dδ u σ s π ε s dx = + δ v dx E s 34 33 34 35 36 ε s σ s π + E a 1 σs σcr.13 σ s π Z s s 1 σ ε + E ( s ) A σ f f 4π EI π EI σ cr = σ cr = 35 A A λ = λ =1 36 σ E elasto-plastic point CRS cross point 4 E CRS η stress reduction factor η σ σ s, ep σ s, crs σ max σ s, ep η ( η 1) 37 σs, s, crs σ s, ep s, ep s, nax 8
cr ep u s f s,crs s,ep E CRS s,ep s,crs s 9
5 95 η η =1. f s a a E s Model D f s Ma mm a mm 1 16 A 19 95 fixed-fixed 5 5. 3 4 35 B 19 fixed-fixed 5 5. 6 345 C 7 19 95 hinged-hinged 8 fixed-fixed 5 5. 9 5 D 1 19 95 fixed-fixed 5 5. E 13 5. 11 75 1.5 19 95 fixed-fixed 5 14 7.5 1
a - - elasto-plastic point convex side cross point 1 elasto-plastic point cross point - elasto-plastic point cross point - 3 elasto-plastic point cross point - 4-5 - 11
oad(kn) 15 1 D D19 D16 elasto-plastic point D16 D19 D cross point D16 D19 D 5 D D19 D16 5 1 15 5 Axial Displacement(mm) 35 3 Axial Stress(Ma) 5 15 1 D D19 D16 5 elasto-plastic uckling model i-linear model.5.1.15. Axial Strain 1
oad(kn) 15 1 5 345(Ma) 95(Ma) elasto-plastic point 35(Ma) 95(Ma) 345(Ma) cross point 35(Ma) 95(Ma) 345(Ma) 35(Ma) 35 5 1 15 5 Axial Displacement(mm) 3 Axial Stress(Ma) 5 15 1 345(Ma) 95(Ma) 35(Ma) 5 elasto-plastic uckling model i-linear model.5.1.15. Axial Strain 13
oad(kn) 15 1 5 fixed-fixed fixed-fixed elasto-plastic point hinged-hinged fixed-fixed cross point hinged-hinged fixed-fixed hinged-hinged hinged-hinged 5 1 15 5 Axial Displacement(mm) 35 Axial Stress(Ma) 3 5 15 1 5 elasto-plastic uckling model i-linear model fixed-fixed hinged-hinged.5.1.15. Axial Strain 14
oad(kn) 15 1 5(mm) 5(mm) 75(mm) elasto-plastic point 5(mm) 5(mm) 75(mm) cross point 5(mm) 5(mm) 75(mm) 5 5(mm) 5(mm) 75(mm) 5 1 15 5 Axial Displacement(mm) 35 3 Axial Stress(Ma) 5 15 1 5 5(mm) 5(mm) 75(mm) elasto-plastic uckling model i-linear model.5.1.15. Axial Strain 15
.5(mm) 5.(mm) oad(kn) 15 1 5 7.5(mm) elasto-plastic point.5(mm) 5.(mm) 7.5(mm) cross point.5(mm) 5.(mm) 7.5(mm) 5 1 15 5 Axial Displacement(mm) 35 Axial Stress(Ma) 3 5 15 1.5(mm) 5.(mm) 7.5(mm) 5 elasto-plastic uckling model i-linear model.5.1.15. Axial Strain 16
- 1,,, :,, pp. 33-4, 199.5, : 7, 9,,, 1983 3 : 9, 3,,, 1983 17