AASHTO Fig. Different cross-sections of stiffeners 6 7 Bleich 30 w = Y m sin mπx 8 Y m y m 3 3 F sz z F sx x b T c b ηb η 9 σ p F sy y m s 3b 3 4 Fig.

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1 * DOI /j. gyjz06006 EQUIVALENT RIGIDITY OF ONE-SIDE STIFFENERS PLACED IN ARBITRARY POSITION OF STEEL SHEAR WALL Yng Zhng Tong Genshu Zhng Lei. Deprtment of Civil Engineering Zhejing University Hngzhou Chin. The Architecturl Design & Reserch Institute of Zhejing University Co. Ltd Hngzhou 3008 Chin Abstrct It ws nlyzed the buckling of pltes with one-side stiffener in rbitrry position under uniform compression. Anlyses were crried out for the isolted stiffener nd the plte cted by their interctive forces nd they re combined to stisfy the continuity conditions in the longitudinl strins nd the deflections on the connecting line the effect of the free nd wrping torsion nd the sher deformtion in the stiffener were included. The eqution of buckling ws thus obtined. Compring the buckling eqution of plte with double sided stiffener nlytic expression of effective bending stiffness nd twisting stiffness of the one-side stiffener ws obtined the effective width of the plte tking prt in the function of the stiffener ws found. Compring with the results of ANSYS nlysis it ws found tht the nlytic solution hd excellent ccurcy regrdless of the shpe of the stiffener. Using the effective rigidities the one-side stiffened pltes could be nlyzed s if it ws double side stiffened plte. Keywords steel sher wll one-side stiffener torsion equivlent rigidity effective bredth JGJ * woodchuck8@ 63. com Industril Construction Vol. 46 No

Ltd Hngzhou 3008 Chin Abstrct It ws nlyzed the buckling of pltes with one-side stiffener in rbitrry position under uniform compression.

2 AASHTO Fig. Different cross-sections of stiffeners 6 7 Bleich 30 w = Y m sin mπx 8 Y m y m 3 3 F sz z F sx x b T c b ηb η 9 σ p F sy y m s 3b 3 4 Fig. Plte stiffened with one-side stiffener b t 3 Fig. 3 Discrete nlysis of the stiffened pltes h s T. b e b e Timoshenko x

3 4 σ p Q s F sz h ss v s y θ s x F sx F sz F sx = A zm sin mπx = A xm cos mπx A zm A xm 4 Fig. 4 Stiffener nlysis h c F sz b F sz M M P s = A zm mπx m sin π = h ca xm mπx sin mπ = - A xm mπx sin mπ 3 4 4b σ p M 3 = σ p A s w s 5 4 θ s E s I sω - G A s w s z x 4 s J s - σ p A s i s θ s = m x s + F sy h ss w sb w st 6 w s = w sb + w st 6 Timoshenko γ s = w st x 7 γ s Q s 0 Q s = G sa s k s γ s 8 G s k s Q s = A zm mπx cos mπ w st = k sa zm G s A s mπ sin mπx 0 y I s z E s I s w sb x = - M + M + M 3 E s w s = + mπ A zm + h c A xm E s I s - m π σ p A s = k se s I s G s A s mπ 3 mπx m 3 3sin π 7 Timoshenko x ε sx top = P s E s A s ε sx top + w sb x h c 3 θ s F sx θ s = sin mπx Y m 4 y y = ηb y v s = - h ss θ s 5 y 4 v s v E s I sz + σ x 4 p A s θ s s + y x 0 = F sy 6b x y 0 = h ss - h c I sω i s γ s J s I sz z T

+ F sy h ss w sb w st 6 w s = w sb + w st 6 Timoshenko γ s = w st x 7 γ s Q s 0 Q s = G sa s k s γ s 8 G s k s Q s = A zm mπx cos mπ 9 9 8 7 w st = k sa zm G s A s mπ sin mπx 0 y I s z E s I s w sb x

4 m s 4 6 m π = G s J s eff - σ p A s i s + h c h ss θ s 7 F sy = f y sin mπx J s eff = J s + + μ s I sω + I sz h ss m π f y = m π 7b 7c σ p A s h c - m π E s I sz h Y ss m 7d y y = ηb μ s. + μ γ ixy = τ E ixy c E μ x y 5 u F sx i v i F sy u i = ε ix dx 3 Fig. 5 5 Plne stress nlysis of plte σ ix σ iy τ ixy i φ i σ ix σ iy τ ixy = φ i y = φ i x = φ i x y 8 8b 8c φ i 4 φ i x φ i x y + 4 φ i y 4 = 0 9 φ i = Φ i y sin mπx im C im + mπy im Φ i y = A im + mπy B mπy sinh D mπy cosh A im B im C im D im ε ix ε iy γ ixy - ε ix = σ ix - μσ iy E ε iy = σ iy - μσ ix E b v i = ε iy dy 3b y = - b / σ y y = -b / = 0 4 τ xy y = -b / = 0 4b y = b / σ y y = b / = 0 4c τ xy y = b / = 0 4d 3y = ηb σ y y = ηb - σ y y = ηb = - F sy /t 4e τ xy y = ηb - τ xy y = ηb = - F sx /t 4f u y = ηb = u y = ηb 4g v y = ηb = v y = ηb 4h x ε px y = ηb = ζ Et A xmsin mπx λ = mb + ζ mπx Et f y sin ξ 6 + 4ξ 4 δ + 3 ξ 4 + ξ - ξ 3 μ 4δ δ ξ 4 ξ λ π ξ ξ 5 4δ 4 - ξ + 4ξ 3 δ + 4 ξ 3 - ξ 5 - ξ 4 μ 4δ 4 δ ζ = - ξ 3 ξ λ π ξ ξ 4δ δ ζ = - ξ 3 ξ λ π ξ ξ 4δ 4 + 5

5 5 Plne stress nlysis of plte σ ix σ iy τ ixy i φ i σ ix σ iy τ ixy = φ i y = φ i x = φ i x y 8 8b 8c φ i 4 φ i x 4 + 4 φ i x y + 4 φ i y 4 = 0 9 φ i = Φ i y sin mπx 0 9 0 im C im + mπy im Φ i y = A

5 δ δ 3 ξ ξ ξ 3 ξ 4 ξ 5 ξ 6 ξ 6 + 4ξ 4 δ + 3 ξ 3 + ξ - ξ 4 μ 4δ δ ξ 4 ξ λ π ξ ξ 6 4δ 4 - ξ + 4ξ 3 δ 4 ξ 4 - ξ 6 + μ - ξ 3 4δ = sinh λπ - λπ δ = sinh λπ + λπ = cosh λπ + δ 4 = cosh λπ - = + μ ληπsinh ληπ + - μ cosh ληπ = + μ ληπcosh ληπ - sinh ληπ = + μ sinh ληπ = + μ cosh ληπ = + μ ληπcosh ληπ + - μ sinh ληπ = + μ ληπsinh ληπ - cosh ληπ ζ ζ 5 F sy 5 ε px y = ηb = ζ Et A xmsin mπx 6 D 4 w i = - σ p t w i ζ λ 6 x ζ λ 6 Fig. 6 η = /4 η = /6 η = 0 ζ μ = 0. 3 ζ chnge by spect rtio of plte μ = x z w s = w y = ηb 7 ε sx top = ε px y = ηb 7b A xm = - Eth c λ π Y m y = ηb + Etb3 E s A s λπ + b ζ A zm = + E si s eff - σ pa s b λ π 8 λ 4 π 4 b 4 Y m y = ηb 8b Eb c t I s eff = I s + A E s A s + Etb s h c 8c c b c = λπζ b 8d. 4 7 F sz m s Fig Bending nlysis of plte w i i D = Y im w i Et 3 - μ = Y im sin mπx 9 = P i coshβy + Q i sinhβy + M i cosγy + N i sinγy β = mπ 槡 σ p t 槡 D + mπ mπ γ = σ p t 槡槡 D - mπ P i Q i M i N i y M yi 9 30 = - D w i + μ w i 3 y x F pi [ ] = - D 3 w i + - μ 3 w i y 3 x y y = - b 3b w y = -b / = 0 3

ληπ = + μ cosh ληπ = + μ ληπcosh ληπ + - μ sinh ληπ = + μ ληπsinh ληπ - cosh ληπ ζ ζ 5 F sy 5 ε px y = ηb = ζ Et A xmsin mπx 6 D 4 w i = - σ p t w i ζ λ 6 x ζ λ 6 Fig. 6 η = /4 η = /6 η = 0 ζ μ = 0.

6 w y y = -b / = 0 3b y = b / I s eff w y = b / = 0 33 J s eff w I = 0 33b s eff J s eff 8c 7c y y = b / 9 8d b c 3y = ηb w y = ηb = w y = ηb 34 b w = w e = b c = b 37 λπζ y y = ηb 34b y y = ηb λ e = b e /b M y y = ηb - M y y = ηb + m s = 0 34c λ e = 38 F p - F p + F sz = 0 34d λπζ 30 8 λ f K + θ f K + θ f 3 K + θ θ f 4 K = 0 K = tb σ p cr π D θ = + θ = G sj s eff bd f K = 4K E s I s eff bd - K A s btλ f K = λ 槡 K bβκ - K π A s i s + h c h ss bt b K 槡 λ - sinh βb sin γb - bγκ 35 f 3 K = 槡 K - λ K bβκ 3 - bγκ 4 f 4 K = λ bβκ 5 - bγκ 6 bβκ 7 - bγκ 8 κ κ κ 3 κ 4 κ 5 κ 6 κ 7 κ 8 η η = sinh βb sin η γb sin η γb = sinh η βb sinh η βb sin γb = cosh η βb cosh η βb sin γb = sinh βb cos η γb cos η γb = cosh η βb sin η γb = sinh η βb cos η γb = cosh η βb sin η γb = sinh η βb cos η γb = η = η K σ p cr k s = A st s 8 h 60I s - h e h e - h e 4 h e - s eff 35 0 h s - h e h 3 e + 3h 5 e 40 θ θ h c h ss = 0 T k s = A st s h I s - h s b 3 s h s - h e 5 - s eff E θ' = s I s + bd - K A χ h 3 s - 3h s h e + 3h s h e + 3χ h s h 5 e s 36 bt 40b λ θ' = G sj s bd - K π A s tb i s b η = /4 η = /6 η = 0 8 Fig. 8 36b λ e μ = 0. 3 λ e chnge by spect rtio of plte μ = k s k s 9 k s t b s h e h e = A s E /E s b e t + A s h c

btλ f K = λ 槡 K bβκ - K π A s i s + h c h ss bt b K 槡 λ - sinh βb sin γb - bγκ 35 f 3 K = 槡 K - λ K bβκ 3 - bγκ 4 f 4 K = λ bβκ 5 - bγκ 6 bβκ 7 - bγκ 8 κ κ κ 3 κ 4 κ 5 κ 6 κ 7 κ 8 η η = sinh βb sin η

7 k s = A st s h s - h e b 3 s h s - h e 5-6I s eff χ h 3 s - 3h s h e + 3h s h e + 3χ h s h 5 e 40c χ = b s h s - h e + h s - h e χ = b s h s - h e + h s - h e ANSYS ANSYS. ANSYS 00 T t s h s b s η /4 /6 Shell 63 Shell 8 4 Shell 8 E s 0. 3 = E =. 0 5 MP μ s = μ = ANSYS 0. %. K 35 9 K ANSYS 9b ANSYS K ANSYS η = /4 b η = /6 ANSYS ANSYS % 0 T % K ANSYS 0b T K ANSYS K ANSYS b T ANSYS K ANSYS Fig. 9 9 t s /t = Comprison of plte-strip stiffeners t s /t = h s /b s = 3 η = /4 b h s /b s = η = /6 0 Fig. 0 T t s /t = Comprison of T-stiffeners t s /t = 3

ANSYS 00 T t s h s b s η /4 /6 Shell 63 Shell 8 4 Shell 8 E s 0. 3 = E =. 0 5 MP μ s = μ = 60 60 ANSYS 0. %.

8 3 ANSYS 4 t s /t = 0. 8 η = /4 b t s /t = 0. 6 η = /6 Fig. ANSYS h s /b s = Comprison of closed-form Stiffeners h s /b s = ANSYS 4% ANSYS M ANSYS. 9 I sω I sz 0 M η. J J J J JGJ S. D Bleich F. Buckling Strength of Metl Structures M. New York McGrw Hill 95.. J ANSYS M

9 I sω I sz 0 M η. J. 00 7 6 5-3.. J. 03 43 5 37-43. 3. J. 03 43 4-7. 4. J. 03 30 9-9.

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