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Outline_10 - 1.054/1.541 Mechanics and Design of Concrete...

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1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk 1 / 8 1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 10 Torsion, Shear, and Flexure ± Torsion o Stress distribution on a cross section subject to torsion T T Massachusetts Institute of Technology max τ y x x: narrow side y: wide side o Maximum shear stress, max max 2 T x y τη = where η = shape factor, T = torque, , x y = dimensions of the cross section. The shape factor is different for linear and nonlinear cases.
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1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 10 ± Failure mode o Torsion failure of plain concrete occurs suddenly with an inclined tension crack in one of the wider faces, then extending into the narrow faces. Concrete crushing occurs in the opposite wider face. ± Torsional strength, T up , of plain concrete o Several theories have been presented for computing torsional strength of plain concrete including elastic, plastic, and skew bending theories. o Skew bending: T tw T 4 π M b y x Æ T is the applied torque and M , T tw , are the bending and twisting moments, respectively, on the 4 plane. Æ 2 T M = , 2 by = , ( ) 2 2 2 6 32 == yx xy S 2 2 3 2 up up t T T M Sx y σ = , where = ultimate torsion for plain concrete when up T reaches t . Æ 2 3 up t x y T = ( ) '' 0.85 0.85 7.5 6 =≈ = tr cc f ff 2 / 8
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1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 10 Æ 2 '2 ' 62 3 cr c c up xy Tf x y f =⋅ = = T ± Torsional strength contributed by steel o
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This note was uploaded on 11/29/2011 for the course CIVIL 1.018j taught by Professor Markusbuehler during the Fall '08 term at MIT.

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Outline_10 - 1.054/1.541 Mechanics and Design of Concrete...

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