o_06_dcty_dflctn - 1.054/1.541 Mechanics and Design of...

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1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk 1 / 9 Massachusetts Institute of Technology 1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 6 Ductility and Deflections Ductility o Toughness, deformability, energy absorption capacity s A d b y ϕ c ε kd u ε u ϕ s y ε ε > c s y ε ε = o For beams failing in flexure the ductility ratio can be defined as the ratio of the curvature at ultimate moment to the curvature at yield. Yield condition: ( ) 1 1 y y s f E d k ϕ = Ultimate condition: 1 u u u c a ε ε β ϕ = = Æ Ductility = ( ) 1 1 u u y y s d k f E a ϕ ε ϕ β = Æ The ratio gives a measure of the curvature ductility of the cross section. o Ductility characterizes the deformation capacity of members (structures) after yielding, or their ability to dissipate energy. o In general, ductility is a structural property which is governed by fracture and depends on structure size.
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