o_06_dcty_dflctn

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 u s y > c s y = 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. ² Yield condition: () 1 1 y y s f E dk = ² Ultimate condition: 1 uu u ca εβ == Æ Ductility = ( ) 1 1 yy s fE a ϕε 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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1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 6 o The defined ductility (ratio) shown above does not give information about effects of a moderate number of cycles nor about the shape of the descending branch in moment-rotation curves. o For doubly reinforced cross section, () 1/2 '' 2 '2 2 d kn d ρ ρρ ⎡⎤ ⎛⎞ =+ + + ⎢⎥ ⎜⎟ ⎝⎠ ⎣⎦ n ys y M Af jd = ' ' 0.85 s c y A fA f a f b = and the curvature ductility ratio factor is given ' 2 2 1 2 ' 0.85 12 us c c y y Ef d nn n d f ϕβ ε ϕ ⎧⎫ ⎪⎪ + + + + ⎨⎬ ⎩⎭ o Effect of axial load on flexural ductility Ductility of unconfined column sections: s A ' s A P = ' ' Given , , ss scy AA Aff b d d’ h c σ 0.85 ' c f distribution 0.85 ' c f distribution c =0.003 y u c 2 / 9
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1.054/1.541 Mechanics and Design of Concrete Structures Spring 2004 Prof. Oral Buyukozturk Outline 6 Curve 1: Combinations of P and M and ϕ h that cause the column to reach u ε (ultimate concrete strain) without confinement Curve 2: Combinations of P and M and h at which the tension steel first reaches the yield strength.
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o_06_dcty_dflctn - 1.054/1.541 Mechanics and Design of...

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