Vietnam Institute for Building Science and Technology (IBST) Building Code Requirements for Structural Concrete (ACI 318M-11) Design of Slender Columns by ACI 318 David Darwin Vietnam Institute for Building Science and Technology (IBST) Hanoi and Ho Chi Minh City December 12-16, 2011

This morning Slender columns Walls High-strength concrete

Slender columns Notation Effective length factors and effect of slenderness on strength Moment magnification ACI design criteria Design procedures Nonlinear second order analysis Linear second order analysis Moment magnification procedure

Notation l, l = column length I = moment of inertia A = area of cross section r = radius of gyration = l, l = column length k = slenderness ratio = kl/r Et = tangential modulus of elasticity

Braced columns: effective length factor ½ ≤ k ≤ 1

Unbraced columns: effective length factor k ≥ 1

Effect of slenderness on column strength

Frames kl(braced) < kl(unbraced) Braced frame Unbraced frame Pc2 << Pc1

Moment magnification – the P- effect

Moment magnification For a column in single curvature:

Moment magnification For a column in double curvature with equal end moments:

Moment magnification More generally, when the end moments are not equal:

ACI design criteria Braced (nonsway): Neglect slenderness when klu/r ≤ 34 – 12M1/M2 ≤ 40 where lu = unsupported length (clear distance) Unbraced (sway): klu/r ≤ 22

Alignment charts to determine k

Alignment charts to determine k  = ratio of (EI/lc) of compression members to (EI/l) of flexural members in a plane at one end of a compression member lc, l = span length of column or flexural member center-to-center of joints

Design procedures Nonlinear second-order analysis Linear second-order analysis Moment magnifier procedure

Nonlinear second-order analysis

Linear second order analysis

Section properties Moments of inertia: Beams 0.35Ig Columns 0.70Ig Walls – uncracked 0.70Ig – cracked 0.35Ig Flat plates and flat slabs 0.25Ig Area 1.0Ag Modulus of elasticity Ec  next slide

Modulus of elasticity Ec For members under sustained lateral load, divide I by (1 + ds), where Sustained load

Moment magnification procedure Mmax = M0

Nonsway versus sway structures Nonsway if

Nonsway frames Stiffness reduction factor

EI

Sway frames

When calculating s k ≥ 1.0 ds is substituted for dns when calculating EI ds is most often = 0 Pu and Pc summed for all columns on floor

Summary Notation Effective length factors and effect of slenderness on strength Moment magnification ACI design criteria Design procedures Nonlinear second order analysis Linear second order analysis Moment magnification procedure

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The University of Kansas David Darwin, Ph.D., P.E. Deane E. Ackers Distinguished Professor Director, Structural Engineering & Materials Laboratory Dept. of Civil, Environmental & Architectural Engineering 2142 Learned Hall Lawrence, Kansas, 66045-7609 (785) 864-3827 Fax: (785) 864-5631 daved@ku.edu

Slender columns