1. 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

2. This morning
Slender columns
Walls
High-strength concrete

3. 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

4. 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

5. Braced columns: effective length factor ½ ≤ k ≤ 1

6. Unbraced columns: effective length factor k ≥ 1

7. Effect of slenderness on column strength

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

9. Moment magnification – the P- effect

10. Moment magnification
For a column in single curvature:

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

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

13. 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

14. Alignment charts to determine k

15. 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

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

17. Nonlinear second-order analysis

18. Linear second order analysis

19. 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

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

21. Moment magnification procedure
Mmax = M0

22. Nonsway versus sway structures
Nonsway if

24. Nonsway frames
Stiffness reduction factor

25. EI

26. Sway frames

27. 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

28. 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

30. Figures copyright  2010 by McGraw-Hill Companies, Inc
Figures copyright  2010 by McGraw-Hill Companies, Inc Avenue of the America New York, NY USA Figures copyright  2011 by American Concrete Institute Country Club Drive Farmington Hills, MI USA Duplication authorized for use with this presentation only.

31. 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,
(785) Fax: (785)

32. Slender columns