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2. Design of Concrete Structure II University of Palestine
بسم الله الرحمن الرحيم
Lecture # 3
Instructor:
Eng. Mazen Alshorafa

3. Design of Concrete Structure II University of Palestine
Page 1
University of Palestine
Columns
According to ACI Code a structural element with a ratio of height-to least lateral dimension exceeding three used primarily to support compressive loads is defined as column. P h b l h b
Instructor:
Eng. Mazen Alshorafa

4. Design of Concrete Structure II University of Palestine
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University of Palestine
Columns
Columns are vertical compression members of a structural frame intended to support the load-carrying beams. They transmit loads from the upper floors to the lower levels and then to the soil through the foundations.
Loads
Sec A-A
Column
Column
Beam
Sec A
Sec A
Main beam
Instructor:
Eng. Mazen Alshorafa

5. Design of Concrete Structure II University of Palestine
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University of Palestine
Columns
Usually columns carry bending moment as well, about one or both axes of the cross section, and the bending action may produce tensile forces over a part of the cross section
The main reinforcement in columns is
longitudinal, parallel to the direction of
the load and consists of bars arranged
in a square, rectangular, or circular
Instructor:
Eng. Mazen Alshorafa

6. Design of Concrete Structure II University of Palestine
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University of Palestine
Types of Columns
1- Form and arrangement of reinforcement
Columns are divided into three types
1- Tied Columns
It is a column in which the longitudinal reinforcement bars are tied together with separate smaller diameter transverse bars (ties) spaced at some interval along the column height. (Figure a)
2- Spirally-Reinforced Columns
It is a column in which the longitudinal bars are arranged in a circle surrounded by a closely spaced continuous spiral. (Figure b)
3- Composite Columns
It is a column made of structural steel shapes or pipes surrounded by or filled by concrete with or without longitudinal reinforcement. (Figure c)
Instructor:
Eng. Mazen Alshorafa

7. Design of Concrete Structure II University of Palestine
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University of Palestine
Types of Columns
Instructor:
Eng. Mazen Alshorafa

8. Design of Concrete Structure II University of Palestine
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University of Palestine
Types of Columns
2- Length of the column in relation to its lateral dimensions.
Columns may be divided into two categories
1- Short Columns, for which the strength is governed by the strength of the materials and the geometry of the cross section
2- Slender columns, for which the strength may be significantly reduced by lateral deflections.
3- Position of the load on the cross-section
Columns can be classified as
1-Concentrically loaded columns, are subjected to axial force only
2-Eccentrically loaded columns, are subjected to moment in addition to the axial force.
Instructor:
Eng. Mazen Alshorafa

9. Design of Concrete Structure II University of Palestine
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University of Palestine
Columns
Behavior of Tied and Spirally-Reinforced Columns
Failure of a tied column
Failure of a spiral column
Deformation
Instructor:
Eng. Mazen Alshorafa

10. Design of Concrete Structure II University of Palestine
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University of Palestine
Columns
Factored Loads and Strength Reduction Factors
Factored Loads
For gravity loads only,
Pu = 1.2 PD+1.6 PL
For dead, live and wind loads,
Pu = 1.2 PD+1.0 PL+1.6 PW
For dead and wind loads,
Pu = 0.9 PD PW or Pu = 1.2 PD PW
For dead, live and earthquake loads,
Pu = 1.2 PD+1.0 PL+1.0 PE
For dead and earthquake loads,
Pu = 0.9 PD PE
Instructor:
Eng. Mazen Alshorafa

11. Design of Concrete Structure II University of Palestine
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University of Palestine
Columns
Strength Reduction Factors
ACI Code specifies Φ values or strength reduction factors for most situations as in the following table
Tension-controlled sections (εt ≥ 0.005)
Compression-controlled sections (εt ≤ 0.002)
Members with spiral reinforcement
Other reinforced members
Strength condition Φ
Instructor:
Eng. Mazen Alshorafa

12. Sway and Nonsway Frames
Design of Concrete Structure II
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University of Palestine
Sway and Nonsway Frames
1- Nonsway Frames (braced)
It is a structural frames whose joints are restrained against lateral displacement by attachment to rigid elements or bracing
According to ACI Code
a column in a structure is nonsway if
Columns
Shear wall
Columns
Brace X
Beams
Beams P M ∆ lc
Instructor:
Eng. Mazen Alshorafa

13. Sway and Nonsway Frames
Design of Concrete Structure II
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University of Palestine
Sway and Nonsway Frames
1- Nonsway Frames (braced)
Moreover, ACI Code assumes a story within a structure is nonsway if:
Where,
Q is the stability index which is the ratio of secondary moment due
to lateral displacement and primary moment,
ΣPu is the total vertical load in the story,
Vu is the story shear in the story under consideration,
Lc is length of column measured center-to center of the joints in the
frame, and
Δ is the first-order relative deflection between the top and bottom
of that story.
Instructor:
Eng. Mazen Alshorafa

14. Sway and Nonsway Frames
Design of Concrete Structure II
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University of Palestine
Sway and Nonsway Frames
2- Sway Frames (Unbraced)
Structural frames, not attached to an effective bracing element, but depend on the bending stiffness of the columns and girders to provide resistance to lateral displacement are called “sway frames”
Instructor:
Eng. Mazen Alshorafa

15. Design of Concrete Structure II University of Palestine
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University of Palestine
Slenderness effect
The slenderness of columns is based on their geometry and on their lateral bracing. As their slenderness increases, their bending stresses increase, and thus buckling may occur.
Several items involved in the calculation of slenderness ratios, these item unsupported column lengths, effective length factors and radii of gyration.
Unsupported lengths (lu)
It is clear distance between floor slabs, beams, or other members capable of providing lateral support as shown in figure.
Instructor:
Eng. Mazen Alshorafa

16. Design of Concrete Structure II University of Palestine
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University of Palestine
Slenderness effect
Effective length factors K
The effective length is the distance between points of zero moment in the column Thus, the effective length factor k, is the ratio of the effective length to the original length of column.
Typical cases illustrating the buckled shape of the column for several end conditions and the corresponding length factor K
Points of inflection
Instructor:
Eng. Mazen Alshorafa

17. Design of Concrete Structure II University of Palestine
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University of Palestine
Slenderness effect
Effective length factors K
For members in a structural frame, the end restraint lies between the hinged and fixed conditions. The actual k value can be estimated from the Jackson and Moreland alignment charts
The effective length factor k is a function of the relative stiffness at each end of the column. In these charts, k is determined as the intersection of a line joining the values of ψ at the two ends of the column. The relative stiffness of the beams and columns at each end of the column ψ is given by the following equation
Instructor:
Eng. Mazen Alshorafa

18. Design of Concrete Structure II University of Palestine
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University of Palestine
Braced frame
Instructor:
Eng. Mazen Alshorafa

19. Design of Concrete Structure II University of Palestine
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University of Palestine
Unbraced frame
Instructor:
Eng. Mazen Alshorafa

20. Design of Concrete Structure II University of Palestine
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University of Palestine
Slenderness effect
Effective length factors K
where,
lc = length of column center-to-center of the joints
lb = length of beam center-to-center of the joints
Ec = modulus of elasticity of column concrete
Eb = modulus of elasticity of beam concrete
Ic =moment of inertia of column cross section about an axis perpendicular to the plane of buckling being considered.
Ib =moment of inertia of beam cross section about an axis perpendicular to the plane of buckling being considered.
Σ indicates a summation of all member stiffness connected to the joint
and lying in the plane in which buckling of the column is being considered
Instructor:
Eng. Mazen Alshorafa

21. Design of Concrete Structure II University of Palestine
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University of Palestine
Slenderness effect
Effective length factors K
Consider the two-story frame shown in Figure. To determine the effective length factor k for column EF
and
For ψ = and for ψ =
ACI Code specifies that for columns in nonsway frames, the effective length factor k should be taken as 1.0 A C B D F E G I H h1 h2 L1 L2
Instructor:
Eng. Mazen Alshorafa

22. Design of Concrete Structure II University of Palestine
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University of Palestine
Slenderness effect
Effective length factors K
To calculate the ψ values it is necessary to use realistic moments of inertia. Usually, the girder will be appreciably cracked on their tensile sides, whereas the columns will probably have only a few cracks.
In the ACI code, it is stated that for determining ψ values for use in evaluating K factors, the rigidity for beams = 0.35 Ig and for columns= 0.7 Ig as follows
Where, Ig is the gross moment of inertia
Instructor:
Eng. Mazen Alshorafa

23. Design of Concrete Structure II University of Palestine
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University of Palestine
Slenderness effect
Effective length factors K
ACI Code provides the following simplified equations for computing the effective length factors for nonsway and sway frame members
For Nonsway frames,
K is the smaller of
Where, ψA and ψB are the values of ψ at the two ends of the column,
ψmin is the smaller of the two values.
Instructor:
Eng. Mazen Alshorafa

24. Design of Concrete Structure II University of Palestine
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University of Palestine
Slenderness effect
Effective length factors K
For Sway frames,
a) Restrained at both end
For ψm > 2.0 ,
For ψm ≥ 2.0 ,
Where, ψm is the average of ψ at the two ends of the column
b) Hinged at one end
Where, ψ is the values at the restrained end of the column
Instructor:
Eng. Mazen Alshorafa

25. The ACI Procedure for Classifying Short and Slender Columns
Design of Concrete Structure II
Page 23
University of Palestine
The ACI Procedure for Classifying Short and Slender Columns
According to ACI Code, columns can be classified as short when their effective slenderness ratios satisfy the following criteria:
For Nonsway frames
For sway frames
Where,
k = effective length factor
lu = unsupported length of member
r = radius of gyration, for rectangular cross sections r = 0.30 h, and
for circular sections, r = 0.25 h
h = column dimension in the direction of bending.
Instructor:
Eng. Mazen Alshorafa

26. The ACI Procedure for Classifying Short and Slender Columns
Design of Concrete Structure II
Page 24
University of Palestine
The ACI Procedure for Classifying Short and Slender Columns
M1 = smaller factored end moment on column, positive if member is
bent single curvature, negative if bent in double curvature.
M2 = larger factored end moment on column, always positive.
[M1/M2] = ratio of moments at two column ends [Range -1 to 1]
Single curvature
Double curvature
Instructor:
Eng. Mazen Alshorafa

27. Chart summarizes the process of column design as per the ACI Code
Design of Concrete Structure II
Page 25
University of Palestine
Chart summarizes the process of column design as per the ACI Code
Non-sway frame
Neglect
Slenderness
[ Short ]
Moment
magnification
[ long ]
Exact P ∆
analysis
Column Design
Instructor:
Eng. Mazen Alshorafa

28. Design of Concrete Structure II University of Palestine
بسم الله الرحمن الرحيم
Example # 1
Instructor:
Eng. Mazen Alshorafa

29. Design of Concrete Structure II University of Palestine
بسم الله الرحمن الرحيم
Example # 1
The frame shown in Figure consists of members with rectangular cross sections, made of the same strength concrete. Considering buckling in the plane of the figure.
Categorize column bc as long or short if the frame is:
Nonsway
Sway
270 kN.m
0.6x0.3
0.6x0.3
4.0 m
0.3x0.35
0.6x0.3
0.6x0.3
400 kN.m
4.5 m
0.3x0.35
9.0 m
7.5 m
Instructor:
Page Ex1-1
Eng. Mazen Alshorafa

30. Design of Concrete Structure II University of Palestine
بسم الله الرحمن الرحيم
Solution
a- Nonsway
For a column to be short,
Lu = =3.40 m
k is conservatively taken as 1.0
Instructor:
Page Ex1-2
Eng. Mazen Alshorafa

31. Design of Concrete Structure II University of Palestine
بسم الله الرحمن الرحيم
Solution
b- Sway
For a column to be short,
Using the appropriate alignment chart, k = 1.21, and
i.e., column is classified as being slender
Instructor:
Page Ex1-3
Eng. Mazen Alshorafa

32. Short axially loaded columns
Design of Concrete Structure II
Page 26
University of Palestine
Short axially loaded columns
For tied reinforced columns
For spirally reinforced columns
Instructor:
Eng. Mazen Alshorafa

33. Page 27 Design of Concrete Structure II University of Palestine
Design Considerations
Maximum and Minimum Reinforcement Ratios
Instructor:
Eng. Mazen Alshorafa