unit 12 ( reinforced concrete columns )

REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT12/

UNIT 12

REINFORCED CONCRETE COLUMNS

GENERAL OBJECTIVE

To understand the basic definitions used in the design of reinforced concrete

columns.

At the end of this unit you will be able to: -

a) differentiate the following:

i) a column and a wall

ii) braced and unbraced columns

iii) short and slender columns

b) calculate the following:

i) the effective height of columns

ii) the minimum and the maximum longitudinal

reinforcement

iii) minimum size and maximum distance of ties

c) arrange the reinforcement according to BS 8110 requirements.

1

OBJECTIVES

SPECIFIC OBJECTIVES


12.1 Definition

This unit is concerned with the design of reinforced concrete columns. The

function of a column is to act as a vertical support to suspend structural

elements and to transmit building loads from these elements to the foundation.

As it is a structural unit, its strength is the capacity to resist compressive

stresses. Clause 3.8.2, BS8110 defines a column as a vertical load-bearing

member whose greatest lateral dimension is not greater than four times its

least lateral dimension. A structure above these limits would be classed as a

wall. This is simplified as follows;

When h < 4b, the design is classified as a wall

When h > 4b, the design is classified as a column

2

INPUT 1


h and b are the dimensions as shown below;

The minimum size of a column is dependent upon fire resistance, nominal

cover and durability requirements. This is given in Table 3.4 Part 1 of

BS8110.

3

h=longer side

b=shorter side

Figure 12.1: Column Dimensions


Classify the given figures whether it is a column or a wall

12.1

12.2

4

3000 mm

500 mm

ACTIVITY 12a


PLEASE CHECK YOUR ANSWERS

12.1 b = 700 mm, h = 3000 mm

4b = 4 x 500 = 2000 mm

Since h = 3000 mm > 4b, it is a wall.

12.2 b = 200 mm, 4b = 800mm

h = 500 mm

Since h < 4b, therefore it is a column.

5

500 mm

200 mm

FEEDBACK 12a


12.3 Braced and Unbraced Columns

A column is classified in relation to the type of force, which may be applied to

it. Earlier we assumed that all loads are applied vertically to a column.

However, horizontal forces such as wind forces when applied to a column will

also cause deflection. The result is that the load is no longer applied axially

throughout the length of the column. Therefore, it is important that when

designing reinforced concrete columns to define whether or not a column may

be classed as braced or unbraced column. The following points should be

taken into account:

a) If vertical supports consist of columns alone the effects of a horizontal

force will be able to deflect all columns sideways. This is termed as an

unbraced column in which the stiffness of the column is assumed to

resist lateral movement.

6

INPUT 2


b) If other structural elements such as shear walls, diagonal bracing, etc

provide a considerable greater resistance to horizontal forces, then the

column is termed braced.

The difference between the braced and unbraced column is stated in clause

3.8.1.5.of BS 8110. Please refer to this clause for your clarification.

12.4 Short and slender columns

The strength of a column could be stated in terms of the ultimate strength in

compression and on facts for a very short column This is true. However, the

ultimate strength of a column depends upon the tendency of the member to

buckle under load, i.e. the slenderness of the column.

According to clause 3.8.1.3 of BS 8110, a column is considered as short when

both the ratios and is less than 15 (for braced column) and less than 10

(for unbraced column). Above these limits, a column is considered as slender.

and are the effective height of columns, with respect to the x and y axis.

The x and y axis are indicated in figure 12.2 on the next page.

7


At the design stage, h is taken as the dimension parallel to the direction of

bending irrespective whether it is the greater or smaller dimension. b is the

other dimension of the column.

8

xx

y

h

b

y

Figure 12.2: Short and slender columns


Answer the following questions by filling in the blanks with the correct

answers.

12.3 Reinforced concrete columns, which depend on their stiffness to resist

deflection, are termed as __________________ columns.

12.4 Columns in which the lateral stability is provided by walls or bracing

are considered as __________________ columns.

12.5 Short column fails through ___________________________.

12.6 Slender column fails through _________________________.

12.7 A braced column is considered as short when both the ratios and

are less than _______________________________.

9

ACTIVITY 12b


Check your answers here:

12.3 unbraced

12.4 braced

12.5 crushing

12.6 deflection

12.7 15

10

FEEDBACK 12b


12.8 Effective Height of Columns

The height of deflection or buckling of column is affected by its end restraint.

This height is called the effective height and is calculated using equation 30 of

BS 8110. This is given below;

Where = effective height of column

β = effective height coefficient (From

Table 3.21, BS 8110 for braced column and Table 3.22 for

unbraced column)

= clear height between end restraints.

Values of β are dependent upon the end conditions (restraints) and are

explained in the following notes.

11

INPUT 3


12.9 End Conditions

The degree of restraint afforded at the ends of the columns is classified into

four types. They are as follows;

12.2 Condition 1

Braced columns are properly restrained in direction at both ends and are

jointed monolithically together. The depth of the beam should at least be equal

to the column’s dimension in the plane considered. The joint between the

column and foundation is designed to carry bending moments. Figure 12.3

explains condition 1 diagrammatically;

12

Designed for moments

hb ≥ hc

hb ≥ hc

hc

hc

Note :hb = beam overall depthhs = slab thicknesshc = column dimensions

Figure 12.3: Braced columns at condition 1


12.3 Condition 2

There are beams monolithically joined to both sides at the end of a beam

column. The depth of the beam is less than the column’s dimension in the

plane considered. This is a braced column imperfectly restrained in direction

at one or both ends. This is shown in figure 12.4.

12.4 Condition 3

Unbraced or partially braced columns is properly restrained in direction at one

end but imperfectly restrained in direction at the other end. The adjoining

elements provide only nominal restraint. An example of this is a beam

designed and detailed as simply supported beam. For the junction between the

13

hb < hc or hs < hc

hc

hb < hc

Note :hb = beam overall depthhs = slab thicknesshc = column dimensions

Figure 12.4: Braced column at condition 2


column and the foundation, it is not designed to carry bending moments.

Figure 12.5 shows this condition;

12.5 Condition 4

The end of the column is not restrained from lateral movements and torsion.

An example of this is the free end of a cantilever column of an unbraced

structure. This is shown in Figure 12.6.

14

Joint not designed for moments

Simply supported beam

Figure 12.5: Braced column at condition 3


However, BS 8110 only specifies the end condition where there are beams on

both sides of the column in a given plane. When there is one beam on one side

of the column, the effective height of the column is obtained using equation 3

to 6, Part2 of the code.

12.10 Main Reinforcement (longitudinal reinforcement)

Table 3.27 of BS 8110 gives the requirements for minimum percentages of

reinforcement to be provided in a column. For a rectangular column, the

minimum to be provided is 0.4 %bh for both steel grades (fy = 250 N/mm2 & fy

= 460 N/mm2). Minimums of four bars are provided and the minimum

diameter is 12 mm for a rectangular column. For a circular column, the

minimum number of bars is 6 .

The maximum area of longitudinal reinforcement is 6 % for vertically cast

column, 8% for horizontally cast and 10% at laps. These requirements are

stated in Clause 3.12.6.2 of the code.

15

Free end

Figure 12.6 Braced column at condition 4


12.11 Ties or Links

The minimum diameter of ties is one quarter of the biggest longitudinal bar in

diameter but not smaller than 6 mm. The maximum distance is 12 times the

smallest longitudinal bar diameter. These requirements are stated in clause

3.12.7.1 of the code.

Every corner and alternate bar should be restrained by a link passing round the

bar. All other bars should be within 150 mm of a restrained bar. These

requirements are stated in clause 3.12.7.2 of the code. This is shown in figure

12.7 below;

16

x

x

θ

X < 150 mm θ < 135◦

ACTIVITY 12c

Figure 12.7: Arrangement of links for containment of beam’s or columns compressive reinforcement.


Answer the following questions;

12.8 Write down the equation that is used to calculate the effective height of

a column.

12.9 What is Table 3.21 used for?

12.10 What is meant by “end conditions”?

12.11 How many types of end conditions are there?

12.12 If b = 250mm and h = 250 mm, what is the minimum area of

longitudinal reinforcement?

12.13 What is the maximum area of longitudinal reinforcement of the column

in question 5?

12.14 What is the minimum size of link to be provided in column in question

5, if 4T20 are used as the main bars?

12.15 What is the maximum distance of the link in question 7?

12.16 What is the maximum angle contained by ties?

12.17 What is the maximum distance that a bar should be within a restrained

bar?

17

FEEDBACK 12c


Now, check the answers together:

12.8

12.9 Table 3.21 is used to determine the values of β.

12.10 End conditions mean the degree of restraint that is present at

the ends of columns.

12.11 4 types

12.12 Minimum area of reinforcement = 0.4%bh

=

= 250 mm 2

12.13 Maximum area of reinforcement = 6% bh

=

= 3,750 mm 2

12.14 Minimum size of link

=

= 5 mm (must not be smaller than 6 mm.)

Suitable link is 6 mm diameter.

12.15 Maximum distance of link = 12 x 20

= 240 mm centres.

12.16 135 º

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12.17 150 mm

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SUMMARY


1. A column is considered braced in a given plane if walls or other

suitable bracing to resist all lateral forces in that plane provides

the lateral stability to the structure as a whole.

2. A column is considered unbraced in a given plane when the

column provides lateral stability in that plane.

3. Failure of a column is due to buckling rather than pure

compression.

4. The effective height is a convenient method for dealing with

buckling.

5. The effective height can be found from clause 3.8.1.6 of BS

8110.

6. The minimum percentage area of reinforcement in a column is

0.4% of the column size.

7. The maximum percentage areas of reinforcement in a column

are 6% and 8% for vertically cast and horizontally cast columns

respectively with 10% at laps for both columns.

8. Links or ties should be at least be one quarter the size of the

largest compression bar or 6mm, whichever is the greater.

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9. The maximum spacing of links is 12 times the smallest

compression bar.

10. Every corner bar and each alternate bar should be supported by

a link passing round the bar and having an angle of not more

than 135◦

11. There should be no bars further than 150 mm from a restrained

bar.

21

SELF-ASSESSMENT


There are 20 questions. Answer all the questions by circling the correct

answers. Please read the questions carefully before you answer them. Good

Luck!

1. If b and h are the width and overall depth of a section respectively, it

can be designed as a column when …

A. h = 4b

B. h < 4b

C. h > 4b

D. h < 6b

2. A braced column is said to be short if the effective height to the least

side ratio is less than…

A. 20

B. 15

C. 12

D. 10

3. An unbraced column is said to be slender if the effective height to the

least side ratio is less than…

A. 20

B. 15

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C. 12

D. 10

4. When walls provide the lateral stability of a structure or bracing, the

column of the structure can be categorised as…

A. short

B. slender

C. braced

D. unbraced

5. Which of the following equations represent the effective height of a

column?

A.

B.

C.

D.

6. The end of a cantilever column can be categorised as…

A. condition 1

B. condition 2

C. condition 3

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D. condition 4

7. In a monolithic connection between a beam and a column, when the

depth of the beam is greater than the overall dimension of a column,

what is the end condition?

A. Condition 1

B. Condition 2

C. Condition 3

D. Condition 4

8. The minimum percentage area of reinforcement in a reinforced

concrete column is…

A. 0.2 %

B. 0.4%

C. 0.13%

D. 0.15%

9. The maximum percentage area of reinforcement in a horizontally cast

reinforced concrete column is…

A. 6%

B. 8%

C. 10%

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D. 4%

10. The minimum number of main steel bars in a rectangular reinforced

concrete column must be…

A. 2

B. 4

C. 6

D. 8

11. The minimum number of main steel bars in a reinforced concrete

circular column must be…

A. 2

B. 4

C. 6

D. 8

12. The minimum size of main reinforcement in reinforced concrete

column is…

A. 8mm

B. 12mm

C. 16mm

D. 20mm

25


13. The maximum spacing of longitudinal bars without a bend around

alternate bars in reinforced concrete column is…

A. 150 mm

B. 100 mm

C. 75 mm

D. nil as there is no such limitation

14. What is the minimum size of ties suitable for a column reinforced with

4T32 longitudinal bars?

A. 6 mm

B. 8 mm

C. 10 mm

D. 12 mm

15. What is the maximum spacing of the ties for a column reinforced with

4T32 bars?

A. 284 mm centres

B. 384 mm centres

C. 484 mm centres

D. 584 mm centres

26


16. In the case of more than one row of longitudinal bars in each face of a

reinforced concrete column, the bars must be tied …

A. not necessarily in groups

B. in groups and then the groups be inter connected

C. in groups

D. in any way, as there is no fixed limitation

17. Which of the statements is correct? In the case of two rows of

longitudinal bars at a face in R.C columns, the ties for the inner row …

A. must be provided separately

B. must be connected to the outer row

C. need not be provided in all cases

D. must be tied to the both ends.

18. A column is considered unbraced in a given plane when lateral

stability in that plane is provided by the…

A. column

B. beam

C. slab

D. foundation

27


19. The failure of column is due to _____________ rather than pure

compression.

A. crushing

B. buckling

C. shear

D. cracking

20. If both ends of a braced column is of type “end condition 1”, the

effective height is ________________ times the clear height.

A. 1.00

B. 0.95

C. 0.85

D. 0.75

All the answers are given below. For every correct answer award one

point. If you can answer all the questions correctly, you will get 20

points for this test. What are you waiting for? Let’s check it out!

28

11. C

12. B

13. A

14. B

15. B

16. A

17. C

18. A

19. B

20. D

FEEDBACK ON SELF-ASSESSMENT


1. B

2. B

3. D

4. C

5. D

6. D

7. A

8. B

9. B

10. B

YOU SHOULD SCORE 80% OR MORE TO PASS THIS UNIT. IF

YOUR SCORE IS LESS THAN 80%, YOU SHOULD WORK

THROUGH THIS UNIT OR PARTS OF THIS UNIT AGAIN. GOOD

LUCK!

GLOSSARY

ENGLISH MALAY

two-way slab papak dua hala

one way slab papak satu hala

simply supported slab papak tertupang mudah

restrained slab papak terhalang

uplifting effect kesan terangkat

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End of Unit 12


non-monolithic tak-sekata

moment coefficient pekali momen

panel petak

bay ruang

continuous slab papak selanjar

distribution steel tetulang agihan

modification factor factor pengubahsuai

interior span rentang dalaman

deflection of slab pesongan papak

boundary condition keadaan sempadan

edge strip jalur pinggir

middle strip jalur tengah

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“Learn to stand back from your troubles and take a calm

survey of them. The best way to do this is through the

practice of quietness. In quietness and peace, take a look

at your problems.”

unit 12 ( reinforced concrete columns )

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