Unit 12 (REINFORCED CONCRETE COLUMNS) [PDF]

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REINFORCED CONCRETE STRUCTURAL DESIGN

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UNIT 12 REINFORCED CONCRETE COLUMNS

OBJECTIVES

GENERAL OBJECTIVE To understand the basic definitions used in the design of reinforced concrete columns. SPECIFIC OBJECTIVES

At the end of this unit you will be able to: a) differentiate the following: i) a column and a wall

)

braced and unbraced columns

i)

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.

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INPUT 1

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

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h and b are the dimensions as shown below;

h=longer side

b=shorter side Figure 12.1: Column Dimensions

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.

REINFORCED CONCRETE STRUCTURAL DESIGN

ACTIVITY 12a

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

12.1

3000 mm

500 mm

12.2

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500 mm

200 mm

FEEDBACK 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.

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INPUT 2

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.

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b)

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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

l l ex and ey is less than 15 (for braced column) and less than h b

10 (for unbraced column). Above these limits, a column is considered as slender. l ex and l ey 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.

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y

h x

x

b

y Figure 12.2: Short and slender columns

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.

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ACTIVITY 12b

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

l ey b

are less than _______________________________.

l ex h

and

REINFORCED CONCRETE STRUCTURAL DESIGN

FEEDBACK 12b

Check your answers here: 12.3

unbraced

12.4

braced

12.5

crushing

12.6

deflection

12.7

15

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INPUT 3

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;

l e = βl o

Where l e = effective height of column β = effective height coefficient (From Table 3.21, BS 8110 for braced column and Table 3.22 for unbraced column) l o = clear height between end restraints.

Values of β are dependent upon the end conditions (restraints) and are explained in the following notes.

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12.9

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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;

hb ≥ hc

hc hb ≥ hc

hc

Designed for moments Note : hb = beam overall depth hs = slab thickness hc = column dimensions

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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.

hb < hc or hs < hc

hc hb < hc Note : hb = beam overall depth hs = slab thickness hc = column dimensions Figure 12.4: Braced column at condition 2

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

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column and the foundation, it is not designed to carry bending moments. Figure 12.5 shows this condition;

Simply supported beam

Joint not designed for moments

Figure 12.5: Braced column at condition 3

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.

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Free end

Figure 12.6 Braced column at condition 4

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.

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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;

x

θ

x

X < 150 mm θ < 135◦ Figure 12.7: Arrangement of links for containment of beam’s or columns compressive reinforcement.

ACTIVITY 12c

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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?

FEEDBACK 12c

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Now, check the answers together:

12.8

l e = βl o

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 =

0.4 × 250 × 250 100

= 250 mm2

12.13 Maximum area of reinforcement = 6% bh =

6 × 250 × 250 100

= 3,750 mm2 12.14 Minimum size of link =

1 × 20 4

= 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

REINFORCED CONCRETE STRUCTURAL DESIGN

12.17 150 mm

SUMMARY

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1.

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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.

REINFORCED CONCRETE STRUCTURAL DESIGN

9.

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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.

SELF-ASSESSMENT

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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. l e =

β lo

B. β = l e l o C. l o = βl e D. l e = βl o

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

REINFORCED CONCRETE STRUCTURAL DESIGN

13.

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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

REINFORCED CONCRETE STRUCTURAL DESIGN

16.

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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

REINFORCED CONCRETE STRUCTURAL DESIGN

19.

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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

11. C 12. B FEEDBACK ON SELF-ASSESSMENT 13. A 14. B All the answers are given below. For every correct answer award one 15. B point. If you can answer all the questions correctly, you will get 20 16. A points for this test. What are you waiting for? Let’s check it out! 17. C 18. A 19. B 20. D

REINFORCED CONCRETE STRUCTURAL DESIGN

1.

B

2.

B

3.

D

4.

C

5.

D

6.

D

7.

A

8.

B

9.

B

10.

B

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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!

End of Unit 12 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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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

“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.”