design of rcc columns

8/18/2019 Design of RCC columns

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Prepared by Dr. Prashanth J. Page 1

UNIT 6: DESIGN OF COLUMNS

6.1 GENERAL

A ‘compression member’ is a structural element which is subjected (predominantly) to axial

compressive forces. Compression members are most commonly encountered in reinforcedconcrete buildings as columns (and sometimes as reinforced concrete walls), forming part of the

‘vertical framing system’. Other types of compression members include truss members (‘struts’),

inclined members and rigid frame members.

The ‘column’ is representative of all types of compression members, and hence, sometimes, the

terms ‘column’ and ‘compression member’ are used interchangeably. The Code [Cl. 25.1.1 of

the Code] defines the column as a compression member, the ‘effective length’ of which exceeds

three times the least lateral dimension. The term ‘pedestal’ is used to describe a vertical

compression member whose ‘effective length’ is less than three times it’s least lateral dimension

[Cl. 26.5.3.1(h) of the Code].

6.2 CLASSIFICATION OF COLUMNS

6.2.1 Based on Type of Reinforcement

Reinforced concrete columns may be classified into the following three types based on the type

of reinforcement provided:

1) Tied columns: where the main longitudinal bars are enclosed within closely spaced lateral

ties [Fig. 1(a)];2) Spiral columns: where the main longitudinal bars are enclosed within closely spaced and

continuously wound spiral reinforcement [Fig. 1(b)];

3) Composite columns: where the reinforcement is in the form of structural steel sections or

pipes, with or without longitudinal bars [Fig. 1(c)].

6.2.2 Based on Type of Loading

Columns may be classified into the following three types, based on the nature of loading:

1. Columns with axial loading (applied concentrically) [Fig. 2(a)];

2.

Columns with uniaxial eccentric loading [Fig. 2(b)];

3. Columns with biaxial eccentric loading [Fig. 2(c)].


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Fig. 1: Types of columns — tied, spiral and composite

Fig. 2: Different loading situations in columns


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6.2.3 Based on Slenderness Ratios

Columns (i.e., compression members) may be classified into the following two types, depending

on whether slenderness effects are considered insignificant or significant:

1.

Short columns;

2. Slender (or long) columns.

‘Slenderness’ is a geometrical property of a compression member which is related to the ratio of

its ‘effective length’ to its lateral dimension. This ratio, called slenderness ratio, also provides a

measure of the vulnerability to failure of the column by elastic instability (buckling) — in the

plane in which the slenderness ratio is computed. Columns with low slenderness ratios, i.e.,

relatively short and stocky columns, invariably fail under ultimate loads with the material

(concrete, steel) reaching its ultimate strength, and not by buckling. On the other hand, columns

with very high slenderness ratios are in danger of buckling (accompanied with large lateraldeflection) under relatively low compressive loads, and thereby failing suddenly. Design codes

attempt to preclude such failure by specifying ‘slenderness limits’ to columns.

According to the IS Code (Cl. 25.1.2), a compression member may be classified as a ‘short

column’ if its slenderness ratios with respect to the ‘major principal axis’ ( l ex /D) as well as the

‘minor principal axis’ (l ey /b) are both less than 12; otherwise, it should be treated as ‘slender

column’. Here l ex and D denote the effective length and lateral dimension (‘depth’) respectively

for buckling in the plane passing through the longitudinal centroidal axis and normal to the major

principal axis; i.e. causing buckling about the major axis [refer Fig. 2(c)]; likewise, l ey and b refer

to the minor principal axis.

6.3 EFFECTIVE LENGTH OF COLUMN

When relative transverse displacement between the upper and lower ends of a column is

prevented, the frame is said to be braced (against sideway). In such cases, the effective length

ratio k varies between 0.5 and 1.0, as shown in Fig. 3. The extreme value k = 0.5 corresponds to

100 percent rotational fixity at both column ends [Fig. 3(a)] (i.e., when the connecting floor

beams have infinite flexural stiffness), and the other extreme value k = 1.0 corresponds to zero

rotational fixity at both column ends (‘pinned’) [Fig. 3(c)] (i.e., when the beams have zero

flexural stiffness). When one end is fully ‘fixed’ and the other ‘pinned’, k = 0.7 [Fig. 3(b)].

These values are tabulated in Table 28 of Annex E of the Code.


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Fig. 3: Effective lengths of columns braced against sideway

6.3.1 Code Recommendations

Although, in design practice, it is convenient to assume the idealized boundary conditions of

either zero or full restraint (rotational and translational) at a column end, the fact is that such

idealizations cannot generally be realized in actual structures. For this reason, the Code (Cl. E –

1), while permitting these idealizations, recommends the use of ‘effective length ratios’ k = l e /l

that are generally more conservative than those obtained from theoretical considerations [Fig. 3].

These recommended values of k are as follows:

a) Both ends ‘fixed’ rotationally [Fig. 3 (a)] : 0.65 (instead of 0.5)

b) One end ‘fixed’ and the other ‘pinned’[Fig. 3 (b)] : 0.80 (instead of 0.7)

c) Both ends ‘free’ rotationally (‘pinned’) [Fig. 3 (c)] : 1.00

6.4 LOADS ON COLUMNS

Columns in a building frame are subjected to the following loads:

Live loads on the floor supported by column.

Dead weight of floor and beams supported by the column.

Self weight of the column.


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6.5 BRACED AND UNBRACED COLUMNS

It is desirable that the columns do not have to resist any horizontal loads due to wind or

earthquake. This can be achieved by bracing the columns as in the case of columns of a water

tank or tall buildings (Fig. 4). Lateral tie members for the columns of water tank or shear walls

for the columns of tall buildings resist the horizontal forces and these columns are called braced

columns. Unbraced columns are supposed to resist the horizontal loads also. The bracings can be

in one or more directions depending on the directions of the lateral loads. The effect of bracing

has been taken into account by the IS code in determining the effective lengths of columns (vide

Annex E of IS 456).

Fig. 4: bracing of columns

6.6 CODAL REQUIREMENTS

6.6.1 Slenderness Limits

Slenderness effects in columns effectively result in reduced strength, on account of the additional

‘secondary’ moments introduced. In the case of very slender columns, failure may occur

suddenly under small loads due to instability (‘elastic buckling’), rather than due to material

failure. The Code attempts to prevent this type of failure (due to instability) by specifying certain

‘slenderness limits’ in the proportioning of columns.

The Code (Cl. 25.3.1) specifies that the ratio of the unsupported length (l) to the least lateral

dimension (d) of a column should not exceed a value of 60 (i.e., l/d ≤ 60). Furthermore, in case

one end of a column is free (i.e., cantilevered column) in any given plane, the Code (Cl. 25.3.2)

specifies that l ≤ 100b2 /D where D is the depth of the cross-section measured in the plane of the

cantilever and b is the width (in the perpendicular direction).


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6.6.2 Minimum Eccentricities

Eccentricities not explicitly arising out of structural analysis calculations act on the column due

to various reasons, such as:

• Lateral loads not considered in design;

•

Live load placements not considered in design;

• Accidental lateral/eccentric loads;

• Errors in construction (such as misalignments); and

• Slenderness effects underestimated in design.

For this reason, the Code (Cl. 25.4) requires every column to be designed for a minimum

eccentricity emin (in any plane) equal to the unsupported length/500 plus lateral dimension/30,

subject to a minimum of 20 mm. For a column with a rectangular section, this implies:

(Whichever is greater)

(Whichever is greater)

For non-rectangular and non-circular cross-sectional shapes, it is recommended that, for any

given plane,

where l e is the effective length of the column in the plane considered.

6.6.3 Reinforcement and Detailing

Longitudinal Reinforcement (refer Cl. 26.5.3.1 of the Code)

• Minimum Reinforcement: The longitudinal bars must, in general, have a cross-sectional area

not less than 0.8 percent of the gross area of the column section. Such a minimum limit is

specified by the Code:

To ensure nominal flexural resistance under unforeseen eccentricities in loading; and

To prevent the yielding of the bars due to creep and shrinkage effects, which result in

a transfer of load from the concrete to the steel.

In very large-sized columns (where the large size is dictated, for instance, by architectural

considerations, and not strength) under axial compression, the limit of 0.8 percent of gross area

may result in excessive reinforcement. In such cases, the Code allows some concession by

permitting the minimum area of steel to be calculated as 0.8 percent of the area of concrete

required to resist the direct stress, and not the actual (gross) area.


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• Maximum Reinforcement: The maximum cross-sectional area of longitudinal bars should not

exceed 6 percent of the gross area of the column section. However, a reduced maximum limit

of 4 percent is recommended in general in the interest of better placement and compaction of

concrete — and, in particular, at lapped splice locations.

In tall buildings, columns located in the lowermost storeys generally carry heavy reinforcement

(∼ 4 percent). The bars are progressively curtailed in stages at higher levels.

• Minimum diameter / number of bars and their location: Longitudinal bars in columns (and

pedestals) should not be less than 12 mm in diameter and should not be spaced more than

300 mm apart (centre-to-centre) along the periphery of the column [Fig. 5 (a)]. At least 4 bars

(one at each corner) should be provided in a column with rectangular cross-section, and at

least 6 bars (equally spaced near the periphery) in a circular column. In ‘spiral columns’

(including noncircular shapes), the longitudinal bars should be placed in contact with the

spiral reinforcement, and equidistant around its inner circumference [Fig. 5 (b)]. In columnswith T-, L-, or other cross-sectional shapes, at least one bar should be located at each corner

or apex [Fig. 5 (c)].

Longitudinal bars are usually located close to the periphery (for better flexural resistance), but

may be placed in the interior of the column when eccentricities in loading are minimal. When a

large number of bars need to be accommodated, they may be bundled, or, alternatively, grouped,

as shown in [Fig. 5 (d)].

• Cover to reinforcement: A minimum clear cover of 40 mm or bar diameter (whichever is

greater), to the column ties is recommended by the Code (Cl. 26.4.2.1) for columns ingeneral; a reduced clear cover of 25 mm is permitted in small-sized columns (D ≤ 200 mm

and whose reinforcing bars do not exceed 12mm) and a minimum clear cover of 15 mm (or

bar diameter, whichever is greater) is specified for walls. However, in aggressive

environments, it is desirable, in the interest of durability, to provide increased cover but

preferably not greater than 75 mm.

Transverse Reinforcement (refer Cl. 26.5.3.2 of the Code)

• General : All longitudinal reinforcement in a compression member must be enclosed within

transverse reinforcement, comprising either lateral ties (with internal angles not exceeding

135o) or spirals. This is required:

To prevent the premature buckling of individual bars;

To confine the concrete in the ‘core’, thus improving ductility and strength;

To hold the longitudinal bars in position during construction; and

To provide resistance against shear and torsion, if required.


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Fig. 5: Some Code recommendations for detailing in columns

• Lateral Ties: The arrangement of lateral ties should be effective in fulfilling the above

requirements. They should provide adequate lateral support to each longitudinal bar, thereby

preventing the outward movement of the bar. The diameter of the tie φt is governed byrequirements of stiffness, rather than strength, and so is independent of the grade of steel.

The pitch st (centre-to-centre spacing along the longitudinal axis of the column) of the ties

should be small enough to reduce adequately the unsupported length (and hence, slenderness

ratio) of each longitudinal bar. The Code recommendations are as follows:

where φlong,max denotes the diameter of longitudinal bar to be tied and D denotes the least lateral

dimension of the column.

Ideally, the tie must turn around (and thereby provide full lateral restraint to) every longitudinal

bar that it encloses — particularly the corner bars. When the spacing of longitudinal bars is less

than 75 mm, lateral support need only be provided for the corner and alternate bars [Fig. 5 (e)].


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The straight portion of a closed tie (between the corner bars) is not really effective if it is large,

as it tends to bulge outwards when the concrete core is subjected to compression. For this reason,

supplementary cross ties are required for effective confinement of the concrete. If the

longitudinal bars spaced at a distance not exceeding 48φt are effectively tied in two directions,

then the additional longitudinal bars in between these bars need be tied only in one direction by

open ties [Fig. 5 (f)].

• Spirals: Helical reinforcement provides very good confinement to the concrete in the ‘core’

and enhances significantly the ductility of the column at ultimate loads. The diameter and

pitch of the spiral may be computed as in the case of ties except when the column is designed

to carry a 5 percent overload (as permitted by the Code), in which case

The ends of the spiral should be anchored properly by providing one and a half extra turns.

6.7 DESIGN OF SHORT COLUMNS UNDER AXIAL COMPRESSION

The main assumptions made for limit state design of columns failing under pure compression as

specified in Cl. 39.1 of IS: 456-2000 are as follows:

1. The maximum compressive strain in concrete in axial compression is 0.002.

2. Plane sections remain plane in compression.

3. The design stress-strain curve of steel in compression is taken to be the same as in tension.

The design stress in steel is 0.87fy in Fe 250, 415 and 500 grade steels. Accordingly, under pure

axial loading conditions the design strength of the short column is expresses as,

Where, f sc = 0.87f y

The code requires that all columns are to be designed for minimum eccentricity of 0.05 times thelateral dimension. Hence, the final expression for the ultimate load is obtained by reducing the

value of Pu by 10 percent in the above equation specified as,

Where, Pu = axial ultimate load on the member.

f ck = characteristic compressive strength of concrete


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Ac = area of concrete

f y = characteristic compressive strength of steel

Asc = Area of longitudinal reinforcement

Short columns with helical reinforcement (spiral columns) have increased ductility prior to

collapse and hence the code permits 5% increase in the load carrying capacity of spiral columns.

However, the ratio of the volume of helical reinforcement to the volume of the core shall not be

less than,

according to Cl. 39.4.1 of IS:456-2000.

Where, Ag = gross area of the section,

Ac = area of the core of the helically reinforced column measured to the outside

diameter of the helix.

6.8 DESIGN PROCEDURE TO FIND AREA OF COMPRESSION REINFORCEMENT

GIVEN THE DIMENSIONS

1. Slenderness ratio

If, L/D < 12

Design the column as short column.

2. Minimum eccentricity

Calculate,

Calculate, e per = 0.05D

emin < e per . Therefore codal formula can be used.

3. Calculate Pu = 1.5P

4. Area of column, A = b X D

5. Area of concrete, Ac = A- Asc

6. Design of longitudinal reinforcement,

Pu = 0.4 f ck Ac + 0.67 f y Asc

Substitute value of Ac as (A – Asc)

Find Asc

7.

Assuming dia of bars ( ) (12 mm, 16 mm, 20 mm, 25mm, 32 mm)

Area of one bar, asc = *2/4

No. of bars = Asc/asc

8. Design of lateral ties

Diameter ranges from /4 to 16 mm

Pitch is least of following,

i) Least lateral dimension: b or D


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ii) 16 times diameter of longitudinal bar ( )

iii) 300 mm

9. Sketch the reinforcement details.

6.9 DESIGN PROCEDURE TO FIND DIMENSIONS AND COMPRESSIONREINFORCEMENT

1. Area of concrete, Ac = A – Asc

Assuming 0.8% percent of reinforcement = 0.008A

Ac = A – 0.008A

2. Size of column

Pu = 0.4f ck Ac + 0.67f yAsc

Substitute Ac and Asc

Find the area of column required A

i)

If square column, then size of column, D = sqrt(A)

ii) If rectangular column, then assume b = 300 mm to 500 mm then D = A/b

iii) If circular column, diameter, D = sqrt(4A/ )

3. Slenderness ratio check, L/D < 12. Therefore short column.

If L/D > 12, redesign.

4. Minimum eccentricity check

Calculate,

Calculate, e per = 0.05D

emin < e per . Therefore codal formula can be used.

If emin > e per revise the dimensions.

5. Design of longitudinal reinforcement

Calculate area of steel, Asc = 0.008A

Assuming dia of bars ( ) {12 mm, 16 mm, 20 mm, 25 mm, 32 mm}

Area of one bar, asc =2/4

No. of bars = Asc/ asc

10. Design of lateral ties

Diameter ranges from /4 to 16 mm

Pitch is least of following,

i)

Least lateral dimension: b or Dii) 16 times diameter of longitudinal bar ( )

iii) 300 mm

11.

Sketch the reinforcement details.


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6.10 DESIGN OF SHORT COLUMNS UNDER COMPRESSION WITH UNIAXIAL

BENDING

The external columns of multistoried buildings and columns supporting crane loads through

corbels are subjected to direct loads and bending moments. The compression members should be

designed for axial load and bending moment based on the assumptions prescribed in IS: 456-2000 code Cls. 39.1 and 39.2.

The analytical design of members subjected to combined axial load and uniaxial bendinginvolves lengthy calculation by trial and error and the method uses equilibrium equal to

determine the area of reinforcement required to resist direct loads and uniaxial moment. In orderto overcome these difficulties, IS code recommends the use of interaction diagrams involving

non-dimensional parameters in SP: 16 – design aids for reinforced concrete.

The following cases are covered in the SP: 16 design charts:1. Rectangular section reinforced with equal number of bars on opposite sides parallel to

that axis of bending (Charts 27 to 38).2.

Rectangular sections reinforced with equal number of bars on all the four sides (Charts 39

to 50).3. Circular sections reinforced with 8 bars symmetrically spaced (Charts 51 to 62) and these

charts can also be used for bars not less than 6.

The charts for each of these types have been given for three grades of steel (Fe-250, Fe-415 andFe-500) and four values of the ratio (d`/D). The dotted lines in these chats indicate the stress in

bars nearest to the tension face of the member. It is pertinent to note that all these stress valuesare at the failure condition corresponding to the limit state of collapse and not at working loads.

The construction of these design charts are based on the equilibrium equations at the limit statecollapse as outlined in SP: 16.

Fig. 6: Compression with bending-Rectangular section-Reinforcement distributed equally

on two sides (SP: 16 chart 32)


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6.11 DESIGN OF SHORT COLUMNS UNDER COMPRESSION WITH BIAXIAL

BENDING

Columns located at the corners of a multistoried building with rigidly connected beams at right

angles, develop biaxial moments together with the axial compression load transmitted from

beams. Fig. 7 (a) shows the column section subjected to the axial compressive load Pu and themoments Mux and Muy about the major and minor axis respectively. Fig. 7 (b) shows the axis of bending and the resultant moment Mu acts about this axis inclined to the two principal axes. The

resultant eccentricity is computed as e = Mu/Pu and this can also be expressed as,

where, and

The possible neutral axis lies in the X-Y plane as shown in Fig. 7 (c).

By choosing the neutral axis which is in the X-Y plane, calculations are made from fundamentals

to satisfy the equilibrium of load and moments about both the axes. This procedure is tedious andis not generally recommended for routine design.

Fig. 7: Biaxial bending of short column


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6.11.1 Codal method for design of compression members subjected to biaxial bending

The simplified procedure adopted by the code (Cl. 39.6) based on Bresler’s empirical

formulation is expressed by the relation,

Where Mux, Muy are the moments about X and Y axes respectively due to design loads. Mux1 and

Muy1 are the maximum uniaxial moment capacities with an axial load Pu, bending about X and Y

axes respectively. n is an exponent whose value depends on the ratio of Pu/Puz where,

Puz = 0.45f ck Asc + 0.75f yAsc i.e., value of Pu when M = 0

Alternative to this equation chart 63 of SP: 16 can be used to get Puz. For different values of

Pu/Puz, the appropriate values of n has been taken and curves for the equation,

have been plotted in Chart 64 of SP: 16.

design of rcc columns

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