chapter 5 column design

Nasir Shafiq

IntroductionIntroduction

The columns in a structure carry the loads from beams and slab down to the foundations, and therefore they are primarily compression members, although they may also have to resist bending forces due to continuity of the structure.

IntroductionIntroduction

Loading and MomentLoading and Moment

Braced Column

Braced Column – where the lateral loads resisted by wall or some other form of bracing. With a braced column the axial forces and moments are caused by the dead and imposed load only. For a braced column the critical arrangement of the ultimate load is usually that which causes the largest moment in the column, together with a large axial load.

Loading and MomentLoading and Moment

Unbraced Column

Unbraced Column - where the lateral loads are resisted by the bending action of the columns. With an unbraced column the loading arrangements which include the effects of the lateral loads must also be considered. When the moments in column are large and particularly with unbraced column, it may also be necessary to check the case of maximum moment combined with the minimum axial load.

Unbraced Column

Classification of Column and Classification of Column and Failure ModesFailure Modes

Classification of ColumnGenerally, a column can be classified as two types:

• Short Column and

• Slender Column.

Most columns are termed short columns and fail when the material reaches its ultimate capacity under the applied loads and moments. Slender columns buckle and the additional moments caused by deflection must be taken into account in design. Since short columns are more common than slender.

Classification of Column and Classification of Column and Failure ModesFailure Modes

Effective Length

According to BS 8110 the effective length le of a column is defined as:

Where lo is the actual length (height) of column and is the coefficient which depends on the degree of end restraints that defined as End Fixity Condition 1, 2 and 3 as below:

oe ll

Effective Length

Effective LengthThe effective length or height of a column depends on its end conditions, i.e. the degree of fixity at each end discussed as above. Four (4)Four (4) end condition categories are defined in the design codes as BS 8110 are:

End condition-1: The end of the column is connected monolithically to beams or slabs that are deeper than the column dimension in the relevant plane.

End condition-2: The end of the column is connected monolithically to beams or slabs which are shallower than the overall column dimension in the relevant plane.

End condition-3: The end of the column is connected to members that provide some nominal restraint. In the context of this program, this condition is regarded as pinned.

End condition-4: The end of the column has no lateral or rotational restraint, i.e. a free end of a cantilever column. In the context of this program, this condition is regarded as free.

Effective Length

Slenderness

According to BS 8110 slenderness demonstrate the type of column as short and/or slender, it is expressed in the table below:

Design of RC ColumnsConfiguration/Type of ColumnConfiguration/Type of ColumnAs depicted in the following diagram:

Design of Short Columns

Short columns are divided into three categories according the degree of eccentricity of the loading as described in the following sections.

Short braced axially loaded columnsShort braced axially loaded columnsThis type of column can occur in pre-cast concrete construction when there is no continuity between the members. Also it can be considered to occur when the columns support a symmetrical and very rigid structure.When the load is perfectly axial the ultimate axial resistance according to BS 8110-1997 is:

Design of Short Columns

Design of Short Columns

Where Ac is the net area of the concrete and Asc is the area of the longitudinal reinforcement. Perfect conditions never exist and to allow for a small eccentricity (BS 8110 allows emin 0.05Dm or 20 mm) the ultimate load should be calculated from:

Short braced columns supporting an approximately Short braced columns supporting an approximately symmetrical arrangement of beamssymmetrical arrangement of beams

The moments of these columns will be small and due primarily to unsymmetrical arrangement of the live load. Provided the beam spans do not differ by more than 15 per cent of the longer, and the loading on the beams is uniformly distributed, the column may be designed to support the axial load only. The in the design equation for short columns the effect of the eccentricity of the load is taken into account by reducing the capacity for axial load by about 10%. The ultimate load by BS 8110 is given by the expression.

Short braced columns supporting an approximately Short braced columns supporting an approximately symmetrical arrangement of beamssymmetrical arrangement of beams

To taken account of the area of concrete displaced by the reinforcement the equation for a rectangular section may be written as:-

The area of longitudinal steel for the columns is determined by:

1. Using design chart or constructing M-N interaction diagrams

2. A solution of the basic design equations, or

3. An approximate method.

Since design equations are not suitable for direct solution and

the design of a column with symmetrical reinforcement in each

face is best carried out using design charts which are published

in Part 3 of BS 8110, the reinforcement of column is determined

by M-N interaction diagram using development of spread sheet

(as attached one).

Short columns subjected to axial load Short columns subjected to axial load and momentsand moments

Short columns subjected to axial load Short columns subjected to axial load and momentsand moments

Short columns subjected to axial load Short columns subjected to axial load and momentsand moments

Short columns subjected to axial load Short columns subjected to axial load and momentsand moments