What is columnThe columns in a structure carry the loads from the beams and slabs down to the foundations and therefore they are primarily compression members , although they may also have to resist bending forces and to the continuity structure.

What is columnThe columns in a structure carry the loads from the beams and slabs down to the foundations and therefore they are primarily compression members , although they may also have to resist bending forces and to the continuity structure.

h – larger of the two cross-section dimension

b – Smaller of the two cross-section dimension

Lex - Effective height w.r.t major axis of bending

Ley –Effective height w.r.t minor axis of bending

Lox- Clear height between restrains w.r.t major axis

Loy –Clear height between restrains w.r.t minor axis

Main classification of columns

Effective height of a column

beam

End 1

End 2

non-failing column

failing column

non-failing column

For braced members

𝓵𝟎 = 𝟎.𝟓𝓵ඨ൬𝟏 + 𝒌𝟏𝟎.𝟒𝟓+ 𝒌𝟏൰൬𝟏 + 𝒌𝟐𝟎.𝟒𝟓+ 𝒌𝟐൰

For unbraced members

𝓵𝟎 = 𝓵ටቀ𝟏 + 𝟏𝟎𝒌𝟏× 𝒌𝟐𝒌𝟏+ 𝒌𝟐ቁ and 𝓵𝟎 = 𝓵ቀ𝟏 + 𝒌𝟏𝟏+𝒌𝟏ቁቀ𝟏 + 𝒌𝟐𝟏+𝒌𝟐ቁ

For braced membersFor braced members

For un-braced membersFor un-braced members

Effective length for isolated membersEffective length for isolated members

Column effective lengths

Effective length factor ,F , for braced columns

300 mm

500 mm

Slenderness ratio of a column

Effective lengths for isolated membersEffective lengths for isolated members

Euercode 2 states that second order effects may be ignored if they are less that 10% of the first order effects. As an alternative, if the slenderness is less than the slenderness limit , then second order effects may be ignored.

Euercode 2 states that second order effects may be ignored if they are less that 10% of the first order effects. As an alternative, if the slenderness is less than the slenderness limit , then second order effects may be ignored.

Limiting slenderness ratio- short or slender columns

∅𝑒𝑓 = effective creep ratio( if not known A can be taken as 0.7)

𝑤= 𝐴𝑠𝑓𝑐𝑑 𝐴𝑐𝑓𝑐𝑑ൗ� ( if not known B can be taken as 1.1 )

fyd = the design yield strength of the reinforcement

𝑓𝑐𝑑 = design compressive strength of the reinforcement 𝐴𝑠 = the total area of longitudinal reinforcement

Calculating factor ‘C’ Calculating factor ‘C’

𝑁𝐸𝑑 = the design ultimate axial load in the column

𝑟𝑚 = 𝑀01 𝑀02ൗ� ( if 𝑟𝑚 not known then C can be taken as 0.7 )

𝑀01, 𝑀02 are the first order moments at the end of the column

with ȁ!𝑀01ȁ!≥ ȁ!𝑀02ȁ! Design bending momentsDesign bending moments

Short columns resisting moments and axial forces

• The area of longitudinal steel for these columns is determined by,

1. using design charts or constructing M-N interaction diagrams2. a solution of the basic design equations3. an approximate method

• The area of longitudinal steel for these columns is determined by,

1. using design charts or constructing M-N interaction diagrams2. a solution of the basic design equations3. an approximate method

Moment M

Moment M

Load N

Load N

• The basic equations derived for a rectangular section as shown in figure and with a rectangular stress block are,

1. For the depth to the neutral axis x determine the strain εsc in the compression steel and the strain εst in the tension steel.

2. Determine the steel stresses fsc in compression and fst in tension from the stress-strain diagram .The forces in the steel are Cs= fscAs ′ in compression and T=fstAs in tension.

𝑁𝐸𝑑 − design ultimate axial load 𝑀𝐸𝑑 − design ultimate moment 𝑠− the depth of the stress block = 0.8x 𝐴′𝑠 − the area of longitudinal reinforcement in the more highly compressed face 𝐴𝑠 = the area of reinforcement in the other face 𝑓𝑠𝑐 − the stress in reinforcement 𝐴′𝑠 𝑓𝑠 − the stress in reinforcement 𝐴𝑠 ,negative when tesile.

• For most column,biaxial bending will not govern the design.

• Building’s internal and edge columns will not usually cause large moments in both directions.

• Corner columns may have to resist significant bending about both axes,but the axial loads are usually small and a design similar to the adjacent edge columns is generally adequate.

• For members with a rectangular cross section,separate checks in the two principal planes are permissible if the ratio of the corresponding eccentricities satisfies one of the following conditions.

Subject to the following conditions;

a) if 𝑀𝑧ℎ′ ≥ 𝑀𝑦𝑏′

then the increased single axis design moment is

𝑀𝑧′ = 𝑀𝑧 + 𝛽ℎ′𝑏′ × 𝑀𝑦

b) if 𝑀𝑧ℎ′ < 𝑀𝑦𝑏′

then the increased single axis design moment is

𝑀𝑦′ = 𝑀𝑦 + 𝛽ℎ′𝑏′ × 𝑀𝑧

𝛽 = 1− 𝑁𝐸𝑑𝑏ℎ𝑓𝑐𝑘

Values of coefficient

Design of slender columns

1. A general method based on a non-linear analysis of the structure and allowing for second-order effects that necessitates the use of computer analysis.

2. A second-order analysis based on nominal stiffness values of the beams and column that,again,requires computer analysis using a process of iterative analysis.

3. The ‘moment magnification’ method where the design moment are obtained by factoring the first-order moment.

4. The ‘norminal curvature’ method where second-order moments are determined from an estimation of the column curvature.These secon-order moments are added to the first-order moments to give the total column design moment

1. A general method based on a non-linear analysis of the structure and allowing for second-order effects that necessitates the use of computer analysis.

2. A second-order analysis based on nominal stiffness values of the beams and column that,again,requires computer analysis using a process of iterative analysis.

3. The ‘moment magnification’ method where the design moment are obtained by factoring the first-order moment.

4. The ‘norminal curvature’ method where second-order moments are determined from an estimation of the column curvature.These secon-order moments are added to the first-order moments to give the total column design moment