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 β larger of the two cross-section dimension
b β Smaller of the two cross-section dimension
Lex - Effective height w.r.t major axis of bending
Ley βEffective height w.r.t minor axis of bending
Lox- Clear height between restrains w.r.t major axis
Loy βClear 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
π΅π = π.ππ΅ΰΆ¨ΰ΅¬π + πππ.ππ+ ππࡰ࡬π + πππ.ππ+ ππΰ΅°
For unbraced members
π΅π = π΅ΰΆ§απ + ππππΓ ππππ+ ππα and π΅π = π΅απ + πππ+ππααπ + πππ+ππα
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
β ππ = effective creep ratio( if not known A can be taken as 0.7)
π€= π΄π πππ π΄ππππΰ΅οΏ½ ( if not known B can be taken as 1.1 )
fyd = the design yield strength of the reinforcement
πππ = design compressive strength of the reinforcement π΄π = the total area of longitudinal reinforcement
Calculating factor βCβ Calculating factor βCβ
ππΈπ = the design ultimate axial load in the column
ππ = π01 π02ΰ΅οΏ½ ( if ππ not known then C can be taken as 0.7 )
π01, π02 are the first order moments at the end of the column
with Θ!π01Θ!β₯ Θ!π02Θ! Design bending momentsDesign bending moments
Short columns resisting moments and axial forces
β’ 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
β’ 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
β’ 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 Ξ΅sc in the compression steel and the strain Ξ΅st 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 β² in compression and T=fstAs in tension.
ππΈπ β design ultimate axial load ππΈπ β design ultimate moment π β the depth of the stress block = 0.8x π΄β²π β the area of longitudinal reinforcement in the more highly compressed face π΄π = the area of reinforcement in the other face ππ π β the stress in reinforcement π΄β²π ππ β the stress in reinforcement π΄π ,negative when tesile.
β’ For most column,biaxial bending will not govern the design.
β’ Buildingβs internal and edge columns will not usually cause large moments in both directions.
β’ 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.
β’ 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 ππ§ββ² β₯ ππ¦πβ²
then the increased single axis design moment is
ππ§β² = ππ§ + π½ββ²πβ² Γ ππ¦
b) if ππ§ββ² < ππ¦πβ²
then the increased single axis design moment is
ππ¦β² = ππ¦ + π½ββ²πβ² Γ ππ§
π½ = 1β ππΈππβπππ
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 βmoment magnificationβ method where the design moment are obtained by factoring the first-order moment.
4. The βnorminal curvatureβ 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 βmoment magnificationβ method where the design moment are obtained by factoring the first-order moment.
4. The βnorminal curvatureβ 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
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