BCGBC4010A Apply structural principles to residential low-rise constructions

Structural principles - Structural members

Columns

Columns - further considerations
Axially loaded column
When the load is central to the centre of gravity axis, it produces a direct compressive stress within the column. Axially loaded columns are sometimes referred to as 'concentric columns'.
A diagram shows the load is applied to the middle of the column where the centre of gravity axis is.
Non-axially loaded column
When the load is off-centre the column is called an 'eccentric column'. This results in bending and compressive stress being applied to the column.
A diagram shows the load applied to the right of the centre of gravity axis on a column. The distance between the centre of gravity axis and the point at which the load is applied is labelled 'Eccentricity'.
Buckling
Buckling is a major consideration in designing all compression members. Buckling is deformation (deflection, bending) at right angles to the direction of the applied load.
Buckling will always occur about the weakest axis unless some form of lateral (sideways) restraint is used to prevent it. The longer and/or more slender the member, the more likely it is to buckle under compressive forces. Therefore a long member can carry less load than a short one of the same cross-section.
The tendency to buckle increases with the strength of the material. As the material gets stronger, the cross-sectional area required to carry the stress decreases. This produces more slender struts which are more likely to buckle. 
Image 1
A picture of load applied to a thin column. The column bends under the pressure. 
The failure of long slender columns is due to buckling (typically timber or steel columns).

Image 2
A picture of load applied to a thick column. The column bulges outwards as the pressure is applied.
The failure of short squat columns is due to crushing (typically reinforced concrete columns). 
Slenderness ratio
The maximum load a column can be allowed to support depends on the slenderness ratio and the material from which the column is made. The slenderness ratio involves:
•	the height of the column
•	the size and shape of its cross-section
•	the manner in which the two ends of the columns are supported or fixed.
Slenderness for the cross-sectional area of general shapes is calculated using the following formula: 
slenderness = effective length divided by least radius of gyration
                     = l divided by r.
In the case of a rectangular cross-section where b = breadth and d = depth,
slenderness = effective length divided by least width of column
                     = effective length divided by b.
End fixity and effective length
The way in which a column buckles is affected by how rigidly it is connected to other members at the top and the bottom. The term for the type of end fixing is end fixity and this affects the way a column buckles. The length of a column which may buckle is defined as the effective length. 
Types of fixity
For the following four images L = Effective length
Image 1
Type A column is encased in a concrete at the top and bottom. Buckling only occurs at the middle of the column as the concrete holds the top and bottom of the column firmly. The equation to calculate the effective length for a type A column is 
L = h divided by 2 (ie the column buckles along half of its length).
Image 2
Type B column has pinned joints at the top and bottom. Buckling occurs for the whole length and the equation to calculate the effective length for a type B column is 
L = h (ie the column buckles along its entire length).

Image 3
Type C column has a pinned joint at the top and is fixed at the bottom. The bottom third of the column is not affected by buckling. Buckling occurs along the top two thirds of the column. The equation for finding the effective length for a type C column is L = 2/3 h.
Image 4
Type D is pinned at the bottom and is an extreme case, eg a flagpole which is bolted to a steel plate. The column bends to the right. The equation used to calculate the effective length of the column is L = 2 h.
Notice that the less a structure is fixed, the more it will buckle. This gives a higher value for L, the effective length.

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