College of Engineering and Technology
Framed structures are either described as braced where horizontal loads are resisted by shear walls or unbraced where horizontal loads are carried in the structure through rigid joints between beams and columns.
Most framed structures are braced and only braced columns are considered here.
The slenderness of columns gives a further classification and columns are described as short or slender
Slenderness depends on the effective length lo and the radius of gyration i
The slenderness l = lo/i
lo is the clear height x a factor depending on its end fixity determined from a table.
The fixity at the base of columns at the bottom of a multi-storey buildings are assumed to be End condition 1
Beam deeper than column.
Beam smaller than column
Beams assumed simply supported
End condition 1
End Condition 2
End Condition 3
Fixity factors
End condition at top
End condition at bottom
1
2
3
0.75
0.80
0.90
0.85
0.95
1.00
IStructE Manual for the Design of Reinforced Concrete Structures to Eurocode 2
Limiting factors for slenderness l determine the slenderness classification. (see later)
Dimensions and nomenclature
N Axial load N kN
e Nominal eccentricity e
Main steel As carries compressive load
Links hold the main steel in position and are
described by their diameter and pitch
1. Select Materials
Choose a concrete grade (say fck = 30N/mm2)
Choose type of steel (say fyk = 500N/mm2 for main steel and links)
2. Find Design Action, axial force N and applied moments Mapp
Use factored actions. Self weight may be a significant factor and is part of the permanent action. Concrete has a volume density of 25kN/m3 so a column 300mm ´ 300mm has a self weight of 2.25kN/m
Column actions will generally be derived from loads already calculated for beams.
3. Size the Column
Architectural requirements may determine the dimensions. Otherwise estimates of size can be made by assuming that 3% of the area will be main reinforcement. Practical minimum 200 x 200 but fire resistance requirements may require larger.
· Estimate the area of the column
Determine dimensions. For a square column b = h =
4. Determine slenderness and check that column is short
1. Determine effective length lo = clear height x fixity factor
2. For rectangular columns limiting ratio is lo/b
Most columns are short and slender columns are not considered here
For a short braced rectangular column l0b≤6.19bhfckN
5. Calculate Main Steel
Axially loaded columns
These are very unusual and can only be considered if the ends of the column are truly pinned and no moment is applied. Tables may be used to determine the amount of main reinforcement.
N/bhfck
<0.45
0.5
0.6
0.7
0.8
0.9
As/bhfck
0
0.17x10-3
0.51x10-3
0.85x10-3
1.19x10-3
1.53x10-3
1.87x10-3
5.1 Calculate design Moment M
Columns should be designed to resist the applied moment from beams and a nominal moment due to the axial load which is caused by slight deformations of the column and the fact that the axial load may not truly be axial and is applied eccentrically
· eccentricity e = h or lo or 20mm whichever is greatest.
30 400
· Design moment M = Nxe + MApp
5.2 Find d2...
Shangri_La1993