Unformatted text preview: Chapter Seven
_____________________________________________________________________ Design of Reinforced Concrete Columns 7.1 Columns in Buildings 7.1.1 Types of columns
• Columns in a building carry loads from the beams and slabs down
to the foundations. They are primarily compression members.
• In general, columns also have to resist bending moments due to the
continuity of the structure. M
N N M
N Fig. 7.11 Loading and internal forces in columns • Two common types of columns
(i) braced column – where the lateral loading is resisted by walls or
some other form of bracing. A braced column is designed to
resist vertical loads only (such as dead and imposed loads).
(ii) unbraced column – where the lateral loading is resisted by the
bending action of columns. An unbraced column is designed to
resist both vertical and horizontal (wind/earthquake) loads.
246 wind shear
walls (b) (a)
wind (c) Fig. 7.12 (a) Plan; (b) braced frame; (c) unbraced frame 7.1.2 Reduction of imposed floor loads
• Critical loading arrangement For a braced column: the critical loading arrangement is usually
that which causes the largest moment in + largest axial force.
Fig. 7.13 shows the critical arrangement of the ultimate loads for
the design of (1) the centre column at the 1stfloor level, and (2)
the lefthand column at all floor level. Fig. 7.13 A critical loading
arrangement 247 • Reduction of total imposed floor loads
Table 7.1 Reduction of total imposed floor loads on columns, walls and
foundations.
British code difference Hong Kong Building Regulations (CAP. 123) 7.2 Column Classification and Failure Modes 7.2.1 Classification
Table 7.2 Short and slender columns (BS 8110: Part 1: 1997, clause 3.8.1.3) where lex – effective height with respect to major axis bending
ley – effective height with respect to minor axis bending
248 7.2.2 Effective height
• The effective height of a column is specified as l e = β lo (7.1) where
lo – the clear distance between the column end restraints β − a coefficient which depends on the degree of end restraints y
x lox x loy
y to T.O.S. column crosssection Fig. 7.21 Clear distances lox and loy between the column end restraints with
respect to major and minor axis bending 249 Table 7.3 Values of b for braced and unbraced columns 7.2.3 Failure modes
• A short column usually fails by crushing, but a slender column is liable to fail by buckling.
o The crushing load Nuz of a truly axially loaded column Nuz = 0.45fcuAc + 0.95fyAsc
where Ac – concrete area and Asc – longitudinal steel area.
o The additional moment Neadd of a slender column causes further lateral deflection. If the applied load N exceeds a critical value
Ncritical, the column buckles.
Eüler formula for the critical load of
a pinended strut: N critical = π 2 EI
l2 250 Fig. 7.22 Column
failure modes l
h 7.3 Reinforcement Details 7.3.1 Longitudinal steel
• A minimum of four bars, which are not less than size 12, is required in a rectangular column and six bars in a circular column. • Asc/Ac ≤ 6%, to avoid congestion and hence unsatisfactory compaction of concrete (IStructE: ρmax = 4% is preferable.)
• Asc/Ac ≥ 0.4%, to resist bending moment which may exist:
emin N N
M Mmin = N emin
where emin = 0.05 h ( > 20 mm)
M
N N 251 • Splices of reinforcement column Fig. 7.31 Details of splices in column reinforcement 7.3.2 Links (stirrups) (b)
(a) Fig. 7.31 Links in column
• Minimum size = 1
× size of the largest compression steel, but not
4 less than 6 mm.
• Maximum spacing = 12 × size of the smallest compression bars. (I StructE recommends that link spacing be not greater than the
smallest crosssectional dimension of the column).
252 • The links should be arranged so that every corner bar and alternate bar or group in an outer layer of longitudinal steel is supported by a
link passing round the bar and having an included angle not greater
than 135°.
• No bar not restrained by a link is to be further than 150 mm from a restrained bar (Fig. 7.31a).
7.4 Design of Short Columns 7.4.1 Braced axiallyloaded columns
This type of columns can be considered to occur when they support a
symmetrical and very rigid structure.
(1) Typical modes of failure
premature
buckling (a) (b) Fig. 7.41 (a) Short axiallyloaded column; (b) reinforcement buckling after
ultimate strength is reached To prevent premature buckling of longitudinal reinforcement:
o Links should be sufficiently closely spaced.
o Link size should be adequate.
253 (2) Ultimate load capacity N = 0.45fcuAc + 0.95fyAsc (7.2) Ac – the net area of the concrete
Asc – the area of the longitudinal reinforcement
To allow for eccentricity of the loading (Mmin = N emin, where emin =
0.05h or 20 mm, whichever is the lesser), BS 8110 limits the
capacity for axial load to about 90% of that from Eq. (7.2); thus
N = 0.4 f cu Ac + 0.8 f y Asc (7.3) For a rectangular column and to allow for the area of concrete
displaced by the longitudinal steel, Eq. (7.3) becomes
N = 0.4 f cu bh + Asc (0.8 f y − 0.4 f cu ) (7.4) Example 7.41: Axially loaded short column
A short braced axially loaded column 300 mm square in section is
reinforced with four 25 mm diameter bars. Find the ultimate axial load
that the column can carry and the pitch and diameter of the links required.
The materials are grade 30 concrete and grade 460 reinforcement.
Steel area Asc = 1963 mm2
Concrete area Ac = 3002 – 1963 = 88037 mm2
N= 0.4 × 30 × 88037 0.8 × 1963 × 460
+
= 1056 + 722 = 1778 kN
10 3
10 3 254 The links are not to be less than 6 mm in diameter or onequarter of the
diameter of the longitudinal bars. The spacing is not to be greater than 12
times the diameter of the longitudinal bars.
Provide 8 mm diameter links at 300 mm centres ([email protected]). The column
section is shown in the following figure. From the code the cover for
mild exposure is 25 mm. T8300 Example 7.42: Axially loaded short column
A short braced column has to carry a design axial load of 1366 kN. The
column size is 250 mm × 250 mm. Determine the steel area required for
the longitudinal reinforcement and select suitable bars. The materials are
grade 30 concrete and grade 460 reinforcement.
Substitute in the expression for the ultimate load,
1366 ×103 = 0.4 × 30 × (250 2 − Asc ) + 0.8 × 460 Asc
Asc = 1730 mm 2
Provide four 25 mm diameter bars to give a steel area of 1963 mm2.
Check:
100 As 100 × 1963
=
= 3.14 . This is satisfactory.
bd
250 2
255 7.4.2 Braced columns supporting an approximately symmetrical arrangement of beams
• The moments of these columns are small due primarily to
unsymmetrical arrangement of the live load.
• The ultimate load capacity
N = 0.35 f cu Ac + 0.70 f y Asc (7.5) 7.4.3 Columns resisting moments and axial forces
In practice, the area of longitudinal steel for these columns is determined
using design charts in BS 8110: Part 3 or in the IStructE design manual. (a) (b)
Fig. 7.42 (a) Column section; (b) BS 8110 column design charts
256 • Text Example 9.3 (pp.228232): Column design using design charts.
• Example 7.43: Short column subjected to axial load and moment using design chart
A short braced column is subjected to a design axial load of 1480 kN and
a design moment of 54 kNm. The column section is 300 mm × 300 mm.
Determine the area of steel required. The materials are grade 30 concrete
and grade 460 reinforcement.
Assume 25 mm diameter bars for the main reinforcement and 8 mm
diameter links. The cover on the links is 25 mm.
d = 300 – 25 – 8 –12.5 = 255 mm
d/h = 255/300 = 0.85
Use the chart in BS 8110 shown below, where d/h = 0.85.
N 1480 × 10 3
M
54 × 10 6
=
= 16.4 ;
=
= 2. 0
bh
300 2
bh 2
300 3 100Asc / bh = 2.0. Then Asc = 2.0 × 3002/100 = 1800 mm2
Provide four 25 mm diameter bars to give an area of 1963 mm2. 257 ...
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 Spring '06
 JSKUANG
 Structural Engineering, Trigraph, Column, Buckling, short columns

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