1 reinforced concrete design lecture 14 dr. nader okasha
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1
Reinforced Concrete Design
Lecture 14
Dr. Nader Okasha
Design of Short Axially Loaded Columns
2
According to ACI Code, a structural element with a ratio of height-to least lateral
dimension exceeding three used primarily to support compressive loads is defined as
column.
Columns are vertical compression members of a structural frame intended to support the
load-carrying beams. They transmit loads from the upper floors to the lower levels and then
to the soil through the foundations.
bl
P
h
b
h
Column
Beam
Loads
Footing
Soil
Slab
Slab
Beam Beam
Beam Beam
Beam Beam
Column
3
Columns
Usually columns carry bending moment as well, about one or both axes of the cross
section, and the bending action may produce tensile forces over a part of the cross
section
The main reinforcement in columns is
longitudinal, parallel to the direction of
the load and consists of bars arranged
in a square, rectangular, or circular shape
Columns
Columns may be divided into two categories
1- Short Columns, for which the strength is governed by the strength of the materials
and the geometry of the cross section
2- Slender columns, for which the strength may be significantly reduced by lateral
deflections.
Length of the column in relation to its lateral dimensions
3- Position of the load on the cross-section
Columns can be classified as
1-Concentrically loaded columns, are subjected to axial force only
2-Eccentrically loaded columns, are subjected to moment in addition to the axial
force.
5
Column Load: Tributary area method
6
Column Load: Beam reaction method
7
Load Summation on Column Section for Design
8
Analysis and Design of Short Columns
Column Types:
1. Tied
2. Spiral
3. Composite
9
Behavior of Tied and Spirally-Reinforced Columns
Axial loading tests have proven that tied and spirally reinforced columns
having the same cross-sectional areas of concrete and steel reinforcement
behave in the same manner up to the ultimate load.
At that load tied columns fail suddenly due to excessive cracking in the
concrete section followed by buckling of the longitudinal reinforcement
between ties within the failure region. For spirally reinforced columns, once
the ultimate load is reached, the concrete shell covering the spiral starts to peel
off. Only then, the spiral comes to action by providing a confining force to the
concrete core, thus enabling the column to sustain large deformations before
final collapse occurs.10
Behavior of Tied and Spirally-Reinforced Columns
Failure of a tied column Failure of a spiral column
Deformation
11
Nominal Capacity and Design under Concentric Axial loads
0 c g st y st0.85 *P f A A f A
Ag = gross area = b*h
Ast = area of long steel
fc = concrete compressive strength
fy = steel yield strength
12
Nominal Capacity and Design under Concentric Axial loads
Maximum Nominal Capacity for Design Pn
n 0P rP
r = Reduction factor to account for accidental eccentricity
r = 0.80 ( tied )
r = 0.85 ( spiral )ACI 10.3.6.3
13
un PP
= 0.65 for tied columns
= 0.75 for spiral columns (was 0.70 in ACI318-05)
ACI 9.3.2.2r = 0.80 ( tied )
r = 0.85 ( spiral )
ACI 10.3.6.3
Nominal Capacity and Design under Concentric Axial loads
ucystcgn
steel
85.0
concrete
85.0 PffAfArP
14
ucystcgn
steel
85.0
concrete
85.0 PffAfArP
or
ucygcgn 85.085.0 PfffArP
Nominal Capacity and Design under Concentric Axial loads
un PP
15
u
g
c g y c
0.85 0.85
PA
r f f f
* when g is known or assumed:
Nominal Capacity and Design under Concentric Axial loads
16
un PP
Reinforcement Requirements (Spiral)
sD
A
c
sps
4
Core of Volume
Spiral of Volume
Spiral Reinforcement Ratio, rs
sD
DA
41
:from
2c
csps
17
Nominal Capacity and Design under Concentric Axial loads
Reinforcement Requirements (Spiral)
y
c
c
gs *1*45.0
f
f
A
A
sp
2c
c
c
y
cross-sectional area of spiral reinforcement
core area
4 core diameter: outside edge to outside edge of spiral
spacing pitch of spiral steel (center to center)
yield strength of sp
A
DA
D
s
f
iral steel 420Mpa
18
Nominal Capacity and Design under Concentric Axial loads
4
'0.45 1
sp
g cc
c y
Aa
A fD
A f
Reinforcement Requirements (Longitudinal Steel Ast)
ACI Code 10.9.1 requires
g st g0.01 0.08A A A
19
Design Considerations
- Minimum Number of Bars ACI Code 10.9.2
min. of 6 bars in spiral arrangement
min. of 4 bars in rectangular or circular ties
min. of 3 bars in triangular ties
Reinforcement Requirements (Longitudinal Steel Ast)
20
Design Considerations
ACI Code 7.10.5.1
Reinforcement Requirements (Lateral Ties)
8 bar if longitudinal bar 30 bar 12 bar if longitudinal bar 32 bar 12 bar if longitudinal bars are bundled
size
21
Design Considerations
Reinforcement Requirements (Lateral Ties)
Vertical spacing: (ACI 7.10.5.2)
16 db ( db for longitudinal bars ) 48 dstirrup least lateral dimension of column
s s s
22
Design Considerations
Reinforcement Requirements (Lateral Ties)
Arrangement Vertical spacing: (ACI 7.10.5.3)
At least every other longitudinal bar shall have lateral support from the corner of a tie with an included angle 135o.
No longitudinal bar shall be more than 15cm clear on either side from “support” bar.
1.)
2.)
23
Design Considerations
Examples of lateral ties
24
Design Considerations
ACI Code 7.10.4.2
Reinforcement Requirements (Spirals )
10 mm diametersize
clear spacing between spirals
7.5cmACI 7.10.4.3
2.5cm 25
Design Considerations
ACI Code specify that for tied or spirally reinforced columns, clear
distance between bars, shown in Figure, is not to be less than the
larger of 1.50 times bar diameter or 4 cm. This is done to ensure free
flow of concrete among reinforcing bars.
Clear Distance between Reinforcing Bars
Design Considerations
26
Concrete Protection Cover
ACI Code specifies that for reinforced columns, the clear concrete cover is not to be
taken less than 4 cm for columns not exposed to weather or in contact with ground. It is
essential for protecting the reinforcement from corrosion or fire hazards.
Minimum Cross Sectional Dimensions
The ACI Code does not specify minimum cross sectional dimensions for columns.
Column cross sections 20 × 25 cm are considered as the smallest practicable sections.
For practical considerations, column dimensions are taken as multiples of 5 cm.
Lateral Reinforcement
Ties are effective in restraining the longitudinal bars from buckling out through the
surface of the column, holding the reinforcement cage together during the construction
process, confining the concrete core and when columns are subjected to horizontal
forces, they serve as shear reinforcement.
Design Considerations
27
Factored Loads
For gravity loads only,
Pu = 1.2 PD+1.6 PL
For dead, live and wind loads,
Pu = 1.2 PD+1.0 PL+1.6 PW
For dead and wind loads,
Pu = 0.9 PD + 1.3 PW or Pu = 1.2 PD + 0.8 PW
For dead, live and earthquake loads,
Pu = 1.2 PD+1.0 PL+1.0 PE
For dead and earthquake loads,
Pu = 0.9 PD + 1.0 PE
28
Design Considerations
1. Evaluate the factored axial load Pu acting on the column.
2. Decide on a reinforcement ratio ρg that satisfies ACI Code limits. Usually a 1 %
ratio is chosen for economic considerations.
3. Determine the gross sectional area Ag of the concrete section.
4. Choose the dimensions of the cross section based on its shape.
5. Readjust the reinforcement ratio by substituting the actual cross sectional area in the
respective equation. This ratio has to fall within the specified code limits.
6. Calculate the needed area of longitudinal reinforcement ratio based on the adjusted
reinforced ratio and the chosen concrete dimensions.
Design Procedure for Short Axially Loaded Columns
29
Design Procedure for Short Axially Loaded Columns
7. From reinforcement tables, choose the number and diameters of needed
reinforcing bars. For rectangular sections, a minimum of four bars is
needed, while a minimum of six bars is used for circular columns.
8. Design the lateral reinforcement according to the type of column, either
ties or spirals.
9. Check whether the spacing between longitudinal reinforcing bars satisfies
ACI Code requirements.
10. Draw the designed section showing concrete dimensions and with required
longitudinal and lateral reinforcement.
30
OK%8ρ1.21%ρ%1ρ
1.21%0.0124025
2.016
A
Aρ
maxgmin
g
sg
cm1512.82
3(1.6)2(0.8)2(4)40Sc
Example 1The cross section of a short axially loaded tied column is shown in
Figure. It is reinforced with 6 16mm bars. Calculate the design load
capacity of the cross section.
Use fc′=280 kg/cm2 and fy = 4200 kg/cm2.
Solution:
Clear distance between bars Sc
Only, one ties is required for the cross section
Figure [1]
6Φ1625
40
Ties Φ8@25cm
6Φ1625
40
Ties Φ8@25cm
Sc=12.8 cm
6Φ1625
40
31
Example 1 The spacing between ties is not exceed the smallest of 16 db =16(1.6) = 25.4 cm 48 ds = 48(0.8) = 38.4 cm 25 cmThus, ACI requirements regarding reinforcement ratio, clear distance between bars and tie spacing are all satisfied.
The design load capacity ΦPn
Φ 8mm ties spaced @ 25 cm
tons.148.7kg148,688PΦ
2800.8542000.01212800.8525400.52PΦ
'0.85ffρ'0.85f0.52APΦ
n
n
cygcgn
32
n g c g y c 0.65(0.8) 0.85 0.85P A f f f
Example 2
Design a short tied column to support a factored concentric load of 1000 kN, with one side of the cross section equals to 25
cm. 30cf Mpa 420yf Mpa 1%g
33
3
g
2
1000 10
0.65 0.8 0.85 30 0.01 420 0.85 30
65311g
A
A mm
Solution
u
g
c g y c
0.65 0.8 0.85 0.85
PA
f f f
34
2
2s
65311
250
261
column 25cm 40cm
A 0.01(25 40) 10
8 14
gA mm
b mm
h mm
use
cm
use
b stirrupNo. of bars 2 cover
No. of bars 1
40 4 1.4 2 4 0.8
38.267cm < 15cm ok
h d ds
Check spacing
35
b
max stirrup
16 16 1.4cm 22.4cm
48 48 0.8 38.4cm
smaller or
go
2
verns
5
d
s d
b d cm
Stirrup design
Example 3
Design a short, spirally reinforced column to support a service dead load of 800 kN and a service live load of 400 kN.
30cf Mpa 420yf Mpa 1%g
1.20 1.60 1.2 800 1.6 400 1600u D LP P P kN
u
g
c g y c
0.75 0.85 0.85 0.85
PA
f f f
Solution
3
g
2
1600 10
0.75 0.85 0.85 30 0.01 420 0.85 30
85237g
A
A mm
36
2
2s
85237
for circular column d= =329mm4
column with d = 35cm
A 0.01 (35 35) 9.624
7 14
g
g
A mm
A
use
cm
use
Solution
Check spacing between longitudinal bars
37
D’ =35-2(4)-2(0.8)-1.4=24cm
4cm
1.5(1.4)9.01cm1.410.41S
cm10.412
51.43sin24
2
360/NsinD'S
c
Design the needed spiral, try 8
38
center.tocenter3.5cm ofpitch a withspiral8mmΦUse
7.5cm)&2.5cm(limit codeACIwithin i.ecm,2.70.83.5S
center)to(centercm3.50astakencm,3.63S
4200280
127π/4
35π/4270.45
0.54
f
'f1
A
A0.45D
α4S
cm274435D
c
2
2
y
c
c
gc
s
c
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