CD1_Lect14

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


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


ucystcgn

steel

85.0

concrete

85.0 PffAfArP

14

ucystcgn

steel

85.0

concrete

85.0 PffAfArP

or

ucygcgn 85.085.0 PfffArP


un PP

15

u

g

c g y c

0.85 0.85

PA

r f f f

* when g is known or assumed:


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


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


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


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



Vertical spacing: (ACI 7.10.5.2)

16 db ( db for longitudinal bars ) 48 dstirrup least lateral dimension of column

s s s

22



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


Examples of lateral ties

24


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


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


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.


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


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

Documents

CD1_Lect14