COLUMNS

According to ACI Code 21 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 support vertical loads from the floor and roof slabs and transfer these loads to the footingsColumns usually support compressive loads with or without bendingDepending on the magnitude of the bending moment and the axial forcecolumn behavior will vary from pure beam action to pure column actionColumns are classified as short or long depending on their slenderness ratios Short columns usually fail when their materials are overstressed and long columns usually fail due to buckling which produces secondary moments resulting from the P minus Δ effectColumns are classified according to the way they are reinforced into tied and spirally reinforced columns Columns are usually reinforced with longitudinal and transverse reinforcement

IntroductionIntroduction

Types of ColumnsTypes of Columns

Columns are divided into three types according to the way they are reinforced

Tied ColumnsTied Columns

Tied column

Spirally-Reinforced ColumnsSpirally-Reinforced Columns

Spirally-reinforced column

Composite ColumnsComposite Columns

Composite column

Factored Loads and Strength Reduction FactorsFactored Loads and Strength Reduction FactorsFactored LoadsFactored Loads

WDu

W

WLDu

L

D

u

LDu

PPP

P

PPPP

P

P

P

PPP

301900

loads windand deadFor 3

load windservice

where

)701701401(750

loads windand live deadFor 2

load live service

load dead service

load factored

where

701401

only loadsgravity For 1

Strength Reduction FactorsStrength Reduction Factors

ACI Code 9322 specifies that for tied columns the strength reduction factors Φ is taken as 070 For spirally reinforced columns the strength reduction factor Φ is taken as 075 This factor is larger for spirally reinforced columns than for tied columns due to the ductility that spirally reinforced columns show before collapse takes place For columns under axial tension and axial tension with flexure both axial load and moment nominal strengths are multiplied by a strength reduction factor Φ of 090The basic equation is given by

nU PP

load axial nominal

factorreduction strength

load axial factored

where

P

Φ

P

n

u

When axial compressive loads are applied through the centroid of the cross section of a short column concrete and steel reinforcement are shortened by the same amount due to their composite action From equilibrium of forces in the vertical direction

yssgcno

nsncno

fAAAfP

PPP

)(

days-28at strength ecompressiv concrete

entreinforcem of area sectional cross

column of area sectional gross

entreinforcem steelby carried load axial nominal

concreteby carried load axial nominal

section ofcapacity axial nominal

Where

c

s

g

ns

nc

no

f

A

A

P

P

P

Short Axially Loaded ColumnsShort Axially Loaded Columns

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

According to ACI Code 21 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 support vertical loads from the floor and roof slabs and transfer these loads to the footingsColumns usually support compressive loads with or without bendingDepending on the magnitude of the bending moment and the axial forcecolumn behavior will vary from pure beam action to pure column actionColumns are classified as short or long depending on their slenderness ratios Short columns usually fail when their materials are overstressed and long columns usually fail due to buckling which produces secondary moments resulting from the P minus Δ effectColumns are classified according to the way they are reinforced into tied and spirally reinforced columns Columns are usually reinforced with longitudinal and transverse reinforcement

IntroductionIntroduction

Types of ColumnsTypes of Columns

Columns are divided into three types according to the way they are reinforced

Tied ColumnsTied Columns

Tied column

Spirally-Reinforced ColumnsSpirally-Reinforced Columns

Spirally-reinforced column

Composite ColumnsComposite Columns

Composite column

Factored Loads and Strength Reduction FactorsFactored Loads and Strength Reduction FactorsFactored LoadsFactored Loads

WDu

W

WLDu

L

D

u

LDu

PPP

P

PPPP

P

P

P

PPP

301900

loads windand deadFor 3

load windservice

where

)701701401(750

loads windand live deadFor 2

load live service

load dead service

load factored

where

701401

only loadsgravity For 1

Strength Reduction FactorsStrength Reduction Factors

ACI Code 9322 specifies that for tied columns the strength reduction factors Φ is taken as 070 For spirally reinforced columns the strength reduction factor Φ is taken as 075 This factor is larger for spirally reinforced columns than for tied columns due to the ductility that spirally reinforced columns show before collapse takes place For columns under axial tension and axial tension with flexure both axial load and moment nominal strengths are multiplied by a strength reduction factor Φ of 090The basic equation is given by

nU PP

load axial nominal

factorreduction strength

load axial factored

where

P

Φ

P

n

u

When axial compressive loads are applied through the centroid of the cross section of a short column concrete and steel reinforcement are shortened by the same amount due to their composite action From equilibrium of forces in the vertical direction

yssgcno

nsncno

fAAAfP

PPP

)(

days-28at strength ecompressiv concrete

entreinforcem of area sectional cross

column of area sectional gross

entreinforcem steelby carried load axial nominal

concreteby carried load axial nominal

section ofcapacity axial nominal

Where

c

s

g

ns

nc

no

f

A

A

P

P

P

Short Axially Loaded ColumnsShort Axially Loaded Columns

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Types of ColumnsTypes of Columns

Columns are divided into three types according to the way they are reinforced

Tied ColumnsTied Columns

Tied column

Spirally-Reinforced ColumnsSpirally-Reinforced Columns

Spirally-reinforced column

Composite ColumnsComposite Columns

Composite column

Factored Loads and Strength Reduction FactorsFactored Loads and Strength Reduction FactorsFactored LoadsFactored Loads

WDu

W

WLDu

L

D

u

LDu

PPP

P

PPPP

P

P

P

PPP

301900

loads windand deadFor 3

load windservice

where

)701701401(750

loads windand live deadFor 2

load live service

load dead service

load factored

where

701401

only loadsgravity For 1

Strength Reduction FactorsStrength Reduction Factors

ACI Code 9322 specifies that for tied columns the strength reduction factors Φ is taken as 070 For spirally reinforced columns the strength reduction factor Φ is taken as 075 This factor is larger for spirally reinforced columns than for tied columns due to the ductility that spirally reinforced columns show before collapse takes place For columns under axial tension and axial tension with flexure both axial load and moment nominal strengths are multiplied by a strength reduction factor Φ of 090The basic equation is given by

nU PP

load axial nominal

factorreduction strength

load axial factored

where

P

Φ

P

n

u

When axial compressive loads are applied through the centroid of the cross section of a short column concrete and steel reinforcement are shortened by the same amount due to their composite action From equilibrium of forces in the vertical direction

yssgcno

nsncno

fAAAfP

PPP

)(

days-28at strength ecompressiv concrete

entreinforcem of area sectional cross

column of area sectional gross

entreinforcem steelby carried load axial nominal

concreteby carried load axial nominal

section ofcapacity axial nominal

Where

c

s

g

ns

nc

no

f

A

A

P

P

P

Short Axially Loaded ColumnsShort Axially Loaded Columns

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Spirally-Reinforced ColumnsSpirally-Reinforced Columns

Spirally-reinforced column

Composite ColumnsComposite Columns

Composite column

Factored Loads and Strength Reduction FactorsFactored Loads and Strength Reduction FactorsFactored LoadsFactored Loads

WDu

W

WLDu

L

D

u

LDu

PPP

P

PPPP

P

P

P

PPP

301900

loads windand deadFor 3

load windservice

where

)701701401(750

loads windand live deadFor 2

load live service

load dead service

load factored

where

701401

only loadsgravity For 1

Strength Reduction FactorsStrength Reduction Factors

ACI Code 9322 specifies that for tied columns the strength reduction factors Φ is taken as 070 For spirally reinforced columns the strength reduction factor Φ is taken as 075 This factor is larger for spirally reinforced columns than for tied columns due to the ductility that spirally reinforced columns show before collapse takes place For columns under axial tension and axial tension with flexure both axial load and moment nominal strengths are multiplied by a strength reduction factor Φ of 090The basic equation is given by

nU PP

load axial nominal

factorreduction strength

load axial factored

where

P

Φ

P

n

u

When axial compressive loads are applied through the centroid of the cross section of a short column concrete and steel reinforcement are shortened by the same amount due to their composite action From equilibrium of forces in the vertical direction

yssgcno

nsncno

fAAAfP

PPP

)(

days-28at strength ecompressiv concrete

entreinforcem of area sectional cross

column of area sectional gross

entreinforcem steelby carried load axial nominal

concreteby carried load axial nominal

section ofcapacity axial nominal

Where

c

s

g

ns

nc

no

f

A

A

P

P

P

Short Axially Loaded ColumnsShort Axially Loaded Columns

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Composite ColumnsComposite Columns

Composite column

Factored Loads and Strength Reduction FactorsFactored Loads and Strength Reduction FactorsFactored LoadsFactored Loads

WDu

W

WLDu

L

D

u

LDu

PPP

P

PPPP

P

P

P

PPP

301900

loads windand deadFor 3

load windservice

where

)701701401(750

loads windand live deadFor 2

load live service

load dead service

load factored

where

701401

only loadsgravity For 1

Strength Reduction FactorsStrength Reduction Factors

ACI Code 9322 specifies that for tied columns the strength reduction factors Φ is taken as 070 For spirally reinforced columns the strength reduction factor Φ is taken as 075 This factor is larger for spirally reinforced columns than for tied columns due to the ductility that spirally reinforced columns show before collapse takes place For columns under axial tension and axial tension with flexure both axial load and moment nominal strengths are multiplied by a strength reduction factor Φ of 090The basic equation is given by

nU PP

load axial nominal

factorreduction strength

load axial factored

where

P

Φ

P

n

u

When axial compressive loads are applied through the centroid of the cross section of a short column concrete and steel reinforcement are shortened by the same amount due to their composite action From equilibrium of forces in the vertical direction

yssgcno

nsncno

fAAAfP

PPP

)(

days-28at strength ecompressiv concrete

entreinforcem of area sectional cross

column of area sectional gross

entreinforcem steelby carried load axial nominal

concreteby carried load axial nominal

section ofcapacity axial nominal

Where

c

s

g

ns

nc

no

f

A

A

P

P

P

Short Axially Loaded ColumnsShort Axially Loaded Columns

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Factored Loads and Strength Reduction FactorsFactored Loads and Strength Reduction FactorsFactored LoadsFactored Loads

WDu

W

WLDu

L

D

u

LDu

PPP

P

PPPP

P

P

P

PPP

301900

loads windand deadFor 3

load windservice

where

)701701401(750

loads windand live deadFor 2

load live service

load dead service

load factored

where

701401

only loadsgravity For 1

Strength Reduction FactorsStrength Reduction Factors

ACI Code 9322 specifies that for tied columns the strength reduction factors Φ is taken as 070 For spirally reinforced columns the strength reduction factor Φ is taken as 075 This factor is larger for spirally reinforced columns than for tied columns due to the ductility that spirally reinforced columns show before collapse takes place For columns under axial tension and axial tension with flexure both axial load and moment nominal strengths are multiplied by a strength reduction factor Φ of 090The basic equation is given by

nU PP

load axial nominal

factorreduction strength

load axial factored

where

P

Φ

P

n

u

When axial compressive loads are applied through the centroid of the cross section of a short column concrete and steel reinforcement are shortened by the same amount due to their composite action From equilibrium of forces in the vertical direction

yssgcno

nsncno

fAAAfP

PPP

)(

days-28at strength ecompressiv concrete

entreinforcem of area sectional cross

column of area sectional gross

entreinforcem steelby carried load axial nominal

concreteby carried load axial nominal

section ofcapacity axial nominal

Where

c

s

g

ns

nc

no

f

A

A

P

P

P

Short Axially Loaded ColumnsShort Axially Loaded Columns

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Strength Reduction FactorsStrength Reduction Factors

ACI Code 9322 specifies that for tied columns the strength reduction factors Φ is taken as 070 For spirally reinforced columns the strength reduction factor Φ is taken as 075 This factor is larger for spirally reinforced columns than for tied columns due to the ductility that spirally reinforced columns show before collapse takes place For columns under axial tension and axial tension with flexure both axial load and moment nominal strengths are multiplied by a strength reduction factor Φ of 090The basic equation is given by

nU PP

load axial nominal

factorreduction strength

load axial factored

where

P

Φ

P

n

u

When axial compressive loads are applied through the centroid of the cross section of a short column concrete and steel reinforcement are shortened by the same amount due to their composite action From equilibrium of forces in the vertical direction

yssgcno

nsncno

fAAAfP

PPP

)(

days-28at strength ecompressiv concrete

entreinforcem of area sectional cross

column of area sectional gross

entreinforcem steelby carried load axial nominal

concreteby carried load axial nominal

section ofcapacity axial nominal

Where

c

s

g

ns

nc

no

f

A

A

P

P

P

Short Axially Loaded ColumnsShort Axially Loaded Columns

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

When axial compressive loads are applied through the centroid of the cross section of a short column concrete and steel reinforcement are shortened by the same amount due to their composite action From equilibrium of forces in the vertical direction

yssgcno

nsncno

fAAAfP

PPP

)(

days-28at strength ecompressiv concrete

entreinforcem of area sectional cross

column of area sectional gross

entreinforcem steelby carried load axial nominal

concreteby carried load axial nominal

section ofcapacity axial nominal

Where

c

s

g

ns

nc

no

f

A

A

P

P

P

Short Axially Loaded ColumnsShort Axially Loaded Columns

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Eq yields larger values than those obtained from laboratory testing due to the better quality of the tested concrete cylinders Reducing the compressive strength in Eq by 15 gives results in close agreement with those obtained through testing schemes

yssgcno fAAAfP )(850

The above equation is appropriate for determining axial load capacities of already designed columns

ggs AA

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

where ρg is the reinforcement ratio

)]850(850[

)(850

cygcgno

ygggggcno

fffAP

fAAAfP

ACI Code 1035 reduces the strength of tied columns by 20 and spirally reinforced columns by 15 For capacity calculations of tied and spirally reinforced columns respectively the following equations are to be used

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Columns Subjected To Pure Axial TensionColumns Subjected To Pure Axial Tension

The strength under pure axial tension is computed assuming that the section is completely cracked and subjected to a uniform strain equal to or less than εy The axial capacity of the concrete is ignored and the axial strength in tension is given by the following equation

ysu fAP

where Φ is the strength reduction factor for axial tension = 090 and As is the area of column reinforcement

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Design ConsiderationsDesign Considerations

Maximum and Minimum Reinforcement RatiosMaximum and Minimum Reinforcement Ratios

ACI Code 1091 specifies that a minimum reinforcement ratio of 1 is to be used in tied or spirally reinforced columns Maximum reinforcement ratio is limited to 8 for columns For compression member with a cross section larger than required by consideration of loading ACI Code 1084 permits the minimum area of steel reinforcement to be based on the gross sectional area required by analysis The reduced sectional area is not to be less than one half the actual cross sectional dimensions

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Minimum Number of Reinforcing BarsMinimum Number of Reinforcing Bars

ACI Code 1092 specifies a minimum of four bars in rectangular tied columns or one bar in each corner of the cross section for other shapes and a minimum of six bars in spirally reinforced columns

Clear Distance between Reinforcing BarsClear Distance between Reinforcing Bars

ACI Code 763 and 764 specify that for tied or spirally reinforced columns clear distance between bars is not to be less than the larger of 150 times bar diameter or 4 cm This is done to ensure free flow of concrete among reinforcing bars The clear distance limitations also apply to the clear distance between lap spliced bars and adjacent lap splices since the maximum number of bars occurs at the splices

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Concrete Protection CoverConcrete Protection Cover

ACI Code 771 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 DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Minimum Cross Sectional DimensionsMinimum Cross Sectional Dimensions

The ACI Code does not specify minimum cross sectional dimensions for columns Column cross sections 20 times 25 cm are considered as the smallest practicable sections For practical considerations column dimensions are taken as multiples of 5 cm

Lateral ReinforcementLateral 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

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

TiesTies

According to ACI Code 71051 for longitudinal bars 32 mm or smaller lateral ties 10 mm in diameter are used In our country and in some neighboring countries ties 8 mm in diameter are used in column construction Tests have proven that spacing between ties has no significant effect on ultimate strength of columnsACI Code 71052 specifies that vertical spacing of ties is not to exceed the smallest of1048707 16 times longitudinal bar diameter1048707 48 times tie diameter1048707 Least cross sectional dimension

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Design Procedure for Short Axially Loaded ColumnsDesign Procedure for Short Axially Loaded Columns

1 Evaluate the factored axial load Pu acting on the column2 Decide on a reinforcement ratio ρg that satisfies ACI Code limitsUsually a 1 ratio is chosen for economic considerations3 From equations for tied and spirally reinforced columns respectively determine the gross sectional area Ag of the concrete section 4 Choose the dimensions of the cross section based on its shape For rectangular sections the ratio of the longer to shorter side is recommended to not exceed 35 Readjust the reinforcement ratio by substituting the actual cross sectional area This ratio has to fall within the specified code limits6 Calculate the needed area of longitudinal reinforcement ratio based on the adjusted reinforced ratio and the chosen concrete dimensions

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

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 columns8 Design the lateral reinforcement according to the type of column either ties or spirals as explained in the previous sections of this chapter9 Check whether the spacing between longitudinal reinforcing bars satisfies ACI Code requirements10 Draw the designed section showing concrete dimensions and with required longitudinal and lateral reinforcement

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Example (92)Example (92)

SolutionSolution

The cross section of a short axially loaded tied column is shown in FigureIt is reinforced with 6φ 16mm barsCalculate the design load capacity of the cross section Use fcrsquo= 280kgcm2 and fy = 4200 kgcm2

211)25)(40(

)100(1012g

Clear distance between bars

cm80122

)601(3)800(2)4(240

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Since the clear distance between bars is less than 15 cm only one tie is required for the cross sectionThe spacing between ties is not to exceed the smallest of1048707 16 (16) = 2560 cm1048707 48 (080) = 3840 cm1048707 25 cmφ 8 mm ties spaced 25 cm (one set since only corner bars are used)Thus ACI requirements regarding reinforcement ratio clear distance between bars and tie spacing are all satisfied

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Example (93)Example (93)

SolutionSolution

The cross section of a short axially loaded tied column is shown in Figure (Ex 9-2)It is reinforced with 6φ 16mm barsCalculate the design tensile load capacity of the cross section Use fc prime = 280kgcm2 and fy = 4200 kgcm2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

Example (94)Example (94)

SolutionSolution

Design a short tied column to support a factored concentric load of 80 tons with one side of the cross section equals to 25 cmUse fc prime = 280 kgcm2 fy = 4200 kgcm2 and = ρg 1

1- The factored load Pu is given as 80 tons2- The reinforcement ratio ρg is given as 13- Determine the gross sectional area Ag of the concrete section

• Slide 1
• Slide 2

• Slide 1
• Slide 2