8.2 Design of reinforcement for 1D members (beams, beams as slab, columns)

There is different procedure for design of longitudinal and shear reinforcement for beams, beams as slab and for columns.

8.2.1 Beams and beams as slab – design of reinforcement

8.2.1.1 Method for calculation strength reduction factor

There are three basic methods for design of longitudinal reinforcement. The decision which method will be used depends on the setting in concrete setup and in concrete member data. There are new options Use iterative calculation for design reinforcement in Concrete setup>General >Calculation and Type of strength reduction factor in concrete member data.

The three methods are the following:

Method 1 (User input value of Phi) – Use iterative calculation for design reinforcement is not important for this method and concrete member data is defined and Strength reduction factor Phi = User input

Method 2 (Iterative calculation value Phi) – Use iterative calculation for design reinforcement is ON and concrete member data is not defined or concrete member data is defined but Strength reduction factor Phi = Calculated

Method 3 (Non-iterative calculation value Phi) – Use iterative calculation for design reinforcement is OFF and concrete member data is not defined or concrete member data is defined but Strength reduction factor Phi = Calculated

Method Use iterative calculation for design reinforcement Concrete member data defined Strength reduction factor
Method 1 Not important YES User input
Method 2 ON YES or NO Calculated
Method 3 OFF YES or NO Calculated
8.2.1.1.1 Method 1 (User input value of Phi)

This method is used when Strength reduction factor Phi = User input in concrete member data


and

8.2.1.1.2 Method 2 (Iterative calculation value Phi)

The iterative method is used for calculation of strength reduction factor (). The procedure of this method is the following:


and

Strain

Estimation

 

Estimation of strength reduction factor is OK

 

Estimation is NOT OK and iterative calculation starts running

Iteration will be finished if (value from concrete setup

 

Estimation is NOT OK and calculation is finished with error (the cross-section is not ductile)
8.2.1.1.3 Method 3 (Non-iterative calculation value Phi)

The design reinforcement without iteration run according to following procedure:


and

Strain

Estimation

 

Estimation of strength reduction factor is OK

 

Estimation is OK BUT calculation finishes with warning (W301 - The section is in transition zone, but strength reduction factor for tension-controlled section is used)

 

 

Estimation is NOT OK and calculation is finished with error (E916 - the cross-section is not ductile)

Value is value equal to 0,004 (see chapter 4.1.4.3 Maximum strain for non-prestressed flexural member)

Output with W301

Output with E916

Explanation of values printed in the preview

Value

Description

Member

Name of the checked member

dx

Position of the checked section on member

Case

Loadcase/combination or class which is selected for check

f

Strength reduction factor

εst

Calculated strain in reinforcement

Nu

Factored normal force

Muy

Factored bending moment around y axis

Muz

Factored bending moment around z axis

c

Depth of the compression zone

d

Effective depth

As,add

Area of additional longitudinal reinforcement

W/E

Warning and errors

8.2.1.2 Longitudinal reinforcement

There is only one difference between design of reinforcement for “Beam” and “Beam as slab”. The shear reinforcement is not designed for member type “beam as slab”. The design of longitudinal reinforcement is the same for “beam” and “beam slab” too.

When shear reinforcement is designed for member type “beam slab” then special warning appears (W90 – No shear reinforcement calculated, since the beam is considered to be floor without shear reinforcement)

The procedure of design of longitudinal reinforcement is based on the calculation of equilibrium between internal forces and external load. This is general method independent on the used method.

There are the following preconditions:

8.2.1.2.1 Design of compressive reinforcement

The different procedure is used when it is necessary to design also compressive reinforcement. This procedure is applied when:

Then design of reinforcement is provided as the following:

8.2.1.2.2 Maximum reinforcement factor (chapter 10.3.5 from ACI 318-05)

When user switches ON this checkbox then the strain in reinforcement has to be higher than inputted value 0,004=. Otherwise the section is not ductile.

8.2.1.2.3 Detailing provisions

Detailing provisions for beams are verified. These detailing provisions are done for longitudinal and shear reinforcement separately.

8.2.1.2.3.1 Minimum reinforcement factor (chapter 10.5.1 from ACI 318-05)

When the designed are of reinforcement is too low then minimum are of reinforcement has to be used. Settings for this verification are explained in chapter "4 Global setting ". If the first two checkboxes are switch ON then calculation logic is the following

The existence of the tensile zone is checked.

8.2.1.2.3.2 Minimal clear distance between bars (chapter 7.6.1 from ACI 318-05)

When user switches ON the checkboxes related to minimal clear distance between bars then this detailing provision is verified during the design procedure.

Minimal clear distance between bars is set as

8.2.1.2.3.3 Maximal clear distance between bars (chapter 10.6.4 from ACI 318-05)

Maximal clear distance between bars is also checked. There are two items related to maximal clear distance between bars (see chapter "4 Global setting "). Maximal allowed centre to centre bars spacing between longitudinal bars is based on the chapter 10.6.4 from ACI 318-05 and on user defined value


Where

fs – stress in reinforcement closest to the tension face; can be taken as 2/3 fy

cc – the least distance from the surface of the bar to the tensile surface of cross-section

8.2.1.2.4 Table in document for member check

Member

dx

Case

φ

Nu

Mu

c

d

As,add

Reinf.

W/E

 

[m]

 

 

[kN]

[kNm]

[mm]

[mm]

[mm2]

 

 

Explanation of symbol

f

Strength reduction factor

Nu

Factored axial normal force

Mu

Factored bending moment

c

Distance from extreme compression fibre to neutral axis

d

Distance from extreme compression fibre to centroid of longitudinal tension reinf.

As,add

Theoretical reinforcement area

 

 

Table composer

εc

Max. compression strain in concrete

εsc

Max. compression strain in reinforcement

εst

Max. tension strain in reinforcement

σc

Max. compression stress in concrete

σsc

Max. compression stress in reinforcement

σst

Max. tension stress in reinforcement

db

Nominal diameter of longitudinal bar

#bars

Number of needed bars

As,user

User defined reinforcement area

As,perc

Percentage of reinforcement in upper/lower zone

cbal

Distance from extreme compression fibre to neutral axis for balanced strain conditions

8.2.1.3 Shear reinforcement

General principles for design is the following:

Design procedure:

Vu ≥ 0,5Vc

s – user defined value in concrete member data

In case Vs ≥ Vs,max/2

              8.2.1.3.1 Detailing provisions

Check detailing provisions for beams and shear reinforcement

8.2.1.3.1.1 Maximal centre to centre spacing of stirrups legs (chapter 11.5.5 from "10 Literature")

Maximal centre to centre spacing of stirrups legs is checked if the checkbox in concrete setup is switched ON. There are two different values dependent on shear reinforcement resistance of and maximal shear capacity of cross-section

Unit format

Formula

spacing

US

 

Metric

 

Where values mean

– shear reinforcement resistance of concrete section

- maximal shear resistance of concrete section

When reinforcement is designed according to this provision then warning appears (W52 - The  shear  reinforcement  was  designed  according  to  code  longitudinal  distance  of  stirrups). 

8.2.1.3.1.2 Minimal percentage of shear reinforcement (chapter 11.5.6 from "10 Literature")

Minimal percentage of shear reinforcement is checked if the checkbox in concrete setup is switched ON. There are two different values dependent on shear resistance of cross-section and maximal shear capacity

Unit format

Formula

spacing

US

 

Metric

 

Where values mean

– factored shear force acting on structure

- maximal shear resistance of concrete section

When reinforcement is designed according to this provision then warning appears (W46 - The shear reinforcement was designed according to percentage of shear reinforcement). 

8.2.1.3.1.3 Minimal diameter of shear reinforcement

Minimal allowed diameter of shear reinforcement is checked if the checkbox in concrete setup is switched ON. This check depends on defined diameter of longitudinal reinforcement in concrete member data and diameter of stirrup.

When lesser diameter of shear reinforcement is defined in concrete member data then warning appears. (W163 – The profile of the shear reinforcement is lesser than permitted)

8.2.1.3.1.4 Maximal transverse spacing of the legs

Maximal transverse spacing of the legs is checked if the checkbox in concrete setup is switched ON. This value is code independent and it is user value. Default is 12 inch. The check is performed in Concrete member data. When the checkbox user defined number of cuts is set ON then maximal transverse spacing of the stirrups legs is checked.

Minimal number of cuts is calculated based on this distance and user is not allowed to input less value then calculated by program. Otherwise the following message appears.

Shear  reinforcement for selected members

Member

dx

Case

φ

Vu

bw

d

Vc

Av

Reinf.

W/E

 

[m]

 

 

[kN]

[mm]

[mm]

[kN]

[mm2]

 

 

Explanation of symbol

f

Strength reduction factor for shear

Vu

Factored shear force

bw

Width of section for shear

d

Distance from extreme compression fiber to centroid of longitudinal tension reinf.

Vc

Nominal shear strength provided by concrete

Av

Area of shear reinforcement

 

 

Table composer

Nu

Factored axial normal force

Mu

Factored bending moment

Mm

Factored moment modified to account for effect of axial compression

Vs

Nominal shear strength provided by shear reinforcement

Vs.max

Maximal nominal shear strength provided by shear reinforcement

Av,min

Minimum area of shear reinforcement

ds

Nominal diameter of shear reinforcement

s

Centre to centre spacing of shear reinforcement

fyt

Specified yield strength of shear reinforcement

8.2.2 Column – design of reinforcement

8.2.2.1 Method for calculation strength reduction factor

There are three basic methods for design of longitudinal reinforcement. The decision which method will be used depends on the setting in concrete setup and in concrete member data. There are new options Use iterative calculation for design reinforcement in Concrete setup > General > Calculation, see chapter "4.1 Concrete setup for 1D member" and Type of strength reduction factor in concrete member data, see chapter "5.2 Member data 1D (beams, beams as slab, columns)".

Concrete setup >General > Calculation

Concrete member data

The three methods are the following:

Method

Use iterative calculation for design reinforcement

Concrete member data defined

Type of strength reduction factor

Method 1

-

YES

User input

Method 2

ON

YES or NO

Calculated

Method 3

OFF

YES or NO

Calculated
8.2.2.1.1 Method 1 (User input value of φ)

This method is used when Strength reduction factor Phi = User input in concrete member data. The following procedure is used:

8.2.2.1.2 Method 2 (Iterative calculation value φ)

This method is used, if  check box Use iterative calculation for design reinforcement is ON and concrete member data is not defined or concrete member data is defined and Type of strength reduction factor Phi = Calculated. The iterative calculation for calculation strength reduction factor is used, it mean that the calculation takes longer time, but the results are more precise. The value φ are calculated from values defined in concrete setup depending on strain in mots-tensioned reinforcement (value εt) and on axial force. It follows, that for each section of the member different value strength reduction factor can be used. The following procedure is used:

For tensile axial force and pure bending (Pu ³ 0)

Strain

Calculation and result of calculation

 

Estimation of strength reduction factor is OK and calculation is OK

 

Estimation is NOT OK and iterative calculation is used

Iteration will be finished if strain in most tensioned reinforcement in two consecutive steps is lesser than precision of calculation or number of iteration setup is exceeded

 

Estimation is NOT OK and new value of strength reduction factor will be used (the value for compression controlled section φ=φcc )

 

For compressive axial force (Pu < 0)

Strain

Calculation and result of calculation

 

Estimation of strength reduction factor NOT OK and new value of strength reduction factor will be used (the value for tension- controlled section φ=φtc)

 

 

Estimation is NOT OK and iterative calculation is used

Iteration will be finished if strain in most tensioned reinforcement in two consecutive steps is lesser than precision of calculation or number of iteration setup is exceeded

Estimation of strength reduction factor is OK and calculation is OK

 

where

Pu

Axial factored force

Muy(z)

factored bending moment about  y (z) axis of LCS. If magnified moments have to be taken into account, then Muy(z) =Muy(z),rec

Muy(z),rec

Recalculated factored bending moment with slenderness effect (magnified moments), see chapter "7.2 Internal forces for 1D members (beam, beam as slab, column)"

For strain in most tensioned reinforcement in cross-section is SEN is used symbol εst instead of value εt

8.2.2.1.3 Method 3 (Non-iterative calculation value φ)

This method is used check box Use iterative calculation for design reinforcement is ON and concrete member data is not defined or concrete member data is defined and Type of strength reduction factor Phi = Calculated. The value φ are loaded from concrete setup depending on value of axial force (Pu) in section. It follows, that for each section of the member different value strength reduction factor can be used. The following procedure is used:

For tensile axial force and pure bending (Pu³ 0)

Strain

Result of calculation

 

The strength reduction factor is correct and calculation is OK

 

The strength reduction factor is  incorrect and calculation finishes with warning 301 (The section is in transition zone, but strength reduction factor for tension-controlled section is used)

The strength reduction factor is  incorrect and calculation finishes with warning 302 (The section is compression-controlled, but strength reduction factor for tension-controlled section is used)

For compressive axial force (Pu < 0)

Strain

Result of calculation

 

The strength reduction factor is incorrect and calculation finishes with warning 303 (The section is tension-controlled , but strength reduction factor for  compression-controlled section is used)

 

The strength reduction factor is  incorrect and calculation finishes with warning 301 (The section is in transition zone, but strength reduction factor for tension-controlled section is used)

The strength reduction factor is correct and calculation is OK

 

where

Pu

Axial factored force

Muy(z)

factored bending moment about  y (z) axis of LCS. If magnified moments have to be taken into account, then Muy(z) =Muy(z),rec

Muy(z),rec

Recalculated factored bending moment with slenderness effect (magnified moments), see chapter 7.2.2 Column

For strain in most tensioned reinforcement in cross-section is SEN is used symbol εst instead of value εt

In the table below are compared results of design reinforcement with using Method 2 (iterative calculation of value φ) and Method 3 (non-iterative calculation of value φ) for column with different values internal forces.

Method 2

Method 3

8.2.2.2 Longitudinal reinforcement

The design of longitudinal reinforcement depends on method for calculation strength reduction factor and on method for design reinforcement in the main. For detailed procedure of calculation strength reduction factor see chapter "8.2 Design of reinforcement for 1D members (beams, beams as slab, columns)"

8.2.2.2.1 Method for design of reinforcement for column

There is supported following methods and cross-sections for design longitudinal reinforcement for column:

Method

Mark

Supported cross-section

Only corner design

C

Rectangular, T, I, L sections

Uniaxial bending calculation (sum)

Us

Rectangular cross-section

Uniaxial bending calculation (max)

Um

Rectangular cross-section

Biaxial bending calculation

B

Rectangular cross-section

Design for circular column

C

Circular cross-section

Automatic calculation

B or Um

Rectangular cross-section

If compression member (column) is loaded only by axial force (bending moment about y and z axis of compression member are zero), then reinforcement is designed only for this axial load and method of calculation is N/A

Five methods of design reinforcement is supported for rectangular column, therefore it is very important select the correct method of calculation depending on values of bending moments or used automatic calculation. In the table below are compared results of design reinforcement for rectangular columns for different method (B1-only corner design, B2- Uniaxial bending calculation (sum), B3 - Uniaxial bending calculation (max) , B4 – biaxial bending calculation, B5- automatic calculation )

The following preconditions are used for all methods:

Member without concrete member data

Member with concrete member data

The results of design longitudinal reinforcement are presented in numerical and graphical output and detailed results for each section can be presented via action button Single check

The numerical output is available after clicking on action button Preview. The numerical output does depend on selected value. The table of longitudinal reinforcement is presented, if values As,total, req; As user define; As add,req is presented

There is available more detailed tables for columns (for example table with detailed presentation of area of reinforcement, or table with detailed presentation of number of bars ). These detailed tables can be selected after clicking on the header of the table and by selecting the type of the table from the combo box (see picture below)

Existing table can be edit via icon Table composer   or via double clicking on the header of the table, see picture above

The new table can be created via icon Table manager

The following values can be presented in numerical output:

Value

Explanation

Nu

Factored axial normal force

Muy

Factored bending moment around y axis (with influence of slenderness effect, if is taken into account)

Muz

Factored bending moment around z axis (with influence of slenderness effect, if is taken into account)

db

Nominal diameter of longitudinal bar

#bars

Number of needed bars

As,add

Theoretical reinforcement area (additional required area which is required to be added to user defined reinforcement to cross-section satisfies)

As,perc

Percentage of  longitudinal reinforcement in whole cross-section

Reinfreq

Number of required reinforcement bars (required number of bars which is required to be added to user defined reinforcement to cross-section satisfies).

For rectengular column:

String: nreq(nreq,y /n nreq,z )x db, for example 20(12/12)x0,5

For other column:

String: nreqx db, for example 20x0,5

nreq,y – number of bars of required reinforcement in direction y

nreq,z – number of bars of required reinforcement in direction z

nreq – total number of bars  of required reinforcement nreq = nreq,y + nreq,z – 4

Calc. type

Column calculation type: Us = uni-axial(sum) (diagram), Um = uni-axial(max) (diagram), B = bi-axial (formula), N/A = Not available, C = Circle column, O = Only corner design

Ratio y/z

Ratio of reinforcement in y and z direction calculated for designed area

Interaction check

Result of the interaction formula (Only for biaxial calculation )

W/E

Number that refers to the list of typical errors

Φ

Strength reduction factor

As,req,cor

Required reinforcement area in corner of rectangular cross-section (it is always reinforcement area of 4 bars)

As,req,ed,y

Required reinforcement area on edges in y direction (only for rectangular cross-section)

As,req,ed,z

Required reinforcement area on edges in z direction  (only for rectangular cross-section)

As,req,y

Required reinforcement area in y direction (only for rectangular cross-section)

As,req,y = As,req,ed,y +0,5· As,req,cor

As,req,z

Required reinforcement area in z direction (only for rectangular cross-section)

As,req,z = As,req,ed,z +0,5· As,req,cor

As,req

Required reinforcement area  As,req = As,req,y + As,req,z

As,user,cor

User reinforcement area in corner (only for rectangular cross-section). It is always reinforcement area of 4 bars)

As,user,ed,y

User reinforcement area on edges in y direction (only for rectangular cross-section)

As,user,ed,z

User reinforcement area on edges in z direction (only for rectangular cross-section)

As,user,y

User reinforcement area in y direction (only for rectangular cross-section)

As,user,y = As,user,ed,y + 0,5·As,user,cor

As,user,z

User reinforcement area in z direction (only for rectangular cross-section)

As,user,z = As,user,ed,z + 0,5·As,user,cor

As,user

User reinforcement area As,user = As,user,y + As,user,z

Reinfcor

Number of reinforcement bars in corner (only for rectangular column).

Content: 4 x db(As,user,cor) + 4x db(As,req,cor)  for example 4x0,5 (0,79) + 4x0,5 (0,79)

Reinfed,y

Number of reinforcement bars on edges in direction y (only for rectangular column)

String: nuser,ed,y x db(As,user,ed,y)+nreq,ed,y xdb(As,user,ed,y),for example 6x0,5(1,17)+4x0,5 (0,79)

nreq,ed,y – number of bars of required reinforcement on edges in direction y

nuser,ed,y – number of bars of user reinforcement on edges in direction y

Reinfed,z

Number of reinforcement bars on edges in direction y (only for rectangular column)

String: nuser,ed,z x db(As,user,ed,z)+nreq,ed,z xdb(As,user,ed,z),for example 4x0,5(0,79)+4x0,5 (0,79)

nreq,ed,z – number of bars of required reinforcement on edges in direction z

nuser,ed,z – number of bars of user reinforcement on edges in direction z

Reinfy

Number of reinforcement bars in direction y (only for rectangular column)

String: nreg,y x db(As,user,y)+nuser,y  xdb(As,req,y),for example 8x0,5(1,58)+6x0,5 (1,17)

nreq,y – number of bars of required reinforcement on edges in direction y: nreq,y = nreq,ed,y+2

nuser,y – number of bars of user reinforcement on edges in direction y:   nuser,y = nuser,ed,y+2

Reinfz

Number of reinforcement bars in direction z (only for rectangular column)

String: nreg,z x db(As,user,z)+nuser,z xdb(As,req,z),for example 8x0,5(1,58)+6x0,5 (1,17)

nreq,z – number of bars of required reinforcement on edges in direction z: nreq,z = nreq,ed,z+2

nuser,z – number of bars of user reinforcement on edges in direction z:   nuser,z = nuser,ed,z+2

Reinftot

Total number of reinforcement bars

String: nreg x db(As,user)+nuser xdb(As,req,),for example 8x0,5(1,58)+6x0,5 (1,17)

nreq– number of bars of required reinforcement (for rectangular column nreq = nreq,y + nreq,z )

nuser  – number of bars of user reinforcement :   (for rectangular column nreq = nreq,y + nreq,z )

Design Type

Design calculation type: UI = User input of value Phi, IC = Iterative calculation of value Phi, NC = Non-iterative calculation of value Phi, ND = Not defined

Poy

Axial resistance for bending moment Mu  (Only for biaxial calculation, Bresler reciprocal method )

Poz

Axial resistance for bending moment Muz (Only for biaxial calculation, Bresler reciprocal method )

Po

Maximum axial resistance without bending moments (Only for biaxial calculation, Bresler reciprocal method )

Mnoy

Nominal uniaxial moment resistance about the local y-axis of the member (Only for biaxial calculation, Bresler and  PCA load contour method )

Mnoz

Nominal uniaxial moment resistance about the local z-axis of the member (Only for biaxial calculation, Bresler and  PCA load contour method )

εst

Max. tension strain in reinforcement

The values in graphical output is always presented around axis of LCS , if the item More comp from combo box Values is not selected. If the item More comp. is selected, then user can select if the values will be presented around local axis (Drawing = 3D) or in one plane (Drawing = Screen)

Drawing = 3D

Drawing = Screen

8.2.2.2.2 Only corner design

This method is used for design of longitudinal reinforcement:

Only corner design is special type of calculation, where the reinforcement is designed only in corner of cross-section with internal angle 90deg. It is an iterative calculation, where number of bars is same, but the diameter of bars increases. The way of increasing diameter depends on setting of radio button Design reinforcement  by using (biaxial and only corner design) in Concrete setup, item Calculation > Column > Advanced setting, see chapter 4.1.3.1.5.7 Group Design reinforcement using (biaxial and only corner design)

Diameter d

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Imperial [inch]

0.375

0.5

0.625

0.75

0.875

1

1.128

1.27

1.41

1.693

2.257

-

-

-

-

Soft metric [inch]

9.5

12.7

15.9

19.1

22.2

25.4

28.7

32.3

35.8

43

57.3

-

-

-

-

European [mm]

6

8

10

12

14

16

18

20

22

25

26

28

30

32

40

where

ΔA 

is value of delta area set in concrete setup, see chapter 4.1.3.1.5.7.2 Delta area of reinforcement

i

is number of iteration step

In both cases the calculation finishes with error 508 (The number of iteration is exceeded) if designed reinforcement does not satisfy for maximum diameter defined in table above.

The position of corner bars in both cases is calculated from parameters defined in concrete setup (item Design default > Column, see chapter "4.1 Concrete setup for 1D member"), if concrete member data is not defined or from concrete member data (see chapter "4.1 Concrete setup for 1D member") otherwise.  The position is not changed during the iteration calculation.

Only the basic concrete section (Cross-section > Concrete) is supported for this calculation. The number of bars (ns) depends on shape of cross-section

Section

Rectangular section

I section

T section

L section with lower flange

L section with upper flange

ns

4

8

6

5

5

Shape

In the table below is designed longitudinal reinforcement to columns with different shape of cross-section loaded by compressive axial force and biaxial bending moment with using method Only corner design (initial value of diameter is 12 mm).

8.2.2.2.3 Uniaxial bending calculation

This method is available only for rectangular cross-section and there is supported two types of Uniaxial bending calculation:

 

Uniaxial bending moment (sum)

Direction

y axis

z axis

Resultant

Dimensional forces

Pu/φ, Muy/φ

Pu/φ, Muyz/φ

Pu/φ, Muy/φ, Muyz/φ

Arae of reinforcement

Asy

Asz

As = Asy+Asz

Picture

Uniaxial bending moment (max)

Condition

Muy ≥ Muz

Muy < Muz

Dimensional forces

Pu, Muy

Pu, Muz

Area of reinforcement

As = Asy

As = Asz

Picture

Uniaxial calculation is taken into account if check box Only corner design in concrete setup or in concrete member data is OFF

The procedure of design of longitudinal reinforcement is based on the calculation of equilibrium between internal forces and external load. The following preconditions are used

In the table below are compared results of design reinforcement with using Uniaxial bending calculation (sum) and Uniaxial bending calculation (max) for column with different values of bending moments Muy and Muz.

Uniaxial (sum)

Uniaxial (max)

8.2.2.2.4 Biaxial bending calculation for rectangular column

This method is available only for rectangular cross-section and  is used for member (column) without concrete member data, if Calculation method for design reinf. with rectangular css = Biaxial bending calculation(interaction formula) in   Concrete setup (General > Calculation > column > Advanced), see chapter "4.1 Concrete setup for 1D member" and for member with concrete member data, if Type of calculation = biaxial , see chapter "5.2 Member data 1D (beams, beams as slab, columns)".

Biaxial calculation is taken into account if check box Only corner design in concrete setup or in concrete member data is OFF

It is an iterative calculation, where number of bars is changed. The way of increasing number of bars of reinforcement in direction of y and z axis of LCS in each step depends on ratio of reinforcement in y and z direction of LCS of the column (see chapter 4.1.3.1.5.9 Group Ratio y/z or "5.2 Member data 1D (beams, beams as slab, columns)")   and on results of interaction formula. At first initial check of interaction formula for minimum number of bars is checked, it mean one bar in each corner of rectangular column. If interaction formula satisfies, the calculation is finisher. Otherwise iterative calculation according to scheme below is used.

where

nin 

The initial number of bars in one edge of rectangular cross-section. Default value is 32

ny(z)

number of bars at one edge of rectangular cross-section in y or z direction of LCS of the compression member

ratio_y/z

Ratio of reinforcement in y and z direction of LCS of compression member for biaxial calculation. Three type of method for calculation of this ratio are supported and this method and value can be set:

 

The number of bars in direction of z and y axis  of LCS of compression member does not depend on value ratio_y/z (the scheme above is not used), if check box  Optimize the number of  bars in c-s for biaxial calculation  (Concrete setup > General > Calculation, see chapter "4.1 Concrete setup for 1D member" ) is ON. In this case program checked all possible arrangements of bars of reinforcement  in z and y directions and select this one, which result of interaction formula is the nearest to one

If it is not possible to input designed number of bars too cross-section (problem with minimum bars distance) during to iterative calculation, the program finishes with  warning 115 (Maximum number of bars was placed into cross-section and the design basic condition is not fullfiled)

The area of one reinforcement bar used in biaxial calculation depends on setting of radio button Design reinforcement  by using (biaxial and only corner design) in Concrete setup, item Calculation > Column > Advanced setting, 4.1.3.1.5.7 Group Design reinforcement using (biaxial and only corner design)

In both cases the number of bars from designed area of reinforcement area calculated from the diameter defined in concrete setup, if member data is not defined on the member or from diameter defined in concrete member data, if member data is defined. 

    Three type methods (interaction formula) can be used for biaxial calculation of rectangular cross-section. This type of method can be set

 

Method

Interaction formula

Bressler reciprocal load method

Bressler load contour method

 

PCA load contour method

 

where

Pu/φ

factored axial force

Poy

Maximum uniaxial resistance of the column with a moment of Muy/φ, it means axial resistance for bending moment Muy/φ .It is intersection of Pn-Mn diagram  and  vertical line ( parallel with axis P) across the point with coordinate [Pu/φ, Muy/φ,0]

Poz

Maximum uniaxial resistance of the column with a moment of Muz/φ, it means axial resistance for bending moment Muz/φ. It is intersection of Pn-Mn diagram and  vertical line ( parallel with axis P) across the point with coordinate [Pu/φ,0, Muz/φ]

Po

Is maximum axial resistance without bending moments. It is intersection of interaction diagram and  vertical line ( parallel with axis P) across the point with coordinate [Pu/φ,0, 0]

Muy(z)/ φ

Factored (magnified) moment at section about  the y (z) axis of LCS of the member

f

Strength reduction factor calculated by iterative calculation, loaded from concrete setup or from concrete member data, see chapter "4.1 Concrete setup for 1D member"

Mnoy(z) 

nominal uniaxial moment resistance about the y (z) axis of LCS of the member

α

Exponent of interaction formula, which can be set in concrete setup, 4.1.3.1.5.8.1 Alpha

b

Exponent of interaction formula, which can be set in concrete setup, 4.1.3.1.5.8.2 Beta

In the table below are compared results of design reinforcement with using Biaxial bending calculation (interaction diagram) for column with rectangular cross-section and for different methods.

Input data

b =12 inch; h=20inch;c=1.5 inch; Pu=197,4 kip; Muy =129,8kipft; Muz =76kipft

 

σy =Muy/Wc,B,y =129.8/433.5 =0.00358 ksi ; σz =Muz/Wc,B,z =76/229.5 =0,003974 ksi

Ratio y/z =

Result

Bressler reciprocal load method

Initial check with minimum number of bars satisfies, iterative calculation is not necessary

 

Bressler load contour method  α = 1.5

Initial check with minimum number of bars does not satisfy, iterative calculation is necessary

PCA load contour methodβ = 0.65

Initial check with minimum number of bars does not satisfy, iterative calculation is necessary
    Design of reinforcement for circular column

This method is used for column with circular cross-section and for this cross-section is always used the following interaction formula

where

Muy(z)/ φ

Factored (magnified) moment at section about  the y (z) axis of LCS of the member

f

Strength reduction factor calculated by iterative calculation, loaded from concrete setup or from concrete member data, see chapter "4.1 Concrete setup for 1D member"

Mnoy(z) 

nominal uniaxial moment strength about the y (z) axis of LCS of the member

 

It is an iterative calculation, where number of bars is changed. The way of increasing number of bars in each steps depends on result of interaction formula, see scheme below

In the table below is presented iterative calculation and result of design reinforcement for column with circular cross-section.

Result

Iterative calculation

8.2.2.2.6 Automatic calculation

             This automatic determination of method for design reinforcement is supported only for rectangular column and it is used

Type of method, which will be used for design reinforcement, if Calculation Method =Automatic determination is selected, depends on ratio bending moments.

                                                                Ratio(My/Mz) =

where

Muy(z)/ φ

Factored (magnified) moment at section about  the y (z) axis of LCS of the member

Ratiolim

Limit value of ratio biaxial bending moment, which can be set

  •  

 

Member without concrete member data

Member with concrete member data

There is comparison of results for automatic determination of calculation moment for column with different value of bending moment column with the same load, but with different size of diameter of longitudinal reinforcemen.

If bending moments in both direction are zero, then reinforcement is designed only for normal force and calculation type =N/A

8.2.2.2.7 Detailing provisions

The following detailing provisions are checked for longitudinal reinforcement

8.2.2.2.7.1 Min. reinf. percentage

This detailing provisions is taken into account for design of reinforcement, if check box Min. reinf. percentage is ON (Concrete setup > Detailing provisions > Columns ), see chapter 4.1.5.2.1.1 Min. reinf. percentage. If this check box is ON and area of longitudinal reinforcement is lesser than minimum area of reinforcement.

As = As,min = x·Ag /100

then design of longitudinal reinforcement finishes with error 2 (The main reinforcement area was designed according to min. Required reinforcement percentage)

where

Ag

gross area of concrete section

x

Value of minimum percentage loaded from edit box

The minimum diameter of longitudinal reinforcement for Corner design only which can be used in calculation, if this detailing provisions ON, is calculated according to formula:

                                              

  where

ns

number of bars depending on shape of cross-section, see chapter Only corner design

The recalculation minimum area of reinforcement to direction y (area Asy) and z (area Asz) of LCS of rectangular compression member depends on type of calculation and values of bending moments

Type of calculation

Bending moments

 Asy Asz

Uni-axial calculation

Muy =0

Muz =0

0,5·As,min

0,5·As,min

Muy ≠ 0

Muz =0

As,min

0

Muy = 0

Muz ≠0

0

As,min

Muy ≠0

Muz ≠0

0,5·As,min

0,5·As,min

Bi-axial calculation

-

-

0,5·As,min

0,5·As,min

Percentage of reinforcement can be presented graphically and numerically, if in service Design As value Reinforcement ratio is selected

There is presented minimum area of reinforcement for different shape of cross-section and automatic determination of method for rectangular column.

8.2.2.2.7.2 Max. reinf. percentage

This detailing provision is taken into account for design of reinforcement, if check box Max. reinf. percentage is ON (Concrete setup > Detailing provisions > Columns), see chapter 4.1.5.2.1.2 Max. reinf. percentage. If this check box is ON and area of longitudinal reinforcement is greater than maximum area (As > As,max = x·Ag /100). Then design of longitudinal reinforcement finishes with warning 502 (The percentage of designed reinforcement  is higher than the maximum percentage))

where

Ag

gross area of concrete section

x

Value of maximum percentage loaded from edit box
8.2.2.2.7.3 Mini clear bars spacing

This detailing provisions is taken into account for design of reinforcement, if one from two check boxes Min.clear bars spacing is  ON (Concrete setup > Detailing provisions > Columns ), see chapter 4.1.5.2.1.3 Min. clear bars spacing or 4.1.5.2.1.4 Min. clear bars spacing .

Setting of calculation

Minimum clear bars spacing

 

where

db

diameter of longitudinal reinforcement loaded

  • from concrete setup (Design default > Column >main), if member data is not defined on the member or
  • from concrete member data (Design > Main >diameter) , if concrete member data is defined on the member

x,y

Values of minimum clear distance loaded form edit boxes, see chapter 4.1.5.2.1.3 Min. clear bars spacing or 4.1.5.2.1.4 Min. clear bars spacing

 

     If one from check boxes for check minimum clear bars spacing is ON  and  the clear bars spacing between bars is lesser than minimum, program finishes with the following warning:

Warning

Description

Cause

134

Tha bar distance for the  Y-direction is too small

The minimum spacing of bars  in direction of y-axis of LCS of the member for rectangular cross-section does not satisfy

136

Tha bar distance for the  Z-direction is too small

The minimum spacing  of bars in direction of z-axis of LCS of the member for rectangular cross-section does not satisfy

138

The bars distance is too small

The minimum spacing of bars in circular cross-section is does not satisfy

Minimal clear distance between bars is set as

The minimum spacing of bars is not checked for Only corner design

If for biaxial calculation , it is not possible to input designed number of bars too cross-section (problem with minimum bars distance) during to iterative calculation, the program finishes with  warning 115 (Maximum number of bars was placed into cross-section and the design basic condition is not fullfiled)

8.2.2.2.7.4 Max. bars spacing

This detailing provisions is taken into account for design of reinforcement, if check box Max.bars spacing is  ON (Concrete setup > Detailing provisions > Columns ), see chapter 4.1.5.2.1.5 Max. bars spacing . If this check box is ON, then centre-centre spacing between bars is checked. This is code independently check. If this centre-centre spacing of bars is bigger than maximum spacing then design of longitudinal reinforcement finishes with the following warnings

Warning

Description

Cause

133

Tha bar distance for the  Y-direction is too big

The centre-centre maximum  spacing of bars  in direction of y-axis of LCS of the member for rectangular cross-section does not satisfy

135

Tha bar distance for the  Z-direction is too big

The centre-centre maximum  spacing of bars in direction of z-axis of LCS of the member for rectangular cross-section does not satisfy

137

The bars distance is big

The centre-centre maximum  spacing of bars in circular cross-section does not satisfy

The maximum spacing of bars is not checked for Only corner design

8.2.2.2.7.5 Minimum number of bars

This detailing provisions is taken into account for design of reinforcement, if check box Min.number of bars is ON (Concrete setup > Detailing provisions > Columns), see chapter 4.1.5.2.1.6 Min. number of bars . If this check box is ON, then in design of reinforcement minimum number of bars set in concrete setup is used for design of reinforcement, though number of bars of statically required reinforcement is lesser. For rectangular column minimum numbers of bars is always 4, independently on value defined in the concrete setup. This check is used for circular column.

8.2.2.3 Shear reinforcement

Transverse (shear) reinforcement is designed as ties and vertical spacing of ties is designed according to detailing provisions.  The same shape of cross-section are supported for shear reinforcement as for longitudinal reinforcement

The results of shear reinforcement is presented in numerical and graphical output and detailed results for each section can be presented via action button Single check

The numerical output is available after clicking on action button Preview. The numerical output of shear reinforcement is presented, if values Ass is selected

8.2.2.3.1 Design of shear reinforcement

The vertical spacing of ties depends on:

Maximum spacing defined in Concrete setup

Basic distance in concrete data

The final vertical spacing of ties are calculated according to formula:

  ss,min = min ss,min,1 = x·db if check box is ON
ss,min,2 = min (b;h) if check box is ON
ss,min,3 = x·ds if check box is ON
ss if ss≠ 0

 

The area of shear reinforcement per meter is calculated according to formula

where

db

diameter of longitudinal reinforcement loaded

  • from concrete setup (Design default > Column >main), if member data is not defined on the member or
  • from concrete member data (Design > Main >diameter) , if concrete member data is defined on the member

ds

diameter of shear reinforcement (tie diameter)

  • from concrete setup (Design default > Column >Stirrup), if member data is not defined on the member or
  • from concrete member data (Design > Stirrups >Diameter) , if concrete member data is defined on the member

b,h

The dimensions of cross-section of compression member in direction of y(z) axis of LCS. For different shape of cross-section as than rectangular shape, the dimensions of circumscribed rectangular is taken into account

x

values of maximum spacing  loaded from edit box

ns

Number of cuts of ties, which can be calculated :

  • automatically , if concrete member data are not defined

 

bcen

width of cross-section in centroid of concrete cross-section

hcen

height of cross-section in centroid of concrete cross-section

c

The nominal value of concrete cover, value presented in property Concrete cover

st,max

the maximum transverse spacing of the legs, the value is defined in concrete setup (Concrete setup > Detailing provisions >Columns >Transverse reinforcement), see chapter 4.1.5.2.2.5 Max transverse spacing of the legs

The diameter of longitudinal reinforcement for calculation of vertical spacing of shear reinforcement is always loaded from concrete setup or concrete member data, though diameter of this longitudinal reinforcement is increased  during Only corner design

In the table below is presented results of calculation vertical spacing of ties for compression member with different input data

Input data and manually calculation

Results in SEN

8.2.2.3.2 Detailing provisions

Shear reinforcement is designed according to detailing provisions – maximum vertical spacing. Except the program is able to check minimum value of  diameter of shear reinforcement.

8.2.2.3.2.1 Check diameter of shear reinforcement

This detailing provisions is taken into account for design of shear reinforcement, if check box Check diameter is ON (Concrete setup > Detailing provisions > Columns), see chapter 4.1.5.2.2.4 Check diameter. If this check box is ON, then minimum diameter of shear reinforcement (ties)   according to clause 7.10.5.1 in ACI 318-05 is checked during design of shear reinforcement. Minimum diameter of shear reinforcement depends on diameter of longitudinal reinforcement, which enclosed, see table below

Unit format

Diameter of longitudinal reinforcement

Minimum shear diameter

US

Metric

 

where

db

diameter of longitudinal reinforcement loaded

  • from concrete setup (Design default > Column >main), if member data is not defined on the member or
  • from concrete member data (Design > Main >diameter) , if concrete member data is defined on the member

The diameter of longitudinal reinforcement for calculation of vertical spacing of shear reinforcement is always loaded from concrete setup or concrete member data, though diameter of this longitudinal reinforcement is increased  during Only corner design

If diameter of shear reinforcement   is lesser than minimum shear diameter, then design of shear reinforcement with warning 163 (The profile diameter of shear reinforcement is lesser than permitted). In this case, value shear reinforcement has to be increased in :