BEAM DESIGN CALCULATION

Project Name

:

Unassigned

Client Name

:

Unassigned

Engineer Name

:

Unassigned

Design File

:

D:\Bentley\Common data\Bentley Communities\IS\Validation Sheets\IS code_Validation problem_Updated\Coupler Beam\Coupling beam-testing-model-2-Beam-1-15 m.rcdx

Analysis File

:

D:\Bentley\Common data\Bentley Communities\IS\Validation Sheets\IS code_Validation problem_Updated\Coupler Beam\Coupling beam-testing-model-2.std

Analysis Last Modified

:

10/28/2021 2:15:51 PM

Level Designed

:

15 m,20 m

 

 

Sr.No.

Symbol

Definitions

1

α

=

Angle formed with horizontal by diagonal reinforcement

2

ε1

=

Strain at level considered, Calculated ignoring the stiffening of the concrete in tension zone

3

εm

=

Average steel strain at level considered

4

Acr

=

Distance from the point considered to the surface of the nearest longitudinal bar

5

Adr

=

Area of diagonal reinforcement in coupler beam

6

AstCalc

=

Area of Tension reinforcement required in sqmm

7

Ast comp

=

Ast at compression side

8

AstCrack

=

Area of Tension reinforcement for Crack Width required in sqmm

9

AstPrv

=

Area of reinforcement provided at given section in sqmm

10

Asv

=

Area of shear reinforcement required per meter length in sqmm

11

Asv Reqd

=

Min area shear reinforcement as per clause 41.4.3

12

Asv Total Prv

=

Total area of shear reinforcement provided, including that for torsion

13

Asv Torsion

=

Area of Stirrups over the corner bars to resist shear and torsion as per clause 41.4.3

14

Asv Torsion Prv

=

Area of shear reinforcement resisting torsion (outer legs only)

15

b

=

Width of the Beam in mm

16

bw

=

Width of Web in mm

17

Ceff

=

Effective Cover of Beam in mm

18

Cmin

=

Clear cover

19

d

=

Effective depth of Beam in mm

20

d'

=

Clear cover to reinforcement at compression side.

21

D

=

Depth of Beam in mm

22

D'

=

Distance (c/c) between top-most and bottom-most layer

23

Df

=

Thickness of Flange in mm

24

Ec

=

Modulus of elasticity of concrete

25

Es

=

Modulus of elasticity of steel

26

FcPerm

=

Permissible Stress in Concrete required in N/sqmm

27

Fst

=

Stress in steel

28

FstPerm

=

Permissible Stress in Steel required in N/sqmm

29

Legs

=

Number of legs of the shear reinforcement

30

lo

=

Effective Length of Beam in mm

31

Mh

=

Hogging Moment of Resistance in kNm

32

Ms

=

Sagging Moment of Resistance in kNm

33

MTu

=

Converted Bending Moment due to Torsion at a section in kNm

34

Mu

=

Factored Bending Moment in Limit State at a section in kNm

35

Mud

=

Total Design Moment = Mu + MTu in kNm

36

MuLim

=

Limiting Moment of Resistence of Singly Reinforced Section

37

NA angle (φ)

=

It is a neutral axis angle corresponding to load angle to find out MCap

38

Pcclc

=

Calculated percentage compression steel

39

Ptclc

=

Calculated percentage tension steel

40

Ptmin

=

Minimum percentage steel as per code

41

PtPrv

=

provided percentage steel

42

R

=

Moment Ratio Mud/Bd2

43

Reinf

=

Rebar arrangement provided

44

sp

=

Spacing Between bars at outer most layer

45

Spc1 to Spc6

=

Max Stirrup Criteria in mm

46

Stirrup Dia

=

Diameter of shear stirrups in mm

47

SvCalc

=

Stirrup spacing calculated as per Asv in mm

48

SvPrv

=

Stirrup spacing provided in m

49

Tc

=

Permissible Shear stress in concrete at a given section in N/sqmm Calculated as per Tensile reinforcement

50

Τce

=

Earthquake inducted shear stress in N/sqmm

51

Τcep

=

Permissible value of shear stress for checking of coupling action in N/sqmm

52

Tu

=

Factored Torsional Moment in Limit State at a section in kNm

53

Tv

=

Shear stress due to Vud in N/sqmm

54

VD+L

=

Shear force 1.2x(Dead Load + Live Load) in kN

55

Vc

=

Shear capacity of concrete section due to Tc in kN

56

Vu

=

Factored Shear Force in Limit State at a section in kN

57

Vu-A1

=

VD+LLeft - 1.4 x (MsLeft + MhRight)/L in kN

58

Vu-A2

=

VD+LLeft + 1.4 x (MhLeft + MsRight)/L in kN

59

Vu-B1

=

VD+LRight + 1.4 x (MsLeft + MhRight)/L in kN

60

Vu-B2

=

VD+LRight - 1.4 x (MhLeft + MsRight)/L in kN

61

Vud

=

Design Shear Force (Max of Vus and Vu-sway) in kN

62

Vue

=

Earthquake inducted shear in kN

63

Vu-sway

=

Max of (Vu-A1 and Vu-A2) & (Vu-B1 and Vu-B2) in kN

64

Vus

=

Vud - Vc Design Shear Force for reinforcement, in kN

65

Vut

=

Total Shear Force = Vu + VTu in kN

66

VTu

=

Converted Shear Force due to Torsion at a section in kN

67

Wcr

=

Surface Crack Width

68

WcrPerm

=

Permissible Crack Width required in mm

69

X1

=

Smaller c/c dimension of outermost Stirrups

70

Y1

=

Larger c/c dimension of outermost Stirrups

All 6mm diameter bars are assumed 250 grade with fy = 250 N/sqmm

 

All Forces are in 'kN', 'kNm', Stress in 'N/sqmm' & Dimension are in 'mm'.

 

Code References

 

IS 456

Sr.No.

Item

Clause / Table

1.

Ptmax

:

26.5.1.1

2.

Ptmin

:

26.5.1.1

3.

MTu

:

41.4.2

4.

VTu

:

41.3.1

5.

Ptclc

:

38

6.

Tc

:

40.2.1

7.

Tcmax

:

40.2.3

8.

Asv

:

40.4

9.

Min Shear Reinf

:

26.5.1.6

10.

Max Stirrup Spacing

:

26.5.1.5

11.

Shear Reinf - Torsion

:

26.5.1.7

12.

Side Face Reinforcement

:

26.5.1.3

13.

crack width calculation

:

Annex-F

14.

cracking

:

Clause 35.3.2

                                

IS 13920 - 2016

Sr.No.

Item

Clause / Table

1.

Ptmax

:

6.2.2

2.

Ptmin

:

6.2.1

3.

Astmin

:

6.2.3 & 6.2.4

4.

Svclc

:

6.3.5

5.

Shear Capacity

:

6.3.4

6.

Coupling Beams

:

10.5


Group

:

G2

 

Beam No

:

B2

 

Analysis Reference (Member)

15 m

:

1304

 

20 m

:

1404

 

Beam Length

:

1000

mm

Breadth (B)

:

450

mm

Depth (D)

:

900

mm

Effective Depth (d)

:

845

mm

Design Code

:

IS 456

Beam Type

:

Coupling Beam

Grade Of Concrete (Fck)

:

M25

N/sqmm

Grade Of Steel

:

Fe415

N/sqmm

Clear Cover (Cmin)

:

25

mm

Es

:

2x10^5

N/sqmm

 

Check for coupling action

 

Clear Span of Beam, (Ls)

=

1000

mm

Beam Depth, (D)

=

900

mm

D'

=

850

mm

Shear, (Vue)

=

471.989

kN

Tce

=

Vue/BD

=

1.165

N/sqmm

Tcep

=

(0.1xLsxsqrt(Fck))/D

=

0.556

N/sqmm

Tce > Tcep

Hence, Beam is 'Coupling Beam'

Design of diagonal reinforcement

Angle with horizontal, (α)

=

40.365

deg

Adr

=

1514

sqmm

Reinforcement provided

=

4-T16
4-T16 Both diagonals

    

Flexure Design (For Vertical Load Only)

Beam Bottom

Beam Top

Left

Mid

Right

Left

Mid

Right

Critical L/C - RCDC

-

-

-

-

-

-

Mu (kNm)

-

-

-

-

-

-

Tu (kNm)

0

0

0

0

0

0

MTu (kNm)

0

0

0

0

0

0

Mud (kNm)

0

0

0

0

0

0

MuLim (kNm)

1109

1109

1109

1109

1109

1109

R

0

0

0

0

0

0

   Ptmin (%)

0.2

0.2

0.2

0.2

0.2

0.2

   Ptclc (%)

0.2

0.2

0.2

0.2

0.2

0.2

   Pcclc (%)

0

0

0

0

0

0

  PtPrv (%)

0.212

0.212

0.212

0.212

0.212

0.212

AstCalc (sqmm)

760.5

760.5

760.5

760.5

760.5

760.5

AstPrv (sqmm)

804.24

804.24

804.24

804.24

804.24

804.24

Reinforcement Provided

4-T16

4-T16

4-T16

4-T16

4-T16

4-T16

 

Shear Design (For Vertical Load Only)

Left

Mid

Right

Critical L/C - RCDC

-

-

0

PtPrv (%)

0.212

0.212

0.212

Vu (kN)

0

0

0

Tu (kNm)

0

0

0

VTu (kN)

0

0

0

Vut (kN)

0

0

0

Tv (N/sqmm)

0

0

0

Tc (N/sqmm)

0.34

0.34

0.34

Vc (kN)

128.91

128.91

128.91

Vus=Vut-Vc (kN)

0

0

0

Legs

2

2

2

Stirrup Rebar

8

8

8

Asv Torsion (sqmm)

-

-

-

Asv Torsion Prv (sqmm)

-

-

-

Asv Reqd (sqmm/m)

498.55

498.55

498.55

SvCalc (mm)

200

200

200

SvPrv (mm)

200

200

200

Asv Total Prv (sqmm)

502.7

502.7

502.7

 

 

Maximum Spacing Criteria

 

    

 

       Basic                               

                Spc1 =0.75d

=

634

mm

                Spc2

=

300

mm

 

SFR Design

 

  

 

Beam Width

=

450

mm

Beam Depth

=

900

mm

Beam Depth >750 Or Torsion > 0,

Hence SFR Provided

Asr

=

405

sqmm

SFR Provided

=

2-T12EF

ASFR Provided

=

452.4

sqmm

  

Spacing Criteria

           

Provided Spacing

=

272.7

mm

1.<= beam Width

=

450

mm

2. Not Greater Than

=

300

mm