Roofdeck Beam Ok 105

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beam rc1

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BEAM 1

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 2.5MPa; tS = 115mm

WTransmitted =WS3

=(5.20)(4.5)3

= 7.8kN/m

WT = 7.8kN/m + 3.17kN/m = 10.97kN/m

SPAN 2:

DL = 0MPa; LL = 2.5MPa; tS =110mm

WTransmitted = WS3

=(5.09)(4.5)3

= 7.64kN/m

WT = 7.64kN/m + 3.17kN/m = 10.81kN/m

SPAN 3:

DL = 0MPa; LL = 3MPa; tS = 105mm

WTransmitted = WS3

=(5.47)(4)

3= 7.29kN/m

WT = 7.29kN/m+ 3.17kN/m = 10.46kN/m

SPAN 4:

DL = 0MPa; LL = 3MPa; tS = 105mm

WTransmitted = WS3

=(5.47)(4)

3= 7.29kN/m

WT = 7.29kN/m+ 3.17kN/m = 10.46kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 125mm

WTransmitted = WS3

=(6.44)(4 )3

= 8.59kN/m

WT = 8.59kN/m+ 3.17kN/m = 11.76kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 10.97×4.52

16(1.30)

= 18.05kN-m

-MB1 = wL2

10(1.30) = 10.97×4.52

10(1.30)

= 28.88kN-m

-MB2 = wL2

11(1.30) = 10.81×42

11(1.30)

= 20.44kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 10.97×4.52

14(1.30)

= 20.63kN-m

Design for R.S.B

For Section 1-1, MEX = 28.88kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

28.88kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

As = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

= 50.50kN/m > 19kN/m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 20.63kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

20.63kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 10.97×4.52

10(1.30)

= 28.88kN-m

-MB2 = wL2

11(1.30) = 10.81×4.52

11(1.30)

= 25.87kN-m

-MC1 = wL2

11(1.30) = 10.81×4.52

11(1.30)

=25.87kN-m

-MC2 = wL2

11(1.30) = 10.46×42

11(1.30)

= 19.78kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 10.81×4.52

16(1.30)

= 17.79kN-m

Design for R.S.B

For Section 2-1, MEX = 28.88kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

28.88kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 17.79kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

17.79kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 10.81×4.52

11(1.30)

= 25.87kN-m

-MC2 = wL2

11(1.30) = 10.46×42

11(1.30)

= 19.78kN-m

-MD1 = wL2

11(1.30) = 10.46×42

11(1.30)

= 19.78kN-m

-MD2 = wL2

11(1.30) = 10.46×42

11(1.30)

= 19.78kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 10.46×42

16(1.30)

= 13.60kN-m

Design for R.S.B

For Section 3-1, MEX =25.87kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

25.87kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 13.60kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.60kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 10.46×42

11(1.30)

= 19.78kN-m

-MD2 = wL2

11(1.30) = 10.46×42

11(1.30)

= 19.78kN-m

-ME1 = wL2

11(1.30) = 10.46×42

11(1.30)

=19.78kN-m

-ME2 = wL2

10(1.30) = 11.76×42

10(1.30)

= 24.46kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 10.46×42

16(1.30)

= 13.60kN-m

Design for R.S.B

For Section 4-1, MEX = 24.46kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

24.46kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 13.60kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.60kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 10.46×42

11(1.30)

=19.78kN-m

-ME2 = wL2

10(1.30) = 11.76×42

10(1.30)

= 24.46kN-m

-MF = wL2

16(1.30) = 11.76×42

16(1.30)

= 15.29kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 11.76×42

14(1.30)

= 17.47kN-m

Design for R.S.B

For Section 5-1, MEX =24.46kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

24.46kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 17.47kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

17.47kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2BEAM 2

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 5MPa; tS = 105mm

WTransmitted =WS3

=7.47×4.53 = 11.21kN/m

WT = 11.21kN/m+ 3.17kN/m = 14.38kN/m

SPAN 2:

DL = 0.5MPa; LL = 5MPa; tS = 105mm

WTransmitted = WS

3 = 7.97× 4.5

3 = 11.96kN/m

WT = 11.96kN/m+ 3.17kN/m = 15.13kN/m

SPAN 3:

DL = 1MPa; LL = 5MPa; tS = 100mm

WTransmitted = WS

3 = 8.35× 4

3 = 11.13kN/m

WT = 11.13kN/m+ 3.17kN/m =14.30kN/m

SPAN 4:

DL = 1MPa; LL = 5MPa; tS = 100mm

WTransmitted = WS

3 = 8.35 × 4

3 = 11.13kN/m

WT = 11.13kN/m+ 3.17kN/m = 14.30kN/m

SPAN 5:

DL = 0.5MPa; LL = 5MPa; tS = 110mm

WTransmitted = WS

3 = 8.09 × 4

3 = 10.79kN/m

WT = 10.79kN/m+ 3.17kN/m = 13.96kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 14.38×4.52

16(1.30)

= 23.66kN-m

-MB1 = wL2

10(1.30) = 14.38×4.52

10(1.30)

= 37.86kN-m

-MB2 = wL2

11(1.30) = 15.13×42

11(1.30)

= 28.61kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 14.38×4.52

14(1.30)

= 27.04kN-m

Design for R.S.B

For Section 1-1, MEX = 37.86kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

37.86kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 27.04kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

27.04kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 14.38×4.52

10(1.30)

= 37.86kN-m

-MB2 = wL2

11(1.30) = 15.13×42

11(1.30)

= 28.61kN-m

-MC1 = wL2

11(1.30) = 15.13 x 4.52

11(1.30)

= 36.21kN-m

-MC2 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 15.13×4.52

16(1.30)

= 24.89kN-m

Design for R.S.B

For Section 2-1, MEX = 37.86kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

37.86kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 24.89kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

24.89kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 15.13 x 4.52

11(1.30)

= 36.21kN-m

-MC2 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-MD1 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-MD2 = wL2

10(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 14.30×42

16(1.30)

= 18.59kN-m

Design for R.S.B

For Section 3-1, MEX = 36.21kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

36.21kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M2 = 18.59kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

18.59kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-MD2 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-ME1 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-ME2 = wL2

10(1.30) = 13.96×42

10(1.30)

= 29.04kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 14.30×42

16(1.30)

= 18.59kN-m

Design for R.S.B

For Section 4-1, MEX = 29.04kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

29.04kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 18.59kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

18.59kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-ME2 = wL2

10(1.30) = 13.96×42

10(1.30)

= 29.04kN-m

-MF = wL2

16(1.30) = 11.76×42

16(1.30)

= 15.29kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 11.76×42

14(1.30)

= 17.47kN-m

Design for R.S.B

For Section 5-1, MEX = 29.05kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

29.05kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 17.47kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

17.47kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

BEAM 3

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 2.5MPa; tS = 100mm

WTransmitted =WS3

=(4.85)(4.5)3

= 7.28kN/m

WT = 7.28kN/m + 3.17kN/m = 10.45kN/m

SPAN 2:

DL = 0MPa; LL = 2.5MPa; tS = 95mm

WTransmitted = WS3

=(4.73)(4.5)3

= 7.10kN/m

WT = 7.10kN/m + 3.17kN/m = 10.27kN/m

SPAN 3:

DL = 0MPa; LL = 3MPa; tS = 90mm

WTransmitted = WS3

=(5.12)(4)

3= 6.83kN/m

WT = 6.83kN/m+ 3.17kN/m = 10.0kN/m

SPAN 4:

DL = 0MPa; LL = 3MPa; tS = 90mm

WTransmitted = WS3

=(5.12)(4)

3= 6.83kN/m

WT = 6.83kN/m+ 3.17kN/m = 10.0kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 95mm

WTransmitted = WS3

=(5.73)(4)

3 = 7.64kN/m

WT = 7.64kN/m+ 3.17kN/m = 10.81kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 10.45×4.52

16(1.30)

= 17.19kN-m

-MB1 = wL2

10(1.30) = 10.45×4.52

10(1.30)

= 27.51kN-m

-MB2 = wL2

11(1.30) = 10.27×42

11(1.30)

= 24.58kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 10.45×4.52

14(1.30)

= 19.65kN-m

Design for R.S.B

For Section 1-1, MEX = 27.51kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

27.51kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

= 50.50kN/m > 19kN/m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 19.65kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

19.65kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 10.45×4.52

10(1.30)

= 27.51kN-m

-MB2 = wL2

11(1.30) = 10.27×42

11(1.30)

= 24.58kN-m

-MC1 = wL2

11(1.30) = 10.27×4.52

11(1.30)

= 24.58-m

-MC2 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 10.27×4.52

16(1.30)

= 16.90kN-m

Design for R.S.B

For Section 2-1, MEX = 27.51kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

27.51kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 16.90kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

16.90kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 10.27×4.52

11(1.30)

= 24.58kN-m

-MC2 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

-MD1 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

-MD2 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 10×42

16(1.30)

= 13.0kN-m

Design for R.S.B

For Section 3-1, MEX = 24.58kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

24.58kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 13.0kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.0kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

-MD2 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

-ME1 = wL2

11(1.30) = 10×42

11(1.30)

=18.91kN-m

-ME2 = wL2

10(1.30) = 10.81×42

10(1.30)

= 22.48kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 10×42

16(1.30)

= 13.0kN-m

Design for R.S.B

For Section 4-1, MEX = 22.48kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

22.48kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 13.0kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.0kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 10×42

11(1.30)

=18.91kN-m

-ME2 = wL2

10(1.30) = 10.81×42

10(1.30)

= 22.48kN-m

-MF = wL2

16(1.30) = 10.81×42

16(1.30)

= 14.05kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 10.81×42

14(1.30)

= 16.06kN-m

Design for R.S.B

For Section 5-1, MEX = 22.48kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

22.48kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 16.06kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

16.06kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

BEAM 4

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 5MPa; tS = 100mm

WTransmitted =WS3

=7.35×4.53 = 11.03kN/m

WT = 11.03kN/m+ 3.17kN/m = 14.20kN/m

SPAN 2:

DL = 0.5MPa; LL = 5MPa; tS = 95mm

WTransmitted = WS

3 = 7.73 × 4.5

3 = 11.60kN/m

WT = 11.60kN/m+ 3.17kN/m = 14.77kN/m

SPAN 3:

DL = 1MPa; LL = 5MPa; tS = 90mm

WTransmitted = WS

3 = 8.12× 4

3 = 10.83kN/m

WT = 10.83kN/m+ 3.17kN/m =14.0kN/m

SPAN 4:

DL = 0MPa; LL = 5MPa; tS = 90mm

WTransmitted = WS

3 = 7.12 × 4

3 = 9.49kN/m

WT = 9.49kN/m+ 3.17kN/m = 12.66kN/m

SPAN 5:

DL = 0.5MPa; LL = 5MPa; tS = 95mm

WTransmitted = WS

3 = 7.73 × 4

3 = 10.31kN/m

WT = 10.31kN/m+ 3.17kN/m = 13.48kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 14.20×4.52

16(1.30)

= 23.36kN-m

-MB1 = wL2

10(1.30) = 14.20×4.52

10(1.30)

= 37.38kN-m

-MB2 = wL2

11(1.30) = 14.77×4.52

11(1.30)

= 35.35kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 14.20×4.52

14(1.30)

= 21.10kN-m

Design for R.S.B

For Section 1-1, MEX = 37.38kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

37.38kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 21.10kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

21.10kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 14.20×4.52

10(1.30)

= 37.38kN-m

-MB2 = wL2

11(1.30) = 14.77×4.52

11(1.30)

= 35.35kN-m

-MC1 = wL2

11(1.30) = 14.77 x 4.52

11(1.30)

= 35.35kN-m

-MC2 = wL2

11(1.30) = 14×42

11(1.30)

= 26.47kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 14.77×4.52

16(1.30)

= 19.20kN-m

Design for R.S.B

For Section 2-1, MEX = 37.38kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

37.38kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 19.20kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

19.20kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 14.77x 4.52

11(1.30)

= 35.35kN-m

-MC2 = wL2

11(1.30) = 14×42

11(1.30)

= 26.47kN-m

-MD1 = wL2

11(1.30) = 14×42

11(1.30)

= 26.47kN-m

-MD2 = wL2

10(1.30) = 12.66×42

11(1.30)

= 23.94kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 14×42

16(1.30)

= 18.20kN-m

Design for R.S.B

For Section 3-1, MEX = 35.35kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

35.35kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 18.20kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

18.20kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 14×42

11(1.30)

= 26.47kN-m

-MD2 = wL2

10(1.30) = 12.66×42

11(1.30)

= 23.94kN-m

-ME1 = wL2

11(1.30) = 12.66×42

11(1.30)

= 23.94kN-m

-ME2 = wL2

10(1.30) = 13.48×42

10(1.30)

= 28.04kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 12.66×42

16(1.30)

= 16.46kN-m

Design for R.S.B

For Section 4-1, MEX = 28.04kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

28.04kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 16.46kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

16.46kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 12.66×42

11(1.30)

= 23.94kN-m

-ME2 = wL2

10(1.30) = 13.48×42

10(1.30)

= 28.04kN-m

-MF = wL2

16(1.30) = 13.48×42

16(1.30)

= 17.52kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 13.48×42

14(1.30)

= 20.03kN-m

Design for R.S.B

For Section 5-1, MEX = 28.04kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

28.04kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 20.03kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

20.03kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

BEAM 5

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 2.5MPa; tS = 100mm

WTransmitted =WS3

=(4.85)(4.5)

3 = 7.28kN/m

WT = 7.28kN/m + 3.17kN/m = 10.45kN/m

SPAN 2:

DL = 0MPa; LL = 2.5MPa; tS = 95mm

WTransmitted = WS3

=(4.73)(4.5)3

= 7.10kN/m

WT = 7.10kN/m + 3.17kN/m = 10.27kN/m

SPAN 3:

DL = 0MPa; LL = 3MPa; tS = 90mm

WTransmitted = WS3

=(5.12)(4)3

= 6.83kN/m

WT = 6.83kN/m+ 3.17kN/m = 10.0kN/m

SPAN 4:

DL = 0MPa; LL = 3MPa; tS = 90mm

WTransmitted = WS3

=(5.12)(4)3

= 6.83kN/m

WT = 6.83kN/m+ 3.17kN/m = 10.0kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 95mm

WTransmitted = WS3

=(5.73)(4)

3 = 7.64kN/m

WT = 7.64kN/m+ 3.17kN/m = 10.81kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 10.45×4.52

16(1.30)

= 17.19kN-m

-MB1 = wL2

10(1.30) = 10.45×4.52

10(1.30)

= 27.51kN-m

-MB2 = wL2

11(1.30) = 10.27×42

11(1.30)

= 21.36kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 10.45×4.52

14(1.30)

= 15.53kN-m

Design for R.S.B

For Section 1-1, MEX = 27.51kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

27.51kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

= 50.50kN/m > 19kN/m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 15.53kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

15.53kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 10.45×4.52

10(1.30)

= 27.51kN-m

-MB2 = wL2

11(1.30) = 10.27×42

11(1.30)

= 21.36kN-m

-MC1 = wL2

11(1.30) = 10.27×4.52

11(1.30)

=24.58kN-m

-MC2 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 10.27×4.52

16(1.30)

= 16.90kN-m

Design for R.S.B

For Section 2-1, MEX = 27.51kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

27.51kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 16.90kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

16.90kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 10.27×4.52

11(1.30)

=24.58kN-m

-MC2 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

-MD1 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

-MD2 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 10×42

16(1.30)

= 13.0kN-m

Design for R.S.B

For Section 3-1, MEX =24.58kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

24.58kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 13.0kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.0kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

-MD2 = wL2

11(1.30) = 10×42

11(1.30)

= 18.91kN-m

-ME1 = wL2

11(1.30) = 10×42

11(1.30)

=18.91kN-m

-ME2 = wL2

10(1.30) = 10.81×42

14(1.30)

= 16.06kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 10×42

16(1.30)

= 13.0kN-m

Design for R.S.B

For Section 4-1, MEX = 18.91kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

18.91kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 13.0kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.0kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 10×42

11(1.30)

=18.91kN-m

-ME2 = wL2

10(1.30) = 10.81×42

14(1.30)

= 16.06kN-m

-MF = wL2

16(1.30) = 10.81×42

16(1.30)

= 15.05kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 10.81×42

14(1.30)

= 16.06kN-m

Design for R.S.B

For Section 5-1, MEX = 18.91kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

18.91kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 5-2, MEX = +M = 16.06kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

16.06kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

BEAM 6

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 5MPa; tS = 105mm

WTransmitted =WS3

=7.47×4.53 = 11.21kN/m

WT = 11.21kN/m+ 3.17kN/m = 14.38kN/m

SPAN 2:

DL = 0.5MPa; LL = 5MPa; tS = 100mm

WTransmitted = WS

3 = 7.85 × 4.5

3 = 11.78kN/m

WT = 11.78kN/m+ 3.17kN/m = 14.95kN/m

SPAN 3:

DL = 1MPa; LL = 5MPa; tS = 100mm

WTransmitted = WS

3 = 8.35× 4

3 = 11.13kN/m

WT = 11.13kN/m+ 3.17kN/m =14.30kN/m

SPAN 4:

DL = 1MPa; LL = 5MPa; tS = 100mm

WTransmitted = WS

3 = 8.35 × 4

3 = 11.13kN/m

WT = 11.13kN/m+ 3.17kN/m = 14.30kN/m

SPAN 5:

DL = 0.5MPa; LL = 5MPa; tS = 105mm

WTransmitted = WS

3 = 7.97 × 4

3 = 10.63kN/m

WT = 10.79kN/m+ 3.17kN/m = 13.80kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 14.38×4.52

16(1.30)

= 23.66kN-m

-MB1 = wL2

10(1.30) = 14.38×4.52

10(1.30)

= 37.86kN-m

-MB2 = wL2

11(1.30) = 14.95×42

11(1.30)

= 28.27kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 14.38×4.52

14(1.30)

= 27.04kN-m

Design for R.S.B

For Section 1-1, MEX = 37.86kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

37.86kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 27.04kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

27.04kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 14.38×4.52

10(1.30)

= 37.86kN-m

-MB2 = wL2

11(1.30) = 14.95×42

11(1.30)

= 28.27kN-m

-MC1 = wL2

11(1.30) = 14.95 x 4.52

11(1.30)

= 37.78kN-m

-MC2 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 14.95×4.52

16(1.30)

= 24.60kN-m

Design for R.S.B

For Section 2-1, MEX = 37.86kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

37.86kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 24.60kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

24.60kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 14.95 x 4.52

11(1.30)

= 37.78kN-m

-MC2 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-MD1 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-MD2 = wL2

10(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 14.30×42

16(1.30)

= 18.59kN-m

Design for R.S.B

For Section 3-1, MEX = 37.78kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

37.78kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M2 = 18.59kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

18.59kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-MD2 = wL2

10(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-ME1 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-ME2 = wL2

10(1.30) = 13.80×42

10(1.30)

= 28.70kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 14.30×42

16(1.30)

= 18.59kN-m

Design for R.S.B

For Section 4-1, MEX = 28.70kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

28.70kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 18.59kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

18.59kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 14.30×42

11(1.30)

= 27.04kN-m

-ME2 = wL2

10(1.30) = 13.80×42

10(1.30)

= 28.70kN-m

-MF = wL2

16(1.30) = 11.76×42

16(1.30)

= 15.29kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 13.80×42

14(1.30)

= 17.47kN-m

Design for R.S.B

For Section 5-1, MEX = 28.70kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

28.70kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 20.50kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

20.50kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

BEAM 7

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 2.5MPa; tS = 105mm

WTransmitted =WS3

=(4.97)(4)3

= 7.46kN/m

WT = 7.28kN/m + 3.17kN/m = 10.63kN/m

SPAN 2:

DL = 0MPa; LL = 2.5MPa; tS = 100mm

WTransmitted = WS3

=(4.85)(4 )

3 = 7.28kN/m

WT = 7.28kN/m + 3.17kN/m = 10.45kN/m

SPAN 3:

DL = 0MPa; LL = 3MPa; tS = 100mm

WTransmitted = WS3

=(5.35)(4)

3= 7.13kN/m

WT = 7.13kN/m+ 3.17kN/m = 10.30kN/m

SPAN 4:

DL = 0MPa; LL = 3MPa; tS = 100mm

WTransmitted = WS3

=(5.35)(4)3

= 7.13kN/m

WT = 7.13kN/m+ 3.17kN/m = 10.30kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 105mm

WTransmitted = WS3

=(5.97)(5)3

= 7.96kN/m

WT = 7.96kN/m+ 3.17kN/m = 11.13kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 115mm

WTransmitted = WS3

=(6.20)(5)

3 = 8.27kN/m

WT = 8.27kN/m+ 3.17kN/m = 11.44kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 10.63×42

16(1.30)

= 13.82kN-m

-MB1 = wL2

10(1.30) = 10.63×42

10(1.30)

= 22.11kN-m

-MB2 = wL2

11(1.30) = 10.45×42

11(1.30)

= 21.74kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 10.63×42

14(1.30)

= 15.79kN-m

Design for R.S.B

For Section 1-1, MEX = 22.11kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

22.11kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

= 50.50kN/m > 19kN/m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 15.79kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

15.79kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 10.63×42

10(1.30)

= 22.11kN-m

-MB2 = wL2

11(1.30) = 10.45×42

11(1.30)

= 21.74kN-m

-MC1 = wL2

11(1.30) = 10.45×42

11(1.30)

= 19.76kN-m

-MC2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 10.45×42

16(1.30)

= 13.59kN-m

Design for R.S.B

For Section 2-1, MEX = 22.11kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

22.11kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 13.59kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN--m

Check if MEX < MC

13.59kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 10.45×42

11(1.30)

= 19.76kN-m

-MC2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD1 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 10.30×42

16(1.30)

= 13.39kN-m

Design for R.S.B

For Section 3-1, MEX = 19.76kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

19.76kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 13.39kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.39kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-ME1 = wL2

11(1.30) = 10.30×42

11(1.30)

=19.48kN-m

-ME2 = wL2

10(1.30) = 11.13×52

10(1.30)

= 32.88kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 10.30×42

16(1.30)

= 13.39kN-m

Design for R.S.B

For Section 4-1, MEX = 32.88kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

32.88kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 13.39kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.39kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 10.30×42

11(1.30)

=19.48kN-m

-ME2 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF1 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF2 = wL2

10(1.30) = 11.44×52

10(1.30)

= 37.18kN-m

For Positive Moment:

+M5 = wL2

16(1.30) = 11.13×52

16(1.30)

= 22.61kN-m

Design for R.S.B

For Section 5-1, MEX = 37.18kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

37.18kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 22.61kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

22.61kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

SPAN 6: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MF1 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF2 = wL2

10(1.30) = 11.44×52

10(1.30)

= 37.18kN-m

-MG1 = wL2

16(1.30) = 11.44×52

16(1.30)

= 23.24kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 11.44×52

14(1.30)

= 26.56kN-m

Design for R.S.B

For Section 6-1, MEX = 37.18kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

46.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-1

Design for R.S.B

For Section 6-2, MEX = +M6 = 26.56kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

26.56kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-2

BEAM 8

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 2.5MPa; tS = 100mm

WTransmitted =WS3

=(4.85)(4 )3

= 6.46kN/m

WT = 6.46kN/m + 3.17kN/m = 9.63kN/m

SPAN 2:

DL = 0MPa; LL = 2.5MPa; tS = 95mm

WTransmitted = WS3

=(4.73)(4 )

3 = 6.31kN/m

WT = 6.31kN/m + 3.17kN/m = 9.48kN/m

SPAN 3:

DL = 0MPa; LL = 3MPa; tS = 95mm

WTransmitted = WS3

=(4.73)(4 )3

= 6.31kN/m

WT = 6.31kN/m+ 3.17kN/m = 9.48kN/m

SPAN 4:

DL = 0MPa; LL = 3MPa; tS = 95mm

WTransmitted = WS3

=(4.73)(4 )3

= 6.31kN/m

WT = 6.31kN/m+ 3.17kN/m = 9.48kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 105mm

WTransmitted = WS3

=(5.97)(5)

3 = 7.96kN/m

WT = 7.96kN/m+ 3.17kN/m = 11.13kN/m

SPAN 5:

DL = 0MPa; LL = 3MPa; tS = 125mm

WTransmitted = WS3

=(5.94)(5)

3 = 9.9kN/m

WT = 9.9kN/m + 3.17kN/m = 13.07kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the

beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 9.63×42

16(1.30)

= 12.52kN-m

-MB1 = wL2

10(1.30) = 9.63×42

10(1.30)

= 20.03kN-m

-MB2 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 9.63×42

14(1.30)

= 14.31kN-m

Design for R.S.B

For Section 1-1, MEX = 20.03kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

20.03kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

= 50.50kN/m > 19kN/m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 14.31kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

14.31kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 9.63×42

10(1.30)

= 20.03kN-m

-MB2 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

-MC1 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

-MC2 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 9.48×42

16(1.30)

= 12.32kN-m

Design for R.S.B

For Section 2-1, MEX = 20.03kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

20.03kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 12.32kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN--m

Check if MEX < MC

12.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load

that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

-MC2 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

-MD1 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

-MD2 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 9.48×42

16(1.30)

= 12.32kN-m

Design for R.S.B

For Section 3-1, MEX = 17.93kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

17.93kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 12.32kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

12.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

-MD2 = wL2

11(1.30) = 9.48×42

11(1.30)

= 17.93kN-m

-ME1 = wL2

11(1.30) = 9.48×42

11(1.30)

=17.93kN-m

-ME2 = wL2

10(1.30) = 11.13×52

10(1.30)

= 32.88kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 9.48×42

16(1.30)

= 12.32kN-m

Design for R.S.B

For Section 4-1, MEX = 32.88kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

32.88kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 12.32kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

12.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 9.48×42

11(1.30)

=17.93kN-m

-ME2 = wL2

10(1.30) = 11.13×52

10(1.30)

= 32.88kN-m

-MF1 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF2 = wL2

10(1.30) = 13.07×52

10(1.30)

= 42.48kN-m

For Positive Moment:

+M5 = wL2

16(1.30) = 11.13×52

16(1.30)

= 22.61kN-m

Design for R.S.B

For Section 5-1, MEX = 42.48kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

42.48kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 22.61kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

22.61kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

SPAN 6: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MF1 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF2 = wL2

10(1.30) = 13.07×52

10(1.30)

= 42.48kN-m

-MG1 = wL2

16(1.30) = 13.07×52

16(1.30)

= 26.55kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 13.07×52

14(1.30)

= 30.34kN-m

Design for R.S.B

For Section 6-1, MEX = 42.48kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

42.48kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-1

Design for R.S.B

For Section 6-2, MEX = +M6 = 30.34kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

30.34kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-2

BEAM 9

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 2.5MPa; tS = 100mm

WTransmitted =WS3

=(4.85)(4 )

3 = 6.47kN/m

WT = 6.47kN/m + 3.17kN/m = 9.64kN/m

SPAN 2:

DL = 0MPa; LL = 2.5MPa; tS = 90mm

WTransmitted = WS3

=(4.62)(4)

3 = 6.16kN/m

WT = 6.16kN/m + 3.17kN/m = 9.33kN/m

SPAN 3:

DL = 0MPa; LL = 3MPa; tS = 90mm

WTransmitted = WS3

=(5.12)(4)

3= 6.83kN/m

WT = 6.83kN/m+ 3.17kN/m = 9.9kN/m

SPAN 4:

DL = 0MPa; LL = 3MPa; tS = 90mm

WTransmitted = WS3

=(5.12)(4)3

= 6.83kN/m

WT = 6.83kN/m+ 3.17kN/m = 9.9kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 100mm

WTransmitted = WS3

=(5.85)(5)

3 = 9.75kN/m

WT = 9.75kN/m+ 3.17kN/m = 12.92kN/m

SPAN 5:

DL = 0MPa; LL = 2MPa; tS = 105mm

WTransmitted = WS3

=(4.47)(5)3

= 7.45kN/m

WT = 7.45kN/m+ 3.17kN/m = 10.62kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 9.64×42

16(1.30)

= 12.53kN-m

-MB1 = wL2

10(1.30) = 9.64×42

10(1.30)

= 20.05kN-m

-MB2 = wL2

11(1.30) = 9.33×42

11(1.30)

= 17.64kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 9.64×42

14(1.30)

= 14.32kN-m

Design for R.S.B

For Section 1-1, MEX = 20.5kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

20.05kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

= 50.50kN/m > 19kN/m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 14.32kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

14.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 9.64×42

10(1.30)

= 20.05kN-m

-MB2 = wL2

11(1.30) = 9.33×42

11(1.30)

= 17.64kN-m

-MC1 = wL2

11(1.30) = 9.33×42

11(1.30)

= 17.64kN-m

-MC2 = wL2

11(1.30) = 9.9×42

11(1.30)

= 18.72kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 9.33×42

16(1.30)

= 12.13kN-m

Design for R.S.B

For Section 2-1, MEX = 20.05kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

20.05kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 12.13kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN--m

Check if MEX < MC

12.13kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 9.33×42

11(1.30)

= 17.64kN-m

-MC2 = wL2

11(1.30) = 9.9×42

11(1.30)

= 18.72kN-m

-MD1 = wL2

11(1.30) = 9.9×42

11(1.30)

= 18.72kN-m

-MD2 = wL2

11(1.30) = 9.9×42

11(1.30)

= 18.72kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 9.9×42

16(1.30)

= 12.87kN-m

Design for R.S.B

For Section 3-1, MEX = 18.72kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

18.72kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 12.87kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

12.87kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 9.9×42

11(1.30)

= 18.72kN-m

-MD2 = wL2

11(1.30) = 9.9×42

11(1.30)

= 18.72kN-m

-ME1 = wL2

11(1.30) = 9.9×42

11(1.30)

=18.72kN-m

-ME2 = wL2

11(1.30) = 12.92×52

11(1.30)

= 38.17kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 9.89×42

16(1.30)

= 12.87kN-m

Design for R.S.B

For Section 4-1, MEX = 38.17kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

38.17kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 12.87kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

12.87kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 9.9×42

11(1.30)

=18.72kN-m

-ME2 = wL2

11(1.30) = 12.92×52

11(1.30)

= 38.17kN-m

-MF1 = wL2

11(1.30) = 12.92×52

11(1.30)

= 38.17kN-m

-MF2 = wL2

10(1.30) = 10.62×52

10(1.30)

= 34.52kN-m

For Positive Moment:

+M5 = wL2

16(1.30) = 12.92×52

16(1.30)

= 26.24kN-m

Design for R.S.B

For Section 5-1, MEX = 38.17kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

38.17kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 26.24kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

26.24kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

SPAN 6: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MF1 = wL2

11(1.30) = 12.92×52

11(1.30)

= 38.17kN-m

-MF2 = wL2

10(1.30) = 10.62×52

10(1.30)

= 34.52kN-m

-MG1 = wL2

16(1.30) = 10.62×52

16(1.30)

= 21.57kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 10.62×52

14(1.30)

= 24.65kN-m

Design for R.S.B

For Section 6-1, MEX = 38.17kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

38.17kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-1

Design for R.S.B

For Section 6-2, MEX = +M6 = 24.65kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

24.65kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-2

BEAM 10

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 2.5MPa; tS = 105mm

WTransmitted =WS3

=(4.97)(4.5)3

= 7.46kN/m

WT = 7.28kN/m + 3.17kN/m = 10.63kN/m

SPAN 2:

DL = 0MPa; LL = 2.5MPa; tS = 100mm

WTransmitted = WS3

=(4.85)(4.5)

3 = 7.28kN/m

WT = 7.28kN/m + 3.17kN/m = 10.45kN/m

SPAN 3:

DL = 0MPa; LL = 3MPa; tS = 100mm

WTransmitted = WS3

=(5.35)(4)

3= 7.13kN/m

WT = 7.13kN/m+ 3.17kN/m = 10.30kN/m

SPAN 4:

DL = 0MPa; LL = 3MPa; tS = 100mm

WTransmitted = WS3

=(5.35)(4)3

= 7.13kN/m

WT = 7.13kN/m+ 3.17kN/m = 10.30kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 105mm

WTransmitted = WS3

=(5.97)(4)3

= 7.96kN/m

WT = 7.96kN/m+ 3.17kN/m = 11.13kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 115mm

WTransmitted = WS3

=(6.20)(4)

3 = 8.27kN/m

WT = 8.27kN/m+ 3.17kN/m = 11.44kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 10.63×42

16(1.30)

= 13.82kN-m

-MB1 = wL2

10(1.30) = 10.63×42

10(1.30)

= 22.11kN-m

-MB2 = wL2

11(1.30) = 10.45×42

11(1.30)

= 21.74kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 10.63×42

14(1.30)

= 15.79kN-m

Design for R.S.B

For Section 1-1, MEX = 22.11kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

22.11kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

= 50.50kN/m > 19kN/m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 15.79kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

15.79kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 10.63×42

10(1.30)

= 22.11kN-m

-MB2 = wL2

11(1.30) = 10.45×42

11(1.30)

= 21.74kN-m

-MC1 = wL2

11(1.30) = 10.45×42

11(1.30)

= 19.76kN-m

-MC2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 10.45×42

16(1.30)

= 13.59kN-m

Design for R.S.B

For Section 2-1, MEX = 22.11kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

22.11kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 13.59kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN--m

Check if MEX < MC

13.59kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the

beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 10.45×42

11(1.30)

= 19.76kN-m

-MC2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD1 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 10.30×42

16(1.30)

= 13.39kN-m

Design for R.S.B

For Section 3-1, MEX = 19.76kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

19.76kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 13.39kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.39kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-ME1 = wL2

11(1.30) = 10.30×42

11(1.30)

=19.48kN-m

-ME2 = wL2

10(1.30) = 11.13×52

10(1.30)

= 32.88kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 10.30×42

16(1.30)

= 13.39kN-m

Design for R.S.B

For Section 4-1, MEX = 32.88kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

32.88kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 13.39kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.39kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 10.30×42

11(1.30)

=19.48kN-m

-ME2 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF1 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF2 = wL2

10(1.30) = 14.44×52

10(1.30)

= 46.32kN-m

For Positive Moment:

+M5 = wL2

16(1.30) = 11.13×52

16(1.30)

= 22.61kN-m

Design for R.S.B

For Section 5-1, MEX = 46.32kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

46.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 22.61kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

22.61kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

SPAN 6: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MF1 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF2 = wL2

10(1.30) = 14.44×52

10(1.30)

= 46.32kN-m

-MG1 = wL2

16(1.30) = 14.44×52

16(1.30)

= 29.33kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 14.44×52

14(1.30)

= 33.52kN-m

Design for R.S.B

For Section 5-1, MEX = 46.32kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

46.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 33.52kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

33.52kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-2

BEAM 11

fc’ = 21MPa k = 0.31

fs = 210MPa j = 0.90

b = 300mm h= 450mm

n = 10

Solve for Loadings

WT = WTransmitted + WB

WB = bhWC

= 0.300 × 0.450 × 23.5kN/m

= 3.17kN/m

Load Transmitted from Slab to Beam

SPAN 1:

DL = 0MPa; LL = 2.5MPa; tS = 105mm

WTransmitted =WS3

=(4.97)(4.5)

3 = 7.46kN/m

WT = 7.28kN/m + 3.17kN/m = 10.63kN/m

SPAN 2:

DL = 0MPa; LL = 2.5MPa; tS = 100mm

WTransmitted = WS3

=(4.85)(4.5)3

= 7.28kN/m

WT = 7.28kN/m + 3.17kN/m = 10.45kN/m

SPAN 3:

DL = 0MPa; LL = 3MPa; tS = 100mm

WTransmitted = WS3

=(5.35)(4)

3= 7.13kN/m

WT = 7.13kN/m+ 3.17kN/m = 10.30kN/m

SPAN 4:

DL = 0MPa; LL = 3MPa; tS = 100mm

WTransmitted = WS3

=(5.35)(4)

3= 7.13kN/m

WT = 7.13kN/m+ 3.17kN/m = 10.30kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 105mm

WTransmitted = WS3

=(5.97)(4)

3 = 7.96kN/m

WT = 7.96kN/m+ 3.17kN/m = 11.13kN/m

SPAN 5:

DL = 0.5MPa; LL = 3MPa; tS = 115mm

WTransmitted = WS3

=(6.20)(4)

3 = 8.27kN/m

WT = 8.27kN/m+ 3.17kN/m = 11.44kN/m

SPAN 1: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MA = wL2

16(1.30) = 10.63×42

16(1.30)

= 13.82kN-m

-MB1 = wL2

10(1.30) = 10.63×42

10(1.30)

= 22.11kN-m

-MB2 = wL2

11(1.30) = 10.45×42

11(1.30)

= 21.74kN-m

For Positive Moment:

+M1 = wL2

14(1.30) = 10.63×42

14(1.30)

= 15.79kN-m

Design for R.S.B

For Section 1-1, MEX = 22.11kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

22.11kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

= 50.50kN/m > 19kN/m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-1

Design for R.S.B

For Section 1-2, MEX = +M1 = 15.79kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

15.79kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45 x 106

210×0.9×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-16mm ∅

Ass = ⫪ (16 )2

4(3) = 603.19mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 1-2

SPAN 2: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MB1 = wL2

10(1.30) = 10.63×42

10(1.30)

= 22.11kN-m

-MB2 = wL2

11(1.30) = 10.45×42

11(1.30)

= 21.74kN-m

-MC1 = wL2

11(1.30) = 10.45×42

11(1.30)

= 19.76kN-m

-MC2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

For Positive Moment:

+M2= wL2

16(1.30) = 10.45×42

16(1.30)

= 13.59kN-m

Design for R.S.B

For Section 2-1, MEX = 22.11kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

22.11kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-1

Design for R.S.B

For Section 2-2, MEX = +M2 = 13.59kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN--m

Check if MEX < MC

13.59kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 2-2

SPAN 3: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MC1 = wL2

11(1.30) = 10.45×42

11(1.30)

= 19.76kN-m

-MC2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD1 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

For Positive Moment:

+M3 = wL2

16(1.30) = 10.30×42

16(1.30)

= 13.39kN-m

Design for R.S.B

For Section 3-1, MEX = 19.76kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

19.76kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-1

Design for R.S.B

For Section 3-2, MEX = +M3 = 13.39kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.39kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 3-2

SPAN 4: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MD1 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-MD2 = wL2

11(1.30) = 10.30×42

11(1.30)

= 19.48kN-m

-ME1 = wL2

11(1.30) = 10.30×42

11(1.30)

=19.48kN-m

-ME2 = wL2

10(1.30) = 11.13×52

10(1.30)

= 32.88kN-m

For Positive Moment:

+M4= wL2

16(1.30) = 10.30×42

16(1.30)

= 13.39kN-m

Design for R.S.B

For Section 4-1, MEX = 32.88kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

32.88kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.9 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-1

Design for R.S.B

For Section 4-2, MEX = +M4 = 13.39kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12×(0.45×21)×0.31×0.9×300×3502

= 48.45kN-m

Check if MEX < MC

13.39kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.9×350 = 732.43mm2

Try using 20mm ∅

N = AsA∅ =

732.43⫪ (20 )2

4 = 2.33 ≈ 3 pcs.

As = ⫪ (20 )2

4(3) = 942.48mm2

Using 3-18mm ∅

Ass = ⫪ (18 )2

4(3) = 763.41mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 4-2

SPAN 5: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-ME1 = wL2

11(1.30) = 10.30×42

11(1.30)

=19.48kN-m

-ME2 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF1 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF2 = wL2

10(1.30) = 14.44×52

10(1.30)

= 46.32kN-m

For Positive Moment:

+M5 = wL2

16(1.30) = 11.13×52

16(1.30)

= 22.61kN-m

Design for R.S.B

For Section 5-1, MEX = 46.32kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

46.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 22.61kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

22.61kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 5-2

SPAN 6: Design of R.S.B

Solve for External Moments

Using Moment Coefficient from ACI Codes:

Note: Additional 30% will be added in each moment for the seismic and wind load that can be developed within the beam. Largest moment in the section on the beam adjacent to the column will govern in designing the R.S.B.

For Negative Moments:

-MF1 = wL2

11(1.30) = 11.13×52

11(1.30)

= 32.88kN-m

-MF2 = wL2

10(1.30) = 14.44×52

10(1.30)

= 46.32kN-m

-MG1 = wL2

16(1.30) = 14.44×52

16(1.30)

= 29.33kN-m

For Positive Moment:

+M5 = wL2

14(1.30) = 14.44×52

14(1.30)

= 33.52kN-m

Design for R.S.B

For Section 5-1, MEX = 46.32kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

46.32kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

@ Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-1

Design for R.S.B

For Section 5-2, MEX = +M5 = 33.52kN-m

Check for Moment Capacity of Concrete

d = h – m; where m = 100mm

d = 450mm – 100mm = 350mm

MC = 12fckjbd2 × 10-6 kN-m

= 12 ×(0.45×21)×0.31×0.90×300×3502

= 48.45kN-m

Check if MEX < MC

33.52kN-m < 48.45kN-m

∴ SAFE and Beam is S.R.B

Use MC in designing R.S.B in Tension Zone

Tension Bars

MS = ASfsjd

AS = 48.45E6

210×0.90×350 = 732.43mm2

Try using 18mm ∅

N = AsA∅ =

732.43⫪ (18 )2

4 = 2.88 ≈ 3 pcs.

As = ⫪ (18 )2

4(3) = 763.41mm2

Using 3-20mm ∅

Ass = ⫪ (20 )2

4(3) = 942.48mm2

∴ Adopt 3-18mm ∅

Check for the Spacing:

S = (300−100−(3×18))

2 = 73mm

S = 73mm > 25mm

∴ SAFE

Check for Moment Capacity of Reinf.

MS = ASfsjd × 10-6kN-m

= 763.41 × 210 × 0.90 × 350

= 50.50kN-m

Ms > MEX

∴ SAFE

ILLUSTRATION FOR SECTION 6-2

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