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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
