Rc Beam Design (cantilever)
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- Words: 800
- Pages: 8
Proj. Name: Location: Client: Designer: Date:
2 - Storey Resd'l. Lolita Village, Brgy. Caibaan, Tac. City Pitao BL Pitao BL 2/7/2008
General Description: Cantililever Beam 1.5 m span
DOUBLE REINFORCED CANTILEVER BEAM (WSD) AT END - SPAN NEGATIVE MOMENT DESIGN DATA FOR CONCRETE BEAMS: 13.79 ITEM fc' = 2,000.00 fc = .45fc' 6.21 Es 200,000.00 17,564.80 Ec = 4730√fc' n = Es/Ec 11.00 k = n/(n+fs/fc) 0.2481 j = 1 - k/3 0.92 Given: fc': 3,000.00 psi fc = 1,350.00 psi 9.308 mpa fs = 30,000.00 psi 206.85 mpa Concrete Covering: Top = 35 Bottom = 25
17.2 2,500.00 7.74 200,000.00 19,616.67 10.00 0.2723 0.91 Span L: Beam Section: b d Slab Thickness: Slab Width : Wall Ht. : Wall Thk.:
20.7 3,000.00 9.32 200,000.00 21,520.20 9.00 0.2884 0.90 1.5 150 250 0.1 3 1 0.13
DEADLOAD: 1/2L
BEAM : SLAB : WALL : SIESMIC:
LIVELOAD: TOTAL LOAD: W =
1.94
DESIGN MOMENT: Md = COMPUTING FOR M1 = As1 =
0.883 Kn / m 3.546 Kn / m 1.530 Kn / m 0.877 Kn / m 5.82 Kn / m 12.657 Kn / m WL^2/2
14.239
Kn - m
fckjbd^2/2
9.21
Kn - m
M1/fsjd
219.01
sq.mm.
IF: M1 < Md: THEREFORE : PROVIDE COMPRESION BARS COMPUTING FOR M2 =
TOTAL COMPUTE OF As':
As2 = As =
Md - M1 M2/fs(d-d') As1 + As2
5.03
Kn - m
113.01 332.02
sq.mm. sq.mm.
mpa psi mpa mpa
meters mm mm meters meters meters meters
WHERE:
fs' = 2fs(kd-d')/(d-kd) fs' = 103.07 IF: fs' < fs USE: COMPUTED fs' As' = M2/fs'(d-d') 256.63
Mpa sq.mm.
TRY: Tension Compression
No. of Bars 2.00 1.00 2.00 -
Bar Diameter 16 12 16 12
Unit mm mm mm mm
Area 201.06 113.10 201.06 113.10
CHECK FOR SHEAR: V = wL-wd
Allowable va:
16,137.37
v = V/bd va =.09*sqrt(f'c)
0.48 0.41
Newton Mpa Mpa
va
mm
Area = 0.07 2Avfv/v'b
78.54
sq.mm.
Mpa 3,147.55
ACI CODE: MAX. SPACING, Sm = IF: S>Sm : USE ACI CODE: Sm = D/2
mm 125
mm
125.00
mm
sq.mm. sq.mm. sq.mm. sq.mm.
Total Area 402.12 113.10 402.12 -
2.00 pcs. 1.00 pcs.
16 mm. dia. RC Bars 12 mm. dia. RC Bars
250 mm 10 mm dia. Stirrups
2.00 pcs. - pcs. 150 mm.
@ End - span
16 mm. dia. RC Bars 12 mm. dia. RC Bars
Total Area 515.22 OK, SAFE Kana BAY!!!! 402.12 OK, SAFE Kana BAY!!!!
Proj. Name: Location: Client: Designer: Date:
2 - Storey Resd'l. Bldg. Lolita Villaga, Brgy./ Caibaan, Tac. City Pitao BL Pitao BL 2/7/2008
General Description: Cantilever Beam 1.5 m span
INVESTIGATION OF DOUBLE REINF. BEAM AT END - SPAN NEGATIVE MOMENT DESIGN DATA FOR CONCRETE BEAMS: 13.79 ITEM fc' = 2,000.00 fc = .45fc' 6.21 Es 200,000.00 17,564.80 Ec = 4730√fc' n = Es/Ec 11.00 k = n/(n+fs/fc) 0.2481 j = 1 - k/3 0.92 Given: fc': 3,000.00 psi fc = 1,350.00 psi 9.308 mpa fs = 30,000.00 psi 206.85 mpa Concrete Covering: Top = 35 Bottom = 25 DEADLOAD: BEAM : 1/2L SLAB : WALL : SIESMIC: LIVELOAD: 1.94 TOTAL LOAD: W = DESIGN MOMENT: Md =
17.2 2,500.00 7.74 200,000.00 19,616.67 10.00 0.2723 0.91 Span L: Beam Section: b d Slab Thickness: Slab Width : Wall Ht. : Wall Thk.:
20.7 3,000.00 9.32 200,000.00 21,520.20 9.00 0.2884 0.90 1.5 150 250 0.1 3 1 0.13
mpa psi mpa mpa
meters mm mm meters meters meters meters
0.883 Kn / m 3.546 Kn / m 1.530 Kn / m 0.877 Kn / m 5.82 Kn / m 12.657 Kn / m WL^2/2
14.239
Kn - m
TRIAL BARS: Tension Tension Compression
No. of Bars 2 1 2
Diameter 12 12 12
mm. mm. mm.
As = As = As' =
Area,mm^2 226.2 IF: Mc > Md : SAFE, KAAYO BAY !!! 113.10 IF: Ms > Md: SAFE, G'YUD NA BAY !!! 226.20
b (2n-1)As' x (x-d') (d - x)
=
3,845.32 sq.mm.
nAs
=
3,053.64 sq.mm.
By Transformed section method: bx^2/2 + (2n-1)As'(x - d') = nAs(d - x) a = bx^2/2 = b = (2n-1)As'x + nAsx = c = (2n-1)As'd' - nAsd = x = x - d' = d-x =
75 6,898.95 (667,275.84) 58.947 33.95 191.05
mm mm mm
Moment of Inertia' I = bx^3/3 +(2n-1)As'(x-d')^2 +nAs(d - x)^2 I =
126,134,211.24
mm^4
MOMENT CAPACITY FOR CONCRETE: fc = Mc =
Mcx/I fcI/x
19.92
Kn - m
15.17
Kn - m
MOMENT CAPACITY FOR STEEL: fs = Ms =
nMs(d-x)/I fsI/n/(d-x)
2 pcs. 1 pcs.
12 mm. dia. RC Bars 12 mm. dia. RC Bars
2.00 pcs.
12 mm. dia. RC Bars
250 mm
Md : SAFE, KAAYO BAY !!! Md: SAFE, G'YUD NA BAY !!!
150 mm.
@ End - span
2 - Storey Resd'l. Lolita Village, Brgy. Caibaan, Tac. City Pitao BL Pitao BL 2/7/2008
General Description: Cantililever Beam 1.5 m span
DOUBLE REINFORCED CANTILEVER BEAM (WSD) AT END - SPAN NEGATIVE MOMENT DESIGN DATA FOR CONCRETE BEAMS: 13.79 ITEM fc' = 2,000.00 fc = .45fc' 6.21 Es 200,000.00 17,564.80 Ec = 4730√fc' n = Es/Ec 11.00 k = n/(n+fs/fc) 0.2481 j = 1 - k/3 0.92 Given: fc': 3,000.00 psi fc = 1,350.00 psi 9.308 mpa fs = 30,000.00 psi 206.85 mpa Concrete Covering: Top = 35 Bottom = 25
17.2 2,500.00 7.74 200,000.00 19,616.67 10.00 0.2723 0.91 Span L: Beam Section: b d Slab Thickness: Slab Width : Wall Ht. : Wall Thk.:
20.7 3,000.00 9.32 200,000.00 21,520.20 9.00 0.2884 0.90 1.5 150 250 0.1 3 1 0.13
DEADLOAD: 1/2L
BEAM : SLAB : WALL : SIESMIC:
LIVELOAD: TOTAL LOAD: W =
1.94
DESIGN MOMENT: Md = COMPUTING FOR M1 = As1 =
0.883 Kn / m 3.546 Kn / m 1.530 Kn / m 0.877 Kn / m 5.82 Kn / m 12.657 Kn / m WL^2/2
14.239
Kn - m
fckjbd^2/2
9.21
Kn - m
M1/fsjd
219.01
sq.mm.
IF: M1 < Md: THEREFORE : PROVIDE COMPRESION BARS COMPUTING FOR M2 =
TOTAL COMPUTE OF As':
As2 = As =
Md - M1 M2/fs(d-d') As1 + As2
5.03
Kn - m
113.01 332.02
sq.mm. sq.mm.
mpa psi mpa mpa
meters mm mm meters meters meters meters
WHERE:
fs' = 2fs(kd-d')/(d-kd) fs' = 103.07 IF: fs' < fs USE: COMPUTED fs' As' = M2/fs'(d-d') 256.63
Mpa sq.mm.
TRY: Tension Compression
No. of Bars 2.00 1.00 2.00 -
Bar Diameter 16 12 16 12
Unit mm mm mm mm
Area 201.06 113.10 201.06 113.10
CHECK FOR SHEAR: V = wL-wd
Allowable va:
16,137.37
v = V/bd va =.09*sqrt(f'c)
0.48 0.41
Newton Mpa Mpa
va
mm
Area = 0.07 2Avfv/v'b
78.54
sq.mm.
Mpa 3,147.55
ACI CODE: MAX. SPACING, Sm = IF: S>Sm : USE ACI CODE: Sm = D/2
mm 125
mm
125.00
mm
sq.mm. sq.mm. sq.mm. sq.mm.
Total Area 402.12 113.10 402.12 -
2.00 pcs. 1.00 pcs.
16 mm. dia. RC Bars 12 mm. dia. RC Bars
250 mm 10 mm dia. Stirrups
2.00 pcs. - pcs. 150 mm.
@ End - span
16 mm. dia. RC Bars 12 mm. dia. RC Bars
Total Area 515.22 OK, SAFE Kana BAY!!!! 402.12 OK, SAFE Kana BAY!!!!
Proj. Name: Location: Client: Designer: Date:
2 - Storey Resd'l. Bldg. Lolita Villaga, Brgy./ Caibaan, Tac. City Pitao BL Pitao BL 2/7/2008
General Description: Cantilever Beam 1.5 m span
INVESTIGATION OF DOUBLE REINF. BEAM AT END - SPAN NEGATIVE MOMENT DESIGN DATA FOR CONCRETE BEAMS: 13.79 ITEM fc' = 2,000.00 fc = .45fc' 6.21 Es 200,000.00 17,564.80 Ec = 4730√fc' n = Es/Ec 11.00 k = n/(n+fs/fc) 0.2481 j = 1 - k/3 0.92 Given: fc': 3,000.00 psi fc = 1,350.00 psi 9.308 mpa fs = 30,000.00 psi 206.85 mpa Concrete Covering: Top = 35 Bottom = 25 DEADLOAD: BEAM : 1/2L SLAB : WALL : SIESMIC: LIVELOAD: 1.94 TOTAL LOAD: W = DESIGN MOMENT: Md =
17.2 2,500.00 7.74 200,000.00 19,616.67 10.00 0.2723 0.91 Span L: Beam Section: b d Slab Thickness: Slab Width : Wall Ht. : Wall Thk.:
20.7 3,000.00 9.32 200,000.00 21,520.20 9.00 0.2884 0.90 1.5 150 250 0.1 3 1 0.13
mpa psi mpa mpa
meters mm mm meters meters meters meters
0.883 Kn / m 3.546 Kn / m 1.530 Kn / m 0.877 Kn / m 5.82 Kn / m 12.657 Kn / m WL^2/2
14.239
Kn - m
TRIAL BARS: Tension Tension Compression
No. of Bars 2 1 2
Diameter 12 12 12
mm. mm. mm.
As = As = As' =
Area,mm^2 226.2 IF: Mc > Md : SAFE, KAAYO BAY !!! 113.10 IF: Ms > Md: SAFE, G'YUD NA BAY !!! 226.20
b (2n-1)As' x (x-d') (d - x)
=
3,845.32 sq.mm.
nAs
=
3,053.64 sq.mm.
By Transformed section method: bx^2/2 + (2n-1)As'(x - d') = nAs(d - x) a = bx^2/2 = b = (2n-1)As'x + nAsx = c = (2n-1)As'd' - nAsd = x = x - d' = d-x =
75 6,898.95 (667,275.84) 58.947 33.95 191.05
mm mm mm
Moment of Inertia' I = bx^3/3 +(2n-1)As'(x-d')^2 +nAs(d - x)^2 I =
126,134,211.24
mm^4
MOMENT CAPACITY FOR CONCRETE: fc = Mc =
Mcx/I fcI/x
19.92
Kn - m
15.17
Kn - m
MOMENT CAPACITY FOR STEEL: fs = Ms =
nMs(d-x)/I fsI/n/(d-x)
2 pcs. 1 pcs.
12 mm. dia. RC Bars 12 mm. dia. RC Bars
2.00 pcs.
12 mm. dia. RC Bars
250 mm
Md : SAFE, KAAYO BAY !!! Md: SAFE, G'YUD NA BAY !!!
150 mm.
@ End - span
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