Proj. Name: 2 - Storey Resd'l. General Description:Location: Lolita Village, Brgy. Caibaan, Tac. City Cantililever Beam 1.5 m spanClient: Pitao BLDesigner: Pitao BLDate: 2/7/2008

DOUBLE REINFORCED CANTILEVER BEAM (WSD)

AT END - SPAN NEGATIVE MOMENTDESIGN DATA FOR CONCRETE BEAMS:

13.79 17.2 20.7 mpaITEM fc' = 2,000.00 2,500.00 3,000.00 psi

fc = .45fc' 6.21 7.74 9.32 Es 200,000.00 200,000.00 200,000.00 mpa

17,564.80 19,616.67 21,520.20 mpan = Es/Ec 11.00 10.00 9.00

k = n/(n+fs/fc) 0.2481 0.2723 0.2884 j = 1 - k/3 0.92 0.91 0.90

Given: fc': 3,000.00 psi Span L: 1.5 metersfc = 1,350.00 psi Beam Section:

9.308 mpa b 150 mm fs = 30,000.00 psi d 250 mm

206.85 mpa Slab Thickness: 0.1 metersConcrete Covering: Top = 35 Slab Width : 3 meters

Bottom = 25 Wall Ht. : 1 metersWall Thk.: 0.13 meters

DEADLOAD:BEAM : 0.883 Kn / m

1/2L SLAB : 3.546 Kn / mWALL : 1.530 Kn / mSIESMIC: 0.877 Kn / m

LIVELOAD: 1.94 5.82 Kn / mTOTAL LOAD: W = 12.657 Kn / m

DESIGN MOMENT: Md = WL^2/2 14.239 Kn - m

COMPUTING FOR M1 = fckjbd^2/2 9.21 Kn - m

As1 = M1/fsjd 219.01 sq.mm.

IF: M1 < Md: THEREFORE : PROVIDE COMPRESION BARS

COMPUTING FOR M2 = Md - M1 5.03 Kn - m

As2 = M2/fs(d-d') 113.01 sq.mm.TOTAL As = As1 + As2 332.02 sq.mm.

COMPUTE OF As':

Ec = 4730√fc'

WHERE: fs' = 2fs(kd-d')/(d-kd)fs' = 103.07 Mpa

IF: fs' < fs USE: COMPUTED fs'As' = M2/fs'(d-d') 256.63 sq.mm.

TRY:No. of Bars Bar Diameter Unit Area Total Area

Tension 2.00 16 mm 201.06 sq.mm. 402.12 1.00 12 mm 113.10 sq.mm. 113.10

Compression 2.00 16 mm 201.06 sq.mm. 402.12 - 12 mm 113.10 sq.mm. -

CHECK FOR SHEAR:

V = wL-wd 16,137.37 Newton

v = V/bd 0.48 MpaAllowable va: va =.09*sqrt(f'c) 0.41 Mpa

va<v THEREFORE: PROVIDE WEB REINFORCEMENT

10 mm Area = 78.54 sq.mm.

v' = v - va 0.07 Mpa

SPACING, S = 2Avfv/v'b 3,147.55 mm

ACI CODE: MAX. SPACING, Sm = 125 mm

IF: S>Sm : USE ACI CODE: Sm = D/2 125.00 mm

2.00 pcs. 16 mm. dia. RC Bars 1.00 pcs. 12 mm. dia. RC Bars

250 mm10 mm dia. Stirrups

2.00 pcs. 16 mm. dia. RC Bars - pcs. 12 mm. dia. RC Bars

150 mm.

@ End - span

Total Area 515.22 OK, SAFE Kana BAY!!!!

402.12 OK, SAFE Kana BAY!!!!

Proj. Name: 2 - Storey Resd'l. Bldg. General Description:Location: Lolita Villaga, Brgy./ Caibaan, Tac. City Cantilever Beam 1.5 m spanClient: Pitao BLDesigner: Pitao BLDate: 2/7/2008

INVESTIGATION OF DOUBLE REINF. BEAM

AT END - SPAN NEGATIVE MOMENTDESIGN DATA FOR CONCRETE BEAMS:

13.79 17.2 20.7 mpaITEM fc' = 2,000.00 2,500.00 3,000.00 psi

fc = .45fc' 6.21 7.74 9.32 Es 200,000.00 200,000.00 200,000.00 mpa

17,564.80 19,616.67 21,520.20 mpan = Es/Ec 11.00 10.00 9.00

k = n/(n+fs/fc) 0.2481 0.2723 0.2884 j = 1 - k/3 0.92 0.91 0.90

Given: fc': 3,000.00 psi Span L: 1.5 metersfc = 1,350.00 psi Beam Section:

9.308 mpa b 150 mm fs = 30,000.00 psi d 250 mm

206.85 mpa Slab Thickness: 0.1 metersConcrete Covering: Top = 35 Slab Width : 3 meters

Bottom = 25 Wall Ht. : 1 metersWall Thk.: 0.13 meters

DEADLOAD:BEAM : 0.883 Kn / m

1/2L SLAB : 3.546 Kn / mWALL : 1.530 Kn / mSIESMIC: 0.877 Kn / m

LIVELOAD: 1.94 5.82 Kn / mTOTAL LOAD: W = 12.657 Kn / m

DESIGN MOMENT: Md = WL^2/2 14.239 Kn - m

TRIAL BARS:No. of Bars Diameter Area,mm^2

Tension 2 12 mm. As = 226.1952 IF: Mc > Md : SAFE, KAAYO BAY !!!Tension 1 12 mm. As = 113.10 IF: Ms > Md: SAFE, G'YUD NA BAY !!!

Compressio 2 12 mm. As' = 226.20

b(2n-1)As' = 3,845.32 sq.mm.

x (x-d')

(d - x)

nAs = 3,053.64 sq.mm.

By Transformed section method:

Ec = 4730√fc'

bx^2/2 + (2n-1)As'(x - d') = nAs(d - x)

a = bx^2/2 = 75b = (2n-1)As'x + nAsx = 6,898.95 c = (2n-1)As'd' - nAsd = (667,275.84)

x = 58.947 mmx - d' = 33.95 mmd - x = 191.05 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 = Mcx/IMc = fcI/x 19.92 Kn - m

MOMENT CAPACITY FOR STEEL:

fs = nMs(d-x)/IMs = fsI/n/(d-x) 15.17 Kn - m

2 pcs. 12 mm. dia. RC Bars1 pcs. 12 mm. dia. RC Bars

250 mm

2.00 pcs. 12 mm. dia. RC Bars

150 mm.

@ End - span

IF: Mc > Md : SAFE, KAAYO BAY !!!IF: Ms > Md: SAFE, G'YUD NA BAY !!!