Rc Beam Design (cantilever)

  • June 2020
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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

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