RC Beam Design _Cantilever_

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RC Beam Design _Cantilever_ Powered By Docstoc
					Proj. Name:     2 - Storey Resd'l.                                             General Description:
Location:       Lolita Village, Brgy. Caibaan, Tac. City                       Cantililever Beam 1.5 m span
Client:         Pitao BL
Designer:       Pitao BL
Date:           2/7/2008


DOUBLE REINFORCED CANTILEVER BEAM (WSD)
AT END - SPAN NEGATIVE MOMENT
DESIGN DATA FOR CONCRETE BEAMS:
                                       13.79                  17.2                 20.7       mpa
    ITEM               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
                 Ec = 4730√fc'         17,564.80               19,616.67         21,520.20    mpa
                   n = 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       meters
            fc =         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       meters
Concrete Covering: Top =                 35            Slab Width :                  3        meters
                   Bottom =              25            Wall Ht. :                    1        meters
                                                       Wall Thk.:                  0.13       meters
DEADLOAD:
                BEAM :                    0.883        Kn / m
     1/2L       SLAB :                    3.546        Kn / m
                WALL :                    1.530        Kn / m
                SIESMIC:                  0.877        Kn / m
LIVELOAD:                     1.94         5.82        Kn / m
TOTAL 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':

                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 Mpa
Allowable 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 mm
                             10 mm dia. Stirrups



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


  @ End - span
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 span
Client:       Pitao BL
Designer:     Pitao BL
Date:                2/7/2008

INVESTIGATION OF DOUBLE REINF. BEAM
AT END - SPAN NEGATIVE MOMENT
DESIGN DATA FOR CONCRETE BEAMS:
                                  13.79                    17.2              20.7        mpa
   ITEM            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
             Ec = 4730√fc'         17,564.80               19,616.67       21,520.20     mpa
               n = 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        meters
        fc =       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        meters
Concrete Covering: Top =           35               Slab Width :               3         meters
               Bottom =            25               Wall Ht. :                 1         meters
                                                    Wall Thk.:               0.13        meters
DEADLOAD:
          BEAM :                     0.883          Kn / m
   1/2L   SLAB :                     3.546          Kn / m
          WALL :                     1.530          Kn / m
          SIESMIC:                   0.877          Kn / m
LIVELOAD:          1.94               5.82          Kn / m
TOTAL 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 !!!
Compression      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:

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

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

    x =                            58.947         mm
  x - d' =                          33.95         mm
  d-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/I
                  Mc =              fcI/x                 19.92   Kn - m

MOMENT CAPACITY FOR STEEL:

                  fs =           nMs(d-x)/I
                  Ms =           fsI/n/(d-x)              15.17   Kn - m
                                               2 pcs.   12 mm. dia. RC Bars
                                               1 pcs.   12 mm. dia. RC Bars


                250 mm




                                            2.00 pcs.   12 mm. dia. RC Bars

                               150 mm.


                             @ End - span




Md : SAFE, KAAYO BAY !!!
Md: SAFE, G'YUD NA BAY !!!

				
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