mathcad - concrete footing with pedestal

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  • tftg1 1.0 mtftg2 0.5 mdsoil 1.0 m (depth of soil)

    Lftg 2.2 m (latudinal dimension)

    Wftg 2.2 m (longitudinal dimension)

    aw 0.63m (pedestal short dimension)

    aL 0.63m (pedestal long dimension)

    30 (soil angle of friction)

    Mload 85.15kN m conc 24kN

    m3

    Hload 0.46 kNVload1 28.27 kN soil 19

    kN

    m3

    Vload2 25.32kN

  • OVERTURNING MOMENT, MO

    MO Mload Hload tftg1 tftg2 MO 85.84 kN m

    RESISTING MOMENT, MR

    Wtftg conc Lftg Wftg tftg2 aw aL tftg1 Wtftg 67.606 kN

    MR Vload1 Wtftg soil Wftg Lftg aw aL dsoil Wftg2MR 136.13 kN m

    OVERTUNING MOMENT FACTOR OF SAFETY, FOSOT

    FOSOTMRMO

    1.586 > 1.5; OK

    SLIDING FORCE, HSL

    soil 31.5 (angle of internal friction)

    soil tan soil 0.613 (soil coefficient)HSL Hload 0.46 kN (craine sliding force)

    SLIDING RESISING FORCE, HRF

    HRF Vload1 Wtftg soil (sliding resisting force)HRF 24.105 kN

    SLIDING FACTOR OF SAFETY, FOSSL

    FOSSLHRFHSL

    52.402 ; OK

  • SOIL BEARING

    soil1Vload1 Wtftg soil Wftg Lftg aw aL dsoil

    Lftg WftgMO

    Wftg2

    Lftg Wftg3

    12

    soil2Vload1 Wtftg soil Wftg Lftg aw aL dsoil

    Lftg WftgMO

    Wftg2

    Lftg Wftg3

    12

    soil1 73.939 kPa

    soil2 22.801 kPa ;Negative soil pressure is rejected. Use another approach

    ECCENTRICITY OF VERTICAL FORCE

    eOMO

    Vload1 Wtftg soil Wftg Lftg aw aL dsoileO 0.694 m

    rWftg2

    eO

    r 0.406 m

    SOIL BEARING

    f 2( )Vload1 Wtftg soil Wftg Lftg aw aL dsoil

    3r Lftg

    f 92.284 kPa < 200 KPa; OK

  • PUNCHING

    dbar 16 mmcon 0.65d tftg2 75 mm dbar2 0.417 mfc 23 MPa

    Bo aw 2 aL 2d28

    min aL aw max aL aw

    1Bo 4.188 m 1s 40Vult1 39.58 kN Vult2 35.45 kN

    Shear 1.2 conc aw aL tftg1 Vult2Shear 46.881 kNfcmax min fc 70 MPa( ) 23 MPa ACI 318M-08 Sec.11.1.2

    Vc1 0.17 12

    fcMPa

    MPa Bo d ACI 318M-08 Sec.11.11.2.1 Eq. 11-31

    Vc1 4271.465 kN

    Vc2 0.083s dBo

    2

    fcMPa

    MPa Bo d ACI 318M-08 Sec.11.11.2.1 Eq. 11-32

    Vc2 4159.008 kN

    Vc3 0.33 fc

    MPa MPa Bo d ACI 318M-08 Sec.11.11.2.1 Eq. 11-33

    Vc3 2763.889 kNVc con min Vc1 Vc2 Vc3 1796.528 kN > Shear 46.881 kN ;OKONEWAY SHEAR

    Shear 46.881 kN

    Vsc con 0.17 fc

    MPa MPa min Lftg Wftg d

    Vsc 486.166 kN > Shear 46.881 kN ;OK

  • BENDING REINFORCEMENT

    xwWftg aw

    2

    xw 0.785 m

    SOIL STRESS AT PEDESTAL EDGE

    fxf xw3 r

    fx 59.423 kPa

    FOOTING MOMENT

    Mftg 1.6 Lftg fxxw

    2

    2 f fx xw

    2

    3

    Mftg 88.207 kN m