Design of Two Cell Box Structure

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    DESIGN DATA:

    27.160 m

    22.050 m

    20.550 m

    25.485 m

    12.000 m

    11.000 m0.400 m

    0.400 m

    0.400 m

    0.300 m

    0.056 m

    8.000 + 0.350 = 8.350 m

    8.000 + 0.350 = 8.350 m

    5.754 + 0.400 = 6.154 m

    0.500 m

    1.250 x 0.250 m

    1.250 x 0.250 m

    1.675 m

    2.400 t / m

    1.000 t / m

    M 35

    1190 t / m

    20400 t / m

    m - 10

    0.368

    0.877

    192 t / m

    Top slab = 16.70 x 0.40 x 2.40 = 16.032 t / m

    bottom slab = 16.70 x 0.40 x 2.40 = 16.032 t / m

    End Webs = 2 x 6.154 x 0.40 x 2.40 = 11.816 t / m

    Central Web = 1 x 6.154 x 0.30 x 2.40 = 4.431 t / m

    Haunches ( 16 nos.) = 16 x 0.125 x 1.25 x 2.40 = 6.000 t / m

    54.311 t / m

    ( 54.311 / 16.700 ) = 3.252 t / m

    Say, 3.300 t / m

    Wearing Coat (@ 0.20 t / sqm.) = 0.200 t / m

    2 x ( 0.700 / 12.000 ) = 0.117 t / m

    Total = ( 0.200 + 0.117 ) =

    0.317 t / m

    DRY CONDITION

    Due to DL of Box and SIDL = ( 3.300 + 0.317 ) = 3.617 t / m

    Due to LL-70R Wheeled Load = 100 / ( 12 x 16.70 ) = 0.499 t / m

    Due to Earth inside the Box = 1.10 x 2.00 = 2.200 t / m

    Total Base Pressure = ( 3.617 + 0.499 + 2.200 ) = 6.316 t / m

    Eff. horizontal span end cell(upto c/l of web) =

    CALCULATION OF LOADS AND CORRESPONDING BASE PRESSURE:

    Total Weight =

    SUPERIMPOSED DEAD LOAD ( Per metre width ):

    Formation Level along c/l of carriageway (m) =

    Bed Level (m) =

    Founding Level (m) =

    Heighest Flood Level (m) =

    Overall width of bridge =

    width of carriageway =Thickness of top slab =

    Thickness of bottom slab =

    Thickness of Web =

    Thickness of Central Web =

    Tkickness of wearing coat =

    Modular ratio,

    Eff. horizontal span inner cell(upto c/l of web) =

    Eff. vertical span (upto c/l of slab) =

    width of crash barrier =

    Size of haunches in outer webs -

    Size of haunches in inner web -

    Depth of water at HFL. from formation lvl =

    Unit wt of concrete =

    Submerged density of earth =

    Grade of Concrete -

    Permissible Compressive stress in Concrete -

    Permissible Tensile stress in Steel -

    Equivalent upward Base pressure =

    DEAD LOAD-( Per metre width ):

    Equivalent upward Base pressure =

    0.317 t / m

    CHECK FOR BASE PRESSURE

    Crash Barrier ( @ 0.70 t/m on each side ) =

    k -

    Lever arm factor, j -

    Moment of Resistance, Q -

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    HFL CONDITION

    Due to DL of Box, SIDL & LL = ( 3.617 + 0.499 ) = 4.116 t / m

    Due to Water inside the Box = ( 4.423 x 1.000 ) = 4.423 t / m

    Buoyancy = ( 4.823 x - 1.000 ) = - 4.823 t / m

    Total Base Pressure = ( 4.116 + 4.423 - 4.823 ) = 3.716 t / m

    EARTH PRESSURE

    CASE - 1

    Dry Density of Soil = 2.000 t / m

    0.5

    CASE - 2

    Dry Density of Soil = 1.800 t / m

    0.3

    Cooefficient of Earth Pressure at rest =

    Cooefficient of Earth Pressure at rest =

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    Height (m)Location of Earth

    PressureCase - 1

    Surcharge for

    1.2 mCase - 2

    Surcharge for

    1.2 m

    0.256 C/l of top slab 0.256 1.2 0.138 0.648

    1.956 Face of top haunch 1.956 1.2 1.056 0.648

    3.333 Mid. of web 3.333 1.2 1.8 0.648

    4.71 Face of bot. haunch 4.71 1.2 2.543 0.648

    6.41 C/l bottom slab 6.41 1.2 3.461 0.648

    Height (m)Location of Earth

    PressureCase - 1

    Surcharge for

    1.2 mCase - 2

    Surcharge for

    1.2 m

    0.256 C/l of top slab 0.256 1.2 0.138 0.648

    1.675 H.F.L. Level 1.675 1.2 0.905 0.648

    1.956 Face of top haunch 1.956 1.2 1.056 0.648

    3.333 Mid. of web 3.333 1.2 1.8 0.648

    4.71 Face of bot. haunch 4.022 1.2 2.488 0.648

    6.41 C/l bottom slab 4.872 1.2 3.338 0.648

    For Dry Condition

    H.F.L. Condition

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    9.9 0.7

    2 1

    3

    100 mm

    100 mm

    6

    4 5

    5.8 0.8

    S No. t b t F (force) Acting atEccentricity

    e

    1 0.7 1.0 0.08 2.04 0.04 m from top 0.16

    2 9.9 / 2 1.0 0.08 14.41 0.027 m from top 0.173

    3 0.7 / 2 1.0 0.1 1.27 0.113 m from top 0.087

    4 5.8 / 2 1.0 0.08 8.44 0.027 m from bottom -0.173

    5 0.8 1.0 0.08 2.33 0.04 m from bottom -0.16

    6 0.8 / 2 1.0 0.1 1.46 0.113 m from bottom -0.087

    F = 29.95 F.e = 0.97

    2

    t2

    Hence, t = 0.8 C

    0.1

    M = [ F x e ] = Ec x x t x A x e

    0.97 = 36.387 x x 0.0667

    0.08

    0.08

    0.1

    0.08

    0.08

    EFFECT OF TEMPERATURE FALL

    80 mm

    80 mm

    A = b x t

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    Where

    L0=

    a =

    =b / L0= 12 / 8 = 1.5

    2.48

    b1=

    0.5 1.62 2.06 7.32 0.5

    11

    0.5 1.63 1.93 7.44 0.5

    11

    2.48

    Live Load a (m) b1(m) beff(m) beff/2 (m)Max.

    available

    Width (m)

    Load

    Intensity

    70 3.712 0.952 6.065 3.033 7.213 9.705

    70 3.664 0.952 6.051 3.026 7.206 9.715

    70 3.362 0.952 5.933 2.966 7.146 9.795

    70 3.736 0.952 6.072 3.036 7.216 9.701

    63.7 2.08 0.952 4.825 2.413 6.593 9.665

    70 4.012 0.952 6.121 3.061 7.241 9.668

    70 2.285 0.952 5.068 2.534 6.714 10.426

    For Max. BM (Sagging) in Midspan

    For Max. BM (Sagging) at end of haunch 1

    Effective width =beff. .a.[ 1 - a / L0] + b 1

    Hence as per cl. 305.16.2 of IRC:21, =

    breath of loads over the deck slab after 45 dispersion through wearing coat

    the effective span

    A constant depending upon the ratio b/l0, where b is the width of the slab

    the distance of centre of gravity of the concn load from the nearer

    = 0.84 + 2 x 0.056 = 0.952 m (for 70R tracked)

    = 0.81 + 2 x 0.056 = 0.922 m (for 70R wheeled)

    TRANSVERSE POSITION OF LIVE LOAD ( CLASS 70R TRACKED)

    TRANSVERSE POSITION OF LIVE LOAD ( CLASS 70R WHEELED)

    CALCULATION OF EFFECTIVE WIDTH AND LOAD INTENSITY =

    For Max. BM (Hogging) at End web

    Class 70R Tracked Load

    For Max. BM (Hogging) in Midspan

    For Max. BM (Hogging) at start of haunch 2

    For Max. BM (Hogging) at middle web

    For Max. BM (Hogging) at end of haunch 9

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    17.0 1.31 0.92 3.661 1.831 5.591 3.041

    17.0 2.68 0.92 5.435 2.718 6.778 2.508

    17.0 2.62 0.92 5.381 2.69 6.75 2.518

    17.0 1.25 0.92 3.558 1.779 5.488 30.098

    17.0 1.45 0.92 3.894 1.947 5.824 2.919

    17.0 2.82 0.92 5.554 2.777 6.837 2.487

    17.0 2.48 0.92 5.246 2.623 6.683 2.544

    17.0 1.11 0.92 3.309 1.654 5.239 3.245

    17.0 3.9 0.92 6.077 3.038 7.098 2.395

    17.0 3.08 0.92 5.743 2.871 6.931 2.453

    17.0 0.03 0.92 0.996 0.498 1.992 8.533

    17.0 1.34 0.92 3.712 1.856 5.642 3.013

    12.0 3.47 0.92 5.951 2.976 7.036 1.706

    12.0 3.36 0.92 5.902 2.951 7.011 1.712

    12.0 1.86 0.92 4.507 2.254 6.314 1.901

    12.0 3.38 0.92 5.911 2.956 7.016 1.71

    17.0 2.84 0.92 5.57 2.785 6.845 2.484

    17.0 1.47 0.92 3.926 1.963 5.856 2.903

    17.0 1.58 0.92 4.099 2.049 6.029 2.82

    17.0 2.95 0.92 5.653 2.827 6.887 2.469

    17.0 1.75 0.92 4.313 2.156 6.216 2.735

    17.0 3.12 0.92 5.642 2.821 6.881 2.471

    17.0 2.18 0.92 4.855 2.428 6.488 2.62

    17.0 0.81 0.92 2.736 1.368 4.666 3.643

    17.0 2.52 0.92 5.203 2.601 6.661 2.552

    17.0 3.89 0.92 5.878 2.939 6.999 2.429

    12.0 2.33 0.92 5.017 2.509 6.569 1.827

    12.0 0.81 0.92 2.736 1.368 4.666 2.572

    8.0 3.15 0.92 5.787 2.893 6.953 1.515

    17.0 1.63 0.92 4.175 2.088 6.105 2.784

    17.0 3 0.92 5.689 2.844 6.904 2.462

    For Max. BM (Sagging) at end of haunch 1

    Class 70R Wheeled Load

    For Max. BM (Hogging) at End web

    For Max. BM (Sagging) in Midspan

    For Max. BM (Hogging) at end of haunch 9

    For Max. BM (Hogging) at start of haunch 2

    For Max. BM (Hogging) at middle web

    For Max. BM (Hogging) in Midspan

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    9.715 /

    Corresponding base pressure =

    For Max BM (Sagging) at end of haunch 1

    Dispersion width =

    Live load intensity as udl =

    Corresponding base pressure =

    Corresponding base pressure =

    Corresponding base pressure =

    Corresponding base pressure =

    Corresponding base pressure =

    Corresponding base pressure =

    Live load intensity as udl =

    For Max BM (Sagging) at midspan

    Dispersion width =

    Live load intensity as udl =

    For Max BM (hogging) at middle web

    Dispersion width =

    Live load intensity as udl =

    For Max BM (Sagging) at end of haunch 9

    Dispersion width =

    Live load intensity as udl =

    For Max BM (Hogging) at start of haunch 2

    Dispersion width =

    Live load intensity as udl =

    Live load intensity as udl =

    For Max BM (Hogging) in Mid span

    Dispersion width =

    LOAD INTENSITY AND CORRESPONDING BASE PRESSURE FOR CLASS 70R TRACKED:

    Dispersion width = Track length over the span after 45odispersion through wearing coat and slab

    For Max BM (Hogging) at End web

    Dispersion width =

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    ( 0.263 + 0.456 ) = 0.719 m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 3.041 / 1.175 ) = 2.588 t / m

    ( 2.508 / 1.175 ) = 2.134 t / m

    ( 2.518 / 1.175 ) = 2.143 t / m

    ( 3.098 / 1.175 ) = 2.637 t / m

    0.669 t / m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 0.263 + 0.456 ) = 0.719 m

    ( 2.919 / 1.175 ) = 2.484 t / m

    ( 2.487 / 1.175 ) = 2.117 t / m

    ( 2.544 / 1.175 ) = 2.165 t / m

    ( 3.245 / 1.175 ) = 2.762 t / m

    0.670 t / m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 2.395 / 1.175 ) = 2.038 t / m

    ( 2.453 / 1.175 ) = 2.088 t / m

    ( 8.533 / 1.175 ) = 7.262 t / m

    ( 3.013 / 1.175 ) = 2.564 t / m

    ( 1.706 / 1.175 ) = 1.452 t / m

    ( 1.712 / 1.175 ) = 1.457 t / m 1.186 t / m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 1.901 / 1.175 ) = 1.618 t / m

    ( 1.710 / 1.175 ) = 1.455 t / m

    ( 2.484 / 1.175 ) = 2.114 t / m

    ( 2.903 / 1.175 ) = 2.471 t / m

    ( 2.820 / 1.175 ) = 2.400 t / m

    ( 2.469 / 1.175 ) = 2.101 t / m

    0.855 t / m

    for 17 t wheel

    For Max BM (Hogging) at End web

    Corresponding base pressure =

    For Max BM (Hogging) at Start of haunch2

    for 12 t wheel

    for 12 t wheel

    for 17 t wheel

    for 17 t wheel

    for 17 t wheel

    Corresponding base pressure =

    For Max BM (Hogging) at middle web

    Live load intensity as udl

    Disp. width of 17t load at start =

    Disp. width of 17t,12t & 8t load =

    for 17 t wheel

    for 17 t wheel

    for 17 t wheel

    Corresponding base pressure =

    Live load intensity as udl

    Live load intensity as udl

    Disp. width of 17 t &12t wh. =

    Disp. width of 12 t wh.at end =

    for 17 t wheel

    for 17 t wheel

    for 17 t wheel

    for 17 t wheel

    Corresponding base pressure =

    LOAD INTENSITY AND CORRESPONDING BASE PRESSURE FOR CLASS 70R WHEELED:

    Dispersion width = wheel length over the span after 45odispersion through wearing coat and slab

    for 17 t wheel

    for 17 t wheel

    for 17 t wheel

    for 12 t wheel

    for 12 t wheel

    Disp. width of 17t & 12t load =

    Disp. width of 12 t load at end =

    for 17 t wheel

    For Max BM (Hogging) in mid span

    Live load intensity as udl

    Disp. width of 12t load at start =

    Disp. width of 12t & 17t Load =

    for 17 t wheel

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    ( 0.263 + 0.912 ) = 1.175 m

    ( 0.263 + 0.456 ) = 0.719 m

    ( 2.735 / 1.175 ) = 2.328 t / m

    ( 2.471 / 1.175 ) = 2.103 t / m

    ( 2.620 / 1.175 ) = 2.230 t / m

    ( 3.643 / 1.175 ) = 3.100 t / m 0.687 t / m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 2.552 / 1.175 ) = 2.172 t / m

    ( 2.429 / 1.175 ) = 2.067 t / m

    ( 1.827 / 1.175 ) = 1.555 t / m

    ( 2.572 / 1.175 ) = 2.189 t / m

    ( 1.151 / 1.175 ) = 0.980 t / m

    0.631 t / m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 0.263 + 0.912 ) = 1.175 m

    ( 2.784 / 0.912 ) = 3.053 t / m

    ( 2.462 / 0.912 ) = 2.700 t / m

    0.314 t / m

    For Max BM (Sagging) at end of huunch 9

    Live load intensity as udl

    Disp. width of 17t load at start =

    Disp. width of 17t,12t & 8t load =

    Corresponding base pressure =

    for 17 t wheel

    for 17 t wheel

    for 17 t wheel

    for 17 t wheel

    For Max BM (Sagging) in mid span

    Disp. width of 17t load at start =

    Disp. width of 17t,12t & 8t load =

    Live load intensity as udl

    for 17 t wheel

    for 17 t wheel

    for 12 t wheel

    for 12 t wheel

    for 8 t wheel

    Corresponding base pressure =

    For Max BM (Sagging) at end of haunch 1

    Live load intensity as udl

    Corresponding base pressure =

    for 17 t wheel

    for 17 t wheel

    Disp. width of 17t load at start =

    Disp. width of 17t,12t & 8t load =

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    1.1

    1.25

    Max. Max. Max. Max. Max. Max.

    sagging hogging sagging hogging sagging hogging

    At the face of end web -1.914 4.862 -1.788 3.75 -1.914 4.862

    At the end of haunch-1 -3.322 0 -3.175 0 -3.322 0

    mid span -7.128 1.254 -5.95 1.265 -7.128 1.265

    At the start of haunch-2 0 3.322 -0.338 3.375 -0.338 3.375

    At the end of haunch- 2 0 8.492 0 11.938 0 11.938

    At the face of end web 0 1.31 0 1.49 0 1.49

    At the end of haunch-1 -1.82 0 -2.14 0 -2.14 0

    mid span -2.67 0 -3.67 0 -3.67 0

    At the start of haunch-2 0 2.52 0 2.85 0 2.85

    At the end of haunch 0 5.715 0 8.24 0 8.24

    0 1.903 0 3.875 0 3.8750.000

    2.706

    0.000

    3.750

    0.000

    3.750-0.110

    3.960

    0.000

    3.988 -

    0.1103.988-1.045

    5.324 -

    0.863

    5.025 -

    1.045

    5.324

    SUMMARY OF BENDING MOMENT AT DIFFERENT LOCATION

    (I) Due to LIVE LOAD

    Impact factor (I.F.) for class 70R tracked =

    Impact factor (I.F.) for class 70R wheeled =

    CLASS CLASS

    BOTTOM

    SLAB

    70R(Wheeled)70R(Tracked)

    DESIGN BM

    LL

    LOCATION

    TOP

    SLAB

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    -1.936

    6.600 -

    1.800

    5.975 -

    1.936

    6.600

    -2.6732.354 -

    2.513

    2.938 -

    2.673

    2.938

    -0.715

    0.517 -

    0.613

    0.788 -

    0.715

    0.788

    -1.496

    1.474 -

    1.450

    1.550 -

    1.496

    1.550

    -3.663

    3.465 -

    3.500

    3.875 -3.663

    3.875

    -5.665

    5.302 -

    5.400

    6.038 -

    5.665

    6.038

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