ENGM032 Coursework Jesus Rodriguez

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  • ENGM032: COMPOSITE BRIDGE COURSEWORK JESUS RODRIGUEZ RODRIGUEZ

    Initial Data

    Geometry: Materials:

    mm2600Bcarr

    Carriageway

    2mm

    kN205E

    s

    610200

    csshrinkage strain

    mm275Ds

    2mm

    kN31E

    csEcs

    Es

    cs

    Slab 6.6129cs

    mm50esurf

    2mm

    kN15.5E

    clEcl

    Es

    cl

    Road Surfacing 13.2258cl

    m34L Span

    2mm

    N50f

    cu 2mm

    N460f

    y 2mm

    N355

    ycmm500C Cantilever

    2mm

    N345

    yfmm2000Spabeam

    Beam Spacing

    C2Spabeam

    B m3B Slab width

    Loads:

    3m

    kN25

    c

    BDs

    c

    Wslab

    m

    kN20.625W

    slab

    Slab Self Weight

    m

    kN32W

    beam2 Steel Beams Self Weight

    3m

    kN22

    surf

    Bcarr

    esurf

    surf

    Wsurf

    m

    kN2.86W

    surf

    Road Surfacing

    m

    kN2.52W

    rail2 Parapets

    2m

    kN5w

    live

    Bcarr

    wlive

    Wlive

    m

    kN13W

    live

    Footway Live Load

    Section Design:

    mm330bft

    mm20tft

    tft

    bft

    Aft

    2mm6600A

    ft

    Top Flange

    mm465bfb

    mm25tfb

    tfb

    bfb

    Afb

    2mm11625A

    fb

    Bottom Flange

    mm925d mm8tw

    tw

    dAw

    2mm7400A

    w

    Web Plate

    tfb

    tft

    dD mm970D Steel Beam Height

    Ds

    DH m1.245H

    H

    L

    27.3092

    tw

    dw

    115.625w

  • Check Shape Limitations:

    tft

    2

    tw

    bft

    rft

    tfb

    2

    tw

    bfb

    rfb

    8.05rft 9.14r

    fb

    345

    35512r

    lim1 345

    35512r

    lim2

    12.1727rlim212.1727r

    lim1

    Section Classification

    355

    355tft

    7bfo

    mm140bfo

    Flange is not compact

    tft

    m.7652ywc

    Web in compression for plastic neutral axis, calculated later on

    d

    tft

    ywc

    m0.784m

    355

    355tw1m13

    374dlim

    mm325.5004dlim

    Web is not compact

    Calculation of effective areas:

    1Kc

    No reduction of compression flange

    355

    355

    tw

    ywc

    rw

    93.15rw

    No reduction if lower than 68

    tw

    rw

    .006251.425twe

    mm6.7425twe

    Effective web thickness

    twe

    tw

    tw

    dAw

    mm6.7425tw

    i) Stability During Construction

    Lateral Torsional Buckling Analysis

    a) Elastic Properties Analysis of the Steel Beam:

    Aw

    Afb

    Aft

    D0.5Aw

    DAfb

    0

    ye_s

    m0.5846ye_s

    12

    2D

    Aw

    2ye_s

    D0.5Aw

    2ye_s

    DAfb

    2ye_s

    Aft

    Is

    4m0.0045I

    s

    Aw

    Afb

    Aft

    As

    2m0.0245A

    s

  • s

    yf

    fyd_f

    1.11.05s

    MPa298.7013fyd_f Design Yield Strength

    ye_s

    D

    fyd_f

    Is

    Mel_1s

    mkN3513.6804Mel_1s

    ye_s

    fyd_f

    Is

    Mel_2s

    mkN2316.1116Mel_2s

    if

    else

    Mel_2s

    Mel_1s

    Mel_2s

    Mel_1s

    Mel_s

    mkN2316.1116Mel_s

    Elastic Moment Strength for the

    Steel Beam

    As

    Is

    rx

    m0.4305rx

    b) Plastic Properties Analysis for Steel Beam:

    s

    yc

    fyd

    2mm

    N307.3593f

    yd

    fyd_f

    Afb

    Rfb

    kN3472.4026Rfb

    fyd_f

    Aft

    Rft

    kN1971.4286Rft

    fyd

    Aw

    Rw

    kN1916.9424Rw

    Rw

    Rw

    Rft

    Rfb

    2

    dyp_s

    m0.8246yp_s

    d2

    2yp_s

    d

    Rwd2

    2yp_s

    Rw

    yp_s

    Rft

    yp_s

    DRfb

    Mpl_s

    mkN2845.542Mpl_s

    Plastic Moment Strength for the

    Steel Beam

    c) Stability Without self-weight of concrete:

    Effective LTB length without intermediate restraints:

    1k1

    1.2k2

    1ke

    Lke

    k2

    k1

    le

    m40.8le

    Slenderness Parameter:

    2

    tfb

    tft

    tfavg

    1k4

    1 Llw

  • 3tw

    d12

    13bfb

    tfb12

    13bft

    tft12

    1Iy

    4m0.0003I

    y

    Moment of Inertia with respect to Y-axis

    As

    Iy

    ry

    m0.1049ry

    D

    tfavg

    ry

    lw

    F

    7.5153F

    3bft

    tft12

    1Icf

    4mm

    7105.9895I

    cf

    3bfb

    tfb12

    1Itf

    4mm

    8102.0947I

    tf

    Itf

    Icf

    Icf

    i 0.2224i

    From i and F, we obtain the parameter

    0.831

    k4r

    y

    le

    LT 323.0855LT

    Limiting Value of Slenderness:

    Mpl_s

    Mpe

    Mel_s

    Mult

    Section is not compact

    Mult

    Mpe

    355

    35530

    lim33.2525

    lim

    Limiting Moment of Reistance:

    Mpe

    Mult

    355

    355LT

    R

    291.484R

    1.2lw

    le

    0.06 From the graph

    Mult

    MR

    mkN138.9667MR

  • Ultimate Moment due to the Steel Beam Self weight

    8

    2L

    Wbeam

    Mbeam

    mkN867Mbeam1.10

    steel_u

    Mbeam

    steel_u2

    1Mu_2

    mkN476.85Mu_2

    The beam is not stable, since Mu_2 is larger than Mr We need intermediate Restraints

    d) With self-weight of concrete:

    Spacing of LTB restraints:

    This restraints need to be fully effective, with for example cross

    m2.83sLTB

    diagonal bracing in plan view, which brace the compression flanges

    which are prone to LTB instability during construction, until deck

    acts as a restraint

    Effective LTB length with intermediate restraints:

    Lets say le=lw=lr

    sLTB

    le

    Slenderness Parameter:

    2

    tfb

    tft

    tfavg1k

    41 l

    elw

    3tw

    d12

    13bfb

    tfb12

    13bft

    tft12

    1Iy

    4m0.0003I

    y

    As

    Iy

    ry

    m0.1049ry

    D

    tfavg

    ry

    lw

    F

    0.6255F

    3bft

    tft12

    1Icf

    4mm

    7105.9895I

    cf

    3bfb

    tfb12

    1Itf

    4mm

    8102.0947I

    tf

    Itf

    Icf

    Icf

    i 0.2224i

    F

    11.5351.5821.5351

    Linear interpolation from BS tablesF

    11.2661.2911.2662

  • .2i.1

    2

    1

    1

    1.4906

    k4r

    y

    le

    LT 40.1983LT

    Limiting Value of Slenderness:

    Mpl_s

    Mpe

    1.2286Mult

    Mpe

    Mel_s

    Mult

    Mult

    Mpe

    355

    35530

    lim33.2525

    lim

    Limiting Moment of Reistance:

    Mpe

    Mult

    355

    355LT

    R

    36.2665R

    1lw

    le

    .95 From graph

    Mult

    MR

    mkN2200.306MR

    Ultimate Moment due to the Steel Beam and Concrete Deck Self weight

    8

    2L

    Wslab

    Mslab

    8

    2L

    Wbeam

    Mbeam

    1.15conc_u1.10

    steel_umkN867M

    beam

    Mbeam

    steel_u

    Mslab

    conc_u2

    1Mu_1

    mkN2190.5297Mu_1

    The beam is stable, since Mr is larger than Mu

    ii) Stiffeners:

    a) During Construction

    No web stiffeners:

    La m34a

    3

    yc

    y

    MPa204.9593y

    MPa355

    yc

    tw

    dw

    137.1895w

  • da 36.7568 Web panel ratio

    if

    else

    2

    tw

    bft

    yf

    MPa355tft

    10

    2

    tw

    bft

    yf

    MPa355tft

    10bfe

    tw

    2d

    yc2

    2tft

    bfe

    yf

    mfw

    0.0054mfw

    From the graph

    0.24 y

    l

    MPa49.1902l

    s

    l

    ld

    MPa42.589ld

    ld

    Aw

    Vd

    kN265.6193Vd

    2

    LWslab

    conc_u

    Wbeam

    steel_u2

    1Vu_const

    kN257.7094Vu_const

    There is no need of web stiffeners during construction, since Vd is larger than Vu

    b) After Construction

    Web stiffeners every 2m:

    d

    a2

    2

    m2.00a2

    2.16222

    From the graph:

    0.502

    y

    2

    l2

    MPa102.4797l2

    s

    l2

    l2d

    MPa88.727l2d

    l2d

    Aw

    V2d

    kN553.3736V2d

    2

    LWsurf

    surf_u

    Wrail

    rail_u

    Wlive

    live_u

    Wslab

    conc_u

    Wbeam

    steel_u2

    1Vu

    kN517.0019Vu

    Design could be optimised, since this maximum shear only occurs close to the supports.

    In addition, no bending interaction needs to be checked, since this shear force

    occurs where bending moment is equal to zero

  • iii) Ultimate Bending Strength and Ultimate Design Moment

    Plastic Moment of Composite Section

    Effective Slab Width:

    if

    else

    4

    L

    Spabeam

    Spabeam4

    LBeff

    m2Beff

    C2

    Beff

    Be

    m1.5Be

    Ds

    Be

    Ac

    2m0.4125A

    c

    1.11.05s

    s

    yc

    fyd

    2mm

    N307.3593f

    yd

    Steel Design Yield Limit

    s

    yf

    fyd_ff

    cu0.45f

    cd2

    mm

    N22.5f

    cd

    Concrete Design Resistance

    Steel Beam Resistance: Concrete Slab Resistance:

    fcd

    Ac

    Rc

    kN9281.25Rcf

    yd_fAfb

    Rfb

    kN3472.4026Rfb

    fyd_f

    Aft

    Rft

    kN1971.4286Rft

    fyd

    Aw

    Rw

    kN1916.9424Rw kN3888.3709R

    ftRw

    Rw

    Rft

    Rfb

    Rs

    kN7360.7735Rs

    Plastic Neutral Axis:

    Rc is larger than Rs, so PNA lies within the slab depth, as shown in the above figure

    DsR

    c

    Rs

    yp

    m0.2181yp

    yp

    0.5D0.5Ds

    Rw

    yp

    0.5Ds

    DRfb

    yp

    0.5Ds

    Rft

    Mpl

    mkN5519.479Mpl

    Short-term Mechanical Properties for Elastic Analysis

    cs

    Ac

    Aw

    Afb

    Aft

    cs

    Ds

    Ac

    0.5Ds

    D0.5Aw

    Ds

    DAfb

    Ds

    Aft

    ye1

    m0.3409ye1

  • cs

    12

    2Ds

    Ac12

    2D

    Aw

    cs

    2Ds

    0.5ye1

    Ac

    2ye1

    Ds

    D0.5Aw

    2ye1

    Ds

    DAfb

    2Ds

    ye1

    Aft

    Ic1

    4m0.0141I

    c1

    Long-term Mechanical Properties for Elastic Analysis

    cl

    Ac

    Aw

    Afb

    Aft

    cl

    Ds

    Ac

    0.5Ds

    D0.5Aw

    Ds

    DAfb

    Ds

    Aft

    ye2

    m0.4549ye2

    cl

    12

    2Ds

    Ac12

    2D

    Aw

    cl

    2Ds

    0.5ye2

    Ac

    2ye2

    Ds

    D0.5Aw

    2ye2

    Ds

    DAfb

    2Ds

    ye2

    Aft

    Ic2

    4m0.0119I

    c2

    Elastic Moment of Composite Section

    2

    ye2

    ye1

    ye

    2

    Ic2

    Ic1

    Ic

    ye

    Ds

    D

    fyd_f

    Ic

    Mel_1

    mkN4578.4589Mel_1

    fcdy

    e

    Ic

    avg

    Mel_2 2

    cs

    cl

    avg

    mkN7282.5148Mel_2

    if

    else

    Mel_2

    Mel_1

    Mel_2

    Mel_1

    Mel

    mkN4578.4589Mel

    Ultimate Design Moment

    Load Factors for Combination 1:

    At ultimate limit state:

    1.15conc_u

    1.75surf_u

    1.20rail_u

    1.10steel_u

    1.50live_u

    Bending Moments:

    8

    2L

    Wslab

    Mslab

    mkN2980.3125Mslab

    8

    2L

    Wsurf

    Msurf

    mkN413.27Msurf

  • 82L

    Wbeam

    Mbeam

    mkN867Mbeam

    8

    2L

    Wrail

    Mrail

    mkN722.5Mrail

    8

    2L

    Wlive

    Mlive

    mkN1878.5Mlive

    Mlive

    live_u

    Mrail

    rail_u

    Mbeam

    steel_u

    Msurf

    surf_u

    Mslab

    conc_u2

    1Mu

    mkN4394.5159Mu

    The section is non-compact, thus Elastic Moment Capacity is to be used

    Ultimate Bending Strength is larger than Ultimate Bending Moment

    iv) Serviceability Stresses

    Dead Load Stresses

    Partial Safety Factors at Service

    1.00conc_s

    1.20surf_s

    1.00steel_s

    1.00live_s

    1.00rail_s

    Dead Load Bending Moment

    Mrail

    rail_s

    Mbeam

    steel_s

    Msurf

    surf_s

    Mslab

    conc_s2

    1MDL

    mkN2532.8682MDL

    We will use the mechanical properties for long-term loading, since dead loads are

    permanent loads

    ye2

    y1

    Ds

    ye2

    y2

    mm.00001y2

    y3

    m0y4

    Ds

    Dye2

    y5

    cl

    Ic2

    y1

    MDL

    1_d

    clIc2

    y2

    MDL

    2_d I

    c2

    y3

    MDL

    3_d I

    c2

    y4

    MDL

    4_d I

    c2

    y5

    MDL

    5_d

    mm.001y5

    y5

    y4

    y3

    y2

    y1

    mm.001y1

    yDL

    0

    5_d

    4_d

    3_d

    2_d

    1_d

    0

    XDL

    m0.7901

    m0.7901

    0

    m0.1799

    m0.1799

    m0.4549

    m0.4549

    yDL

    MPa

    0

    168.4658

    0

    38.3633

    2.9006

    7.3342

    0

    XDL

  • Dead Load Stresses Graph

    M1

    -256 -128 0 128

    0.5

    0.25

    0

    -0.25

    -0.5

    -0.75

    -1

    x

    y

    Live Load Stresses

    Dead Load Bending Moment

    Mlive

    live_s2

    1MLL

    mkN939.25MLL

    We will use the mechanical properties for short-term loading, since live load is an

    instantaneous load

    ye1

    y1_l

    Ds

    ye1

    y2_l

    mm.00001y2_l

    y3_l

    m0y4_l

    Ds

    Dye1

    y5_l

    cs

    Ic1

    y1_l

    MLL

    1_l

    csIc1

    y2_l

    MLL

    2_l I

    c1

    y3_l

    MLL

    3_l I

    c1

    y4_l

    MLL

    4_l I

    c1

    y5_l

    MLL

    5_l

    mm.001y5_l

    y5_l

    y4_l

    y3_l

    y2_l

    y1_l

    mm.001y1_l

    yLL

    0

    5_l

    4_l

    3_l

    2_l

    1_l

    0

    XLL

    m0.9041

    m0.9041

    0

    m0.0659

    m0.0659

    m0.3409

    m0.3409

    yLL

    MPa

    0

    60.2705

    0

    4.3943

    0.6645

    3.4368

    0

    XLL

  • Live Load Stresses Graph

    M2

    -96 -64 -32 0 32

    0.5

    0.25

    0

    -0.25

    -0.5

    -0.75

    -1

    x

    y

    Total Load Stresses

    Ic1

    ye1

    ye2

    MLL

    4

    mm.001y5

    y5

    y4

    y3

    y2

    y1

    mm.001y1

    yTL

    0

    5_l

    5_d

    4

    4_d

    3_l

    3_d

    2_l

    2_d

    1_l

    1_d

    0

    XTL

    m0.7901

    m0.7901

    0

    m0.1799

    m0.1799

    m0.4549

    m0.4549

    yTL

    MPa

    0

    228.7363

    7.5999

    42.7575

    3.5651

    10.7709

    0

    XTL

    Total Load Stresses Graph

    M3

    -256 -128 0 128

    0.5

    0.25

    0

    -0.25

    -0.5

    -0.75

    x

    y

  • v) Stresses due to shrinkage

    Restrained Shrinkage stresses

    cs

    Ecl

    fo

    MPa3.1fo

    Restrained Tensile Stress in the slab

    Balancing Forces

    Ac

    fo

    Fsh

    kN1278.75Fsh

    Compression Balancing Force

    Ds

    0.5ye2

    Fsh

    Msh

    mkN405.8989Msh Sagging Balancing Moment

    Balancing Axial Stresses

    Aw

    Afb

    Aft

    cl

    Ac

    Acomp Area Composite Section

    Acomp

    Fsh

    f1

    MPa22.9781f1

    Balancing Axial Stress in Steel

    cl

    f1

    f1c

    MPa1.7374f1c

    Balancing Axial Stress in Concrete

    Balancing Bending Stresses

    Ic2

    Ds

    ye2

    Msh

    f2tf

    MPa6.1478f2tf Top Flange, in steel

    cl

    f2tf

    f2bs_c

    MPa0.4648f2bs_c Bottom Slab, in concrete

    cl

    Ic2

    ye2

    Msh

    f2ts_c

    MPa1.1753f2ts_c Top Slab in concrete

    Ic2

    Ds

    Dye2

    Msh

    f2bf

    MPa26.9971f2bf

    Bottom Flange

    Final Stresses

    f2ts_c

    f1c

    fo

    ft_conc

    MPa0.1873ft_conc

    Tensile stress top of slab

    f2bs_c

    f1c

    fo

    fb_conc

    MPa0.8978fb_conc

    Tensile stress bottom of slab

    f1

    f2tf

    ftf

    MPa29.1259ftf

    Compression stress on tof flange

    f1

    f2bf

    fbf

    MPa4.019fbf

    Tensile stress on bottom flange

    Ds

    Dy1

    Dy2

    mm.0001Dy3

    m0y4

  • mm0001y4

    y4

    y3

    y2

    y1

    mm.001y1

    ysh

    0

    fbf

    ftf

    fb_conc

    ft_conc

    0

    Xsh

    m0.001

    0

    m0.97

    m0.97

    m1.245

    m1.245

    ysh

    MPa

    0

    4.019

    29.1259

    0.8978

    0.1873

    0

    Xsh

    Shrinkage Induced Stresses Graph

    M4

    -32 -16 0 16 32

    1.25

    1

    0.75

    0.5

    0.25

    0 x

    y

    vi) Stud Connectors

    Plastic design

    Longitudinal shear force Rq between the steel and concrete:

    if

    else

    Rc

    Rq

    Rs

    Rq

    Rc

    Rs

    Rq

    kN7360.7735Rq

    114Ns

    Total Number of Studs in Half Span mm16stud

    Diameter

    mm75hstud

    HeightkN820.8N

    sRstuds

    kN7478.4Rstuds

    Total Stud Strength

    2

    Ns

    2

    L

    ssc

    mm298.2456ssc

    Spacing if arranged in pairs

    stud

    4stud

    2mm20bflange_min

    m0.12bflange_min

    Minimum flange width

  • 57 pairs of 16mm studs for half span

    Let's check for elastic design:

    Stud resistance per unit length

    ssc

    kN82.82R

    m

    kN439.9059R

    Longitudinal shear force q between the steel and concrete:

    cl

    Ic1

    2

    Ds

    ye1

    Ac

    Vu

    q m

    kN232.8055q

    Studs are OK