CE 156 - HW 3

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  • 7/28/2019 CE 156 - HW 3

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    CE 156 - Homework 3

    Prof. Ulpiano Ignacio

    LRFD:

    Pu = 1.2*(50kips) + 1.6*(135kips)

    = kips

    (KL)x = ft

    (KL)y = ft

    (a) A992

    Fy = ksi Fu = ksi E = ksi

    *choose sections in the AISC is such that local buckling will not occur, Q=1.0

    =

    W8x40

    (kL/r)x =

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    (a) A572 Grade 60

    Fy = ksi Fu = ksi E = ksi

    *sections in the AISC is such that local buckling will not occur, Q=1.0

    =

    W8x40

    (kL/r)x =

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    LRFD:

    Pu = (90kips) + (320kips)

    = kips

    (KL)x = ft

    (KL)y = ft

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    (b) *the first two trials passed it with a value of near 410 kips

    Fy = ksi E = ksi

    *choose sections in the AISC is such that local buckling will not occur, Q=1.0

    =

    W12x53

    (kL/r)x =

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    LRFD:

    Pu = 1.2*(300kips) + 1.6*(500kips)

    = kips

    (KL)x = ft

    (KL)y = ft

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    For Fcr > 2Fy

    Ie/I = [(b/2)^3]/[b^] = Fcr = [^2*Et*(1/8)]/[(kL/r)]1/8

    43.8044885 16.5

    46.5850468 16

    50 15.4439451

    32.1828895 77

    33.3333333 75.6595701

    33.3333333 18.9148925

    16.666667 106.998789

    19.0812352 100

    21.1426429 95

    3.92618008 270

    4.96907166 240

    6.49021605 210

    50 0

    36.8079382 18

    38.9412963 17.5

    34.8452067 18.5

    26.4100141 85

    29.81443 80

    23.5570805 90

    12.7208235 150

    16.666667 131.046218

    8.83390517 180

    Fcr (ksi) kL/r

    3.18020586 300

    0

    10

    20

    30

    40

    50

    60

    0 50 100 150 200 250 300

    Fcr(ksi)

    kL/r ratio

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    (b) LRFD:

    Fy = ksi E = ksi Pu = 1.2*(65kips) + 1.6*(150kips)

    *choose sections in the AISC is such = kips

    that local buckling will not occur, Q=1.0

    (KL)x = ft

    *Use LRFD (KL)y = ft

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    for Fcr < 0.6Fy for Fcr >= 0.6Fy

    Fcr = [^2*E]/[(kL/r)^2] Fcr has linear relation ship with kL/r until yielding

    LRFD:

    Pu = 1.2*(300kips) + 1.6*(500kips)

    = kips

    (KL)x = ft

    (KL)y = ft

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    LRFD:

    Pu = 1.2*(300kips) + 1.6*(900kips)

    = kips

    *Assume design beam is W14x145

    A572, Grade 50: Fy = 50 ksi

    Analysis on the plane of the frame

    GA =

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    *Analysis on the plane perendicular to the frame

    GA = r (128/sqrt(65))

    > , yes Qs => (175/sqrt(65))

    > , no Qs =

    b/t (4.02/.595) > r (95/sqrt(65))

    > ,no

    21.7061 0.73651

    6.7563 11.7833

    216 211

    20.2941 15.8764

    253 250

    285 318

    65

    193.846

    252

    10

    10

    50 65 29000

    0.96

    39.3366 184.971

    113.432 44.6513

    2753

    10

    35.8333

    3.34259

    10.72

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    (kL/r)x = (175/sqrt(50))

    > ,no

    d/t (14/.25) > (253/sqrt(50)) f = ksi

    > ,yes *Fcr with Q=1.0

    dE/t = = Qa = (dE/t)/(d/t) =

    Q = QaQs =

    =

    = ksi

    = 0.9*Fcr*Ag = 0.9*(26.0186ksi)*(13.5in^2) = kips

    0.64572

    26.0186

    316

    45.211 0.80734

    141.16

    20 13.435

    24.7487

    0.79982

    56 35.7796

    62.6122

    35.7941

    4.79985

    2.48479

    17.5005

    67.6113

    29000

    7

    83.3516

    311.021

    13.5

    81.6327 42.9507

    39.7351

    30.7158

    264

    14

    62.8272

    29.5707

    188

    63.8298 70.2507

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    Cruz, Laurenz Luigi B. 2009-22189 February 19, 2012

    Pu = 1.2 D + 1.6 L = 1.2 (3/7 L) + 1.6 L = L = kips

    kips

    kips

    (b) Fy = 60 ksi

    b/t (5/0.25) > (95/sqrt(60))

    > ,yes Qs = =

    > (175/sqrt(60))

    > ,no

    d/t (14/.25) > (253/sqrt(60)) f = ksi

    > ,yes *Fcr with Q=1.0

    dE/t = = Qa = (dE/t)/(d/t) =

    Q = QaQs =

    =

    = ksi

    = 0.9*Fcr*Ag = 0.9*(27.2611ksi)*(13.5in^2) = kips

    Pu = 1.2 D + 1.6 L = 1.2 (3/7 L) + 1.6 L = L = kips

    kips

    kips

    (b) Fy = ksi

    b/t (5/0.25) > (95/sqrt(100))

    > ,yes Qs = => (175/sqrt(100))

    > ,yes

    d/t (14/.25) > (253/sqrt(100)) f = ksi

    > ,yes *Fcr with Q=1.0

    dE/t = = Qa = (dE/t)/(d/t) =

    Q = QaQs =

    =

    = ksi

    = 0.9*Fcr*Ag = 0.9*(27.2634ksi)*(13.5in^2) = kips

    Pu = 1.2 D + 1.6 L = 1.2 (3/7 L) + 1.6 L = L = kips

    kips

    kips

    Live Load 158.918919

    Dead Load 68.1081081

    100

    0.34894

    192.027

    27.634

    336

    2.11429 336

    0.5

    17.5

    51.2487

    56 25.3

    39.0808 0.69787

    Live Load 156.554054

    Dead Load 67.0945946

    20 9.5

    0.57137

    150.064

    27.2611

    331

    2.11429 331

    0.7411

    22.5924

    40.1755

    56 32.6622

    43.1748 0.77098

    Dead Load

    149.459459

    64.0540541

    20 12.2644

    2.11429 316

    Live Load