Vigas - Flexão com Torção 3

TORÇÃO

Neste exemplo, será dimensionada a armadura longitudinal e transversal de uma viga submetida a Flexão Simples combinada com torção utilizando como base a Norma ACI 318-19, conforme dados abaixo:

61cf2f8cada5dc92bcdf8e3fa92ea223.pngb4f4d80dc9f8c38d83328b9e65676519.png

Concreto - C25 (4000 psi) / Aço – ADN420 (60 ksi)

bw: 15,75 in / h: 23,62 in

Mu:

TQS = 3186 kip.inSoftware B = 3491,15 kip.inSoftware C = 3252,82 kip.in


25fb89e34086ff9d112742c5d9b3dca8.png

Flexão:

99a914f756ef79286be3e84c85cd5650.png

e1ecb8caa8900bc95c3ea1911a04e7e1.png

fbfa4dfad2fd78e456672b23a19e3ede.png

92a522ea34ee8d788d27af9c5a82546e.png


4f4e944f326b4cdfcf4ad17648751d28.png



As,min (ACI 318-19 – 9.6.1.2)

4574105fb764fb57bf27ad1a4280332d.png

8c5190e45c7015d993768e976098da00.png

4a717b27548c2dfa2905ca9bb5c52d71.png

TQS = 3,04 in²Software B = 1,42 in²Software C = 1,47 in²

3,04 in² ≥ 3,04 in² → OK!
øMn (3186 kip.in) ≥ Mu (3186 kip.in) → OK!!


Verificação do fator de redução (ACI318-19 – 21.2.2)

5828c6cc9d0d7f42d68aa410520847fe.png

8dc89494aae4d7e770d89d10b112a917.png

aa3efcdd8f24860370ef79006f9f0178.png

0,013 ≥ 0,005 → OK! Tension Controlled! → ø 0,90 OK!


Cortante:


TQSSoftware BSoftware C
Vu = 52,76 kipsVu = 52,57 kipsVu = 52,70 kips
Vu,design = 52,76 kips Vu,design = 44,52 kips Vu,design = 44,59 kips

7bb367397cb7c88332f5a35676605d1d.png

f826c8ce9ac11945e76da4297241ab7d.png

1ad6da52bb253d0ff9f8870ebcb77c23.png

aaf95bfbf1e044110464cb9d26918b8f.png

f0952b8c17778184ff9b68f49671d73d.png

c5ed095bf8bdbcb1488b2c645739de8e.png

2466ad6b595c800efbc6ee6e0631bf8b.png


    Ø0,75 → øVn ≥ Vu → 49,37 ≥ 49,37 → OK!!

    Torção:

    Tu:

    TQS = 539,85 kip.inSoftware B = 534,54 kip.inSoftware C = 538,08 kip.in

    75384bb676cde6418771aa1b3d342fd3.png

    2bcef993c27ac53134d70e70ddaf08b2.png

    3978d73c516ee9ebf7be2024d2f36330.png

    a05f4e263112aaf39ba237317dcd4734.png

    de56f140c13e72b8dff2cbe5adb3c394.png

    cf61c74417fc455a33d25bec0beaf621.png

    Fissuração:

    3c743327b41dddbb27bae6d90231eb80.png

    b740ed6c3716e4aaa95ec247b2dedfab.png

    7933f1f76992ae4be20f0ad5d5987f72.png


    Armaduras Transversal:

    69afa4b2450026aa879bea596d73924b.png

    d8becac269427cdf22ce09d8c1b412ce.png

    77998638c746faa8b9b8881243b70e90.png

    5469b27797bd5235c443b3800d9a5896.png

    Considerando 2 ramos:

    79c627febbeb85694c7cd589deafcb87.png

    1498b28e62b5a7fb00cd36552b55274c.png

    bd5df2f98bdf6ae6c62a42068c783623.png


    Espaçamento:

    06d1e07ea784adbc04a385a9e9430ab3.png

    0a3e75872f87c4980b122644f36de95d.png

    2bdcd12ccf9915b984ec369869858822.png

    8cccee753ab96df7174b4e659b499434.png

    Øt = #4 → Av = 0,080 in²/in → #4 @ 5 in


    øVn (107,55 t) ≥ Vu (52,76 t) → OK!!


    Armadura Longitudinal:

    c502f15d90a349b1f21e10f18b62ae69.png

    a215d85a0ee1f121cfcb25188360a052.png

    a4f32d1602829db949457a83b6de8e56.png

    578b75256aee4d19c83a067c4b52e265.png





    Vigas - Flexão com Torção 2
    Vigas - Cortante