Início Estruturas Índice de Esbeltez de Pilares: O que é? Importância e considerações normativas

Índice de Esbeltez de Pilares: O que é? Importância e considerações normativas

16518
113

No tocante a projetos estruturais de pilares, o índice de esbeltez é um dos parâmetros mais importantes a se avaliar. Isso principalmente porque esse índice remete às propriedades geométricas das peças.  Assim como em qualquer peça estrutural, os pilares devem ter geometria adequada para resistir todas as solicitações (cargas) a eles submetidas.

O conhecimento do índice de esbeltez está diretamente relacionado com a segurança e durabilidade de qualquer estrutura. Para o estado limite de serviço (ELS) a peça deve garantir eficiência quanto ao aspecto de funcionalidade, e para o estado limite último (ELU) a peça deve possuir uma esbeltez equilibrada, a ponto de evitar que quando submetida a um esforço de compressão não ocorra a flambagem, que é o colapso progressivo por perda de estabilidade.

Dentro da engenharia de estruturas o índice de esbeltez deve ser entendido como o parâmetro responsável por prever se um pilar irá ou não sofrer flambagem com as dimensões adotadas para a peça.

Para entender o que é o índice de esbeltez em pilares, como é calculado e todas as variáveis que influenciam na determinação do mesmo, além de entender como este deve ser levado em consideração em cada uma das etapas de projeto previstas pela norma regulamentadora de estruturas de concreto armado no Brasil, leia este artigo até o final.

flambagem-pilares-concreto-armado

O que é índice de esbeltez?

O índice de esbeltez dos pilares é um parâmetro que busca avaliar o quão suscetível a barra comprimida é em relação ao efeito de flambagem. Esse índice consiste basicamente em uma medida mecânica que permite determinar a facilidade que um determinado pilar tem de se encurvar.

O índice de esbeltez depende principalmente do comprimento do pilar e da seção transversal. Isso porque a ANBT NBR 6118:2014 define índice de esbeltez como a razão entre o comprimento de flambagem e o raio de giração do pilar:

esbeltez01

Onde:

λ = índice de esbeltez;

le = comprimento equivalente ou comprimento de flambagem;

i = raio de giração da peça em metros.

 

Comprimento equivalente

O comprimento equivalente de um pilar, ou também chamado de comprimento de flambagem depende exclusivamente da distância entre os pontos que o pilar esteja travado, seja por lajes ou vigas. A distância é dada pelos tipos de apoio presentes no pilar. A ABNT NBR 6118:2014, tratando da análise de elementos estruturais, isolados especifica que em casos onde o pilar é engastado na base e livre no topo, o valor de le é igual a duas vezes o seu comprimento, e nos demais casos deve-se calcular obedecendo a seguinte relação:

comprimento-equivalente-de-flambagem

Onde:

l0 = distância entre as faces internas dos elementos estruturais, supostos horizontais, que vinculam o pilar;

h = altura da seção transversal do pilar, medida no plano da estrutura em estudo;

l = distância entre os eixos dos elementos estruturais aos quais o pilar está vinculado.

Raio de Giração

O raio de giração dos pilares é definido pela relação entre o momento de inércia do pilar e a área da seção transversal:

raio-de-giração

Onde:

i = raio de giração;

I = momento de inércia da seção transversal;

A = área da seção transversal.

Considerando um pilar retangular, com dimensões b e h, o valor do momento de inércia é obtido pela seguinte expressão:

momento-de-inercia-pilar-esbeltez

Classificação dos pilares quanto à esbeltez

Os pilares de uma edificação podem ser classificados de acordo com o índice de esbeltez. Conforme mostra a tabela a seguir:

classificação-de-pilares-esbeltez-nbr6118

Considerações normativas: índice de esbeltez

O máximo valor para o índice de esbeltez permitido pela ABNT NBR 6118:2014 é 200. No entanto, a norma diz ainda que em casos onde o elemento for pouco comprimido com força normal menor que 0,10∙fcd∙Ac a esbeltez pode exceder esse limite.

Relação índice de esbeltez e efeitos de 2ª ordem

Outra especificação importante relacionada ao índice de esbeltez exposta pela norma é que em casos onde o índice ultrapassar o valor de 140 na análise dos efeitos locais de segunda ordem os esforços solicitantes finais devem ser multiplicados por um coeficiente adicional (ɣn).

Para que os efeitos locais de segunda ordem em elementos isolados sejam desconsiderados, o valor do índice de esbeltez deve ser menor que um valor-limite de esbeltez que é calculado da seguinte forma:

esbeltez-limite

Onde:

λ1 = valor-limite de esbeltez e deve ser ≥ a 35 e ≤ a 90;

e1/h = a excentricidade relativa de 1ª ordem na extremidade do pilar onde ocorre  momento de 1ª ordem de maior valor absoluto;

αb = coeficiente relativo a vinculação dos extremos da peça isolada, deve ser obtido da seguinte forma:

ALFA-B-NBR6118

Em relação aos métodos de determinação de efeitos locais de segunda ordem, a norma diz que quando o índice de esbeltez for maior que 90 se faz obrigatória a consideração de fluência. Além disso, para índice de esbeltez maior que 140 é obrigatório a utilização do método geral.

Para pilares de seção retangular submetidos à flexão composta oblíqua cujo índice de esbeltez for menor ou igual a 90 podem ser aplicados os métodos pilar-padrão com curvatura aproximada, pilar-padrão com rigidez aproximada e pilar-padrão acoplado a digramas M, N 1/r simultaneamente, em cada uma das duas direções.

Finalizando

Neste artigo vimos o que é o índice de esbeltez em pilares e qual a sua importância em projetos de estruturas, além disso, foi abordado a forma de como este deve ser obtido e as considerações da norma de estruturas de concreto acerca do assunto.

Caso tenha interesse em saber mais sobre o assunto, acesse meu canal, onde publico frequentemente conteúdos sobre engenharia de estruturas, clicando aqui!

Espero ter contribuído para a evolução do seu conhecimento.

Até a próxima!

113 COMENTÁRIOS

  1. I am curious to find out what blog system you happen to be using?
    I’m having some minor security issues with my latest website and
    I’d like to find something more safe. Do you
    have any solutions?

  2. Howdy! This article couldn’t be written much better!
    Looking through this article reminds me of my
    previous roommate! He always kept talking about this. I’ll send this information to him.

    Pretty sure he’s going to have a great read. Many thanks
    for sharing!

  3. Simply want to say your article is as astonishing.

    The clearness for your submit is just excellent and that i can assume you’re a
    professional on this subject. Fine along with
    your permission allow me to snatch your RSS feed to stay up to date with
    coming near near post. Thank you a million and please keep up the
    enjoyable work.

  4. Hello there, You’ve done an excellent job. I will certainly digg it and personally suggest
    to my friends. I am sure they will be benefited from this website.

  5. Great beat ! I wish to apprentice while you amend your website, how can i subscribe for
    a blog website? The account aided me a acceptable deal.
    I had been tiny bit acquainted of this your broadcast provided bright clear idea

  6. I’m pretty pleased to discover this website.
    I wanted to thank you for your time for this wonderful read!!

    I definitely really liked every bit of it and I have you book marked
    to look at new information on your website.

  7. Very nice post. I just stumbled upon your weblog and wished to say that
    I’ve really enjoyed surfing around your blog
    posts. After all I’ll be subscribing to your rss feed and I hope you
    write again soon!

  8. We stumbled over here from a different website and thought I should check things out.
    I like what I see so now i am following you. Look forward to
    looking into your web page for a second time.

  9. Excellent blog! Do you have any suggestions for aspiring writers?
    I’m hoping to start my own site soon but I’m a little lost on everything.

    Would you propose starting with a free platform like WordPress or go for
    a paid option? There are so many choices out there that I’m totally overwhelmed ..
    Any tips? Thanks!

  10. Greate post. Keep posting such kind of info on your site.
    Im really impressed by it.
    Hi there, You have done a great job. I’ll definitely digg it and in my opinion suggest to my friends.
    I am confident they’ll be benefited from this web site.

  11. Heya i’m for the first time here. I came across this board and I in finding It really useful & it helped me out a lot.
    I’m hoping to give something back and help others such as you aided me.

  12. Admiring the persistence you put into your website and detailed information you present.
    It’s great to come across a blog every once in a while that isn’t the same outdated rehashed information. Excellent read!

    I’ve bookmarked your site and I’m including your RSS feeds to my Google account.

  13. I absolutely love your blog and find a lot of your post’s
    to be what precisely I’m looking for. Would you offer guest writers to write content in your
    case? I wouldn’t mind composing a post or elaborating on a lot of the subjects you
    write in relation to here. Again, awesome site!

  14. Wonderful blog! I found it while searching on Yahoo News.
    Do you have any tips on how to get listed in Yahoo
    News? I’ve been trying for a while but I never seem to get there!
    Many thanks

  15. Greetings, I do think your website could be having browser compatibility issues.
    When I look at your blog in Safari, it looks fine but when opening in IE, it’s got some overlapping issues.
    I just wanted to provide you with a quick heads up! Apart from that,
    great website!

  16. Right here is the perfect site for anyone who
    wants to find out about this topic. You realize a whole
    lot its almost hard to argue with you (not that I really would want to…HaHa).

    You definitely put a new spin on a subject that has been discussed for a long time.
    Excellent stuff, just excellent!

  17. Good day! I know this is kind of off topic but I was wondering if you knew
    where I could locate a captcha plugin for my comment form?

    I’m using the same blog platform as yours and I’m having
    trouble finding one? Thanks a lot!

  18. Solo the very first thing who has fork out to that convergence is a
    emergence with electric know-how. Ones R4 so Red
    R4i card R4i pay as you go card features superb features who may elevate your xbox 360.

    Both decisions R4i Dsi card playing cards enhance the utilization of variety of appliances while you make the most of them for one factor or maybe the previous.

    One of the good capabilities of the Otterbox case is that it comes finish with connects
    for the slots of the S3, so that all the slots are secured however nonetheless fully obtainable.
    They can be found by working with abilities only for transporting information. The cards host the capacity linked with
    filing quite a few sport personal records including coaching movies and as a consequence track selections videos.
    With all this in thoughts, I suggest that we
    explore adding an optionally available type subject to the JSON
    format. In the sector of notebook, if there’s a maker who has been capable to form out a forte for their
    sort title over years, it would be Lenovo with the ThinkPad line
    of merchandise catering typically to the industry skilled together with the highway warrior.
    Still, that is one in every of the first “professional” laptops that may get away with
    having no spinning platter drives.

  19. Sesudah anda seringkali bermain dan mempunyai pengalaman karena itu ada bisa
    secara perlahan-lahan menambahkan modal slot online untuk
    mendapatkan beberapa keuntungan. Mungkin jika kami menyebutkan nama dari
    transaksi tersebut kalian pasti akan terkejut, karena selama ini transaksi itu sudah kita gunakan.
    Ada beberapa persiapan yang harus anda siapkan, sebelum bakal menjalankan taruhan bola online dengan uang asli, karena tanpa melakukan persiapan tersebut maka jalanya taruhan bakal kurang
    lancar. 4. PCIe PCI Express digunakan dalam aplikasi pemakai, server,
    bersama industri, sebagai interkoneksi geladak motherboard (untuk menghubungkan periferal yang terpasang di
    motherboard) dan sebagai antarmuka karcis ekspansi lakukan papan embel-embel.
    Sistem bermain slot sangat sederhana dan dapat dipahami dengan mudah
    oleh semua orang. Sekarang ini yang popular dan bisa anda mainkan diantaranya yaitu Pragmatic, Habanero, CQ9, TTG, PlayStar, RedTiger, Gameplay,
    Isoftbet dan lainnya. Nah, recreation ini cuma ada satu pilihan yang paling
    sempurna, yakni game slot online. Di period fashionable ini hampir semua tipe game judi on-line tersedia secara on-line di internet.
    Originally released in 1995, the loopy adventure of being on the planet of a board
    game grew to become a huge hit, with Jumanji being used as a pop-culture reference for decades to return.

  20. I truly love your blog.. Pleasant colors & theme. Did you build this site yourself?
    Please reply back as I’m attempting to create my very own site and would love to know where you
    got this from or what the theme is called. Thank you!

  21. It might achieve this regardless of the place it appears on the reels
    or whether they’re in the identical pay-line.

    This is identical Nintendo Switch we just opened.
    Three potential odds – every odd modifications your prize consequence.
    Often clubbed with Seo coaching can be the Pay-Per-Click (PPC) module,
    wherein a company can buy a paid slot on a
    writer’s webpage or search engine, such as the highest three outcomes on Google.
    Also, you will note the Ginger the basketball, which add some Splashables, you choose
    to can put along with close by baskets. Website content
    material and app content – Every company needs a effectively written and clear approach to
    explain the brand imaginative and prescient, and to have this displayed
    for customers to see. If you’d just like the societies (your possible prospects) to observe you and your company, you then undoubtedly
    should arrived at their very own discussion board as well as hook up with
    all of them normally. MacXDVD Software is a division of Digiarty Software Company,
    owns an expert multimedia software program development group,
    offering a variety of products for Macintosh Computer customers, together with MacX Video Converter, MacX DVD Ripper,
    DVD Author, DVD backup tools, and so on, series of apps for
    Apple video participant, and iPhone, iPad 2D and 3D video games.

  22. Membaca berita atau kabar terbaru dari sepakbola juga menjadi salah satu termasuk yang bisa kita
    pakai sebelum mencoba memainkana judi first half ini, karena biasanya disini akan membuat
    kita bisa melihat apakah tim yang dipilih memainkan formasi yang terbaiknya, tujuannya agar
    kita nanti tidak salah memilih tim yang ada. Pastikan Anda sebelumnya telah terdaftar untuk
    bermain di agen maxbet, sebelum anda nantinya menggunakan maxbet Slot Board yang akan kami tulis
    dan juga bagikan kepada Anda di bawah ini. Karena permainan ini bisa dikatakan juga sebagai pertaruhan yang tidak
    membutuhkan modal yang besar untuk bermain, sehingga akan membuat kita bermain lebih aman nantinya.
    Saat kita memilih taruhan yang ada, hendaknya kita harus terus memantau kondisi tim yang kita pilih nantinya,
    apakah tim yang kita mainkan dalam kondisi yang baik agar dalam pertandingan nanti akan memainkan permainan yang baik dan bisa membawa kita meraih keuntungan yang besar dalam permainan yang ada.
    Karena kita hanya bermain dalam satu babak pertama saja.
    Sehingga kalian tidak perlu takut karena kami akan memberikan beberapa ideas
    dan panduan bagaimanca cara memainkan permainan yang satu ini sehingga kalian akan bisa meraih kemenangan dengan sempurna tentunya.
    Jika pemain tidak puas dengan kombinasi pemenang, opsi untuk menyimpan kemenangan di mesin ini selalu ada.

  23. Howdy! I simply wish to give you a big thumbs up for
    the excellent info you have got right here on this post.
    I’ll be coming back to your blog for more soon.

  24. Данный процесс довольно длителен, что несет за собой потребление дыма в 100-200 раз больше, нежели при выкуривании сигареты.

    И вот придет ко мне уважаемый Вахид-хан
    и спрашивает, нет ли на продажу белого бачи, и кладет мне на стол сто двадцать тысяч афганей – заметьте, это больше, чем я
    прошу с вас. Он мог назвать эту цену только в одном случае – если он собирается взять твои семьсот тысяч афгани и сбежать с ними.
    Он обещал мне помочь в моей потребности.
    Он был цивилизованным человеком и от
    необходимости есть именно таким способом его просто коробило.
    Затем вынимаем сердцевину или
    мякоть таким образом, чтобы в
    итоге получить форму чаши.
    Курят его особым образом, накручивая
    лист на верхнюю часть курительного прибора.

    Материал, из которого сделана внутрення часть шахты – крайне важная составляющая.
    Часть племен – например киргизское
    племя саваттаров – почти в полном составе
    служили Белому Царю в армии и пограничных дозорах, живя этим,
    части – все же хватало земли
    и воды из ирригационных систем,
    часть занималась пастбищным скотоводством, доходя со
    своими стадами едва ли не до Уральских
    гор. От рынка до городского офиса было совсем рукой подать, из окон кабинета доктора был виден базар была видна старая крепость – но,
    конечно же, они проделали этот
    путь на машине.

  25. Hmm is anyone else encountering problems with the pictures
    on this blog loading? I’m trying to determine if its a problem on my
    end or if it’s the blog. Any feed-back would be greatly
    appreciated.

  26. Howdy just wanted to give you a quick heads up. The
    words in your post seem to be running off the screen in Safari.
    I’m not sure if this is a format issue or something to do with internet browser compatibility but I figured I’d post to let you know.
    The design and style look great though! Hope you get the issue
    fixed soon. Cheers

  27. Thanks for your marvelous posting! I actually enjoyed reading it, you’re a great author.I will ensure that I bookmark your blog and will
    eventually come back very soon. I want to encourage you continue your great writing,
    have a nice day!

  28. Do you mind if I quote a couple of your articles as
    long as I provide credit and sources back to your weblog?
    My blog is in the very same niche as yours and my visitors would certainly
    benefit from some of the information you present here.
    Please let me know if this ok with you. Regards!

  29. prednisone and grapefruit juice interaction snorting viagra sunscreen samples for physician offices atlantic drugstore viagra prices
    gnc vitamins for women energy viagra users group how to make natural viagra plant viagra warnings
    when to take a viagra best male supplements for libido doctor x viagra viagra coupons extenze male enhancement pictures
    sildenafil teva 100 mg capsule anything stronger than viagra viagra women benefits of vitamin e sexually dollar tree coupon policy
    ed medication price comparison german shopping center viagra tablets australia 40 mg cialis ways to prevent headaches
    how to use viagra sildenafil 100mg dapoxetine 60mg red viagra tablets sildenafil citrate pills
    take viagra how long before viagra gum cialis side effects with alcohol my walmart prescription account
    cocaine and viagra interaction viagra tablets viagra face flushing

  30. whoah this blog is excellent i love reading your articles.
    Keep up the good work! You know, lots of
    persons are looking around for this information, you can help
    them greatly.

DEIXE UMA RESPOSTA

Por favor coloque seu comentário!
Por favor coloque seu nome aqui