Determination of optimal cross-section dimensions of rectangular hollow sections under oblique bending: analytical and numerical study

Abstract

An insignificant number of rigorous studies have been devoted to the development of analytical procedures that determine the optimal cross-section dimensions of rectangular hollow section (RHS) members subjected to oblique bending, albeit their ubiquity in numerous application fields. In response to this, an analytical procedure has been developed based on the concept of minimizing maximum effective stress in the RHS caused by an applied oblique bending moment, in order to reduce material costs without compromising strength requirements. The RHS members addressed in this study have been assumed to be produced by hollowing out rectangular solid sections at different cross-section area extraction ratios; therefore, only the wall thicknesses of the RHS members have been taken into consideration as design variables. The minimization of maximum effective stress has been achieved by establishing a functional correlation between the cross-section design variables. The proposed procedure allows specifying the optimal cross-sectional dimensions for given different cross-section area extraction ratios and bringing cost-effective use of materials. After the subtle mathematical calculations, the derived analytical expressions have been made available to practical engineering in simple math forms for use in real design applications. The analytical procedure has been validated against numerical results which have been extracted from finite element analyses carried out in Abaqus engineering software.

Keywords

• Optimum Design
• Rectangular Hollow Section (RHS)
• Rectangular Solid Section
• Oblique Bending
• Finite Element Analysis.

Eğik eğilme altında dikdörtgen içi boş kesitlerin optimal kesit boyutlarının belirlenmesi: analitik ve sayısal çalışma

Abstract

Çok sayıda uygulama alanında yaygın olarak bulunmasına rağmen, eğik eğilmeye maruz kalan dikdörtgen içi boş kesitli (DBK) elemanların optimal kesit boyutlarını belirleyen analitik prosedürlerin geliştirilmesine yönelik az sayıda titiz çalışma yapılmıştır. Buna yanıt olarak, mukavemet gerekliliklerinden ödün vermeden malzeme maliyetlerini azaltmak amacıyla, uygulanan eğik eğilme momentinin neden olduğu DBK'deki maksimum etkili gerilimi en aza indirme konseptine dayalı bir analitik prosedür geliştirilmiştir. Bu çalışmada ele alınan DBK elemanlarının, farklı kesit alanı çıkarma oranlarında dikdörtgen katı kesitlerin içinin boşaltılmasıyla üretildiği varsayılmıştır; bu nedenle tasarım değişkenleri olarak yalnızca DBK elemanlarının duvar kalınlıkları dikkate alınmıştır. Maksimum efektif gerilmenin en aza indirilmesi, kesit tasarım değişkenleri arasında fonksiyonel bir korelasyon kurulmasıyla sağlanmıştır. Önerilen prosedür, verilen farklı kesit alanı çıkarma oranları için en uygun kesit boyutlarının belirlenmesine ve dolayısıyla malzemelerin uygun maliyetli kullanımına olanak sağlamaktadır. Ayrıntılı matematiksel hesaplamalardan sonra, elde edilen analitik ifadeler, gerçek tasarım uygulamalarında kullanılmak üzere basit matematik formlarında pratik mühendisliğe sunulmuştur. Analitik prosedür, Abaqus mühendislik yazılımında gerçekleştirilen sonlu elemanlar analizlerinden elde edilen sayısal sonuçlara göre doğrulanmıştır.

Keywords

• Optimum Tasarım
• Eğik Eğilme
• Sonlu Elemanlar Analizi.
• Dikdörtgen Dolu Kesit
• Dikdörtgen İçi Boş Kesit (DBK)

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