AN ANALYTICAL INVESTIGATION OF RIGID PLASTIC BEAMS UNDER IMPACT LOADING

Öz

Beams might be subjected to impact loading which is a particular type of dynamic loading during their service lives. In this study the behaviour of beams under low speed impact loading has been investigated analytically. Simply supported and fixed ended beams have been analyzed with the assumption of rigid plastic behaviour. The collapse mechanism has been assumed to emerge by the instant formation of plastic hinges, hence, a limit analysis has been performed under dynamic loading considering the conservation principles of energy and momentum. The behaviour of rigid plastic beams under impact loading has been compared to the behaviour of elastic beams under similar loading conditions. 

ÇARPMA YÜKÜ ALTINDAKİ RİJİT PLASTİK KİRİŞLERİN ANALİTİK OLARAK İNCELENMESİ

Öz

Kirişler, kullanım ömürleri boyunca dinamik bir yükleme türü olan çarpma yüklerine maruz kalabilirler. Bu çalışmada kirişlerin düşük hızlı çarpma yükü etkisi altındaki davranışları analitik olarak incelenmiştir. Basit ve ankastre mesnetli kirişler, rijit plastik davranış kabulü yapılarak dinamik yükler altında incelenmiştir. Göçme mekanizmasının ani olarak plastik mafsal oluşumuyla gerçekleştiği kabul edilmiş, enerji ve momentumun korunma ilkeleri dikkate alınarak dinamik yük altında kirişlerin limit analizi yapılmıştır. Darbe yükü altındaki rijit plastik kiriş davranışı, benzer yükleme koşulları altındaki elastik kiriş davranışıyla karşılaştırılmıştır.

Anahtar Kelimeler

• Rijit plastik kirişler
• enerji ve momentumun korunumu
• çarpma yükü
• plastik mafsal

Kaynakça

1. Yu, T.X., Yang, J.L. ve Reid, S.R., “Dynamic behavior of double cantilever beams subjected to impact”, International Journal of Pressure Vessels and Piping, Cilt 78, No 1, 49-57, 2001.
2. Yu, T.X., Yang, J.L. ve Reid, S.R., “Deformable body impact: dynamic plastic behaviour of a moving free-free beam striking the tip of a cantilever beam ”, International Journal of Solids and Structures, Cilt 38, No 2, 261-287, 2001.
3. Yang, J.L., Liu, X.H. ve Reid, S.R., “Dynamic plastic behavior of a free–free beam striking the mid-span of a clamped beam with shear and membrane effects considered”, International Journal of Mechanical Sciences, Cilt 45, No 5, 915–940, 2003.
4. Yang, J.L., Yu, T.X. ve Reid, S.R., “Dynamic behaviour of a rigid, perfectly plastic free-free beam subjected to step-loading at any cross-section along its span”, International Journal of Impact Engineering, Cilt 21, No 3, 165-175 1998.
5. Wen, H.M., Reddy, T. Y. ve Reid, S.R., “Deformation and failure of clamped beams under low speed impact loading”, International Journal of Impact Engineering, Cilt 16, No 3, 435-454, 1995.
6. Liu, J.H. ve Jones, N., “Dynamic response of a rigid plastic clamped beam struck by a mass at any point on the span”, International Journal of Solids and Structures, Cilt 24, No 3, 251-270, 1988.
7. Kantar, E., Arslan. A. ve Anıl, Ö., “Beton dayanımındaki değişimin çarpma davranışına etkisi”, Journal of The Faculty of Engineering and Architecture of Gazi University, Cilt 26, No 1, 115-123, 2011.
8. Kishi, N. ve Bhatti, A.Q., “An equivalent fracture energy concept for nonlinear dynamic response analysis of prototype RC girders subjected to falling-weight impact loading”, International Journal of Impact Engineering, Cilt 37, No 1, 103–113, 2010.

9. Saatci, S. ve Vecchio, F.J., “Effects of shear mechanisms on impact behavior of reinforced concrete beams”, ACI Structural Journal, Cilt 106, No 1, 78-86, 2009.
10. Saatci, S. ve Vecchio, F.J., “Nonlinear finite element modeling of reinforced concrete structures under impact loads”, ACI Structural Journal, Cilt 106, No 5, 717-725, 2009.
11. Harsoor, R. ve Ramachandra, L.S., “Influence of notch on the elastic–plastic response of clamped beams subjected to low velocity impact”, International Journal of Impact Engineering, Cilt 36, No 8, 1058–1069, 2009.
12. Bambacha, M.R., Jamaa, H., Zhaoa, X.L. ve Grzebieta, R.H., “Hollow and concrete filled steel hollow sections under transverse impact loads”, Engineering Structures Cilt 30, No 10, 2859–2870, 2008.
13. Gültop, T., Alyavuz, B. ve Yılmaz, M.C., “Plastic Collapse of Beams under Impact Loading”, 6. Mühendislik ve Teknoloji Sempozyumu, Çankaya Üniversitesi, Ankara, 63-66, 25-26 Nisan 2013.
14. Young, W.C., “Dynamic and Temperature Stresses”, Roark’s Formulas for Stress and Strain, Mc Graw Hill, Sixth Edition, New York, A.B.D., 710-720, 1989.
15. Wasti, S.T., “Yıkılışın Bazı Misalleri”, Limit Analizi, Orta Doğu Teknik Üniversitesi Mühendislik Fakültesi Yayınları, Ankara, Türkiye, 13-24, 1968.
16. Neal, B.G., “Basic Theorems and Simple Examples”, The Plastic Methods of Structural Analysis, Chapman and Hall, Londra, İngiltere, 18-46, 1981.
17. Martin, J.B., “Limit Analysis of Beams and Frames”, Plasticity: Fundamentals and General Results, MIT Press, Londra, İngiltere, 408-420, 1975.