Investigation of Eccentrically-Supported Simple Beam under Point Load

Abstract

According to the classical beam theories, beams are considered as one dimensional element. These theories assume that supports are placed at the mid-plane of the beam. However, in practice, the beams often are supported at the point different from their centers. In this study, an eccentrically simplysupported beam under transverse point load at the center of the beam was solved by the application of the MacLaurin series. This study presents a theoretical approach to the analysis of eccentrically supported beams. The effects of eccentric supports on the flexural rigidity of the beam have been investigated. Analytic equations derived were used to investigate the effect of varying support positions through the thickness on bending analysis of beams under transverse loading. The findings revealed that the flexural rigidity of beams is significantly influenced by eccentric pin-pin support. The accuracy of the equations was verified by comparing the results obtained with the Finite Element solutions.

Keywords

• Eccentric support
• Simple beam
• Beam theory
• modified beam theory
• the MacLaurin series

TEKİL YÜK ETKİSİ ALTINDA EKSANTRİK MESNETLİ KİRİŞLERİN İNCELENMESİ

Abstract

Klasik kiriş teorilerinde kirişler bir boyutlu kabul edilir. Bu teoriye göre mesnetler tarafsız eksendedir. Ancak pratik uygulamalarda kirişler tarafsız eksenlerinden farklı noktalardan mesnetlenmektedir. Literatürde üniform yük etkisinde eksantrik mesnetlenme durumuna sahip kirişler için düzenlenmiş kiriş teorisi geliştirilmiştir. Bu çalışmada tekil yük altındaki eksantrik mesnetli kirişler MacLaurin serileri kullanılarak analitik olarak çözülmüştür. Eksantrik mesnetlerin kirişin eğilme rijitliği üzerindeki etkileri araştırılmıştır. Elde edilen analitik denklemler, mesnetlerin kiriş derinliğinde farklı konumlarında (eksantrisite) kirişlerin eğilme analizi üzerindeki etkisini araştırmak için kullanılmıştır. Bulgular, kirişlerin eğilme rijitliğinin eksantrik mesnet durumundan önemli ölçüde etkilendiğini göstermektedir. Elde edilen sonuçlar Sonlu Eleman çözümleri ile karşılaştırılmıştır.

Keywords

• Eksantrik mesnet
• Basit kiriş
• Kiriş teorisi
• Düzenlenmiş kiriş teorisi
• MacLaurin serileri

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