# Bending of Beams Experiment Report

Lab Report

Experiment # 3

Bending of Beams

Section # ThTh12

Group # 1

Ömer Ege Çalışkan

Serhat Karakuz

Noyan Uğur Renda

Turgut Soydan

20.03.2013

Abstract

In this experiment, a simply supported beam is used and the variations of deflection of a simply supported beam with load, beam thickness and material are investigated. It is found that the deflection of the beam changes linearly with the load and as the beam thickness increases, the beam deflection decreases. In addition, since different materials have different modulus of elasticity, deflection of different materials under a specific load is different. Depending on the results of the experiment, it is observed that the measured deflection values under different loads and for different materials overlap the Euler-Bernoulli Beam Theory.

Introduction

Beams can be described as a structural element that withstands load. Although beams are considered mainly as building structural elements, automobile or machine frames also contain beams to support the structure. Some applications require beams to support loads that can bend the beams, therefore it is important to observe the behavior of the beams under bending forces and which parameters have an effect on this behavior. If the maximum deflection that the beam can resist were not taken into consideration in the design process, there would be some serious failures in structures that can lead to some serious outcomes. In this experiment, an overhanging beam is used, which can be defined as a beam simply supported at two fixed supports and having both ends extended beyond the supports. In order to conduct this experiment and to investigate the variation of deflection of a simply supported beam, an apparatus that contains two support points is used. During the experiment, the relationship between the deflection and the load is to be observed by changing the load applied to the same beam. At the end of the experiment, it is expected that the deflection of the beam is linearly proportional to the applied load as Euler-Bernoulli Beam Theory suggests. The equation of Euler-Bernoulli Beam Theory is as follows:

In this equation, w represents the deflection of the beam, E represents the modulus of elasticity of the material, I represents the second moment of area of the beam and q represents the distributed load, which can also be described as force applied per unit length.

In addition, the effect of the beam thickness on the deflection is another effect to be investigated. Depending on the beam theory, it is anticipated that the deflection of the beam is inversely proportional to the third power of the beam thickness. By this experiment, the relation between the deflection and beam thickness can also be observed and proved. Lastly, the effect of material on the deflection of the beam is to be examined, as well. Euler-Bernoulli Beam Theory suggests that deflection of the beam is inversely proportional to the modulus of elasticity. Since different materials have different elastic modulus, through this experiment, it will be proven that the materials having higher elastic modulus deform less under the same load than the ones having lower modulus of elasticity.

Theory

In construction industry and literature a beam is usually referred to a structural member which is generally horizontal and used to support generally horizontal loads such as floors, roofs, and decks. Similarly, in mechanical engineering applications and in science literature, a beam is explained as a component that is designed to support transverse loads, that is, loads that act perpendicular to the longitudinal axis of the beam. In order to make the building and structure more stable and stronger against impacts and loads, beams are generally applied as a solution. Since there are numerous material types and numerous different shapes of materials, beams can also be...

References: 1- http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm

2- http://paws.wcu.edu/radams/intro_to_beam_theory.pdf

3- http://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory#Boundary_considerations

4- http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm

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