# Beam Bending

Topics: Length, Young's modulus, Graph theory Pages: 11 (2666 words) Published: January 1, 2013
Abstract:

Finding the most adequate and efficient material to perform a certain function in engineering is such a fundamental concern that prompted scientists to investigate and examine the physical and mechanical properties of materials. This report discussed the property of elastic deformation of beams since it’s commonly used in several engineering fields. To begin with, a brief introduction on elasticity is presented, including some related definition and formulae. Then, a guide line to the experiment was explained and followed by the results obtained from the experiment. The results also included graphs to illustrate the general trend line of the recorded measurements. Next, the results are interpreted and measured up to existing data. Finally, a summary of what has been done and what was concluded is provided along with list of references.

Background:

The study of mechanical properties of materials is an absolute necessity in almost all aspects of engineering especially construction, structural and transportation. The urge to understand the way materials behave when an external force is applied to them has lead to the discovery of some important properties such as elasticity, stiffness, strength and ductility.

Elastic deformation:

The concept of elastic deformation refers to the ability of a material to return to its original shape after the force applied to it is removed. However, at a certain point the material will not be able to resist the force applied to it and the material will plastically deform (i.e. will break and not recover its original shape). This point is called the yield point and the stress applied at this point is called the yield stress. The rate of deformation differs from one material to another depending on several factors. The nature of a material is a major factor that determines how elastic it is regardless its geometry and shape. For example, if the same load was applied to two beams of different materials (aluminium and glass) that have the same shape, cross section and separated from the support by equal distance, the glass beam will reach its yield point and hence break first. Therefore, Young’s modulus was incorporated from Hooke’s law to refer to a measure of resistance of a material to elastic deformation when a stress is applied to it and in the previous example, the glass has a smaller young’s modulus, therefore it breaks first (Dobson, 2001). Other factors include the distance from the support, geometry of the beam and the load applied to it.

Stiffness:

The term stiffness describes the opposition of a beam to elastic deformation when it is loaded and it can be calculated using the formula [pic] (1.1)

Where S is the stiffness (N/m), Mg is the load applied to the beam and δ is the resultant deflection (Gere, 1997). The stiffness can also be computed using the formula

[pic](1.2)

Where [pic] is the Young modulus, [pic] is second moment of area and [pic] is the distance from the load to the support (PEME1000).

Experimental Method:

The experiment was carried out by a group of three students. It was divided into five tasks; each task is explained separately as follows:

First of all, the rig was installed so that the wooden block is fixed to the table using a ‘G’-clamp and the ruler was placed in front of the beam to measure the displacement of the beam. Then, the weight hanger and the weights were weighed and the diameters of all the beams were measured and recorded.

Task1: Firstly, the 0.0101 m solid beam was fitted in the wooden block and the ruler was placed at length of 0.8 m to measure the initial height. Then, the weight hanger was placed on the rod at the same length and the final height was recorded. The deflection of the beam was then calculated by subtracting the initial height from the final. The previous steps were repeated by every student in...

References: • DOBSON.K; D.GRACE; D.LOVETT. 2001. Physics. London: Collins Educational.
• DUNCAN.T. 2000. Advanced physics, 5th ed. London: John Murray publishers LTD.
• GERE.J; S.TIMOSHENKO. 1997. Mechanics of materials, 4th ed. London: PWS Publishing Company.
• HUDSON.C. 2009. PEME100 Lecture notes. Retrieved from Leeds University, School of Process, Environment and material Engineering.