BEAM BENDING

Beam Bending



Abstract

If a beam is supported at two points, and a load is applied anywhere on the beam, the resulting deformation can be mathematically estimated. Due to improper experimental setup, the actual results experienced varied substantially when compared against the theoretical values. The following procedure explains how the theoretical and actual values were determined, as well as suggestions for improving upon the experiment. The percent error remained relatively small, around 10%, for locations close to supports. As much as 30% error was experienced when analyzing positions closer to the centre of the beam.

Table of Contents

Abstract2

Introduction & Background4

General Background4

Determination of Curvature4

Central Loading5

Overhanging Loads7

Equipment and Procedure7

Equipment7

Experiment Setup8

Central Loading8

Overhanging Loads8

Data, Analysis & Calculations9

Central Loading9

Overhanging Loads11

Results13

Conclusions14

References15

Raw Notes16

Testing of Materials - Beam Bending

Introduction & Background

Mechanics of Materials is generally the name applied to a discipline in which the stress, strain and deflections of loaded structural elements are considered. This set of notes presents the laboratory aspects of this subject. For nearly all design work it is necessary to know something of the elastic and, often, plastic properties of the material to be used. While these properties are often available from handbooks, sometimes particular properties of less common materials are needed, in which case the engineer must perform his own tests. The performance of these typical tests in this laboratory will give a better feeling for the significance of the various material properties and for the accuracy with which these quantities can be determined (Al-Sulaimani, 1994, 458-64).

The various sections of these notes are concerned with review of the subject of mechanics of materials and related material properties including the laboratory application of these principles to simple structures. In various exercises, the stresses, strains and deflections of a both simply-supported straight and curved beams are measured and compared to analytical predictions. In another exercise, selected mechanical properties and performance of representative engineering materials are measured using standardized test methods and quantitatively compared to handbook values. The effects of stress concentrations are the focus of another exercise in which photoelasticity is used to determine stress raisers for comparisons to values obtained from compendiums. Fracture mechanics and crack interactions are examined in a study of the load carrying reduction of cracks in components (Uomoto, 2002, 191-209).

Time-dependent behaviour is evaluated through measurement and analysis of creep deformation and cyclic fatigue failures. Structural instabilities such as column buckling are compared to material strength in assessing engineering failures. Complex structures are analyzed through experimental measurements and both simple and complex analytical methods to assess the implications of oversimplifications in engineering analysis.

Laboratory Procedure Mechanics of Materials Laboratory, ME 354, is intended to give an experimental understanding and verification of the coursework covered in Mechanics of Materials, CIVE 220 (formerly ENGR 220) and Introduction to Materials Science, MSE 170 (formerly ENGR 170).

No one should be enrolled in this course who has not taken or is not currently taking MSE 170 and CIVE 220 or their equivalents (Al-Sulaimani, 1994, 458-64).

Because of the nature of the laboratory experiments, it is necessary to conduct them as ...