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Beam Deflection

In: Computers and Technology

Submitted By taufik87
Words 617
Pages 3
1.0 INTRODUCTION

1.1 Beam Deflections

1.2 Theory - Calculations

DeflectionF formula for the load given above:

A determination of flexural stress yields:

When rectangular it is

Where;

δ = Deflection (mm) E = Coefficient of Elasticity
L = Span (mm) I = Inertia Factor
Mb = Moment of flexure (Nmm) F1 = Load occasioned by weight
Wb = Resistance to flexure (mm3) of Load Device (N) σb = Flexural Stress (N/mm2) F = Load of occasioned by additional weight (N)

1.3 Objectives

* To investigate the relationship between load, span, width, height and deflection of a beam placed on two bearers and affected by a concentrated load at the center.

* To ascertain the coefficient of elasticity for steel brass and aluminium

2.0 METHODOLOGY

2.1 Procedure - Experiement 1A

* Investigate the relationship between load and deflection.

1) Set the bearers so that a span of 600 mm is obtained. The interval between each groove on the shafts of the apparatus is 100 mm. 2) Place a test specimen with dimensions of 4 x 25 mm, on the bearers and mount the load device in the center of the test specimen. 3) Set the testing device so that the top of the gauge is centered on the upper plane of the load device. Lower the gauge so that its small hand is at about 10 and set the gauge to zero by twisting its outer ring. 4) Load the weights as shown in the table below and read off the deflection. 1 revolution of the large hand of the gauge corresponds to 1 mm deflection. 5) Plot loading, N versus deflection.

2.2 Procedure - Experiment 1B

* Investigate relationship between span and deflection

1) Employ a test specimen with dimensions of 4x25 mm and load with weight 12.5 N. Vary the span as indicated in the table and read off the deflection. 2) Plot span, mm versus deflection, mm.

2.3 Procedure - Experiment 1C

* Investigate the relationship between width and the deflection of the test specimen.

1) Set the bearers for a span of 500 mm, Employ the test specimens indicated in the table below, load with weight 5 N and read off the deflection. 2) Plot width, mm, versus deflection, mm.

2.4 Procedure - Experiment 1D

* Investigate the relationship between the height and deflection of test specimen.

1) Set the bearers for span of 500 mm. Employ the test specimens indicated in the table below, load with weight 5 N and read off the deflection. 2) Plot height, mm, versus deflection, mm.

3.0 RESULTS AND DISCUSSION

Table 1: Investigate the relationship between load and deflection.

Table 2: Investigate relationship between span and deflection

Table 3: Investigate the relationship between width and the deflection of the test specimen.

Table 4: Investigate the relationship between the height and deflection of test specimen.

4.0 QUESTIONS

1. Plot graph deflection as a function of load, span, width and height of a beam. 2. What do you understand with the concept of tensile strength and why it is important to know it? 3. What is happening to the bonded metal atoms during elastic deformation? 4. What is happening to the bonded metal atoms during plastic deformation? 5. Why would engineer be interested in the yield strength of a metal for a particular application?

5.0 CONCLUSION

6.0 REFERENCE

* Ballarini, Roberto (April 18, 2003). "The Da Vinci-Euler-Bernoulli Beam Theory?". Mechanical Engineering Magazine Online. * http://www.memagazine.org/contents/current/webonly/webex418.html. Retrieved 2006-07-22. * Seon M. Han, Haym Benaroya and Timothy Wei (March 22, 1999) (PDF). Dynamics of Transversely Vibrating Beams using four Engineering Theories. final version. Academic Press. * http://csxe.rutgers.edu/research/vibration/51.pdf. Retrieved 2007-04-15.

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