# Mesaurement about deformation of beam

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MEASUREMENTS ABOUT DEFORMATION OF A BEAM

STUDY PROGRAMME:
• Mechanical engineering

Institute:
• Vitus Bering Center Danmark
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MEASUREMENTS ABOUT DEFORMATION OF A BEAM

1. Introduction 1
1. Strain gauges 6
2. Elastic modulus
3. Linear materials
4. Types of gauges
5. Materials commonly used in this construction2. Manual work 8
1. Calculations
28
3. Work with the programme
1. Calculations of the uncertainty

4. Comparation

5. Conclusions 29

1. INTRODUCTION

The beams are structural elements widely used in construction to support loads or to give them stability, to design them is necessary to know perpendicular forces to the axes x, which are exerted along its length.

Inengineering, beam is called a linear construction element works mainly in bending.

1 STRAIN GAUGE

The use of strain gauges is used as instrumental method for:
• Strain measurement

• Measurement of effort

• Measurement of force and weight

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Robert Hook in 1678 established the relationship between stresses and strains in bodies subjected to mechanical stress.If the material is isotropic and homogeneous and does not exceed its elastic limit, then the relationship is linear. Based on this, the extensometer is the method that aims to measure surface deformations of the bodies. The concept of the deformation is the elongation analog unit and is expressed as a dimensionless ratio.
[pic]Usually used as a unit of micro deformation.
The stress or tension[pic] that supports a structure is defined as a ratio between force and area.
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2 ELASTIC MODULUS

The elastic modulus o Young’s modulus is a parameter that characterizes the behavior of an elastic material, according to the direction in which force is applied. For a linear and isotropic elastic material,Young's modulus has the same value for traction than for a compression, being a constant independent of the effort but may not exceed a maximum value called the elastic limit, and is always greater than zero: if a bar is pulled, the length increases, not decreases. This behavior was observed and studied with the English scientist Thomas Young.
Both the Young's modulus and yield strength aredifferent for different materials. The elastic modulus is an elastic constant that, like the elastic limit, can be found empirically based on the material tensile test.
For the specific case of steel Young's modulus is 2 * 10N/mm, the elastic limit (above which the deformation is not proportional and sequelae) is about 3 * 102 N / mm, and rupture reaches 5 +102 N / mm. Below the elastic limitof the ratio, Hook.

1. LINEAR MATERIALS
As described for a linear elastic material the longitudinal elastic modulus is a constant (for values of tension within the range of complete reversibility of deformation). In this case its value is defined by the ratio of the stress and deformation

that appears stretched in a straight bar made of this material for which we intend to estimatethe elastic modulus.
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Where:
E(is the longitudinal elastic modulus.
[pic](is the tension on the bar used to determine the elastic modulus.
[pic](is the strain at any point of the beam.
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Stress-strain diagram: the elastic modulus is the tangent at each point. For materials such as steel is approximately constant within the elastic limit.
Butdeformation don´t occurs only in the direction of the applied force, because the increase in length is accompanied by a decrease in section (Poisson effect).
The ratio defined by the strain in the transverse direction (diameter D) and the strain in the axial direction (length L) is called Poisson's ratio (ν) and must be determined experimentally for each material.

Basically a gauge is an...