보의 처짐 측정

소개글

광섬유 센서를 이용한 보의 처짐을 측정하고 이론값과 비교한 보고서 입니다.

목차

1. Objective
2. Theoretical background
3. Experimental set-ups and procedures
4.Result & analysis
5. Comparison between theoretical expectations and experimental results

본문내용

Comparing the theoretical value with experimental results
v(x)={█(-0.005333x^4+0.02547x^3-0.04413x (0≤x≤0.675)@-0.005333+0.01630x^3+0.01857x^2-0.05667 x+0.002821 (0.675≤x≤1.575)@-0.005333x^4+0.01171x^3+0.04045x^2-0.09147x+0.02126 (1.575≤x≤1.8) )┤
(Unit∶m)
First Theoretical Deflection of beam

v(x)=-0.007208x^4+0.025475x^3-0.04049x (Unit∶ m)
Second Theoretical Deflection of beam

v(x)=-0.005933x^4+0.022052x^3-0.036846x(Unit : m)
Experimental Deflection of beam

Numerical comparison

Table.4 Comparison of experimental and theoretical values
Node Experimental(cm) First Theoretical(cm) Second Theoretical(cm) error rate1(%) error rate2(%)
0 0 0 0 - -
1 -0.8054 -0.9650 -0.8839 -16.53 -8.87
2 -1.4815 -1.7732 -1.6195 -16.45 -8.52
3 -1.9321 -2.2979 -2.0992 -15.92 -7.96
4 -2.0978 -2.4757 -2.2599 -15.26 -7.17
5 -1.9557 -2.2764 -2.0825 -14.09 -6.09
6 -1.5192 -1.7449 -1.5925 -12.93 -4.60
7 -0.8384 -0.9502 -0.8596 -11.76 -2.46
8 0 0 0 - -
Where error rate 1 : the error rate with first theoretical result
error rate 2 : the error rate with second theoretical result

Considering the fact that in the last experiment (Measuring strains in beams using OFS) error rate was in between 10 and 30%, the results of this experimentation came out in acceptable range of error. The values on Node 1 and 2 seem to be calculation wrong-deeds.

Graphical comparison


Fig.8 Comparison of experimental and theoretical values in graph

Rather than assuming that the loads are applied on points, distribution of the loads leads to more accurate results. It is found from both Table.4 and Fig.8, that the difference in values is much lesser. Assumptions must be made in certain range of correctness.

참고 자료

Gere, James M. MECHANICS of MATERIALS. 6th ed. Thompson. Chap.9