Assignment 9 – Beam Deflection Experiment Report

1)
L(mm) L3
680 314432000
700 343000000
800 512000000
900 729000000
1000 1E+09
1100 1.331E+09
1200 1.728E+09

This graph shows a strong linear relationship the deflection and L3. The black line on the graph shows a trend line found from the regression of the data, it lines up very well with the experimental data showing it is fairly accurate. The graph shows y to be proportional to L3 (y ∝ L3), hence y=K L3 where K is a constant found to be 1.08 x10-9.
2)
D 1/d3 y (mm)
6 0.00463 1.59
7.92 0.002013 0.7
10 0.001 0.35

This graph shows an extremely strong linear relationship, however this may be due to a lack of data as the required materials for a more concise test were not available. The graph shows deflection to be inversely proportional to d3 (y ∝ 1/d3). Hence y=K/d3 where K is 341.33 as found from the gradient of the graph.
3)
y(mm) L b d l^3 d^3 W WL3/4bd3
Beam 1
1.72 680 25 6 314432000 216 27.468 399852.6933
1.88 700 25 6 343000000 216 27.468 436181.6667
2.83 800 25 6 512000000 216 27.468 651093.3333
3.98 900 25 6 729000000 216 27.468 927045
5.44 1000 25 6 1E+09 216 27.468 1271666.667
7.2 1100 25 6 1.331E+09 216 27.468 1692588.333
9.17 1200 25 6 1.728E+09 216 27.468 2197440
Beam 2
1.76 900 25.32 7.92 729000000 496.7931 27.468 397974.5768
Beam 3
0.87 900 25 10 729000000 1000 27.468 200241.72

This graph shows the relationship between Y, the deflection of the steel bar, against WL3/4bd3 . The resulting line shows there is a linear relationship, with Y being proportional to the two properties explored in the previous 2 graphs. In this case gradient (constant of proportionality) is found to be 4.293 x 10-6, which when multiplied by 103 to adjust the units gives the young’s modulus of the material which was found to be 4.293 x 10-9 Nm-2. ¬
This value does not seem to correlate with the known values for the young’s modulus for steel, This may be due to the