Asymmetrical Bending Report Updated

Topics: Experiment, Second moment of area, Circle Pages: 17 (1440 words) Published: April 15, 2015
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Asymmetrical Bending Laboratory Report

Date of Laboratory:

Name of Student:

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Summary

Asymmetrical bending is bending couples acting in a plane of symmetric. If loads do not act in plane of symmetry, this leads to deflection in a plane perpendicular to the loading plane as well as in the loading plane. This coupling does not occur if the loading is in principal plane. The experiment was conducted to investigate the deflections of the tip of a cantilever when loaded transversely in directions not coinciding with the principal axes of the cross section, and also to determine:

1. The directions and orientations of the principal axes of an equal section. 2. The sideways of deflections when the deflection is occurred along the line of loading, having maximum and minimum values of load. 3. The values of the principal second moments of area of the section by experiment and by theoretical calculations. First of all, values of deflections (δv, δh) were calculated for various head angles and loads as shown in Table 1-8. These deflection values were plotted against Load and gradients of the graphs of δv/W and δh/W were found out for various angles as shown in Figure 1-8 and stored in table 9. A graph was plotted between δv/W and δh/W which results in a circle. From the circle, values of offset and radius were used to calculate Principal second moments of area and orientation of principal axes. From the experiment results, the values of principal second moment of area obtained from experiment are respectively. Based on theoretical calculations, the values of principal second moment of area for are respectively. The direction of the principal axis of an equal angle section is -30.58⁰.

Results
Experimental

Step (a)

Results obtained from experiment are given below in Tables in which Loads and Head angles are varied.

Angle (⁰)
Load (g)
left dial
right dial
δv (mm)
δh (mm)
0⁰
0
0
0
0.000
0.000

100
0.5
0.44
0.665
0.042

200
2.48
0.94
2.418
1.089

300
3.88
1.39
3.726
1.761

400
5.8
2.03
5.537
2.666

500
6.47
2.53
6.364
2.786
Table 1: Deflection value at 0⁰
Angle (⁰)
Load (g)
left dial
right dial
δv (mm)
δh (mm)
22.5⁰
0
0
0
0.000
0.000

100
0.99
0.58
1.110
0.290

200
2.83
1.64
3.161
0.841

300
4.04
2.55
4.660
1.054

400
6.1
3.7
6.930
1.697

500
7.74
4.89
8.931
2.015
Table 2 Deflection value at 22.5⁰
Angle (⁰)
Load (g)
left dial
right dial
δv (mm)
δh (mm)
45⁰
0
0
0
0.000
0.000

100
1.08
1.08
1.527
0.000

200
2.5
2.49
3.528
0.007

300
4.02
3.99
5.664
0.021

400
5.48
5.48
7.750
0.000

500
7.08
7.06
9.998
0.014
Table 3 Deflection value at 45⁰

Angle (⁰)
Load (g)
left dial
right dial
δv (mm)
δh (mm)
67.5⁰
0
0
0
0.000
0.000

100
0.83
1.4
1.577
-0.403

200
1.87
3.23
3.606
-0.962

300
2.87
4.93
5.515
-1.457

400
3.85
6.64
7.418
-1.973

500
5.04
8.25
9.397
-2.270
Table 4 Deflection value at 67.5⁰

Angle (⁰)
Load (g)
left dial
right dial
δv (mm)
δh (mm)
90⁰
0
0
0
0.000
0.000

100
0.37
1.03
0.990
-0.467

200
0.91
2.74
2.581
-1.294

300
1.39
4.08
3.868
-1.902

400
1.85
5.82
5.424
-2.807

500
2.36
7.27
6.809
-3.472
Table 5 Deflection value at 90⁰

Angle (⁰)
Load (g)
left dial
right dial
δv (mm)
δh (mm)
112.5⁰
0
0
0
0.000
0.000

100
0.22
0.77
0.700
-0.389

200
0.49
1.71
1.556
-0.863

300
0.75
2.65
2.404
-1.344

400
1.02
3.71
3.345
-1.902

500
1.31
4.75
4.285
-2.432
Table 6 Deflection value at 112.5⁰

Angle (⁰)
Load (g)
left dial
right dial
δv (mm)
δh (mm)
135⁰
0
0
0
0.000
0.000

100
0.24
0.56
0.566
-0.226

200
0.7
1.01
1.209
-0.219

300
1.17
1.48
1.874
-0.219

400
1.65
1.9
2.510
-0.177

500
2.13
2.37
3.182
-0.170
Table 7 Deflection value at 135⁰
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