R. sturt buckling - report PDF

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OBJECTIVESa) To examined the critical buckling load for aluminium strut with pinned and fixed for eachboth ends.b) To compared the theoretical and experimental results of critical buckling loads and stressINTRODUCTION & THEORYIn the case of very long columns, the failure happens mainly due t...

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OBJECTIVES a) To examined the critical buckling load for aluminium strut with pinned and fixed for each both ends. b) To compared the theoretical and experimental results of critical buckling loads and stress

INTRODUCTION & THEORY In the case of very long columns, the failure happens mainly due to bending. The Euler’s relations give the crippling load for long columns for various end condition:

Where: E : Modulus of Elasticity of the material (2.1 x 105N/mm2) I : Moment of Inertia of the cross Section of the strut (mm4) L : Effective length of the strut which is equal to total length of the strut (L) when both ends are pinned, 0.5L when the ends are fixed. For this experiment we tested the aluminium strut with condition of both ends pinned and both ends fixed only.

Figure 1 both ends pinned

Figure 2 both ends fixed

PROCEDURES

Figure 3 Euler Buckling Apparatus

1. The aluminium strut diameter was measured with vernier caliper and calculated its second moment of inertia. 2. Then the strut was fitted into the rig with pinned both ends condition. 3. The deflection gauge was set at the midspan of the strut and the reading scale was reset to zero. 4. Some load applied to observed the natural deflection direction. 5. The experiment began by applying loads slowly for pinned both ends. 6. The readings of deflection were heavily recorded for every loads applied. 7. Step 1 until step 6 were repeated for aluminium strut with fixed both ends. 8. Graph of load(N) against deflection(mm) for each condition was plotted. 9. Graph of southwell plot which deflection(mm) against deflection/load for each condition was plotted.

APPARATUS AND MATERIAL Euler Buckling Apparatus, Aluminium strut, and vernier caliper.

DATA AND RESULTS Strut dimension : (20 × 5 × 750) mm Calculation for theoretical critical buckling load : I = (bd 3)/12 —— Equation 2 I = 2.08333⁻¹⁰ m⁴ Where b=2 cm, d=0.5 cm

Pcr = (π 2 EI )/(K L)2 —— Equation 1 Pcr = 189.1671 Pa (both pinned ends) Pcr = 378.3342 Pa (both fixed ends) Where E=69 GPa, K=1(both pinned ends), K=0.5(both fixed ends), L=75 cm Table 1 Deflection in strut with fixed both ends LOAD, (N)

DEFLECTION

READING DIVISION

(mm)

DEFLECTION/ LOAD, (mm/N)

70

0.01

30

0.30(-)

0.004286(-)

140

0.01

31

0.31(-)

0.002214(-)

210

0.01

26

0.26(-)

0.001238(-)

280

0.01

24

0.24(-)

0.0008571(-)

350

0.01

14

0.14(-)

0.0004000(-)

420

0.01

1

0.01

0.00002381

450

0.01

7

0.07

0.0001555

490

0.01

21

0.21

0.0004286

520

0.01

37

0.37

0.0007115

560

0.01

61

0.61

0.001089

580

0.01

76

0.76

0.001310

630

0.01

132

1.32

0.002095

670

0.01

230

2.30

0.003432

700

0.01

485

4.85

0.006929

Table 1 Deflection in strut with pinned both ends LOAD, (N)

DEFLECTION

READING DIVISION

(mm)

DEFLECTION/ LOAD, (mm/N)

10

0.01

0

0.00

0.000000

20

0.01

0

0.00

0.000000

30

0.01

10

0.10

0.003333

40

0.01

16

0.16

0.004000

50

0.01

31

0.31

0.006200

60

0.01

52

0.52

0.008667

70

0.01

70

0.70

0.010000

80

0.01

90

0.90

0.01125

90

0.01

116

1.16

0.01289

100

0.01

150

1.50

0.01560

110

0.01

190

1.90

0.01727

120

0.01

241

2.41

0.02008

130

0.01

305

3.05

0.02346

140

0.01

435

4.35

0.03107

150

0.01

641

6.41

0.04273

ANALYSIS AND DISCUSSIONS Fixed both ends

Pinned both ends

Load (N) against Deflection (mm) 900

Load (N)

675

450

225

0 -1.75

0

1.75

3.5

5.25

7

Deflection (mm) Figure 4 Graph of Load Against Deflection

Based on Figure 4, the graph of load against deflection shows that as the the load increasing, the deflection was also increasing. But the amount of load applied to has the same value of deflection depends on the condition as we can see the strut with fixed ends has higher load applied than strut with pinned ends. Fixed both ends

Critical Load

Pinned both ends

Critical Load

Deflection (mm) Against Deflection/Load (mm/N) 7

Deflection, (mm)

5.25

y = 488.08x + 0.4025 y = 152.81x - 0.5329

3.5 1.75 0 -1.75 -3.5 -0.013

0

0.013

0.025

0.038

Deflection/Load, (mm/N) Figure 5 Southwell plot of Deflection Against Deflection/Load

0.05

Table 3 Critical Loads From Experimental Result Critical load for Fixed ends (N)

488.08

Critical load for Pinned ends (N)

152.81

For the second graph in figure 5, deflection against deflection/load graph is used to examine the experimental critical loads value which 488.08 N for strut with fixed ends and 152.81 for strut with pinned ends. The calculated theoretical critical loads for strut with fixed ends is 378.3342 N and strut with pinned ends is 189.1671 N. Both critical loads from theoretical and experimental for each conditions are different where the experimental critical load for strut with pinned ends has higher value than theoretical while for strut with fixed ends is lower than theoretical value. CONCLUSION In conclusion, the comparison of critical loads between theoretical and experimental for both conditions have been calculated and observed carefully. Besides that, the relationship of critical load and deflection for both conditions also has been examined by observing the graph. REFERENCES McGinty, B. (n.d.). Retrieved February 22, 2020, from https://www.continuummechanics.org/ columnbuckling.html Buckling Experiments Laboratory Report. (n.d.). Retrieved February 22, 2020, from https:// www.ukessays.com/essays/engineering/buckling-experiments-laboratory-report-8868.php Labsheet...