Instability OF Strut Lab Report PDF

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TABLE OF CONTENTS 1 INTRODUCTION CONTENT PAGE 2 OBJECTIVE 3 PROBLEM STATEMENT 4 APPARATUS AND MATERIALS 5 PROCEDURE 6 DATA AND CALCULATION 6 – 7 DISCUSSION 8 CONCLUSION 9 REFERENCES 2 OBJECTIVETo determine the buckling load for the strut.3 PROBLEM STATEMENTColumn is a slender member. It tends to fai...

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TABLE OF CONTENTS

CONTENT

PAGE

1.0 INTRODUCTION

1

2.0 OBJECTIVE

2

3.0 PROBLEM STATEMENT

3

4.0 APPARATUS AND MATERIALS

4

5.0 PROCEDURE

5

6.0 DATA AND CALCULATION

6 – 13

7.0 DISCUSSION

14

8.0 CONCLUSION

15

9.0 REFERENCES

16

INSTABILITY OF STRUTS (BRASS)

1.0 INTRODUCTION If compressive load is applied on a column, the member may fail either by crushing or by buckling depending on its material, cross section, and length. If member is considerably long in comparison to its lateral dimensions, it will fail by buckling. If a member shows signs of buckling the member leads to failure with small increase in load. The load at which the member just buckles is called as crushing load. The buckling load, as given by Euler, can be found by using following expression. Where L α e=L. The following boundary condition: Pined-pined – 1.0 Pined-fixed – 0.7 Fixed-fixed – 0.5

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2.0 OBJECTIVE To determine the buckling load for the strut.

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3.0 PROBLEM STATEMENT Column is a slender member. It tends to fail due to bucking behaviour instead of material itself. Therefore, it is important to determine the buckling load of column so that can serve its primary function.

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4.0 APPARATUS / MATERIAL 1. Strut buckling apparatus 2. Ruler 3. Vernier calliper 4. Brass specimen

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5.0 PROCEDURES 1. A brass specimen and the length, width and thickness were measured at three places. 2. The theoretical buckling load for the strut with pinned end was calculated to ensure that the load applied to the strut does not exceed the buckling load. 3. The knife edge support was placed into the slot of the attachment for the end conditions. 4. Top platen was moved upwards or downwards to bring the distance between the two knife edges closer to the length of the strut. 5. Reading on the digital indicator was noted where the F1 was pressed if not zero until the word “tare” was displayed. 6. Brass was placed on the lower knife edges. 7. The jack was adjusted so that the upper knife edge rests in the groove at the other end of the sample. If the distance between the two knife edges is slightly less than the length of the strut, turn the screw jack handle counter clockwise. If the distance between the two knife edges is slightly greater than the length of the strut, turn the screw jack handle clockwise. 8. Note the reading on the digital indicator. If the compressive load is greater than 10 N turn the jack handle counter clockwise to bring the compressive load to less than 10 N. 9. Check the position of the dial gauge to ensure that it is at the mid-length of the specimen. Set the dial gauge reading to zero. 10. Press F1 until the word “tare” is displayed. 11. Load the specimen at suitable increments by turning the screw jack handle slowly in the clockwise direction. 12. Increase the load and for each load increment record the load and the corresponding mid-span deflection. (Important: please ensure that the applied load is always less than 80% of the buckling load.) 13. Unload the specimen by turning the jack handle in the counter clockwise direction. 14. Carry out the experiment for pinned-pinned, pinned-fixed and fixed-fixed boundary condition.

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6.0 DATA & CALCULATION Specimen Specification = Brass

Length of specimen, L = 0.6m Width of specimen, h = 0.025m Thickness of specimen, t = 0.0035m Modulus of Elasticity, E = 145 GPa Moment of inertia of specimen = bh³/12 = 8.932 x 10ˉ11m⁴

1.

Fixed – Fixed Support Load, P

Mid-Span Deflection, d

d/P (mm/N)

N

div

mm

25

2

0.02

8.0 x 10ˉ⁴

50

11

0.11

2.2 x 10ˉ⁴

75

28

0.28

3.7 x 10ˉ⁴

100

41

0.41

4.1 x 10ˉ⁴

125

59

0.59

4.7 x 10ˉ⁴

150

67

0.67

4.5 x 10ˉ⁴

175

75

0.75

4.3 x 10ˉ⁴

200

89

0.89

4.5 x 10ˉ⁴

225

121

1.21

5.4 x 10ˉ⁴

250

158

1.58

6.3 x 10ˉ⁴

Le = 0.5L = 0.5(0.6) = 0.3m Critical Load, PCR = 𝝅2EI / Le2 = 𝜋2(145 x109)(8.932 x10-11) / (0.3)2 = 1420.28 N

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Deflection(mm) VS Deflection/Load, d/P(mm/N) 1.8 1.6

Deflection (mm)

1.4 1.2 1 y = 723.2x + 0.306

0.8 0.6 0.4 0.2 0 0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

Deflection/Load , d/P (mm/N)

From the graph, the gradient is 723.2N

7

2.

Fixed – Pinned Support Load, P

Mid-Span Deflection, d

d/P (mm/N)

N

div

mm

30

0

0

0

40

0

0

0

50

0

0

0

60

4

0.04

5.0 x 10ˉ⁴

70

9

0.09

9.0 x 10ˉ⁴

80

10

0.10

8.3 x 10ˉ⁴

90

14

0.14

1.0 x 10ˉ³

100

21

0.21

1.3 x 10ˉ³

110

28

0.28

1.6 x 10ˉ³

120

55

0.55

2.8 x 10ˉ³

Le = 0.7L = 0.7(0.6) = 0.42 m

Critical Load, PCR = 𝝅2EI / Le2 = 𝜋2(145 x109)(8.932 x10-11) / (0.42)2 = 724.63 N

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Deflection(mm) VS Deflection/Load,d/P (mm/N) 0.6

0.5 y = 193.15x - 0.0315

Deflection (mm)

0.4

0.3

0.2

0.1

0 0 -0.1

0.0005

0.001

0.0015

0.002

0.0025

0.003

Deflection/Load , d/P (mm/N)

From the graph, the gradient is 193.15N

9

3.

Pinned – Pinned Support Load, P

Mid-Span Deflection, d

d/P (mm/N)

N

div

mm

25 50

0 2

0.00 0.02

0.00 5.6 x 10ˉ⁴

75

20

0.20

2.7 x 10ˉ³

100

60

0.60

6.0 x 10ˉ³

125

110

1.10

8.0 x 10ˉ³

150

150

1.50

1.0 x 10ˉ²

175

190

1.90

1.09 x 10ˉ²

200

220

2.20

1.1 x 10ˉ²

225

260

2.60

1.15 x 10ˉ²

250

300

3.00

1.2 x 10ˉ²

Le = 1.0L = 1.0(0.6) = 0.6 m

Critical Load, PCR = 𝝅2EI / Le2 = 𝜋2(145 x109)(8.932 x10-11) / (0.6)2 = 355.07 N

10

Deflection(mm) VS Deflection/Load,d/P (mm/N) 3.5 3

Deflection (mm)

2.5 y = 221.91x - 0.3004 2 1.5 1 0.5 0 0

0.002

-0.5

0.004

0.006

0.008

0.01

0.012

0.014

Deflection/Load , d/P (mm/N)

From the graph, the gradient is 221.91N

Condition

Fixed – Fixed

Fixed - Pinned

Pinned – Pinned

Experimental Critical Load, PCR EXP (N)

723.2

193.15

221.91

Theoretical Critical Load, PCR THEO (N)

1420.28

724.63

355.07

Different Experimental and Theoretical (%)

49.08%

73.35%

37.50%

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Sample calculation: i.Fixed – Fixed 𝑡ℎ𝑒𝑜𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 − 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 × 100 𝑡ℎ𝑒𝑜𝑟𝑖𝑡ℎ𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒

%𝑒𝑟𝑟𝑜𝑟 = =

1420.28−723.2 723.2

× 100

= 49.08%

ii.Fixed – Pinned

%𝑒𝑟𝑟𝑜𝑟 = =

𝑡ℎ𝑒𝑜𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 − 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 × 100 𝑡ℎ𝑒𝑜𝑟𝑖𝑡ℎ𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 724.63−193.15 724.63

× 100

= 73.35% iii.Pinned – Pinned

%𝑒𝑟𝑟𝑜𝑟 = =

𝑡ℎ𝑒𝑜𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 − 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 × 100 𝑡ℎ𝑒𝑜𝑟𝑖𝑡ℎ𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 355.07−221.91 355.07

× 100

= 37.50%

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7.0 DISCUSSION On this experiment, the sample use is brass sample. It will give the different value of Euler buckling load compare to aluminium and steel because type of materials on this experiment had different in Young’s Modulus. Young’s Modulus are important because it is related with strong of the materials. From the graph deflection against deflection load, the slope represents the buckling load or experimental value. Euler’s formula is used to determine the theoretical critical buckling load using formula:

Pcr =

𝜋²𝜖𝐼 𝐿𝑒²

Where : Pcr = Euler buckling load (N) E = Young’ Modulus (Nm²) I = Second moment of area (mm4) L = Length of struts (m) Length of struts depends on type of boundary condition, which is pinned-pinned use 1.0, pinned-fixed use 0.7 and fixed-fixed use 0.5. For these 3 types of boundaries condition, it will give the different value of Euler buckling and experimental buckling load. For fixed – fixed conditions, the theoretical value of Euler’s critical buckling load is 1420.28 N. From the graph, the actual critical buckling load is 723.2 N which is obtain from the slope of straight line. It can cause error due to different value and the error can be proved by percentage error. The percentage error for both fixed conditions is 49.08%, which is the greater value or error. From the result, the applied load is directly proportional to the deflection when the applied load is increase, the deflection also increase. For fixed – pinned conditions, the theoretical value of Euler’s critical buckling load is 724.63 N. From the graph, the actual critical buckling load is 193.15 N which is obtain from the slope of straight line. It can cause error due to different value and the error can be proved by percentage error. The percentage error for fixed – pinned conditions is 73.35%, which is the greater value or error. From the result, the applied load is directly proportional to the deflection when the applied load is increase, the deflection also increase. 13

For pinned – pinned conditions, the theoretical value of Euler’s critical buckling load is 355.07 N. From the graph, the actual critical buckling load is 221.91 N which is obtain from the slope of straight line. It can cause error due to different value and the error can be proved by percentage error. The percentage error for both pinned conditions is 37.50%, which is the greater value or error. From the result, the applied load is directly proportional to the deflection when the applied load is increase, the deflection also increase. Buckling due to compression can be observed by comparing to the sin curve elongations. The strut tends to buckle in the centre of the length. On this theoretical value of Euler’s critical buckling load, it is higher than the actual critical value. This is due to material imperfection and different support reactions that can create different displacement to the strut (buckling).

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8.0 CONCLUSION At the end of the experiment we manage to identify the buckling load of the struts therefore the objective of the laboratory work achieves. The modulus of elasticity or young’s modulus for various materials was discussed. The data obtained indicate that the longer struts were experiencing a lower buckling load than the shorter struts. Both had the same material properties so due to length of the strut the buckling values vary. It was seen that the brass column has larger capacity to withstand compressive loads for similar crosssectional area and end fixing. The struts were tested, and the results were compared with the Euler theoretical predictions

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9.0 REFERENCES •

Max Rodriguez (May,30). Buckling of Slender Struts/ Columns. Retrieved from

https://www.structuresinsider.com/post/buckling-of-slender-struts-columns-lab-reportexplained •

Madeh Izat Hamakareem, Strut test to determine Euler’s Buckling Load of Strut.

Retrieved from https://theconstructor.org/practical-guide/strut-test/2476/

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