Reaction Beam lab

8/10/2019 Reaction Beam lab

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AEROSPACE LABORATORY II

EAS 3922

Materials

Semester 1 (2013 / 2014)

EXPERIMENT 1

REACTION OF BEAM TEST

Date of Experiment: 20 th September 2013

Name:

Muhammad Azhar Bin Mat Marzuki (164369)

Group Members:

Sivasanghari Karunakaran (165330)

Sarah Munirah Binti Sirajul Huda (162188)

Muhammad Azhar Bin Mat Marzuki (164369)

Lecturers Name : DR. MOHAMAD RIDZWAN ISHAK

Demonstrators Name : MS . NOOR HAZIRA BINTI MOHAMED HAIDZIR

Technicians Name : MR. MAZRUL HISHAM & MR. MOHD WILDAN


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Objective:

The objectives of this experiment are

1. To identify the supports reaction in simply-supported and overhanging beams.

2. To develop an understanding of beam apparatus, and to determine its sensitivity andaccuracy.

Introduction:

Newtons third law of motion stated that For every action force there is an equal andopposite reaction force. Anytime an object applies a force to another object, there is an equaland opposite force back on the original object. This can be seen by pushing a wall by yourhand, if you push on a wall you feel a force against your hand, the wall is pushing back onyou with as much force as you apply to it. Structures also have this kind of characteristic,therefore it is essential for engineers to study the reaction forces on the structures and theeffect of external forces on the structures. In this experiment we had conduct two experimentson three beams (steel, aluminium, and brass) to study their force reaction when being appliedwith certain loaded.

Theory:

Theory Of Beams

If a beam is loaded as at W W W, Fig. 13, the weights produce reactions at the supports.These forces, or reactions, R1, and R2, oppose the action of the weights and their combinedaction must equal the total weight. The weights and reactions, constituting the external forces,tend to produce bending in the beam, and are resisted by the internal forces, consisting of thestrength of the fibers composing the beam. In a simple beam, the effect of loading is toshorten the upper fibers, and to lengthen the lower ones. Somewhere between the top and

bottom of the cross-section are located fibers which are neither shortened nor lengthened; this position is called the neutral axis (see page 75). In steel and like material of homogeneousnature, the neutral axis passes through the center of gravity of the section.


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Reactions:

The reactions or supporting forces of any beam or structure must equal the loads upon it. Ifthe load upon a simple beam is uniformly distributed, applied at the center of the span, orsymmetrically placed and of equal amount upon each side of the center, the reactions R1 andR2 will each be equal to one-half the load. When the loads are not symmetrically placed, thereactions are found by the principle of moments in the following manner:

Fig. 14 represents a simple beam supporting loads W1 W2 , and W3; I is the span or distance between the reactions R1 and R2; a, b, and c are the distances from the reaction R1 to theloads W1, W2 W3.. ively. Then the right-hand reaction, R2 =

(W1x a)+( W2 x b)+(W3.x c) / l

This formula expressed in a general rule is: To find the reaction at either support, multiplyeach load by its distance from the other support, and divide the sum of these products by thedistance between supports.

Since the sum of the reactions must equal the sum of the loads, if one reaction is found, theother can he obtained by subtracting the known one from the sum of the loads.


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Apparatus and Material:

1. Beam apparatus- SM104

2. Vernier calliper3. Load cells4. Dial gauges5. Weight hangers6. Weights: 5 N, 10 N7. Steel blocks8. Beams: Steel / Brass / Aluminium

Procedures

Supports Reaction of The Simply-Supported Beam with Concentrated Loads

1. The thickness and width of the beam were measured.2. The length of the beam was measured and at mid-span and -span points were

marked.

3. Load cells -span was set up to the left and mid span reading was at right, and theknife edge was locked.

4. The beam was placed in position with -span overhang either end.5. Two weight hangers were positioned equidistant from the midpoint of the beam.6. Dial gauge was placed in position on the upper cross-member so that the ball end rests

on the centre-line of the beam immediately above the left-hand support.7. The stem was checked in vertical and bottom O-ring had been moved down the stem.8. The dial gauge was adjusted to zero read and the bezel was locked in position.9. The dial gauge was moved to a position above the right-hand support, the beam was

checked so that it parallels to the cross member, the height of the knife edge wasadjusted so that the dial gauge reads zero.

10. The dial gauge was removed and both knife edges were unlocked. The load cellindicators were adjusted to zero.

11. Loads were applied to the weight hangers in a systematic manner, the beam was tapgently and the readings of the load cells were taken.

12. The results were processed and the graphs were plotted from the experimental results.


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Supports Reaction of the Overhanging Beam with Concentrated and Distributed Loads

1. The thickness and width of the beam were measured2. The load cells -span was set up to the left while 1/8-span to the right of the mid-span

reading and the knife edge was locked.3. A dial gauge was placed in position on the upper cross-member so that the ball end

rests on the centre-line of the beam immediately above the left-hand support.4. The stem was checked in vertical and the bottom O-ring had been moved down to the

stem.5. The dial gauge was adjusted to zero and the bezel was locked in position.6. The dial gauge was moved to a position above the right-hand support, the beam was

checked so that it parallels to the cross member, the height of the knife edge wasadjusted so that the dial gauge reads zero.

7. The dial gauge was removed and both knife edges were unlocked. The load cellindicators were adjusted to zero.

8. A weight hanger 1/8-span was position to the left from the end point of the beam.9. The loads were applied to the weight hanger and steel block in a systematic manner,

and the readings of the load cells were taken.10. The results were processed and the graphs were plotted from the experimental results.


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Supports Reaction of the Simply-Supported Beam with Concentrated Loads

A. RESULT

Beam Beamlength, L(mm)

Beam width, b (mm) Beam thickness, h (mm)1 2 3 Avg. 1 2 3 Avg.

Steel 1351 19.10 19.08 19.10 19.06 6.36 6.38 6.36 6.37Brass 1350 19.16 19.14 19.14 19.15 6.38 6.46 6.48 6.44

Aluminum 1350 19.24 19.26 19.24 19.25 6.54 6.54 6.58 6.55Table1: Measurement of the beam

Steel beam

W 1 (N) W 2 (N) R 1 (N) R 2 (N) R 1 + R 2 (N) (N) %5 0 2.8 0.5 3.3 -1.7 -34.010 0 6.9 1.4 8.3 -1.7 -17.015 0 10.7 2.6 13.3 -1.7 -11.320 0 14.2 3.8 18 -2 -10.025 0 17.2 5.1 22.3 -2.7 -10.830 0 21.8 6.0 27.8 -2.2 -7.30 5 1.0 3.7 4.7 -0.3 -6.00 10 1.6 7.0 8.6 -1.4 -14.00 15 2.4 9.9 12.2 -2.8 -18.70 20 3.8 13.8 17.6 -2.4 -12.00 25 4.7 17.1 21.8 -3.2 -12.80 30 5.9 21.1 27.0 -3 -10.05 5 4.0 4.2 8.2 -1.8 -18.0

10 10 8.7 8.6 17.3 -2.7 -13.515 15 13.4 13.6 27 -3 -10.020 20 18.8 18.7 37.5 -2.5 -6.325 25 23.0 22.8 45.8 -4.2 -8.430 30 29.4 28.9 58.3 -1.7 -2.8

* ( ) ( ) ( )

Table2: Experimental results of simply-supported steel beam with concentrated loads

Brass beamW 1 (N) W 2 (N) R 1 (N) R 2 (N) R 1 + R 2 (N) (N) %

5 0 3.6 1 4.6 -0.4 -8.010 0 7.2 2.4 9.6 -0.4 -4.015 0 10.8 3.4 14.2 -0.8 -5.320 0 13.8 4.6 18.4 -1.6 -8.0

25 0 18.4 5.5 23.9 -1.1 -4.430 0 21.4 6.4 27.8 -2.2 -7.3


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0 5 0.7 2.2 2.9 -2.1 -42.00 10 1.7 5.8 7.5 -2.5 -25.00 15 2.8 9.5 12.3 -2.7 -18.00 20 4 12.1 16.1 -3.9 -19.50 25 5.2 16.6 21.8 -3.2 -12.80 30 6.8 20.5 27.3 -2.7 -9.05 5 4.8 3.6 8.4 -1.6 -16.0

10 10 8.6 7.9 16.5 -3.5 -17.515 15 13.6 13 26.6 -3.4 -11.320 20 19.6 19.9 39.5 -0.5 -1.325 25 24.8 24.1 48.9 -1.1 -2.230 30 28.3 29.3 57.6 -2.4 -4.0

Table3: Experimental results of simply-supported brass beam with concentrated loads

Aluminum BeamW 1 (N) W 2 (N) R 1 (N) R 2 (N) R 1 + R 2 (N) (N) %

5 0 3.1 1 4.1 -0.9 -18.010 0 6.7 1.4 8.1 -1.9 -19.015 0 10.6 2.3 12.9 -2.1 -14.020 0 14.5 3.5 18.0 -2.0 -10.025 0 18.2 4.6 22.8 -2.2 -8.830 0 21.9 6.1 28.0 -2.0 -6.70 5 0.9 2.8 3.7 -1.3 -26.0

0 10 1.6 6.1 7.7 -2.3 -23.00 15 2.8 9.5 12.3 -2.7 -18.00 20 4.6 13.4 18.0 -2.0 -10.00 25 5 17.8 22.8 -2.2 -8.80 30 6.5 20.4 26.9 -3.1 -10.35 5 4 3.8 7.8 -2.2 -22.0

10 10 9.4 8.8 18.2 -1.8 -9.015 15 13.9 13.4 27.3 -2.7 -9.020 20 18.8 17.9 36.7 -3.3 -8.325 25 23.9 21.6 45.5 -4.5 -9.0

30 30 28.4 27.4 55.8 -4.2 -7.0

Table4: Experimental results of simply-supported aluminum beam with concentrated loads


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Graph for Supports Reaction of the Simply-Supported Beam with Concentrated Loads:

y = 0.7394x - 0.6733R = 0.9974

y = 0.2274x - 0.7467R = 0.9972

0

5

10

15

20

25

0 5 10 15 20 25 30 35

R e a c t i o n F o r c e s

[ N ]

W1[N]

Graph of Reaction Forces [N] against W 1[N], whenW2=0 for Steel

R1 (N)

R2 (N)

Linear (R1 (N))

Linear (R2 (N))

y = 0.7177x - 0.0267R = 0.9976

y = 0.2143x + 0.1333R = 0.9941

0

5

10

15

20

25

0 5 10 15 20 25 30 35

R

e a c t i o n F o r c e

[ N ]

W1 [N]

Graph of Reaction Forces [N] against W 1[N], whenW2=0 for Brass

R1 (N)

R2 (N)

Linear (R1 (N))

Linear (R2 (N))

y = 0.7566x - 0.74R = 0.9999

y = 0.2074x - 0.48R = 0.9736

0

5

10

15

20

25

0 5 10 15 20 25 30 35

R e a c t i o n F o r c e

[ N ]

W1 [N]

Graph of Reaction Forces [N] against W 1[N], whenW2=0 for Aluminium

R1 (N)

R2 (N)

Linear (R1 (N))

Linear (R2 (N))


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Graph 1, 2, 3: Reaction forces [N] against W1 [N], when W2=0 for steel, brass, andaluminium.

y = 0.2011x - 0.2867R = 0.987

y = 0.6926x - 0.02R = 0.9979

0

5

10

15

20

25

0 5 10 15 20 25 30 35


[ N ]

W2 [N]

Graph of Reaction Forces [N] against W 2[N], when

W1=0 for Steel

R1 (N)

R2 (N)

Linear (R1 (N))

Linear (R2 (N))

y = 0.2411x - 0.6867R = 0.994

y = 0.7229x - 1.5333R = 0.9962

0

5

10

15

20

25

0 5 10 15 20 25 30 35

R e a c t i o n

f o r c e

[ N ]

W2 [N]

Graph of Reaction Forces [N] against W 2[N], whenW1=0 for Brass

R1 (N)

R2 (N)

Linear (R1 (N))

Linear (R2 (N))


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Graph 4, 5, 6: Reaction forces [N] against W2 [N], when W1=0 for aluminium, steel and brass

y = 0.2286x - 0.4333R = 0.9813

y = 0.7257x - 1.0333R = 0.9966

0

5

10

15

20

25

0 5 10 15 20 25 30 35


[ N

]

W2 [N]

Graph of Reaction Forces [N] against W 2[N], whenW1=0 for Aluminium

R1 (N)

R2 (N)

Linear (R1 (N))

Linear (R2 (N))

y = 0.9783x - 0.9867R = 0.9979

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35


[ N ]

W1=W2 [N]

Graph of Reaction Forces [N] against W 1 = W 2 [N] forSteel

R1 (N)R2 (N)

Linear (R2 (N))


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Graph 7, 8, 9: Reaction forces [N] against W1=W2 [N] for Steel, Brass, and Aluminium.

y = 0.9834x - 0.5933R = 0.9947

y = 1.0514x - 2.1R = 0.9961

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35


[ N ]

W1=W2 [N]

Graph of Reaction Forces [N] against W 1 = W 2 [N] forBrass

R1 (N)

R2 (N)

Linear (R1 (N))

Linear (R2 (N))

y = 0.9737x - 0.64R = 0.9995

y = 0.9194x - 0.6067R = 0.9975

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35


[ N ]

W1=W2 [N]

Graph of Reaction Forces [N] against W 1 = W 2 [N] forAluminium

R1 (N)

R2 (N)

Linear (R1 (N))

Linear (R2 (N))


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Supports Reaction of the Overhanging Beam with Concentrated and Distributed Loads

B. RESULTAluminium

wl [N] W[N] R 1 [N] R 2 [N] R 1+R 2 [N] [N] %0 5 3.9 1.6 5.5 -0.5 -10.00 10 5.8 3.3 9.1 -0.9 -9.00 15 9.7 4.9 14.6 -0.4 -2.70 20 12.2 6.6 18.8 -1.2 -6.0

20 5 10.7 14.6 25.3 0.3 1.220 10 7.8 22.6 30.4 0.4 1.320 15 4.6 30.6 35.2 0.2 0.620 20 1.3 38.6 39.9 -0.1 -0.3

5 5 1.2 9.6 10.8 0.8 8.010 10 0.5 19.3 19.8 -0.2 -1.015 15 0.8 28.8 29.6 -0.4 -1.320 20 1.4 38.4 39.8 -0.2 -0.5

Table 4: Experimental results of Overhanging beam with concentrated and distributed loads

Steel

wl [N] W[N] R 1 [N] R 2 [N] R 1+R 2 [N] [N] %0 5 2.6 1.7 4.3 -0.7 -14.00 10 6.3 3.3 9.6 -0.4 -4.00 15 9.1 5.0 14.1 -0.9 -6.00 20 13.5 6.0 20.1 0.1 2.0

20 5 9.6 14.7 24.3 -0.7 -2.820 10 7.3 22.7 30.0 0.0 0.020 15 3.8 30.8 34.6 -0.4 -1.120 20 0.3 38.8 39.1 -0.9 -2.35 5 0.3 9.7 10.0 0.0 0.0

10 10 0.6 19.5 20.1 0.1 0.515 15 0.4 29.2 29.6 -0.4 -1.3

20 20 0.6 38.9 39.5 -0.5 -1.3Table 5: Experimental results of Overhanging beam with concentrated and distributed loads


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Brass

wl [N] W[N] R 1 [N] R 2 [N] R 1+R 2 [N] [N] %0 5 3.0 2.2 5.2 0.2 10.00 10 5.5 4.4 9.9 -0.1 -1.00 15 8.2 6.6 14.8 -0.2 -1.30 20 10.8 8.8 19.6 -0.4 -2.0

20 5 7.4 16.9 24.3 -0.7 -2.820 10 5.2 25.0 30.2 0.5 1.720 15 2.1 33.1 35.2 0.2 0.620 20 1.0 41.3 42.3 2.3 5.85 5 0.5 10.5 11.0 1.0 10.0

10 10 0.4 21.0 21.4 1.4 7.015 15 1.4 31.5 32.9 2.9 9.7

20 20 2.0 42.1 44.1 4.1 10.3Table 6: Experimental results of Overhanging beam with concentrated and distributed load

Graph for Supports Reaction of the Overhanging Beam with Concentrated and DistributedLoads

y = 0.576x + 0.7R = 0.9841

y = 0.332x - 0.05R = 0.9999

0

2

4

6

8

10

12

14

0 5 10 15 20 25


[ N ]

W [N]

Graph of Reaction Force [N] against W [N] whenwl [N] = 0 for aluminium

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])


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Graph 1, 2, 3: graph of Reaction Force [N] against W [N] when wl [N] = 0 for aluminium,

steel, and brass.

y = 0.71x - 1R = 0.9931

y = 0.292x + 0.35R = 0.9887

0

2

4

6

8

10

1214

16

0 5 10 15 20 25


[ N ]

W [N]

Graph of Reaction Force [N] against W [N] whenwl [N] = 0 for steel

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])

y = 0.522x + 0.35R = 0.9998

y = 0.44xR = 1

0

2

4

6

8

10

12

0 5 10 15 20 25


[ N ]

W [N]

Graph of Reaction Force [N] against W [N] whenwl [N] = 0 for brass

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])


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y = -0.628x + 13.95R = 0.9991

y = 1.6x + 6.6R = 1

0

10

20

30

40

50

0 5 10 15 20 25


[ N ]

W [N]

Graph of Reaction Force [N] against W [N] when wl [N]= 20 for aluminium

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])

y = -0.628x + 13.1R = 0.9913

y = 1.608x + 6.65R = 1

0

10

20

30

40

50

0 5 10 15 20 25

R

e a c t i o n F o r c e

[ N ]

W [N]

Graph of Reaction Force [N] against W [N] when wl [N]= 20 for steel

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])

y = -0.446x + 9.5R = 0.9717

y = 1.626x + 8.75R = 1

0

10

20

30

40

50

0 5 10 15 20 25


[ N ]

W [N]

Graph of Reaction Force [N] against W [N] when wl [N]= 20 for brass

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])


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Graph 4,5,6 : Graph of Reaction Force [N] against W [N] when wl [N] = 20 for aluminium,steel, and brass.

y = 0.018x + 0.75R = 0.0831

y = 1.918x + 0.05R = 1

0

10

20

30

40

50

0 5 10 15 20 25


[ N ]

wl [N]= W [N]

Graph of Reaction Force [N] against wl [N]= W [N] for

aluminum

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])

y = 0.014x + 0.3R = 0.363

y = 1.946xR = 1

0

10

20

30

40

50

0 5 10 15 20 25


[ N ]

wl [N]= W N]

Graph of Reaction Force [N] against wl [N]= W [N] forsteel

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])


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Graph 7,8,9 : Graph of Reaction Force [N] against wl [N]= W [N] for aluminium, steel, and brass.

DISCUSSION:

A) Supports reaction of the simply-supported beam with concentrated loads

1) Verification of equations (3) and (4):

( ) ________ (3)( ) ________ (4)

2) Based on the graph we can observe that the trend line beam reaction toward steel,aluminium, and brass for each case mostly similar to each other. For beamreaction when W 2= 0N the trend line reaction are similar for steel, aluminium, and

brass. The same thing goes to beam reaction when W 1= 0N and W 1=W 2.

3) Below are the table for the theoretical values of R 1 and R 2, by using equations (3)

and (4).

y = 0.11x - 0.3R = 0.8655

y = 2.106x - 0.05R = 1

0

10

20

30

40

50

0 5 10 15 20 25


[ N ]

wl [N]= W[N]

Graph of Reaction Force [N] against wl [N]= W [N] forbrass

R1 [N]

R2 [N]

Linear (R1 [N])

Linear (R2 [N])


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Concentratedload

Theory Steel Brass Aluminum

W 1 (N) W 2 (N) R 1(N) R 2(N) R 1 (N) R 2 (N) R 1 (N) R 2 (N) R 1 (N) R 2 (N)

5 0 3.3 1.7 2.8 0.5 3.6 1 3.1 1

10 0 6.7 3.3 6.9 1.4 7.2 2.4 6.7 1.4

15 0 10.0 4.9 10.7 2.6 10.8 3.4 10.6 2.3

20 0 13.4 6.6 14.2 3.8 13.8 4.6 14.5 3.5

25 0 16.7 8.3 17.2 5.1 18.4 5.5 18.2 4.6

30 0 20.1 9.9 21.8 6.0 21.4 6.4 21.9 6.1

0 5 1.7 3.3 1.0 3.7 0.7 2.2 0.9 2.8

0 10 3.3 6.7 1.6 7.0 1.7 5.8 1.6 6.1

0 15 4.9 10.0 2.4 9.9 2.8 9.5 2.8 9.5

0 20 6.6 13.4 3.8 13.8 4 12.1 4.6 13.4

0 25 8.3 16.7 4.7 17.1 5.2 16.6 5 17.8

0 30 9.9 20.1 5.9 21.1 6.8 20.5 6.5 20.4

5 5 5.0 5.0 4.0 4.2 4.8 3.6 4.0 3.8

10 10 10.0 10.0 8.7 8.6 8.6 7.9 9.4 8.8

15 15 15.0 15.0 13.4 13.6 13.6 13 13.9 13.4

20 20 20.0 20.0 18.8 18.7 19.6 19.9 18.8 17.9

25 25 25.0 25.0 23.0 22.8 24.8 24.1 23.9 21.6

30 30 30.0 30.0 29.4 28.9 28.3 29.3 28.4 27.4

Table 1: Theoretical results compare with experiment results

The graph of theoretical values of R 1 and R 2 are plotted.


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0.000

5.000

10.000

15.000

20.000

25.000

5 10 15 20 25 30

R ( N )

W1(N)

R1 and R 2 against W 1

Theory R1

Theory R2

Steel R1

Steel R2

Brass R1

Brass R2

Aluminium R1

Aluminium R2

0.000

5.000

10.000

15.000

20.000

25.000

5 10 15 20 25 30

R ( N )

W2(N)

R1 and R 2 against W 2

Theory R1

Theory R2

Steel R1

Steel R2

Brass R1

Brass R2

Aluminium R1

Aluminium R2


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Based on the graph plotted by using theoretical value calculated using equation (3)and (4) and the experimental value, we can see that the theoretical values of R 1 are the mostnearer with the experimental values. Compared to theoretical values of R 2, the values showeda lot of different than the values obtained from the experiment. This due to several erroroccurred while conducted the experiment. Basically equation (3) and (4) give more accuratetheoretical values as it were calculated and have no external error. Therefore, we can verifythe experimental values by using both equations.

1) The percentage error is calculated by using the formula below :

Take R 1 of aluminium as an example to calculate percentage error:

0.000

5.000

10.000

15.000

20.000

25.000

30.000

35.000

5 10 15 20 25 30

R ( N )

W1=W2 (N)

R1 and R 2 against W 1=W2

Theory R1

Theory R2

Steel R1

Steel R2

Brass R1

Brass R2

Aluminium R1Aluminium R2


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For the steel beam (R 1),

Concentratedload

Steel,% Brass,% Aluminum,%

W 1 (N) W 2 (N) R 1 (N) R 2 (N) R 1 (N) R 2 (N) R 1 (N) R 2 (N)

5 0 15.2 70.6 -9.1 41.2 6.1 41.2

10 0 -2.9 57.6 -7.5 27.3 0 57.6

15 0 -7 46.9 -8 30.6 -6 53.1

20 0 -5.9 42.4 -2.9 30.3 -8.2 47

25 0 -3 38.6 -10.2 33.7 -8.9 44.6

30 0 -8.5 39.4 -6.5 35.4 -8.9 38.4

0 5 41.2 -12.1 58.8 33.3 47.1 15.2

0 10 51.5 -4.5 48.5 13.4 51.5 9

0 15 51 1 42.9 5 42.9 5

0 20 42.4 -3 39.4 7.5 30.3 0

0 25 43.4 -2.4 37.3 0.6 39.8 -6.6

0 30 40.4 -5 31.3 -2 34.3 -1.5

5 5 15.2 70.6 -9.1 41.2 6.1 41.2

10 10 -2.9 57.6 -7.5 27.3 0 57.6

15 15 -7 46.9 -8 30.6 -6 53.1

20 20 -5.9 42.4 -2.9 30.3 -8.2 47

25 25 -3 38.6 -10.2 33.7 -8.9 44.6

30 30 -8.5 39.4 -6.5 35.4 -8.9 38.4

These results were affected by several errors during the experiment. Those factors are:


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i. The parallax error occurred when we taking the readings from the dial gauge.

ii. The concentrated load might not place on the exact point which it should be

placed according to the lab manual due to some human error when placing the

concentrated load. As a result, the reactions R 1 and R 2 obtained from the

experiment are slightly different from the theoretical values.

iii. There should be some frictions at the contact point between the load cells and

the beam which have caused some errors for the load cell to determine the

exact weight of the concentrated loads.

B) Supports Reaction of the Overhanging Beam with Concentrated and DistributedLoads

1) Verification of equations (7) and (8):Total equation of force: R 1 + R 2 = wl +W __________ (5)

Total moment at R 2: R 1 (l + l) + Wl = wl ( l + l) _________ (6)

R 1 = 2/3 (wl W) _________ (7)

Then substitute R 1 into equation (5): R 2 = wl + W - R 1 R 2 = wl + W 2/3 (wl W)

R 2 = 1/3 (wl - 5W) _________ (8)We know l = L/4Then substitute l = L/4 into R 1 and R 2 equation

R 1 =2/3[(w L/4) W] _______ (10)R 2=1/3 (w L/4- 5W) _______ (11)

The theoretical values of reactions force R 1 and R 2 can obtained from the equations

(10) and (11). Substitute the L, w, and W into the equations in order to get R 1 and R 2.

Length of beam is measured and the distance of R 1 and R 2 from the center of beam is

calculated as below:

R 1 = L/4 from center of beam and R 2 = L/8 from center of beam.

2) According to the graph, we can observe that the trend line of reaction force for steel,aluminium, and brass for each cases almost similar to each other. In experiment ofreaction force when wl= 0N we can observe that the trend line for R 1 for each beam is


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almost similar, however the trend line R 2 for brass does not showed similaritycompared to other. As the trend line for other condition all of it showed similaritywhen compared to each other. Only trend line R 2 for brass when wl= 0N deviatedcompared to other beams, this might due to some error occurred during the

experiment.

3) Theoretical calculation of R 1 and R 2 are by using equation (10) and (11) which are

derived from equation (7) and (8):

( )

Concentratedload

Theory Steel

W 1 (N) W 2 (N) R 1(N) R 2(N) R 1 (N) R 2 (N)

0 5 1.833 0.917 5.970 3.9000 10 -1.500 -7.417 2.270 12.3000 15 -4.833 -15.750 -1.610 20.9000 20 2.750 1.375 8.730 6.000

20 5 -0.583 -6.958 5.100 14.30020 10 -3.917 -15.292 1.450 22.70020 15 -7.250 -23.625 -2.410 31.40020 20 3.667 1.833 11.990 7.6005 5 0.333 -6.500 7.940 16.400

10 10 -3.000 -14.833 4.520 24.60015 15 -6.333 -23.167 0.790 32.80020 20 -9.667 -31.500 -3.090 41.800

Table 10: Theoretical results compare with experiment results

The graph of theoretical values of R 1 and R 2 are plotted.


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Graph 1

Based on graph 1, we can observed that there is not much differ between theoretical andexperimental values for R 1, however for R 2 we can observe a large deviation betweentheoretical and experimental values. These result may be affected due to some error duringthe process of experiment.

Based on this graph we can see that both theoretical and experimental values have different

slope from each other for both R 1 and R 2. To conclude, the experimental result does not obeythe theoretical result.

-20.000

-15.000

-10.000

-5.000

0.000

5.000

10.00015.000

20.000

25.000

30.000

10 15 20

R ( N )

W1

R1 and R 2 against W 1,W2=10

Theory R1

Theory R2

Steel R1

Steel R2

-20

-15

-10-5

0

5

10

15

20

25

0 5 10

R ( N )

W2

R1 and R 2 against W 2,W1=10

Theory R1

Theory R2

Steel R1

Steel R2


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From the graph we can observe that the experimental result and the theoretical result showedthe same pattern and almost similar to each other, but for R 2 both result differ from each otherand have a large gap between them. This might due to error during the experiment.

4) These results were affected by several errors during the experiment. Those factors are:

1) The parallax error occurred when we taking the readings from the dial gauge.

2) The concentrated load might not place on the exact point which it should be

placed according to the lab manual due to some human error when placing the

concentrated load.

3) A level should added to the backboard and the backboard is movable so thatwe can adjust the two supports so that they are at the same level beforestarting the experiment.

-40.000

-30.000

-20.000

-10.000

0.000

10.000

20.000

30.00040.000

50.000

10 15 20 A x i s T i t

l e

Axis Title

R1 and R 2 against W 1=W2

Theory R1

Theory R2

Steel R1

Steel R2


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Conclusion:

The support reaction in simply-supported and overhanging beams has been identified. Theunderstanding of beam apparatus has been understood and the sensitivity also accuracy of

beam has been determined.

Reference:

1. Mechanics of Materials, Seventh SI Edition, R.C Hibbeler, Pearson.

2. Engineering Mechanics Statics, Tenth Edition in SI Units, R.C Hibbeler, Pearson.

3. William D Callister, JR.(1999). Materials Science and Engineering an Introduction,

4th edition. John Willey & Sons, Inc.

Reaction Beam lab

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