reactions final

Beam Reaction Experiment Group 2

1

Table of Contents 1.0. Abstract ............................................................................................................................................ 4

2.0. Introduction ...................................................................................................................................... 4

2.1. Aims ............................................................................................................................................. 4

2.2. Objectives ........................................................................................................................................ 4

3.0. Literature Review ............................................................................................................................. 5

4.0. Methodology .................................................................................................................................. 11

4.1. Apparatus used for this Experiment ........................................................................................... 11

4.2. Procedure ................................................................................................................................... 13

4.3. Special considerations ................................................................................................................ 14

5.0. Results ............................................................................................................................................ 15

6.0. Discussion ...................................................................................................................................... 16

7.0. Experimental errors and limitations ............................................................................................... 19

8.0. Precautions ..................................................................................................................................... 19

9.0. Recommendations .......................................................................................................................... 19

10.0. Health and safety considerations .................................................................................................. 20

11.0. Dissemination of knowledge ........................................................................................................ 20

12.0. Contribution of team members and resource persons .................................................................. 22

13.0. Conclusion ................................................................................................................................... 22


2

List of Figures.

Figure 1.0 ________________________________________________________________________________ 11

Figure 2.0 ________________________________________________________________________________ 11

Figure 3.0 ________________________________________________________________________________ 12

Figure 4.0 ________________________________________________________________________________ 16

Figure 5.0 ________________________________________________________________________________ 17

Figure 6.0 ________________________________________________________________________________ 18


3

List of Table

Table 1.0 __________________________________________________________________________________ 6

Table 2.0 __________________________________________________________________________________ 8

Table 3.0 _________________________________________________________________________________ 10

Table 4.0 _________________________________________________________________________________ 15

Table 5.0 _________________________________________________________________________________ 15

Table 6.0 _________________________________________________________________________________ 15

Table 7.0 _________________________________________________________________________________ 16

Table 8.0 _________________________________________________________________________________ 17

Table 9.0 _________________________________________________________________________________ 18

Table 10.0 ________________________________________________________________________________ 22


4

Beam Reaction Experiment

1.0. Abstract

In this experiment we will record how the reactions of the supports vary when a load is placed at

different positions in the beam. Also, we are going to observe the reactions when the load is beyond

support with changing positions and lastly with an experiment where we have a fixed load and a load

with varying positions.

Calculation of reactions is crucial for the determination of the bending moment and shear force

diagram. These diagrams are needed to calculate deflection of beam, bending stress and the maximum

load it can support.

2.0. Introduction

2.1. Aims

This experiment is carried out to investigate if the experimental value of a beam reaction experiment

is similar to that of the calculated value. The results are plotted to compare the results.

2.2. Objectives

The objective of this experiment is to use the apparatus to measure the reactions at the supports

different types of beam.

For part one, a load is placed at a distance X from the left support. The distance X is varied along the

length of the beam and the reading of the newton meter are noted.

For part 2, a fixed load is placed at a distance m from the left support, and a load is placed at a varied

distance n from the left support, the reaction of both newton meter are again noted.

For part 3, a fixed load is placed at a distance m from the left support, and a load is placed on the right

of the right support (overhanging beam), the load is placed at n cm from the left support and the

length of n is varied making sure that is remains in the overhanging part of the beam. The values at

the supports are noted.

For all three parts the beam must be horizontal before taking readings.


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3.0. Literature Review

Beams are long and slender structures on which are subjected to external forces at right angles

to its axis so they are subjected to bending stress from a direction perpendicular to its length. There

are different types of beams namely, beam hanging at one end only, simply supported beams,

continuous beams and cantilever beams. In this experiment we will investigate the reaction on the

supports of beams, hanging at one end and simply supported beams.

Part 1: To investigate the reaction of a simply supported beam loaded with one

concentrated load of 20N

For the first part of the experiment a uniform 75cm beam of weight 46N is simply supported at both

ends and a loads of 20N is placed at a distance X cm from the left support. The length of x is varied

along the length of the beam between the supports and the reaction is recorded. In theory, when

distance X cm increases the reaction at the left support should decrease and reaction at the right

support should increase.

When X = 0 cm, the reaction at the left support should be (20+46/2) = 33N, and the reaction at the

right support should be 13N.

When X = 75 cm, the reaction at the left support should be 13N and reaction at the right support

should be 33N.

Reaction at both end varies linearly with distance X at which the load is placed, when X increase

The length X is varied across the beam and the reactions R1 and R2 are recorded in a table.

W=20N X cm

L=75cm

Where SW is the self-weight of the beam.

SW=26N

R1 R2


6

Calculations from theory

Using principles of moment:

At equilibrium;

M=0

Taking moments from R1;

clockwise moment = anticlockwise moment

20X + 26x37.5 = 75R2

R2 = +

Equation 1.0

Similarly taking moment from R2;

M=0

Clockwise moment = anticlockwise moment

75R1 = 2x37.5 + 20(75-X)

75R1 = 975 + 1500-20X

=

Equation 2.0

We use these equations and replace the values of X to obtain theoretical values of R1 and R2.

Experiment number X/cm R2/N R1/N 1 37.5 23.00 23.00

2 7.5 15.00 31.00

3 25.0 19.67 26.33

4 65.0 30.33 15.67

Table 1.0


7

Part 2: To investigate the reactions of a simply supported beam with 2 concentric loads

A fixed load is placed at a distance 20 cm from the left support and another load is placed at a

distance n from the left support, the distance n is varied from the left support to the right support.

In theory when the value of n is increased from 0 cm to 75 cm the reaction at support R3 will decrease

linearly, with the maximum reaction at R3 being 37.67N when n = 0cm. And the reaction at R4 will

increase linearly with maximum reaction at R4 being 28.33 N when n = 75cm.

W2=10N n cm

W1=20N

m= 20cm

Length= 75cm

Calculations from theory:


At equilibrium;

M=0

From R3;


R3 R4

SW=26N


8

26x37.5 + 20x20 +10n= 75xR4

= +

Equation 3.0

At equilibrium;

M=0

From R4;

clockwise moment=anticlockwise moment

75XR3=26x37.5+ 10(75-n) + 55x20

=

Equation 4.0


Experiment number n/cm R3/N R4/N

1 32.5 33.33 22.67

2 40.0 32.33 23.67

3 55.0 30.33 26.67

4 67.5 28.67 27.33

Table 2.0


9

W1=20N

Part 3: To find reactions when one load is beyond the RH support.

In part 3 the fixed weight 20N remains at a distance 20 cm from the left support and a load of 10N is

placed beyond the right support at a distance of n cm from the left support. The length of n is varied

but kept beyond the right support.

From theory when the distance n increases the reaction R3 should decrease whereas the reaction R4

increases.

R3 R4

Calculations from theory:


At equilibrium;

M=0

From R3;


26x37.5 + 20x20 +10n= 75xR4

= +

Equation 5.0

W2=10N n cm

75cm

M=20cm

SW=26N


10

To calculate R3, we use

Fy=0

10+-26+-20+R4+R3=0

=

Equation 6.0


Experiment number n/cm R3/N R4/N

1 85 29.33 26.67

2 90 25.67 30.33

3 95 25.00 31.00

4 105 23.67 32.33

Table 3.0


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4.0. Methodology

4.1. Apparatus used for this Experiment

1. Beam Apparatus

Figure 1.0

2. 1400mm beam

3. Four 1kg cast iron weights

4. A spirit level

The spirit level

It is used to check if a surface is horizontal.it consists of a horizontal transparent tube with 2 markings

and a bubble. If surface is horizontal the bubble must be between the 2 marks as shown:

Figure 2.0

If surface is not horizontal then bubble is not between the 2 marks.


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Checking for errors in level.

Place the level on a flat surface and make a mark to show where the level is sitting.

Note the exact position of the bubble in the vial.

Turn the level over to the other side and place it against the mark you made.

Check the exact position of the bubble in the vial again.

If the bubble has returned to the same place, the level is accurate. If it didnt, then it may be

inaccurate. Always double check by repeating the process above.

5. 2 spring balances with adjusting screws

6. Weight hangers

7. 4 rectangular sliders to hook spring balances and weight hangers with beam

Figure 3.0


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4.2. Procedure

The experiment is done in three parts:

Part 1

The 2 spring balances are hooked into position on the supports.

The beam is then simply supported through sliders on the 2 spring balances.

The beam is levelled and the reactions due to self-weight are recorded.

A concentrated load is hooked between the supports on another slider.

The reactions due to this concentrated load at different positions x mm (from the left support),

is investigated.

Part 2

The setup is kept the same as in part 1.

The load is unhooked and a second slider with its weight hanger is inserted on the beam. The

latter is levelled and the reactions due to self-weight are recorded.

The simply supported beam is then loaded with two concentrated loads, one at a fixed

position m mm from the left support and the other was placed at different positions n mm

from the left support to find the respective reactions.

Part 3

One of the supports is moved closed to the other one.

The beam is then hooked again and 2 sliders with weight hangers are inserted; 1 between the

supports and 1 beyond the right support.

The beam is levelled again and the reactions due to self-weight are recorded.

The hangers are loaded; 1 load between each support at a fixed position m mm from the left

support and another load was placed at different positions n mm (measured from the left

support) beyond the right support in cantilever.

The respective reactions were recorded at the supports.


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4.3. Special considerations:

We ensured that the beam is levelled before moving mass and after moving mass and taking

readings and make necessary adjustments.

Before taking readings and checking the level, we waited for the beam to stabilise (beam

makes displacements when disturbed)

Readings were taken by at least 2 persons to minimise gross errors.

The initial weight of beam is measured and recorded. It is equal to sum of readings of the

newton meters (23.0N +23.0N=46.0N)


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5.0. Results

Part 1: To investigate the reaction of a simply supported beam loaded with one concentrated

load of 20N

Experiment number x/cm R1/N R2/N 1 37.5 23.0 23.0

2 7.5 32.0 14.0

3 25.0 27.0 19.0

4 65.0 15.5 30.5

5 55.0 18.5 28.0

Table 4.0


Experiment number n/cm R1/N R2N 1 32.5 35.0 23.5

2 40.0 33.5 24.5

3 55.0 31.0 26.5

4 67.5 29.5 28.5

Table 5.0


Experiment number n/cm R3/N R4/N 1 85.0 35.0 23.5

2 90.0 33.5 24.5

3 95.0 31.0 26.5

4 105.0 29.5 28.5

Table 6.0


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6.0. Discussion

Part 1: To investigate the reaction of a simply supported beam loaded with one concentrated

load of 20N

Table 7.0

Figure 4.0

From the graph we can deduce that the experimental values are reliable, there is a small difference

between the value of the experimental and theoretical values of the experiment, and the maximum

difference between the values is 1N. Both graphs show the same trend. We can conclude the results

are reliable as they are close to what we expected.

Experiment

numberX/cm

Experimental

R1/N

Experimental

R2/N

Theoritical

R1/N

Theoritical

R2/N

1 37.5 23 23 23.00 23.00

2 7.5 32 14 31.00 15.00

3 25 27 19 26.33 19.67

4 65 15.5 30.5 15.67 30.33

5 55 18.5 28 18.33 27.67


17


Table 8.0

Figure 5.0

Both the experimental and theoretical values follow the same trend. However, there is a significant

and almost same difference between the experimental and theoretical values. The maximum

difference between the values is 1.77N. There was a constant error which was present all throughout

this experiment which would cause the experimental reading to deviate constantly from the theoretical

value; this could be due to a defect in the 1Kg load used.

Experiment

numbern/cm

Experimental

R3/N

Experimental

R4/N

Theoritical

R3/N

Theoritical

R4/N

1 32.5 35 23.5 33.33 22.67

2 40 33.5 24.5 32.33 23.67

3 55 31 26.5 30.33 25.67

4 67.5 29.5 28.5 28.67 27.33

20

22

24

26

28

30

32

34

36

25 35 45 55 65

Re

acti

on

s N

/g

Distance from left support

Experimental R3/N

Experimental R4N

TheoreticalR3/N

Theoretical R4/N


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Table 9.0

Figure 6.0

The trend in of the experimental and theoretical values of the experiment is almost the same, however

there is a large percentage of error between the experimental and theoretical values. An error in the

weight used could explain the large difference in readings. The experiment should be repeated with

the mass to be used weighted before use.

Experiment

numbern/cm

Experimental

R3/N

Experimental

R4/N

Theoritical

R3/N

Theoritical

R4/N

1 85 35 23.5 29.33 26.67

2 90 33.5 24.5 25.67 30.33

3 95 31 26.5 25 31

4 105 29.5 28.5 23.67 32.33

22

24

26

28

30

32

34

36

80 85 90 95 100 105 110

Rea

ctio

ns

N/g

Distance from left support (cm)

Experimental R3/N

Experimental R4/N

Theoretical R3/N

Theoretical R4/N


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7.0. Experimental errors and limitations

1) The centre of mass of the beam may not be exactly at the middle of the beam.

2) The pointer on the newton meter was large and the readings were small.

3) The mass of the glide on which the hanger is attached is not included in the calculations.

4) The spirit level was not accurate enough.

5) The beam is made of steel which volume varies greatly with temperature so as the length.

6) The loads are large which prevent it from being placed near the support to obtain very small

reading of m or n.

7) Movement of air around cause the setup to vibrate.

8) The mass of the loads are not exact.

8.0. Precautions

1. The newton meter should be vertical so as to prevent formation of horizontal components of

forces, set square could be used.

2. The beam should be horizontal to prevent formation of horizontal components of forces.

3. The spirit level should be checked before use.

4. The maximum weight of the newton meter should not be exceeded to prevent damage.

5. The beam should be straight and not bend.

6. Precaution should be taken when loading and removing the loads to prevent any loads to fall.

7. The 2nd load used in part 3 (the one which is not fixed) should not exceed the fixed load far

too much as it can overturn the beam.

9.0. Recommendations

1. The pointer should be smaller and the reading on the newton meter should be bigger or a

digital newton meter could be used for more precise and accurate results.

2. The mass of the glider should be used in the calculations.

3. The spirit level should be more sensitive.

4. A newton meter with a higher maximum weight could be used to determine reaction using

heavier masses.

5. For all three part more the reading of the balance should be taken in more than 4 position to

obtain accurate and more reliable results.

6. The loads used could be weighted before being used.


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7. The experiment is carried away from fans and windows.

10.0. Health and safety considerations

Heavy masses should be handled carefully. Bucket of sand on floor can be used to avoid

masses falling on feet.

Gloves to be used when handling beam. Pointed ends can cause injuries.

11.0. Dissemination of knowledge

The graphs of part 1 and part 2, show very small deviations between the theoretical and the actual

values. This is mainly because of small errors. The reactions R1 and R2, varies linearly with load.

This shows that the reactions of a constant load between its supports vary linearly with distance.

In part 1, the gradient is calculated as shown:

M of R1= (23-18.33)/ (37.5-55) =-0.267.

M of R2= (23-27.67)/ (37.5-55) =+0.267

The +ve and ve signs shows that as we increase distance from R1 we have a reduction in reaction

atR1 and an increase in reaction at R2.

The gradient being equal in magnitude shows that the decrease in reaction at R1 is equal to the

increase in reaction at R2.

At x =0,

The max reaction at R1 is y int=23+0.267x37.5=33.00N

The min reaction atR2 is y int=12.99N

At max value of x=75.0cm.

The max R1=12.99N

The min R2= 33.00N

In part 2, the setup is similar but with addition of a constant fixed load on the beam.


21

M of R3= (33.33-28.67)/ (32.5-67.5) = -0.133

M of R4= (22.67-27.33)/ (32.5-67.5) = +0.133

-VE sign at R3 and +VE sign at R4 shows decrease in reaction at R3 and increase in reaction at R4.

The equal magnitude of gradient shows decrease in R3=increase in R4.

At x =0,

Max reaction at R3=37.65

Max reaction at R4= 29.00

Min reaction atR3=27.68 and R4=38.98

The addition of a constant fixed load has cause changes in the graphs.

Compared to case1 case2 has graphs of smaller magnitude of gradient but a higher maximum and

minimum reactions.

In Part 3,

In the graph we can see a very large difference between the theoretical and the experimental values.

This could have been due to the apparatus error (in the Newton meter) which was not suitable for

overhanging loads.

In the graph we can see as distance of W2 increases:

There is a general decrease trend in the reaction at R3 in both experimental and theoretical

values

There is a general increase in the reaction at R4 in both experimental and theoretical values.

Because of the large scattering of points and lines not straight it is difficult to show

mathematical relationships that exist between the reactions.


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12.0. Contribution of team members and resource persons

Table 10.0

We would like to thank to the laboratory technician Mr Gokhool who has given us precious advices.

We have been able to do the practical successfully with his help. We would also like to thank our

lecturer Mr. Nunkoo who has been guiding us throughout our practicals.

13.0. Conclusion

Based on the results of the experiments performed above in three parts, the theoretical values are

obtained from calculations. Hence, within the limit of experimental uncertainty, the values compared

are the same; meaning that the experiments were reliable and almost accurate except for some errors

that were always present.

Task Student

Abstract,

Introduction and

conclusion

Rujub M.Afzar

& Lionel

Gikonyo

Literature review

and discussion

Saif Rhyman

Saib and

Kavish

Sockalingum

Methodology and

results

Abhishek

Jagessur and

Anusha

Bheenuck

Limitations Rujub M.Afzar

Recommendations Saif

Health&Safety

measuresAnusha

Dissemination of

knowledge Abhishek

Contribution of

team members &

Resource person

Lionel Gikonyo

CompilationKavish&

Anusha

reactions final

Documents

beam reaction experiment

safety considerations

special considerations

contribution of team

resource persons

list of figures

table of contents

experimental errors