Experiment Shearing Forces

Shearing Force in Beams Experiment Experiment

Group 2

Table of Contents

List of Tables ................................................................................................................................................ 2 List of Figures ............................................................................................................................................... 3 1.

Abstract ................................................................................................................................................. 4

2.

Introduction ........................................................................................................................................... 4

3.

Literature review ................................................................................................................................... 5

4.

Methodology ......................................................................................................................................... 6 4.1.

Apparatus used .............................................................................................................................. 6

4.2.

Procedures ..................................................................................................................................... 7

5.

Results ................................................................................................................................................... 8

6.

Discussion ........................................................................................................................................... 11

7.

Limitations................... Limitations. .................. ................. .................. ................. .................. ................. .................. ............... 11

8.

Recommendations ............................................................................................................................... 12

9.

Health and safety ................................................................................................................................. 12

10.

Dissemination of knowledge ........................................................................................................... 13

11.

Applications Applications in real life ................................................................................................................... 16

12.

Contribution Contributi on of team members ................. ................. ................. .................. .................. ............... 17

13.

Conclusion Conclusio n .................. ................. ................. .................. ................. .................. .................. ............ 17

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List of Tables

Table 1.................. .................. ................. ................. .................. ................. .................. ................. ............... 8 Table 2.................. .................. ................. ................. .................. ................. .................. ................. ............... 8 Table 3.................. .................. ................. ................. .................. ................. .................. ................. ............... 9 Table 4.................. .................. ................. ................. .................. ................. .................. ................. ............. 10 Table 5.................. .................. ................. ................. .................. ................. .................. ................. ............. 11 Table 6.................. .................. ................. ................. .................. ................. .................. ................. ............. 11 Table 7.................. .................. ................. ................. .................. ................. .................. ................. ............. 15 Table 8.................. .................. ................. ................. .................. ................. .................. ................. ............. 15

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List of Figures

Figure 1 ......................................................................................................................................................... 5 Figure 2 ......................................................................................................................................................... 8 Figure 3 ....................................................................................................................................................... 13 Figure 4 ....................................................................................................................................................... 14 Figure 5 ....................................................................................................................................................... 17

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1. Abstract When simply supported beams are loaded two main forces are created, bending and shear. These forces are internal and cannot easily be seen. This experiment brings these internal forces from inside the beam to outside the beam so that students can visually see the beam deflecting and shear forces acting. Each beam is simply supported on vertical supports which can be easily moved to create varying support positions and beam spans. At the ‘cut’ section, bearings section, bearings in one beam straddle a vertical bearing track in the mating beam. This ensures free vertical movement for monitoring shear forces. Although beam bending is permitted, it is counteracted counteracted by the bearings and a tension spring supported horizontally from underneath the beams .

2. Introduction When a beam is loaded the forces cause the beam to bend and to undergo vertical displacement. These effects are due to vertical component of forces acting perpendicular to the longitudinal axis of the beam. The vertical displacement tends to shear the beam. Shear means relative movement between two parts of a structural member. Any beam must be designed in such a way that it can resist shear and bending. Moving loads on beams are common features of design. Many road bridges are constructed from beam, and as such have to be designed to carry a knife edge load, or a string of wheel loads, or a uniformly distributed load, or perhaps the worst combination of all three. The method of solving the problem is to use influence lines, i.e., shear force diagrams.

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3. Literature review The determination of shear force in a member in civil engineering is the basic part of structural analysis. Shear force is defined as the pair of internal forces at any portion in a member that are formed to resist the load being transferred at that point to maintain equilibrium. Shear force in a member is calculated on a shear force diagram. We can use this diagram to calculate bending moment moment in a section. These diagrams can be used to easily determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure. Another application of shear and moment diagrams is that the deflection of a beam can be easily determined using the moment area method.

Figure 1

If we consider the cantilever beam above with a load, P N acting on the beam end, we can see the shear forces with equal magnitude, Q N acing in opposite directions at section BC. These forces arise as explained below: 

At section AB the net force acting is Q N upwards. In order to bring equilibrium we need a downward force of equal magnitude, Q N. This shear force is provided by the other section of the beam, i.e., CD.



At section CD the net force acting is QN downwards. So in order to bring equilibrium we need an upward shear force of QN. This shear force is provided by the other section of the beam, i.e., AB.

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4. Methodology 4.1.Apparatus used 

Beam



Hangers



Spring Balance



Spirit Level



Measuring tape



Loads

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4.2. Procedures Part 1 1. The beam is installed 300mm from cut part to support A and 600mm from cut part to support B. 2. Initially the beam is made horizontal by tightening/releasing the underslung spring below it,

accordingly to the bubble in the spirit level so that it is central. 3. The height of the Newton meter is adjusted so that the part A and B of the beam are at same level. 4. A measuring tape is used for measurement; a hanger is positioned at the middle of the 300mm

member A1 (A) of beam and another at the middle of the 600mm member B 1 of beam. (B) 5. A hanger is positioned on member A just near the cut part of the beam. 6. The initial reading is recorded on the Newton meter. 7. A load of 10N is first placed on hanger (A). 8. The deflection of the beam is observed. 9. The underslung spring and height of Newton meter is used to level the beam so as to counter the

bending moment moment formed initially. initially. 10. The final value of the Newton meter is recorded. 11. The load is removed. 12. Procedures 3-10 are repeated for the 2 other positions of the beam Part 2

members’ distances and position of hangers are unchanged. 1. The members’ 2. The beam is made horizontal with the spirit level. 3. The initial reading on Newton meter is noted. 4. 10N force is placed on each hanger. 5. The beam is levelled. 6. The final reading on Newton meter is recorded. 7. The load is removed. 8. The experiment is repeated with loads of 15 N and 20 N.

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Group 2 D C B

A

B1 A1

Figure 2

A1-short member B1-long member A-Midpoint of short member B-Midpoint of long member.

5. Results Part 1: Position of 10N load 600mm from Left support (B) 300mm from Left support (D) 150mm form Left Support (A) When placed at C

Initial reading/N 1.50 2.00 2.00

Final reading/N 5.50 9.25 0.75 No reading

Shear force at C/N -1.25 7.25 4.00

Table 1

Part 2: Load on hangers/N 5 10 15

Initial reading/N 2.00 2.00 2.00

Final reading/N 6.50 11.00 17.00

Shear force at C/N 4.50 9.10 15.00

Table 2

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Theoretical shear force diagrams Position of 10N load A

Shear force diagram and force at C SF/N

The theoretical SF at C is +3.33 N B SF/N

The theoretical SF at C is 6.67 N C

SF/N

Theoretical SF at C is -1.67 N Table 3

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Part 2 Load on hangers

SF diagrams and force at C

5

SF/N

Theoretical SF at C is 4.17N 10 SF/N

Theoretical sf at C is 8.33N 15

SF/N

Theoretical SF at C is 12.5N Table 4

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6. Discussion We have shown above how we reached the magnitude of shear force at the point C (cut end of beam) in the diagram. There is small difference in values between the calculated value and experimental value due to the limitations in experiment as shown below. When the load is shifted to position C, the section A of the beam moves upward hence we could not take the any reading on the newton meter. The Newton meter can measure only tensile forces and the shear force is negative at this position and hence compressive. The Newton meter do not enable us to measure this force.

Part 1

A B C

Theoretical value/N 1.67 6.67 3.33

Experimental value/N 1.25 7.25 4.00 Table 5

Part 2 Load 5 10 15



7. Limitations 1)

The pointer of the spring balance was too large.

2)

The loads may have not been well centered on the hanger.

3)

It was difficult difficul t to align the two sections A and B. It was done visually.

4)

Hangers were wide and thus were not placed at exact distances

5)

The beam was not exactly 900mm. The cut has a length.

6)

Friction might occur with the ball bearings at the cut.

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8. Recommendations 

A digital force display meter could be used for more accurate results



Known loads could have been firstly hung to the spring balance to check if it is not damaged.



A compression spring balance could have been used when the spring balance shows no reading (when in compression). compression).



Oil could have been applied to the ball bearings at the cut to eliminate friction.



Grooves could be made at the positions where the hangers were to be suspended.

9. Health and safety



Loads should be handled with care. Shock resisting materials could be placed beneath load hangers if loads were to fall.



Gloves should be used when handling the beam and hangers as pointy ends can cause injuries.



Readings should be taken when beam is at rest.

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10. Dissemination of knowledge Shear force in a beam are forces generated in the beam by the applied loads and by the supports. The forces due to reaction at support push up and forces due to applied forces pushes down. Shear force act along the beam depending on the type of load applied and the reaction at support. The drawing below shows the shear force diagram for different type of loads on a simply supported beam. For this experiment we are using a simple beam with off-set point load.

Figure 3

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Group 2

For this experiment we are using a simple beam with off-set point load. The apparatus used is as shown below.

Figure 4

The beam is cut 300mm from the right hand side of the support and 600mm from the left hand side of the support. The apparatus is set up such as the shear force in the beam can be shown and read from the spring balance attached to the end of left hand side beam.

For the first part the load is applied at different position on the beam: 1) In the middle of the part B of the Beam. 2) In the middle of part A of the Beam 3) In the groove at D The theoretical values of the shear force which would be obtained at the point D when the beam is loaded at those three positions is calculated using the laws of statics. The experimental value is obtained from the spring balance when the beam is levelled.

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The results are shown in the table below:

A B C

Theoretical value value/N 1.67 6.67 3.33


The maximum difference between the theoretical and experimental values of shear force is: 7.25 - 6.67 = - 0.58 N The maximum percentage difference is (0.58/6.67)% = 8.70% From this set of reading we can deduce that the theoretical shear force at the section is similar to the experimental shear force we obtained. For the second part, the hangers are not moved from their position in the Part 1. The experiment is carried out in with 3 different loads, 10N, 15N and 20N, which are placed on all the three hangers. The results are displayed in the table below. Load 5 10 15



The maximum difference between the theoretical and experimental values is: 17.5 – 17.5 – 15.0 15.0 = 2.5N The percentage difference in the reading is: (2.5/15.00)% = 16.67%

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11. Applications in real life

Bending Moment and Shear diagrams are always used by structural engineers or anyone dealing with forces in materials. In steel beam design, bending moment tells the structural engineer what is the lightest shape I can use to carry this bending moment. Shear strength of steel beams are high and typically can be overlooked if there isn’t and isn’t and special loading condition that warrants a look such as a column sitting at the middle of a beam or near the support. At the support, the shear stresses are at its highest and any load near this point would raise a red flag to check the capacity of the steel beam. In concrete, everything has to be checked because concrete is design for bending and the internal couple within the beam must resist the external bending moment placed on it. In addition, the shear in concrete has to be check to make sure it has the capacity and if it doesn’t, doesn’t, stirrups are used to raise the shear capacity to at or above the ultimate strength design of the section. In any case, steel stirrups are always placed in concrete beams. Also, if an engineer is doing a moment frame in concrete or steel, they have to understand how bending moments and shear should look like in the frame. In today’s world, today’s world, the structural engineer uses software to do all the calculation but if they do not know what a bending moment or shear diagram looks like in a loading condition, the analysis is null. Bending moment and shear diagrams are used all the time by engineers design bridges, buildings, boats, cars, planes and any type of structure that has to resist forces.

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12. Contribution of team members

Task Allocation for SHEAR FORCE Work to be

Work

submitted on

submitte submitte d on

Abstract, Introducti Introduction, on, Limitation, recomm rec ommendation,health endation,health and Kavi Ka vish, sh, Rujub Rujub safety, dissemination of and Saif knowledge.contri knowledge.c ontributi bution on of o f team tea m members members and conclusion conclusion

16.04.15

16.04.15

Anusha, Abhishek and Lionel

15.04.15

18.04.15

Task

Literature Review, Methodology and results

Student

Figure 5

13. Conclusion From the results of the experiment we can deduce that the experimental values of shear force are in agreement with the theoretical values calculated. There is a small percentage error in the reading which may be due to several limitations in this experiment; however the results are in consistent with the expected results. The experiment could be repeated with more loads to better compare the results. Overall the experiment was a success and help us a lot to better understand the action of shear force a beam and how to apply this knowledge in practice.

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Experiment Shearing Forces

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