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Contents

1. Objective ........................................................................................................................................................... 2

2. Apparatus .......................................................................................................................................................... 2

3. Background Information ................................................................................................................................... 3

4. Procedure ........................................................................................................................................................... 3

5. Result ................................................................................................................................................................. 4

6. Discussion ......................................................................................................................................................... 5

7. Conclusion ......................................................................................................................................................... 6

8. References ......................................................................................................................................................... 6

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1. Objective1. To determine the relationship between the Bending Moment and the applied load.

2. The effect of variations in distance between hinge and centre line (X) on the Bending Moment.

2.Apparatus- Model beam hinged at the centre.

- Hinged gap to be closed by turnbuckle, spring balance and weights of kgf, beam support.

Figure 1.1 : Model Beam hinged at the centre

Figure 1.2 : Spring balance Figure 1.3 : Spirit level

Figure 1.4 : Load/ Weight of kgf Figure 1.5 : Measuring tape

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Diagram of Experimental Set-up

Theory :

Bending Moment in the beam at section A-A due to applied load (L) can be determined by the product

of the spring balance loading (W) and the distance between hinge and centre line (X).

3. Background InformationTensile stresses andcompressive stresses increase proportionally with bending moment, but are also

dependent on thesecond moment of area of the cross-section of the structural element. Failure in bending

will occur when the bending moment is sufficient to induce tensile stresses greater than theyield stress of

the material throughout the entire cross-section. It is possible that failure of a structural elementinshear may occur before failure in bending, however the mechanics of failure in shear and in bending are

different.

The bending moment at a section through a structural element may be defined as "the sum of the moments

about that section of all external forces acting to one side of that section". The forces and moments on either

side of the section must be equal in order to counteract each other and maintain a state ofequilibrium so the

same bending moment will result from summing the moments, regardless of which side of the section is

selected.

4. Procedure1. The model beam is supported on 2 points at equal distance from centre of hinge.2. Adjusted the turnbuckle to close gap until beam is horizontal by using a spirit level or straight edge.3. Recorded the reading on the spring balance.4. Next load the beam with 1kg weight at a distance L from on support, then repeated step 2 and

recorded the spring balance reading.

5. Repeated using loads of 2kgf and 3 kgf.6. Carried out the above procedure for all the three cases below.

http://en.wikipedia.org/wiki/Tensilehttp://en.wikipedia.org/wiki/Compressivehttp://en.wikipedia.org/wiki/Second_moment_of_areahttp://en.wikipedia.org/wiki/Yield_(engineering)http://en.wikipedia.org/wiki/Shearing_(physics)http://en.wikipedia.org/wiki/Dynamic_equilibriumhttp://en.wikipedia.org/wiki/Dynamic_equilibriumhttp://en.wikipedia.org/wiki/Shearing_(physics)http://en.wikipedia.org/wiki/Yield_(engineering)http://en.wikipedia.org/wiki/Second_moment_of_areahttp://en.wikipedia.org/wiki/Compressivehttp://en.wikipedia.org/wiki/Tensile

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L/4 p L/3

R1 Rr R1 Rr Rr

L L

Case 1 Case 2

L/4 P P L/3

R1 L Rr

Case 3

5. Result

Determine the reactions at the support for the 3 cases and hence find the Bending Moment, M.

Spring reading (kgf)Bending Moment (WX)

(kgf x cm)

Case of

loading

0 1 2 3 1 2 3

1 2.25 2.75 3.50 4.25 14.5 36.25 58.00

2 2.2.5 3.00 4.25 5.00 21.75 58.00 79.75

3 2.50 4.00 6.25 8.00 43.50 108.75 159.50

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1 kgf 2kgf 3kgf

Rr M M

(experimental)

Rr M M

(experimental)

Rr M M

(experimental)

Case 1 0.25 20 14.5 0.5 40 36.25 0.75 60 58

Case 2 0.67 26.41 21.75 1.33 53.6 58 2.0 80 79.75

Case 3 0.91 47.2 43.5 1.83 93.36 108.75 2.75 140 159.5

The bending moment of case 3 may be obtained by using the Principle of Superposition by superimpose

the bending moment of case 1 and case 2 together.

Case of loading 1kgf 2kgf 3kgf

Case 1 14.5 36.25 58

Case 2 21.75 58 79.75

Total (1+2) 36.25 94.25 137.75

Case 3 43.5 108.75 159.5

6. Discussiona) For each case. Construct the experimental and theoretical bending moment diagrams.

b) Compare the superimposed loading of case 1 and case 2 with case 3. Comment on results.

- The superimposed loading (case 1 plus case 2) is slightly different with the case 3 this is because theeffect of the parallax error. The theoretical result is different with the experimental result, theexperimental result is bigger than the theoretical result.

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7. ConclusionIn conclusion, The load increase the bending moment will increase, but the reaction on the bottom of beam wil

increase inconstantly due the position of the load applied on the beam.

8. References1. McMullan,R,(2007),Environmental Science in Building,6

thedition, New York, Palgrave Macmillam,

Resources & Chapters.

2. Nagem Hal, Durka, R, Morgan Williams D.T , Structural Mechanics Loads , Analysis, Design and

materials (1980), UK

3. Chudley, R. & Greeno, R. (2005) Construction Technology(4th

),published by Pearson Education Ltd,

Essex.

4. Domel A. W., (2000).Builders Portable Handbook. New York: McGraw Hill.

5. Denis R. H.,Building: The Process and Product. Published by The Construction Press