Faculty : Civil Engineering And Environment Engineering

Page 01

Department : Structure And Material Engineering

Edition 2

Checking No

Title : BENDING MOMENT IN A BEAM Effective Date

Amendment Date

INTRODUCTION

A structural member which is long when compared with its lateral dimensions, subjected to transverse forces so applied as to induce bending of the member in axial plane and it is called beam.

Bending moment is the algebraic sum of the moment of the forces to the left or to the right of the section taken about the section.

1.0 OBJECTIVE

1.0 To examine how bending moment varies with an increasing point load1.1 To examine how bending moment varies at the cut position of the beam for various

loading condition

2.0 LEARNING OUTCOME

2.0 To application the engineering knowledge in practical application2.1 To enhance technical competency in structural engineering through laboratory

application2.2 To communicate effectively in group

2.4 To identify problem, solving and finding out appropriate solution through laboratory application

3.0 THEORY W

RA a ‘cut’ RB

C

L

Moment at the cut section, Mc = Wa (L-a) . . . equation 1

L

PART 2 :

Use the statement:

“ The bending moment at the ‘ cut ‘ is equal to the algebraic sum of the moment of force acting to the left or to the right of the cut “

4.0 PROCEDURE

PART 11. Digital Force Display meter read was reads zero with no load.2. A hanger with mass 100g was placed to the left of the ‘cut’. Digital Force Display data was

recorded into the table 1. The work was repeated using any masses between 200g and 500g.3. Mass that changed into a load in Newton ( multiply by 9.81 ) and the force reading into a

bending moment (Nm) and used the following expression :Bending moment at a cut (Nm) = Displayed Force x 0.125

4. Theoretical bending moment was calculated in fill into the table 1.

PART 2

1. Digital Force Display with meter zero with no load was checked.2. Beam with the hangers in any positions and loads as example in Figure 2, Figure 3 and Figure 4

was carefully load and complete the table 2.3. The force reading was into bending moment (Nm) using :

Bending moment at a cut (Nm) = Displayed Force x 0.125

4. Support reaction (RA and RB) and theoretical bending moment at the cut was calculated.

Figure 1

Figure 2

Figure 3

5.0 RESULT

Mass (g)

Load(N)

Force(N)

Experimental Bending

Moment (Nm)

Theoretical Bending

Moment (Nm)0 0 0 0 0

100 0.981 0.7 0.088 0.107200 1.962 1.4 0.175 0.214300 2.943 2.0 0.250 0.321400 3.984 2.6 0.325 0.428500 4.905 3.1 0.388 0.535

Table 1

No W1(N)

W2(N)

Force(N)

Experimental Bending

Moment (N)

RA(N)

RB(N)

Theoretical Bending Moment

2 400 0 -1.4 -0.175 1.962 1.962 0.4323 400 100 2.6 0.350 2.363 2.542 0.5204 400 100 2.7 0.338 1.873 3.032 0.464

Table 2

6.0 DISCUSSION

Part 11. Derive equation 1

∑ MR = 0 ∑ ML = 0

MR = - W ( x – a ) + RBx

MR – ML

-W ( x – a ) + RBx = -RAx

-W ( x – a ) = -RAx – RBx

W ( x – a ) = ( RA + RB )x SC = W ( L – a ) L

2. Comment on the shape of the graph. What does it tell you about how bending moment varies due to an increased load?The result of the bending moment varies due to an increased load is directly proportional. This is because when the weight of load is added. The load of weight affects the value of force and the value of bending moment. The bending moment will get higher either in theoretical bending or experimental bending result but the two of the value slightly different value when calculated and sketch on the graph because the theoretical bending is higher than experimental bending moment.

3. Does the equation you used accurately predict the behavior of the beam?Yes. It is because when the weight of load is added, the bending moment of beam will increased too and it will deflect when reach the maximum point load

PART 2

1. Comment on how the results of the experiments compare with those calculated using the theory.The result of the experimental is lower than the theoretical. When applied loads act along a beam, an internal bending moment which varies from point along the axis of the beam is developed. A bending moment is an internal force that is induced in a restrained structural element when external forces are applied. This may be due to some problem that affect our experiment :

1. The readings we take maybe affected by surrounding. This is because the digital force are very sensitive and our member group was touched the apparatus during the experiment happen. So, the reading has an error value each of them.

2. There can be error in the practical readings, possible instruments error, reading error since the values keep on changing for all the members.

3. The reading of the distance of load from support not taken accurately.

2. Does the experiment proof that the moment at the ‘cut ‘is equal to the algebraic sum of the moment of force acting to the left or right of the cut. If not, why?Tests carried out has proved the thesis which states that the moment at a ‘cut’ section of a beam is equal to the algebraic sum of the forces acting to the left or right of the section’.

3. Plot the moment force diagram for load cases in Figure 2, 3 and 4

4. Comment on the shape of the graph. What does it tell you about how Bending Moment varies due to an increased load?From the shape of the graph, we know the value of bending moment depend on the location of the imposed load were placed. Different value of load will get different value of bending moment also and when the load was added, the bending moment value will increased too.

7.0 CONCLUSION

By doing this experiment, we able to prove that the theory of the bending moment at the ‘ cut ‘ section either the right or the left and the value of ‘ x ‘ will be same. Moreover, we will be able to know about the relationship between point load deflection and bending moment. The relationships bending moment is directly proportional to the point load.

8.0 APPENDIX