Bending Moment In A Beam 5e6v1i

FACULTY OF CIVIL ANG ENVIRONMENTAL ENGINEERING DEPARTMENT OF STRUCRURE AND MATERIAL ENGINEERING LAB STRUCTURE

FULL REPORT Subject Code

BFC21201

Code & Experiment Title

BENDING MOMENT IN A BEAM

Course Code

2 BFF

Date

20 SEPTEMBER 2011

Group

GROUP

Name

MUHAMAD ASYRAF BIN AB MALIK (DF100108)

of Group

1. MUHAMMAD IKHWAN BIN ZAINUDDIN (DF100018) 2. AHMAD FARHAN BIN RAKAWI (DF100142) 3. IDAMAZLIZA BT ISA (DF100128) 4. AINUN NAZHIRIN BINTI ABDUL JALIL (DF100076)

Lecturer/Instructor/Tutor EN MOHAMMAD HAIRI BIN OSMAN Received Date

27 SEPTEMBER 2011

Mark

Theory & Objective

/ 20%

Data Analysis

/ 25%

Result

/ 20%

Discussion

/ 20%

Conclusion

/ 10%

References

/ 5%

TOTAL

/ 100%

Comment by examiner

Received

STUDENT CODE OF ETHIC (SCE) DEPARTMENT OF STRUCTURE AND MATERIAL ENGINEERING FACULTY OF CIVIL & ENVIRONMENTAL ENGINEERING

UTHM I, hereby confess that I have prepared this report on my own effort. I also it not to receive or give any help during the preparation of this report and pledge that everything mentioned in the report is true.

___________________________ Student Signature Name

: MUHAMAD ASYRAF BIN AB MALIK

Matric No. : DF100108 Date

: 20/09/2011

STUDENT CODE OF ETHIC (SCE) DEPARTMENT OF STRUCTURE AND MATERIAL ENGINEERING FACULTY OF CIVIL & ENVIRONMENTAL ENGINEERING

UTHM I, hereby confess that I have prepared this report on my own effort. I also it not to receive or give any help during the preparation of this report and pledge that everything mentioned in the report is true.

___________________________ Student Signature Name

: MUHAMMAD IKHWAN BIN ZAINUDDIN

Matric No. : DF100018 Date

: 20/09/2011

STUDENT CODE OF ETHIC (SCE) DEPARTMENT OF STRUCTURE AND MATERIAL ENGINEERING FACULTY OF CIVIL & ENVIRONMENTAL ENGINEERING

UTHM I, hereby confess that I have prepared this report on my own effort. I also it not to receive or give any help during the preparation of this report and pledge that everything mentioned in the report is true.

___________________________ Student Signature Name

: AHMAD FARHAN BIN RAKAWI

Matric No. : DF100142 Date

: 20/09/2011

STUDENT CODE OF ETHIC (SCE) DEPARTMENT OF STRUCTURE AND MATERIAL ENGINEERING FACULTY OF CIVIL & ENVIRONMENTAL ENGINEERING

UTHM I, hereby confess that I have prepared this report on my own effort. I also it not to receive or give any help during the preparation of this report and pledge that everything mentioned in the report is true.

___________________________ Student Signature Name

: IDAMAZLIZA BT ISA

Matric No. : DF100128 Date

: 20/09/2011

STUDENT CODE OF ETHIC (SCE) DEPARTMENT OF STRUCTURE AND MATERIAL ENGINEERING FACULTY OF CIVIL & ENVIRONMENTAL ENGINEERING

UTHM I, hereby confess that I have prepared this report on my own effort. I also it not to receive or give any help during the preparation of this report and pledge that everything mentioned in the report is true.

___________________________ Student Signature Name

:

Matric No. : DF100 Date

: 20/09/2011

1.0

OBJECTIVE 1.1

To examine how bending moment varies with an increasing point load

1.2

To examine how bending moment varies at the cut position of the beam for various loading condition

2.0

LEARNING OUTCOME 2.1

To application the engineering knowledge in practical application

2.2

To enhance technical competency in structural engineering through laboratory application.

2.3

To communicate effectively in group

2.4

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

3.0

INTRODUCTION The bending moment at any point along the beam is equal to the area under the shear force diagram up to that point. (Note: For a simply-ed beam, the bending moment at the ends will always be equal to zero.) To calculate the bending moment the beam must be broken up into two sections: (a) one from x = 0 to x = L/2 and (b) the other from x = L/2 to x = L. The bending moment M(x) at any point x along the beam can be found by using the following equations:

Bending moment diagrams are simply plots of the bending moment (on the y-axis) versus the position of various points along the beam (on the x-axis). Thus, the following is the generalized bending moment diagram for the beam shown above. Bending moment diagrams are simply plots of the bending moment (on the y-axis) versus the position of various points along the beam (on the x-axis). Thus, the following is the generalized bending moment diagram for the beam shown above.

4.0

THEORY

Moment at the cut section, Mc = Mc 

WaL  a  ………….Equation 1 L

Part 2 Use This Statement : “The bending moment at the “cut” is equal to the algebraic sum of the moment of force acting to the left or right of the cut”

5.0

EQUIPMENTS

RA

RB

CUT SECTION

Figure 1: Apparatus for bending moment experiment

Figure 2 : Digital Force Display

Figure 3 : The Loader ( 1piece = 10 gram)

6.0

PROCEDURES 6.1

Part 1 6.1.1

Check the Digital Force Display meter reads zero with no load.

6.1.2

Place a hanger with a 100g mass to the left of the ‘cut’.Record the Digital Force Display reading in Table 1. Repeat using any masses between 200 g and 500 g.

6.1.3

Convert the mass into a load in Newton ( multiply by 9.81 ) and the force reading into a bending moment (Nm) using the following expression: Bending Moment at the cut (N) = Displayed Force x 0.125

6.1.4

Calculate the theoretical Bending Moment at the cut and complete Table 1

Figure 5: Hanger With A 100g Mass

6.2

Part 2 6.2.1

Check the Digital Force Display meter zero with no load.

6.2.2

Carefully load the beam with the hangers in any positions and loads as example in Figure 2, Figure 3 and Figure 4 and complete Table 2.

6.2.3

Convert the force reading into bending moment (Nm) using: Bending moment at a cut (Nm) = Displayed Force x 0.125

6.2.4

Calculate the reaction (RA and RB) and calculated the theoretical bending moment at the cut.

Diagram 1: W1 with 0.98 N

Diagram 2: W1 with 0.98 N and W2 with 1.96 N

Diagram 3: W1 with 0.98 N and W2 with 1.96 N

7.0

RESULTS

Mass

Load

Force

Experimental Bending

Theoretical Bending

(g)

( N)

(N)

Moment (Nm)

Moment (Nm)

0

0

0

0

0

100

0.98

0.7

0.0875

0.0935

200

1.96

1.3

0.1625

0.1871

300

2.94

2.0

0.2500

0.2806

400

3.92

2.5

0.3125

0.3742

500

4.90

3.1

0.3875

0.4677

Table 1

No

W1

W2

Force

Experimental Bending

RA

RB

Theoretical Bending

(N)

(N)

(N)

Moment (Nm)

(N)

(N)

Moment (Nm)

1.

3.92

0

1.3

0.1625

5.17

-1.25

0.1738

2.

3.92

0.98

2.7

0.3375

2.36

2.54

0.3552

3.

3.92

0.98

2.5

0.3125

1.87

3.03

0.3258

Table 2

8.0

ANALYSIS DATA Calculation for Theoretical Bending Moment value.

Part 1 Moment at the cut section , Mc  Example: W=1N

Mc 

0.98 N (0.3m)(0.44m  0.3m) 0.44m

Mc  0.0935Nm

WaL  a  L

Part 2 Example : W= 3.92 N & W=0 N

To calculate the reaction RA and RB : ∑MA = 0 N -3.92N(0.14m)-RB(0.44m) = 0 RB = -1.25N ∑Fy = 0 N RA + RB = 3.92 N RA = 3.92 + 1.25 = 5.17 N

Mc = 5.17 ( 0.44-0.14 ) – 3.92 ( 0.44) Mc = -0.1738 Nm

9.0

DISCUSSION Part 1 1.0

Derive equation 1 +↑∑Fy =

0

+ ∑MA = 0

+↑∑Fy =

R A + RB – W

+ ∑MA = Wa - RBL RB =

Wa L

RA +

Wa -W=0 L

RA = W -

Wa L

RA =

WL Wa L L

RA =

W L  a  L

Mc = RA.a

Mc 

2.0

WaL  a  L

Plot a graph, which compare your experimental result to those you calculated using theory. Refer graph of load versus bending moment figure 1

3.0

Comment on the shape of the graph. What does it tell you about how bending moment varies due to an increased load? From the graph, we can get a linear graph type. When the loads increase, the bending moment will be increase too. This is because, from the normal formula bending moment =Applied Load (P) X Distance. Then, when P is increase, bending moment will increase too. So, this is almost same with the experimental value.

4.0

Does the equation you used accurately predict the behavior of the beam? Yes, from the graph, we know that value between experimental bending moment and theoretical bending moment is almost same the different percentage is only 12.24%. Different percentage when load = 2.943N

0.2806  0.2500 x100% 0.2500  12.24% 

Part 2 1.0

Comment on how the results of the experimental compare with those calculated using the theory. From the result of the experiments, for figure 2 (value bending moment is 0.1625Nm), for figure 3 (value bending moment is 0.3375Nm) and for figure 4 (value bending moment is 0.3125Nm). Compare with using theory method, for figure 2 (bending moment is 0.1738Nm), for figure 3 (value bending moment is 0.3552Nm) and for figure 4 (bending moment is 0.3258Nm).

Different percentage for figure 2

0.1738  0.1625 x100% 0.1625  6.95% 

Different percentage for figure 3

0.3552  0.3375 x100% 0.3375  5.24% 

Different percentage for figure 3

0.3258  0.3125 x100% 0.3125  4.26% 

2.0

Does the experimental 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? Yes, because the bending moment can be calculate based on the data distance. This can be proven by our experiment that distance effect the bending moment.when we look at the different percentage all experiment is small.

3.0

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

MC = 0 MA= - 3.92 (0.14) = - 0.549 MB = - 3.92(0.58) + 5.168(0.44) = 0

OK!!

Figure 3

MA = 0 MC = 2.36 ( 0.22 ) = 0.519 MD = 2.36 ( 0.26 ) – 3.92 ( 0.04 ) = 0.457 MB = 2.36 ( 0.44 ) – 3.92 ( 0.22 ) – 0.98 ( 0.18 ) = 0

OK!!

Figure 4

MA = 0 MC = 1.88 ( 0.24 ) = 0.451 MD = 1.88 ( 0.4 ) – 3.92 ( 0.16 ) = 0.125 MB = 1.88 ( 0.44 ) – 3.92 ( 0.2 ) – 0.98 ( 0.04 ) = 0

OK!!

4.0

Comment on the shape of the graph. What does it tell you about how bending moment varies due to an increased load? From the bending moment diagram we sketch, for the figure 2 (the value bending moment that we can get at the cut is 0.1625Nm), for figure 3 (the value bending moment that we can get at the cut is 0.3375Nm) and for figure 4 (the value bending moment that we can get at the cut is 0.3125Nm). So, we can tell that when the same load applies at the different distance will affect the bending moment value. The value of load is depending to the distance of beam.

10.0

CONCLUSION In conclusion, we can conclude, this experiment proves that the theory of bending moments can be proved by an experiment conducted in the laboratory. Things that affect the value of the bending moment can also be identified.