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)

Members 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

FACULTY OF CIVIL ANG ENVIRONMENTAL

ENGINEERING

DEPARTMENT OF STRUCRURE AND

MATERIAL ENGINEERING

LAB STRUCTURE

FULL REPORT

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 admit 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 admit 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 admit 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 admit 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 admit 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-supported 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 = L

aLWaMc

………….Equation 1

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

Figure 1: Apparatus for bending moment experiment

Figure 2 : Digital Force Display Figure 3 : The Loader ( 1piece = 10 gram)

CUT SECTION

RA RB

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 support 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

(g)

Load

( N)

Force

(N)

Experimental Bending

Moment (Nm)

Theoretical Bending

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

(N)

W2

(N)

Force

(N)

Experimental Bending

Moment (Nm)

RA

(N)

RB

(N)

Theoretical Bending

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 , L

aLWaMc

Example:

W=1N

m

mmmNMc

44.0

)3.044.0)(3.0(98.0

NmMc 0935.0

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 +↑∑Fy = RA + RB – W

+ ∑MA = 0 + ∑MA = Wa - RBL

RB =L

Wa

RA + L

Wa- W = 0

RA = W - L

Wa

RA = L

WL-

L

Wa

RA =

L

aLW

Mc = RA.a

L

aLWaMc

2.0 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

%24.12

%1002500.0

2500.02806.0

x

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

%95.6

%1001625.0

1625.01738.0

x

Different percentage for figure 3

%24.5

%1003375.0

3375.03552.0

x

Different percentage for figure 3

%26.4

%1003125.0

3125.03258.0

x

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.