TABLE OF CONTENT
Content
Page
Person In Charge
1
Umar Akhyar
2-3
Alif Adham
4-6
Abid Amsyari
7
Together
Introduction
Objectives
Learning Outcome
Theoretical Background
Problem statement
Apparatus
Procedure
Results
Analysis
Discussion
Conclusion
TITLE: LAB 2A: REACTION, BENDING MOMENT
AND SHEAR FORCE
1.1 INTRODUCTION
Level 0 laboratory activities refer to condition where the problem and ways & means are
guided and given to the students. However, the answers to the assignment are left to the
students to solve using the group creativity and innovativeness. The activity is designed to
slowly introduce and inculcate independent learning amongst student and prepare them for a
much harder task open-ended laboratory activity.
In this laboratory activity, students will be exposed on the beams experiments for determine
reaction, bending moment and shear force for simply supported and cantilever beams.
1.2 OBJECTIVES
The objective of the experiment is:
To determine the relations among reaction, bending moment and shear force in
simply supported beam.
1.3 LEARNING OUTCAMES
At the end of the laboratory activities, students would be able to:



Identify and use the correct apparatus/tools to carryout experiment on beams;
Work in a group to undertake the task; and
Collect and analyse the data correctly and produce the technical report.
1.4 THEORATICAL BACKGROUND
A beam is subjected to external forces. These are the loads applied to the beam and
reactions to the loads from the supports. The beam transfers the external load set to the
external reaction set by a system of internal forces.
The internal forces as a result of the structural action of the beam are called bending
moments and shear forces. These internal forces may vary along the length of the beam and
are usually represented as separate bending moment and shear force diagrams.
i.
Shear Force
When the load is to the left of x – x,
Shear force at section x – x is;
𝑆𝐹𝑥−𝑥 = 𝑊1 − 𝑅𝐴
Or,
𝑆𝐹𝑥−𝑥 = 𝑅𝐵
= (𝑊 × 𝐿1 )/𝐿
When load is to the right of x – x,
𝑆𝐹𝑥−𝑥 = 𝑅𝐴
= (𝑊 × (𝐿 − 𝐿1 ))/𝐿
ii.
Bending Moment
When the load is to the left of x – x,
Bending moment at section x – x is;
𝐵𝑀𝑥−𝑥 = 𝑊1 𝐿1 − 𝑅𝐴 𝐿𝑋
Or
𝐵𝑀𝑥−𝑥 = 𝑅𝐵 𝐿2
When the load is to the right of x – x,
𝐵𝑀𝑥−𝑥 = 𝑅𝐴 𝐿𝑋
2.1 PROBLEM STATEMENT
Although computers are efficient for structural analysis, it is important for students to be well
versed in the theory and not to simply rely on the computer outputs. Ability to solve structural
analysis problems will come in handy for verifying the computer results. On the other hand,
conducting experiments in the lab can help to develop a deeper understanding of the
mechanics of structures. One can better grasp the way loads are transmitted through
structures and obtain a more complete understanding of the way they deform.
In this experiment, the group will explore the behaviour of various types of beams under
loads to determine their support reaction, bending moment and shear force. The group may
use any suitable software as a tool for understanding the relations between the external and
internal forces.
3.1 APPARATUS
a) Simple Supported Beam
i.
A pair of Simple supports
ii.
Special beam with a cut section.
iii.
A set of weights with several load hangers.
iv.
Digital Force Indicator
3.2 PROCEDURE
a) Simply Supported Beam
i.
The load cell is connected to the digital indicator.
ii.
The indicator is switched on. The reading of indicator is taken after the switch is on
for 10 minutes.
iii.
The two simple supports are fixed to the aluminium base at the distance equal to the
span of the beam to be tested. The support to the base is screwed tightly.
iv.
The load hanger is hanged to the beam.
v.
The beam is placed to the supports.
vi.
The load hanger is placed at 625 mm from the left support.
vii.
The indicator reading is taken. If it is zero, the tare button is pressed on the indicator.
viii.
A load of 5N is placed at the load hanger.
ix.
The indicator reading is taken. This represents the shear force/ force at the cut
section.
x.
Load is added to the load hanger and indicator reading is taken.
xi.
Step 1 to 10 is repeated for another 5 set of readings.
3.3 RESULTS
i.
a) Simple Supported Beam
𝑆ℎ𝑒𝑎𝑟 𝑓𝑜𝑟𝑐𝑒
𝐵𝑒𝑎𝑚 𝑆𝑝𝑎𝑛 = 895 𝑚𝑚
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑠ℎ𝑒𝑎𝑟 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡 𝑠𝑢𝑝𝑝𝑜𝑟𝑡 = 605 𝑚𝑚
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑜𝑎𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡 𝑠𝑢𝑝𝑝𝑜𝑟𝑡 = 312 𝑚𝑚
Table 1 : Shear Force for simply supported beam results
Load (N)
2
4
6
8
10
Shear force At X-X
Experimental Load Cell
Theory 𝑅𝐵 (N)
(N)
0.4
0.697
1.2
1.394
2.0
2.092
3.0
2.789
3.8
3.486
ii.
Bending Moment
𝐵𝑒𝑎𝑚 𝑆𝑝𝑎𝑛, 𝐿 = 895 𝑚𝑚
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑢𝑡 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡 𝑠𝑢𝑝𝑝𝑜𝑟𝑡, 𝐿𝑋 =395 mm
𝐷𝑠𝑖𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑜𝑎𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡 𝑠𝑢𝑝𝑝𝑜𝑟𝑡, 𝐿1 = 625 mm
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑜𝑎𝑑 𝑐𝑒𝑙𝑙 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑒𝑎𝑚 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 = 175 𝑚𝑚
Table 2: Bending Moment for simply supported beam results.
Load (N)
5
10
15
20
25
Load Cell Reading F (N)
0.7
1.7
3.1
4.5
6.0
4.1 ANALYSIS
Theory shear Force for simply supported beam;
𝑆𝐹𝑥−𝑥 = 𝑅𝐵
= (𝑊 × 𝐿1 )/𝐿
Example;
𝑅𝐵 =
2 × 312
895
= 0.697
Theory bending Moment for simply supported beam;
𝑆𝐹𝑥−𝑥 = 𝑅𝐴
= (𝑊 × (𝐿 − 𝐿1 ))/𝐿
𝐵𝑀𝑥−𝑥 = 𝑅𝐴 𝐿𝑋
Bending Moment at A X-X
Experimental
= f * 175 mm
122.5
297.5
542.5
787.5
1050.0
Theory
(Nmm)
595.660
1191.715
1787.375
2383.035
2979.090
Example;
𝑅𝐴 = (5 × (895 − 625))/895
= 1.508
𝐵𝑀𝑥−𝑥 = 𝑅𝐴 𝐿𝑋
= 1.508(395)
= 595.81
4.2 DISCUSSION
From this laboratory experiment, we could identify and use the correct apparatus and tools
to carry out experiment on beams. Besides that, we could also work in group to undertake
the task smoothly with the supervise of the lab technician. From this activity, the accuracy of
the experiment shear force for simply supported beam has an average of 77.84% which
makes it not so distance between the experimented and the theory accuracy. Adding on, the
accuracy for bending moment for simply supported beam has the average of 20% accuracy
between experimental and theory. The accuracy of shear force and bending moment
experiment can be affected by several factors. The equipment used in the experiment should
be calibrated regularly to ensure that it is providing accurate measurements. If the
equipment is not calibrated correctly, it can lead to inaccurate readings. Furthermore,
Parallax error can occur when the observer's eye is not at the same level as the pointer or
scale being read. This can lead to inaccurate readings, and it can occur if the operator is not
careful about their position relative to the measuring equipment. Lastly, Improper alignment
of the apparatus. If the apparatus used in the experiment is not aligned properly, it can affect
the readings of the shear force and bending moment. This can happen if the operator is not
careful when setting up the equipment.
4.3 CONCLUSION
In this experiment, we can conclude that when a load is applied to a beam, it undergoes
deformation or deflection. The amount of deflection depends on the magnitude and type of
load, the length of the beam, the material properties of the beam, and the support conditions.
In a shear force and bending moment lab experiment, a load is applied to the beam, and the
resulting shear force and bending moment are measured at different points along the beam.
Shear force is the force acting perpendicular to the longitudinal axis of the beam, and
bending moment is the moment that tends to bend the beam about an axis perpendicular to
its longitudinal axis.
The load causes the beam to deform and bend, and this results in shear force and bending
moment. The magnitude of the shear force and bending moment at a point along the beam
depends on the load and the location of the point. By measuring the shear force and
bending moment at different points along the beam, the experiment provide insight into the
behaviour of the beam under load.
In this lab, we are using only simple supported beam and not cantilever beam. In the result,
we can see that the higher the load the higher shear force and bending moment. The
reaction force at each support is equal and opposite to the load, and acts perpendicular to
the support.