5035MAA – SOLID MECHANICS AND DYNAMICS
Course Work-1: LAB REPORTS
Dhruvesh Mahida
SID : 11821623
,dd
Contents
LAB-1: Solid Mechanics - Beam Stress and Deflection ............................................................................................................ 2
Abstract ................................................................................................................................................................................... 2
Introduction ............................................................................................................................................................................ 2
Theory ................................................................................................................................................................................. 2
Experimental Procedures ........................................................................................................................................................ 5
Apparatus ............................................................................................................................................................................ 5
Setup and Procedure........................................................................................................................................................... 5
Results ..................................................................................................................................................................................... 6
Experiment data collection ................................................................................................................................................. 6
Experimental Calculations................................................................................................................................................... 7
Analytical Calculations ........................................................................................................................................................ 7
Graphs ................................................................................................................................................................................. 9
Error calculations .............................................................................................................................................................. 10
Discussion.............................................................................................................................................................................. 13
Conclusions ........................................................................................................................................................................... 13
References ............................................................................................................................................................................. 14
Appendix (LAB-1): ................................................................................................................................................................. 15
Appendix A ........................................................................................................................................................................ 15
Appendix B ........................................................................................................................................................................ 15
Appendix C ........................................................................................................................................................................ 15
LAB-2: Dynamic - Balancing Rotating Masses ....................................................................................................................... 16
Abstract ................................................................................................................................................................................. 16
Introduction .......................................................................................................................................................................... 16
Theory ............................................................................................................................................................................... 16
Experimental Procedure........................................................................................................................................................ 19
Apparatus .......................................................................................................................................................................... 19
Set-up and Procedure ....................................................................................................................................................... 19
Results ................................................................................................................................................................................... 21
Graphical Method: ............................................................................................................................................................ 22
Analytical Method: ............................................................................................................................................................ 24
Discussion.............................................................................................................................................................................. 26
Conclusion ............................................................................................................................................................................. 26
References ............................................................................................................................................................................. 27
1
, LAB-1: Solid Mechanics - Beam Stress and Deflection
Abstract
In this experiment, the behaviour of the cantilever beam was observed when subjected to increasing and decreasing
loads to analyse stress, strain, and deflection. A comparison between the experimental and analytical calculations was
carried out, which revealed that there were minor differences due to some potential errors like human error, friction,
temperatures, etc. The error value of increasing and decreasing experimental deflection compared to analytical
deflection calculation was found to be 3.8% and 3.0%, respectively. The error value of increasing experimental stress
compared to analytical stress calculation was 3.49%. The graphs revealed that stress and deflection show a linear
load(weight) relationship. It indicated that the beam experienced increasing stress and deflection with increasing load.
Stress and strain also showed the same relationship. These findings emphasise the importance of precise measurements
and instrument calibration in structural analysis to help design safer structures and machines.
Introduction
Nowadays, there is a wide range of applications for beams, particularly in sectors like engineering and construction. It is
essential to analyse the stresses, strain and deflection experienced by the beams in various infrastructures and
machinery to prevent potential failures or avoid unnecessary wear and tear. Balconies, Roofs, and several other
overhangs are suitable applications of beam mechanics (Cantilever beam) to ensure stability. Even in aeronautical
industries, the geometry of a plane’s wing utilises cantilever beam design (Wings - Aircraft Structures, n.d.).
The primary aim of this experiment was to study the behaviour of the cantilever beam when subjected to increasing and
decreasing load, investigate the strain, stress, and deflection caused by the applied load and compare the experimental
and analytical calculations to provide a comprehensive assessment and discussed the possible factors that could make a
difference.
Theory
Before the actual beginning of the experiment, some of the essential working principles and theories utilised in the
further experiment to develop a better understanding have been mentioned below.
➢ Hooke’s Law: Stretching is directly proportional to the load applied, but if the load is removed, it reverts to its
original shape, known as the elastic region of a material (2004).
𝜎
𝐸=
𝜀
Equation 1 – Hooke’s Law (2004).
E = Young’s modulus, σ = stress and 𝜀 = strain
➢ Strain gauges – The strain gauge operates based on the principle discovered by Lord Kelvin in 1856 that the
electrical resistance of a wire changes when the wire is stretched (Tension) or compressed (Compression) (The
Editors of Encyclopaedia Britannica, 1998). The strain can be measured using resistance strain gauge due to the
material resistance of electrically conductive materials. The resistance of a material(R) is directly proportional to
its length(l) and resistivity (ρ) and inversely proportional to its cross-sectional area(A).
2
Course Work-1: LAB REPORTS
Dhruvesh Mahida
SID : 11821623
,dd
Contents
LAB-1: Solid Mechanics - Beam Stress and Deflection ............................................................................................................ 2
Abstract ................................................................................................................................................................................... 2
Introduction ............................................................................................................................................................................ 2
Theory ................................................................................................................................................................................. 2
Experimental Procedures ........................................................................................................................................................ 5
Apparatus ............................................................................................................................................................................ 5
Setup and Procedure........................................................................................................................................................... 5
Results ..................................................................................................................................................................................... 6
Experiment data collection ................................................................................................................................................. 6
Experimental Calculations................................................................................................................................................... 7
Analytical Calculations ........................................................................................................................................................ 7
Graphs ................................................................................................................................................................................. 9
Error calculations .............................................................................................................................................................. 10
Discussion.............................................................................................................................................................................. 13
Conclusions ........................................................................................................................................................................... 13
References ............................................................................................................................................................................. 14
Appendix (LAB-1): ................................................................................................................................................................. 15
Appendix A ........................................................................................................................................................................ 15
Appendix B ........................................................................................................................................................................ 15
Appendix C ........................................................................................................................................................................ 15
LAB-2: Dynamic - Balancing Rotating Masses ....................................................................................................................... 16
Abstract ................................................................................................................................................................................. 16
Introduction .......................................................................................................................................................................... 16
Theory ............................................................................................................................................................................... 16
Experimental Procedure........................................................................................................................................................ 19
Apparatus .......................................................................................................................................................................... 19
Set-up and Procedure ....................................................................................................................................................... 19
Results ................................................................................................................................................................................... 21
Graphical Method: ............................................................................................................................................................ 22
Analytical Method: ............................................................................................................................................................ 24
Discussion.............................................................................................................................................................................. 26
Conclusion ............................................................................................................................................................................. 26
References ............................................................................................................................................................................. 27
1
, LAB-1: Solid Mechanics - Beam Stress and Deflection
Abstract
In this experiment, the behaviour of the cantilever beam was observed when subjected to increasing and decreasing
loads to analyse stress, strain, and deflection. A comparison between the experimental and analytical calculations was
carried out, which revealed that there were minor differences due to some potential errors like human error, friction,
temperatures, etc. The error value of increasing and decreasing experimental deflection compared to analytical
deflection calculation was found to be 3.8% and 3.0%, respectively. The error value of increasing experimental stress
compared to analytical stress calculation was 3.49%. The graphs revealed that stress and deflection show a linear
load(weight) relationship. It indicated that the beam experienced increasing stress and deflection with increasing load.
Stress and strain also showed the same relationship. These findings emphasise the importance of precise measurements
and instrument calibration in structural analysis to help design safer structures and machines.
Introduction
Nowadays, there is a wide range of applications for beams, particularly in sectors like engineering and construction. It is
essential to analyse the stresses, strain and deflection experienced by the beams in various infrastructures and
machinery to prevent potential failures or avoid unnecessary wear and tear. Balconies, Roofs, and several other
overhangs are suitable applications of beam mechanics (Cantilever beam) to ensure stability. Even in aeronautical
industries, the geometry of a plane’s wing utilises cantilever beam design (Wings - Aircraft Structures, n.d.).
The primary aim of this experiment was to study the behaviour of the cantilever beam when subjected to increasing and
decreasing load, investigate the strain, stress, and deflection caused by the applied load and compare the experimental
and analytical calculations to provide a comprehensive assessment and discussed the possible factors that could make a
difference.
Theory
Before the actual beginning of the experiment, some of the essential working principles and theories utilised in the
further experiment to develop a better understanding have been mentioned below.
➢ Hooke’s Law: Stretching is directly proportional to the load applied, but if the load is removed, it reverts to its
original shape, known as the elastic region of a material (2004).
𝜎
𝐸=
𝜀
Equation 1 – Hooke’s Law (2004).
E = Young’s modulus, σ = stress and 𝜀 = strain
➢ Strain gauges – The strain gauge operates based on the principle discovered by Lord Kelvin in 1856 that the
electrical resistance of a wire changes when the wire is stretched (Tension) or compressed (Compression) (The
Editors of Encyclopaedia Britannica, 1998). The strain can be measured using resistance strain gauge due to the
material resistance of electrically conductive materials. The resistance of a material(R) is directly proportional to
its length(l) and resistivity (ρ) and inversely proportional to its cross-sectional area(A).
2
