1) The document is a lecture on transverse loading on beams and stresses in beams. It covers beam types, shear force and bending moment diagrams, stresses due to bending and shear, and analysis of determinate beams.
2) The lecture defines key concepts like shear force, bending moment, sagging and hogging moments. It demonstrates calculation of bending stresses and shear stresses in beams.
3) Various beam examples are presented including cantilever beams, simply supported beams, overhanging beams, and composite beams. Bending stresses are calculated for different beam loadings and sections.
Springs - DESIGN OF MACHINE ELEMENTS-IIDr. L K Bhagi
Introduction to springs, Types and terminology of springs, Stress and deflection equations, Series and parallel connection, Design of helical springs, Design against fluctuating load, Concentric springs, Helical torsion springs, Spiral springs, Multi-leaf springs, Optimum design of helical spring
Springs - DESIGN OF MACHINE ELEMENTS-IIDr. L K Bhagi
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This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
This section will introduce how to solve problems of axially loaded members such as stepped and tapered rods loaded in tension. The concept of strain energy will also be introduced.
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
This section will introduce how to solve problems of axially loaded members such as stepped and tapered rods loaded in tension. The concept of strain energy will also be introduced.
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Motion and deformation of material under action of
Force
Temperature change
Phase change
Other external or internal agents
These changes lead us to some properties that are called Mechanical properties
Some of the Mechanical Properties
Ductility
Hardness
Impact resistance
Fracture toughness
Elasticity
Fatigue strength
Endurance limit
Creep resistance
Strength of material
Ductility: ductility is a solid material's ability to deform under tensile stress
Hardness of a material may refer to resistance to bending, scratching, abrasion or cutting.
Impact resistance is the ability of a material to withstand a high force or shock applied to it over a short period of time
Plasticity: ability of a material to deform permanently by the
Informacion de vigas y la forma de análisis solución de problemáticas referente a las vigas y su formulación matemática y analítica. Teniendo en cuenta cada una de sus variables como inercia, fuerzas cortantes, flexiones entre muchas más. También se muestran casos de la vida real donde se realiza mal análisis de vigas.
This unit covers Types of stresses & strains,
Hooke’s law, stress-strain diagram,
Working stress,
Factor of safety,
Lateral strain,
Poisson’s ratio, volumetric strain,
Elastic moduli,
Deformation of simple and compound bars under axial load,
Analysis of composite bar with varying cross section.
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Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
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Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
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An Approach to Detecting Writing Styles Based on Clustering Techniquesambekarshweta25
An Approach to Detecting Writing Styles Based on Clustering Techniques
Authors:
-Devkinandan Jagtap
-Shweta Ambekar
-Harshit Singh
-Nakul Sharma (Assistant Professor)
Institution:
VIIT Pune, India
Abstract:
This paper proposes a system to differentiate between human-generated and AI-generated texts using stylometric analysis. The system analyzes text files and classifies writing styles by employing various clustering algorithms, such as k-means, k-means++, hierarchical, and DBSCAN. The effectiveness of these algorithms is measured using silhouette scores. The system successfully identifies distinct writing styles within documents, demonstrating its potential for plagiarism detection.
Introduction:
Stylometry, the study of linguistic and structural features in texts, is used for tasks like plagiarism detection, genre separation, and author verification. This paper leverages stylometric analysis to identify different writing styles and improve plagiarism detection methods.
Methodology:
The system includes data collection, preprocessing, feature extraction, dimensional reduction, machine learning models for clustering, and performance comparison using silhouette scores. Feature extraction focuses on lexical features, vocabulary richness, and readability scores. The study uses a small dataset of texts from various authors and employs algorithms like k-means, k-means++, hierarchical clustering, and DBSCAN for clustering.
Results:
Experiments show that the system effectively identifies writing styles, with silhouette scores indicating reasonable to strong clustering when k=2. As the number of clusters increases, the silhouette scores decrease, indicating a drop in accuracy. K-means and k-means++ perform similarly, while hierarchical clustering is less optimized.
Conclusion and Future Work:
The system works well for distinguishing writing styles with two clusters but becomes less accurate as the number of clusters increases. Future research could focus on adding more parameters and optimizing the methodology to improve accuracy with higher cluster values. This system can enhance existing plagiarism detection tools, especially in academic settings.
An Approach to Detecting Writing Styles Based on Clustering Techniques
Strength of Materials
1. STRENGTH OF MATERIALS FOR
MECHANICAL ENGINEERS (CE8395)
Unit-2
(TRANSVERSE LOADING ON BEAMS AND
STRESSES IN BEAM)
by
Dr. B. Janarthanan
Professor & Head (Research)
Department of Mechanical Engineering
Mohamed Sathak A.J. College of Engineering
08-04-2021 1
2. 08-04-2021 Dr. B. Janarthanan 2
1. To understand the concepts of stress, strain, principal
stresses and principal planes.
2. To study the concept of shearing force and bending
moment due to external loads in determinate beams
and their effect on stresses.
3. To determine stresses and deformation in circular
shafts and helical spring due to torsion.
4. To compute slopes and deflections in determinate
beams by various methods.
5. To study the stresses and deformations induced in thin
and thick shells.
Course Objectives:
3. 08-04-2021 Dr. B. Janarthanan 3
Students will be able to
1. Understand the concepts of stress and strain in simple and
compound bars, the importance of principal stresses and
principal planes.
2. Understand the load transferring mechanism in beams and
stress distribution due to shearing force and bending
moment.
3. Apply basic equation of simple torsion in designing of shafts
and helical spring
4. Calculate the slope and deflection in beams using different
methods.
5. Analyze and design thin and thick shells for the applied
internal and external pressures.
Course outcomes
4. Syllabus Unit-2
UNIT II TRANSVERSE LOADING ON
BEAMS AND STRESSES IN BEAM
Beams – types transverse loading on
beams – Shear force and bending moment
in beams – Cantilevers – Simply supported
beams and over –hanging beams. Theory
of simple bending– bending stress
distribution – Load carrying capacity –
Proportioning of sections – Flitched beams
– Shear stress distribution.
08-04-2021 Dr. B. Janarthanan 4
8. Shear force and Bending Moment
• Shear force
– The shear force at any section is basically the
algebraic sum of the lateral forces acting on either
side of the section.
• Bending moment
– The algebraic sum of the moments about the
section of all forces acting on either side of the
section
08-04-2021 Dr. B. Janarthanan 8
9. Bending moment – sagging and
hogging
• A sagging moment will make the beam
concave (positive) upwards at that section,
and vice versa for a hogging moment (i.e.
negative).
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10. Sign conventions
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Positive shear force
Negative shear force
Positive axial force
Negative axial force
Positive bending moment
Negative bending moment
11. Relation between load intensity, shear
force and bending moment
• The shear force is equal to the rate of change of
bending moment with respect to x.
𝐅 =
𝐝𝐌
𝐝𝐱
• Slope of the moment curve = Shear Force
• The intensity of loading is equal to rate of change of
shear force with respect to x.
𝐖 = −
𝐝𝐅
𝐝𝐱
= −
𝐝𝟐
𝐌
𝐝𝐱𝟐
Slope of the shear diagram = - Value of applied
loading
08-04-2021 Dr. B. Janarthanan 11
18. SFD and BMD for Simply supported beams
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19. SFD and BMD for Simply supported
beams
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20. SFD and BMD for Simply supported
beams
08-04-2021 Dr. B. Janarthanan 20
21. SFD and BMD for Simply supported
beams
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22. SFD and BMD for Simply supported
beams
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23. SFD and BMD for Simply supported
beams
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The maximum bending moment occurs in a beam, when
the shear force at that section is zero or changes the sign
24. Maximum Bending Moment
08-04-2021 Dr. B. Janarthanan 24
Draw the Shear Force Diagram and Bending Moment Diagram for a simply
supported beam of length 8m and carrying a uniformly distributed load of 10 kN/m
for a distance of 4m as shown in figure.
25. SFD and BMD for Simply supported
beams
08-04-2021 Dr. B. Janarthanan 25
27. Over hanging beam
• Draw the SFD and BMD for the overhanging beam carrying
UDL of 2 kN/m over the entire length and a point load of 2 kN
as shown in Fig. Also locate the point of contraflexure
08-04-2021 Dr. B. Janarthanan 27
28. Point of contraflexure
• POINT OF CONTRAFLEXURE
• It is the point on a beam where bending
moment changes its sign and its
value is zero. This point is generally
found in over hanging beam.
08-04-2021 Dr. B. Janarthanan 28
39. • Bending stress
– The stresses produced at the section to resist
bending moment
• Shear stress
– The stresses produced at the section to resist
the shear force
08-04-2021 Dr. B. Janarthanan 39
44. • A cantilever 4 metres long is subjected to a UDL of 1 kN per
metre run over the entire span. The section of the cantilever is
40 mm wide and 60 mm deep. Determine the bending stress
produced. What point load may be applied at the free end to
produce the same bending stress?
08-04-2021 Dr. B. Janarthanan 44
46. • A cantilever 3 m long carries a UDL of 1 kN per metre run over the
whole span. The cross section of the beam is rectangular 60 mm
wide and 100 mm deep with a circular hole of 20 mm diameter at the
centre. Determine the maximum bending stress induced in the beam
08-04-2021 Dr. B. Janarthanan 46
47. • A rectangular beam 120 mm deep and 60 mm wide is simply
supported over a span of 4 m and carries a central load of 10 kN.
Determine the maximum fibre stress in the beam. Also calculate the
stress at a fibre 15 mm from the top surface of the beam.
08-04-2021 Dr. B. Janarthanan 47
48. • A cast iron beam is of T-section as shown in Fig. the beam is simply
supported on a span of 8 m. the beam carries a UDL of 1.5 kN/m
length on the entire span. Determine the max. tensile and max.
compressive stresses.
08-04-2021 Dr. B. Janarthanan 48
49. • A 100 mm x 200 mm rolled steel joist of I-section has flanges
12 mm thick and web 10 mm thick. Find the safe uniformly
distributed load that this section can carry over a span of 6 m
if the permissible skin stress is limited to 160 N/mm^2.
08-04-2021 Dr. B. Janarthanan 49
50. Flitched beam or composite beam
08-04-2021 Dr. B. Janarthanan 50
51. Flitched beam or composite beam
08-04-2021 Dr. B. Janarthanan 51
52. Flitched beam or composite beam
08-04-2021 Dr. B. Janarthanan 52
53. Flitched beam or composite beam
08-04-2021 Dr. B. Janarthanan 53
54. Flitched beam or composite beam
08-04-2021 Dr. B. Janarthanan 54
55. Shear stresses
• 𝜏 =
𝐹𝐴 ത
𝑦
𝐼𝑏
=
𝑄𝐴 ത
𝑦
𝐼𝑏
=
𝑄𝑉
𝐼𝑏
• Where
• F or Q is shear force
• 𝐴 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠ℎ𝑎𝑑𝑒𝑑 𝑝𝑜𝑟𝑡𝑖𝑜𝑛
• ത
𝑦 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑁𝐴 𝑡𝑜 𝑡ℎ𝑒 𝑐𝑒𝑛𝑡𝑟𝑜𝑖𝑑 𝑜𝑓 𝑠ℎ𝑎𝑑𝑒𝑑 𝑎𝑟𝑒𝑎
• 𝑉 = 𝐴ത
𝑦 = moment of shaded area about NA
• 𝐼 = 𝑀𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝐼𝑛𝑒𝑟𝑡𝑖𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑛𝑡𝑖𝑟𝑒 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 𝑎𝑏𝑜𝑢𝑡 𝑁𝐴
• 𝑏 = 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑖𝑏𝑟𝑒
08-04-2021 Dr. B. Janarthanan 55
67. Contact
Dr. B. Janarthanan
Professor & Head (Research)
Department of Mechanical Engineering
Mohamed Sathak A.J. College of Engineering
Email : vbjana@gmail.com,
mech.janarthanan@msajce-edu.in
08-04-2021 Dr. B. Janarthanan 67