The document covers Mohr's stress circle, which is a graphical method to determine normal and tangential stresses on an oblique plane for a material subjected to principal stresses and shear stresses. It also discusses different failure theories, including maximum principal stress, maximum principal strain, maximum shear stress, maximum strain energy, and maximum shear strain energy theories. The different theories predict failure based on the maximum values of stresses, strains, or strain energies for brittle versus ductile materials.
CONTENT:
1. Elastic strain energy
2. Strain energy due to gradual loading
3. Strain energy due to sudden loading
4. Strain energy due to impact loading
5. Strain energy due to shock loading
6. Strain energy due to shear loading
7. Strain energy due to bending (flexure)
8. Strain energy due to torsion
9. Examples
When a body is subjected to gradual, sudden or impact load, the body deforms and work is done upon it. If the elastic limit is not exceed, this work is stored in the body. This work done or energy stored in the body is called strain energy.
When a body is subjected to gradual, sudden or impact load, the body deforms and work is done upon it. If the elastic limit is not exceed, this work is stored in the body. This work done or energy stored in the body is called strain energy.
CONTENT:
1. Elastic strain energy
2. Strain energy due to gradual loading
3. Strain energy due to sudden loading
4. Strain energy due to impact loading
5. Strain energy due to shock loading
6. Strain energy due to shear loading
7. Strain energy due to bending (flexure)
8. Strain energy due to torsion
9. Examples
When a body is subjected to gradual, sudden or impact load, the body deforms and work is done upon it. If the elastic limit is not exceed, this work is stored in the body. This work done or energy stored in the body is called strain energy.
When a body is subjected to gradual, sudden or impact load, the body deforms and work is done upon it. If the elastic limit is not exceed, this work is stored in the body. This work done or energy stored in the body is called strain energy.
Strength of Materials all formulas in pdf
it subject iosd also klnown as mechanics of Soilid.
in this pdf there are formulas of stress strain springs - closed coil helical spring , open coil helical Springs etc.
This document gives the class notes of Unit 3 Compound stresses. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Study of Strain Energy due to Shear, Bending and TorsionJay1997Singhania
Strain Energy-Definition and Related Formulas, Strain Energy due to Shear Loading, Strain Energy due to Bending, Strain Energy due to Torsion and Examples
In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.
The deflection distance of a member under a load is directly related to the slope of the deflected shape of the member under that load, and can be calculated by integrating the function that mathematically describes the slope of the member under that load. Deflection can be calculated by standard formula (will only give the deflection of common beam configurations and load cases at discrete locations), or by methods such as virtual work, direct integration, Castigliano's method, Macaulay's method or the direct stiffness method, amongst others. The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory.
This document gives the class notes of Unit 2 stresses in composite sections. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Lecture slides on the calculation of the bending stress in case of unsymmetrical bending. The Mohr's circle is used to determine the principal second moments of area.
Strength of Materials all formulas in pdf
it subject iosd also klnown as mechanics of Soilid.
in this pdf there are formulas of stress strain springs - closed coil helical spring , open coil helical Springs etc.
This document gives the class notes of Unit 3 Compound stresses. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Study of Strain Energy due to Shear, Bending and TorsionJay1997Singhania
Strain Energy-Definition and Related Formulas, Strain Energy due to Shear Loading, Strain Energy due to Bending, Strain Energy due to Torsion and Examples
In engineering, deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance.
The deflection distance of a member under a load is directly related to the slope of the deflected shape of the member under that load, and can be calculated by integrating the function that mathematically describes the slope of the member under that load. Deflection can be calculated by standard formula (will only give the deflection of common beam configurations and load cases at discrete locations), or by methods such as virtual work, direct integration, Castigliano's method, Macaulay's method or the direct stiffness method, amongst others. The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory.
This document gives the class notes of Unit 2 stresses in composite sections. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Lecture slides on the calculation of the bending stress in case of unsymmetrical bending. The Mohr's circle is used to determine the principal second moments of area.
Theory of metal cutting MG University(S8 Production Notes)Denny John
Theory of metal cutting MG University(S8 Production Notes)
Scenario of manufacturing process – Deformation of metals,
Schmid’s law (review only) – Performance and process parameters – single point cutting
tool nomenclature - attributes of each tool nomenclature - attributes of feed and tool
signature on surface roughness obtainable, role of surface roughness on crack initiation -
Oblique and orthogonal cutting – Mechanism of metal removal - Primary and secondary
deformation shear zones - Mechanism of chip formation, card model, types of chip,
curling of chips, flow lines in a chip, BUE, chip breakers, chip thickness ratio –
Mechanism of orthogonal cutting: Thin zone and thick zone, Merchant’s analysis – shear
angle relationship, Lee and Shaffer`s relationship, simple problems – Friction process in
metal cutting: nature of sliding friction, columb`s law, adhesion theory, ploughing, sublayer
flow – Empirical determination of force component.
Couples presenting to the infertility clinic- Do they really have infertility...Sujoy Dasgupta
Dr Sujoy Dasgupta presented the study on "Couples presenting to the infertility clinic- Do they really have infertility? – The unexplored stories of non-consummation" in the 13th Congress of the Asia Pacific Initiative on Reproduction (ASPIRE 2024) at Manila on 24 May, 2024.
Ozempic: Preoperative Management of Patients on GLP-1 Receptor Agonists Saeid Safari
Preoperative Management of Patients on GLP-1 Receptor Agonists like Ozempic and Semiglutide
ASA GUIDELINE
NYSORA Guideline
2 Case Reports of Gastric Ultrasound
New Directions in Targeted Therapeutic Approaches for Older Adults With Mantl...i3 Health
i3 Health is pleased to make the speaker slides from this activity available for use as a non-accredited self-study or teaching resource.
This slide deck presented by Dr. Kami Maddocks, Professor-Clinical in the Division of Hematology and
Associate Division Director for Ambulatory Operations
The Ohio State University Comprehensive Cancer Center, will provide insight into new directions in targeted therapeutic approaches for older adults with mantle cell lymphoma.
STATEMENT OF NEED
Mantle cell lymphoma (MCL) is a rare, aggressive B-cell non-Hodgkin lymphoma (NHL) accounting for 5% to 7% of all lymphomas. Its prognosis ranges from indolent disease that does not require treatment for years to very aggressive disease, which is associated with poor survival (Silkenstedt et al, 2021). Typically, MCL is diagnosed at advanced stage and in older patients who cannot tolerate intensive therapy (NCCN, 2022). Although recent advances have slightly increased remission rates, recurrence and relapse remain very common, leading to a median overall survival between 3 and 6 years (LLS, 2021). Though there are several effective options, progress is still needed towards establishing an accepted frontline approach for MCL (Castellino et al, 2022). Treatment selection and management of MCL are complicated by the heterogeneity of prognosis, advanced age and comorbidities of patients, and lack of an established standard approach for treatment, making it vital that clinicians be familiar with the latest research and advances in this area. In this activity chaired by Michael Wang, MD, Professor in the Department of Lymphoma & Myeloma at MD Anderson Cancer Center, expert faculty will discuss prognostic factors informing treatment, the promising results of recent trials in new therapeutic approaches, and the implications of treatment resistance in therapeutic selection for MCL.
Target Audience
Hematology/oncology fellows, attending faculty, and other health care professionals involved in the treatment of patients with mantle cell lymphoma (MCL).
Learning Objectives
1.) Identify clinical and biological prognostic factors that can guide treatment decision making for older adults with MCL
2.) Evaluate emerging data on targeted therapeutic approaches for treatment-naive and relapsed/refractory MCL and their applicability to older adults
3.) Assess mechanisms of resistance to targeted therapies for MCL and their implications for treatment selection
Lung Cancer: Artificial Intelligence, Synergetics, Complex System Analysis, S...Oleg Kshivets
RESULTS: Overall life span (LS) was 2252.1±1742.5 days and cumulative 5-year survival (5YS) reached 73.2%, 10 years – 64.8%, 20 years – 42.5%. 513 LCP lived more than 5 years (LS=3124.6±1525.6 days), 148 LCP – more than 10 years (LS=5054.4±1504.1 days).199 LCP died because of LC (LS=562.7±374.5 days). 5YS of LCP after bi/lobectomies was significantly superior in comparison with LCP after pneumonectomies (78.1% vs.63.7%, P=0.00001 by log-rank test). AT significantly improved 5YS (66.3% vs. 34.8%) (P=0.00000 by log-rank test) only for LCP with N1-2. Cox modeling displayed that 5YS of LCP significantly depended on: phase transition (PT) early-invasive LC in terms of synergetics, PT N0—N12, cell ratio factors (ratio between cancer cells- CC and blood cells subpopulations), G1-3, histology, glucose, AT, blood cell circuit, prothrombin index, heparin tolerance, recalcification time (P=0.000-0.038). Neural networks, genetic algorithm selection and bootstrap simulation revealed relationships between 5YS and PT early-invasive LC (rank=1), PT N0—N12 (rank=2), thrombocytes/CC (3), erythrocytes/CC (4), eosinophils/CC (5), healthy cells/CC (6), lymphocytes/CC (7), segmented neutrophils/CC (8), stick neutrophils/CC (9), monocytes/CC (10); leucocytes/CC (11). Correct prediction of 5YS was 100% by neural networks computing (area under ROC curve=1.0; error=0.0).
CONCLUSIONS: 5YS of LCP after radical procedures significantly depended on: 1) PT early-invasive cancer; 2) PT N0--N12; 3) cell ratio factors; 4) blood cell circuit; 5) biochemical factors; 6) hemostasis system; 7) AT; 8) LC characteristics; 9) LC cell dynamics; 10) surgery type: lobectomy/pneumonectomy; 11) anthropometric data. Optimal diagnosis and treatment strategies for LC are: 1) screening and early detection of LC; 2) availability of experienced thoracic surgeons because of complexity of radical procedures; 3) aggressive en block surgery and adequate lymph node dissection for completeness; 4) precise prediction; 5) adjuvant chemoimmunoradiotherapy for LCP with unfavorable prognosis.
Title: Sense of Smell
Presenter: Dr. Faiza, Assistant Professor of Physiology
Qualifications:
MBBS (Best Graduate, AIMC Lahore)
FCPS Physiology
ICMT, CHPE, DHPE (STMU)
MPH (GC University, Faisalabad)
MBA (Virtual University of Pakistan)
Learning Objectives:
Describe the primary categories of smells and the concept of odor blindness.
Explain the structure and location of the olfactory membrane and mucosa, including the types and roles of cells involved in olfaction.
Describe the pathway and mechanisms of olfactory signal transmission from the olfactory receptors to the brain.
Illustrate the biochemical cascade triggered by odorant binding to olfactory receptors, including the role of G-proteins and second messengers in generating an action potential.
Identify different types of olfactory disorders such as anosmia, hyposmia, hyperosmia, and dysosmia, including their potential causes.
Key Topics:
Olfactory Genes:
3% of the human genome accounts for olfactory genes.
400 genes for odorant receptors.
Olfactory Membrane:
Located in the superior part of the nasal cavity.
Medially: Folds downward along the superior septum.
Laterally: Folds over the superior turbinate and upper surface of the middle turbinate.
Total surface area: 5-10 square centimeters.
Olfactory Mucosa:
Olfactory Cells: Bipolar nerve cells derived from the CNS (100 million), with 4-25 olfactory cilia per cell.
Sustentacular Cells: Produce mucus and maintain ionic and molecular environment.
Basal Cells: Replace worn-out olfactory cells with an average lifespan of 1-2 months.
Bowman’s Gland: Secretes mucus.
Stimulation of Olfactory Cells:
Odorant dissolves in mucus and attaches to receptors on olfactory cilia.
Involves a cascade effect through G-proteins and second messengers, leading to depolarization and action potential generation in the olfactory nerve.
Quality of a Good Odorant:
Small (3-20 Carbon atoms), volatile, water-soluble, and lipid-soluble.
Facilitated by odorant-binding proteins in mucus.
Membrane Potential and Action Potential:
Resting membrane potential: -55mV.
Action potential frequency in the olfactory nerve increases with odorant strength.
Adaptation Towards the Sense of Smell:
Rapid adaptation within the first second, with further slow adaptation.
Psychological adaptation greater than receptor adaptation, involving feedback inhibition from the central nervous system.
Primary Sensations of Smell:
Camphoraceous, Musky, Floral, Pepperminty, Ethereal, Pungent, Putrid.
Odor Detection Threshold:
Examples: Hydrogen sulfide (0.0005 ppm), Methyl-mercaptan (0.002 ppm).
Some toxic substances are odorless at lethal concentrations.
Characteristics of Smell:
Odor blindness for single substances due to lack of appropriate receptor protein.
Behavioral and emotional influences of smell.
Transmission of Olfactory Signals:
From olfactory cells to glomeruli in the olfactory bulb, involving lateral inhibition.
Primitive, less old, and new olfactory systems with different path
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journeygreendigital
Tom Selleck, an enduring figure in Hollywood. has captivated audiences for decades with his rugged charm, iconic moustache. and memorable roles in television and film. From his breakout role as Thomas Magnum in Magnum P.I. to his current portrayal of Frank Reagan in Blue Bloods. Selleck's career has spanned over 50 years. But beyond his professional achievements. fans have often been curious about Tom Selleck Health. especially as he has aged in the public eye.
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Introduction
Many have been interested in Tom Selleck health. not only because of his enduring presence on screen but also because of the challenges. and lifestyle choices he has faced and made over the years. This article delves into the various aspects of Tom Selleck health. exploring his fitness regimen, diet, mental health. and the challenges he has encountered as he ages. We'll look at how he maintains his well-being. the health issues he has faced, and his approach to ageing .
Early Life and Career
Childhood and Athletic Beginnings
Tom Selleck was born on January 29, 1945, in Detroit, Michigan, and grew up in Sherman Oaks, California. From an early age, he was involved in sports, particularly basketball. which played a significant role in his physical development. His athletic pursuits continued into college. where he attended the University of Southern California (USC) on a basketball scholarship. This early involvement in sports laid a strong foundation for his physical health and disciplined lifestyle.
Transition to Acting
Selleck's transition from an athlete to an actor came with its physical demands. His first significant role in "Magnum P.I." required him to perform various stunts and maintain a fit appearance. This role, which he played from 1980 to 1988. necessitated a rigorous fitness routine to meet the show's demands. setting the stage for his long-term commitment to health and wellness.
Fitness Regimen
Workout Routine
Tom Selleck health and fitness regimen has evolved. adapting to his changing roles and age. During his "Magnum, P.I." days. Selleck's workouts were intense and focused on building and maintaining muscle mass. His routine included weightlifting, cardiovascular exercises. and specific training for the stunts he performed on the show.
Selleck adjusted his fitness routine as he aged to suit his body's needs. Today, his workouts focus on maintaining flexibility, strength, and cardiovascular health. He incorporates low-impact exercises such as swimming, walking, and light weightlifting. This balanced approach helps him stay fit without putting undue strain on his joints and muscles.
Importance of Flexibility and Mobility
In recent years, Selleck has emphasized the importance of flexibility and mobility in his fitness regimen. Understanding the natural decline in muscle mass and joint flexibility with age. he includes stretching and yoga in his routine. These practices help prevent injuries, improve posture, and maintain mobilit
Ethanol (CH3CH2OH), or beverage alcohol, is a two-carbon alcohol
that is rapidly distributed in the body and brain. Ethanol alters many
neurochemical systems and has rewarding and addictive properties. It
is the oldest recreational drug and likely contributes to more morbidity,
mortality, and public health costs than all illicit drugs combined. The
5th edition of the Diagnostic and Statistical Manual of Mental Disorders
(DSM-5) integrates alcohol abuse and alcohol dependence into a single
disorder called alcohol use disorder (AUD), with mild, moderate,
and severe subclassifications (American Psychiatric Association, 2013).
In the DSM-5, all types of substance abuse and dependence have been
combined into a single substance use disorder (SUD) on a continuum
from mild to severe. A diagnosis of AUD requires that at least two of
the 11 DSM-5 behaviors be present within a 12-month period (mild
AUD: 2–3 criteria; moderate AUD: 4–5 criteria; severe AUD: 6–11 criteria).
The four main behavioral effects of AUD are impaired control over
drinking, negative social consequences, risky use, and altered physiological
effects (tolerance, withdrawal). This chapter presents an overview
of the prevalence and harmful consequences of AUD in the U.S.,
the systemic nature of the disease, neurocircuitry and stages of AUD,
comorbidities, fetal alcohol spectrum disorders, genetic risk factors, and
pharmacotherapies for AUD.
New Drug Discovery and Development .....NEHA GUPTA
The "New Drug Discovery and Development" process involves the identification, design, testing, and manufacturing of novel pharmaceutical compounds with the aim of introducing new and improved treatments for various medical conditions. This comprehensive endeavor encompasses various stages, including target identification, preclinical studies, clinical trials, regulatory approval, and post-market surveillance. It involves multidisciplinary collaboration among scientists, researchers, clinicians, regulatory experts, and pharmaceutical companies to bring innovative therapies to market and address unmet medical needs.
Pulmonary Thromboembolism - etilogy, types, medical- Surgical and nursing man...VarunMahajani
Disruption of blood supply to lung alveoli due to blockage of one or more pulmonary blood vessels is called as Pulmonary thromboembolism. In this presentation we will discuss its causes, types and its management in depth.
Title: Sense of Taste
Presenter: Dr. Faiza, Assistant Professor of Physiology
Qualifications:
MBBS (Best Graduate, AIMC Lahore)
FCPS Physiology
ICMT, CHPE, DHPE (STMU)
MPH (GC University, Faisalabad)
MBA (Virtual University of Pakistan)
Learning Objectives:
Describe the structure and function of taste buds.
Describe the relationship between the taste threshold and taste index of common substances.
Explain the chemical basis and signal transduction of taste perception for each type of primary taste sensation.
Recognize different abnormalities of taste perception and their causes.
Key Topics:
Significance of Taste Sensation:
Differentiation between pleasant and harmful food
Influence on behavior
Selection of food based on metabolic needs
Receptors of Taste:
Taste buds on the tongue
Influence of sense of smell, texture of food, and pain stimulation (e.g., by pepper)
Primary and Secondary Taste Sensations:
Primary taste sensations: Sweet, Sour, Salty, Bitter, Umami
Chemical basis and signal transduction mechanisms for each taste
Taste Threshold and Index:
Taste threshold values for Sweet (sucrose), Salty (NaCl), Sour (HCl), and Bitter (Quinine)
Taste index relationship: Inversely proportional to taste threshold
Taste Blindness:
Inability to taste certain substances, particularly thiourea compounds
Example: Phenylthiocarbamide
Structure and Function of Taste Buds:
Composition: Epithelial cells, Sustentacular/Supporting cells, Taste cells, Basal cells
Features: Taste pores, Taste hairs/microvilli, and Taste nerve fibers
Location of Taste Buds:
Found in papillae of the tongue (Fungiform, Circumvallate, Foliate)
Also present on the palate, tonsillar pillars, epiglottis, and proximal esophagus
Mechanism of Taste Stimulation:
Interaction of taste substances with receptors on microvilli
Signal transduction pathways for Umami, Sweet, Bitter, Sour, and Salty tastes
Taste Sensitivity and Adaptation:
Decrease in sensitivity with age
Rapid adaptation of taste sensation
Role of Saliva in Taste:
Dissolution of tastants to reach receptors
Washing away the stimulus
Taste Preferences and Aversions:
Mechanisms behind taste preference and aversion
Influence of receptors and neural pathways
Impact of Sensory Nerve Damage:
Degeneration of taste buds if the sensory nerve fiber is cut
Abnormalities of Taste Detection:
Conditions: Ageusia, Hypogeusia, Dysgeusia (parageusia)
Causes: Nerve damage, neurological disorders, infections, poor oral hygiene, adverse drug effects, deficiencies, aging, tobacco use, altered neurotransmitter levels
Neurotransmitters and Taste Threshold:
Effects of serotonin (5-HT) and norepinephrine (NE) on taste sensitivity
Supertasters:
25% of the population with heightened sensitivity to taste, especially bitterness
Increased number of fungiform papillae
Recomendações da OMS sobre cuidados maternos e neonatais para uma experiência pós-natal positiva.
Em consonância com os ODS – Objetivos do Desenvolvimento Sustentável e a Estratégia Global para a Saúde das Mulheres, Crianças e Adolescentes, e aplicando uma abordagem baseada nos direitos humanos, os esforços de cuidados pós-natais devem expandir-se para além da cobertura e da simples sobrevivência, de modo a incluir cuidados de qualidade.
Estas diretrizes visam melhorar a qualidade dos cuidados pós-natais essenciais e de rotina prestados às mulheres e aos recém-nascidos, com o objetivo final de melhorar a saúde e o bem-estar materno e neonatal.
Uma “experiência pós-natal positiva” é um resultado importante para todas as mulheres que dão à luz e para os seus recém-nascidos, estabelecendo as bases para a melhoria da saúde e do bem-estar a curto e longo prazo. Uma experiência pós-natal positiva é definida como aquela em que as mulheres, pessoas que gestam, os recém-nascidos, os casais, os pais, os cuidadores e as famílias recebem informação consistente, garantia e apoio de profissionais de saúde motivados; e onde um sistema de saúde flexível e com recursos reconheça as necessidades das mulheres e dos bebês e respeite o seu contexto cultural.
Estas diretrizes consolidadas apresentam algumas recomendações novas e já bem fundamentadas sobre cuidados pós-natais de rotina para mulheres e neonatos que recebem cuidados no pós-parto em unidades de saúde ou na comunidade, independentemente dos recursos disponíveis.
É fornecido um conjunto abrangente de recomendações para cuidados durante o período puerperal, com ênfase nos cuidados essenciais que todas as mulheres e recém-nascidos devem receber, e com a devida atenção à qualidade dos cuidados; isto é, a entrega e a experiência do cuidado recebido. Estas diretrizes atualizam e ampliam as recomendações da OMS de 2014 sobre cuidados pós-natais da mãe e do recém-nascido e complementam as atuais diretrizes da OMS sobre a gestão de complicações pós-natais.
O estabelecimento da amamentação e o manejo das principais intercorrências é contemplada.
Recomendamos muito.
Vamos discutir essas recomendações no nosso curso de pós-graduação em Aleitamento no Instituto Ciclos.
Esta publicação só está disponível em inglês até o momento.
Prof. Marcus Renato de Carvalho
www.agostodourado.com
Novas diretrizes da OMS para os cuidados perinatais de mais qualidade
Lecture 3 mohr’s circle and theory of failure
1.
2. Unit 1- Stress and Strain
Topics Covered
Lecture -1 - Introduction, state of plane stress
Lecture -2 - Principle Stresses and Strains
Lecture -3 - Mohr's Stress Circle and Theory of
Failure
Lecture -4- 3-D stress and strain, Equilibrium
equations and impact loading
Lecture -5 - Generalized Hook's law and Castigliono's
4. Mohr Stress Circle
⎛ σ1 + σ2 ⎞ 2 ⎛ σ1 − σ2 ⎞ 2
⎜σn − ⎟ = ⎜ cos2θ + τ sin2θ ⎟
⎝ 2 ⎠ ⎝ 2 ⎠
2 ⎛ σ1 − σ2 ⎞ 2
(σt ) = ⎜
⎝ 2
sin2θ − τ cos2θ ⎟
⎠
Add above 2 equations. We will equation of circle.
€ 2 2
⎛ σ + σ ⎞
1 2
⎛ σ − σ ⎞
2 1 2 2
⎜σ −
n ⎟ + σ = ⎜ t ⎟ + (τ )
€ ⎝ 2 ⎠ ⎝ 2 ⎠
2 2
( x − a) y r 2
Equation of circle
€
5. Mohr Stress Circle
Graphical method to determine stresses.
Body subjected to two mutually perpendicular principal
stresses of unequal magnitude.
Body subjected to two mutually perpendicular principal
stresses of unequal magnitude and unlike (one tensile
and other compressive).
Body subjected to two mutually perpendicular principal
stresses + simple shear stress.
6. Mohr Stress Circle
Body subjected to two mutually perpendicular
principal stresses of unequal magnitude
(σ1 - σ2 ) length AD = Normal stress on oblique plane
σt
= σn
E length ED = Tangential stress on Oblique plane
= σt
2θ
B length AE = Resultant stress on Oblique plane
θ
σn
O D σ1 2 2
A C = σ +σt n
€
σ2
σ1 €
€
7. Mohr Stress Circle
Body subjected to two mutually perpendicular principal
stresses of unequal magnitude and unlike (one tensile
and other compressive).
(σ1+σ2 )
length AD = Normal stress on oblique plane
σt E = σn
length ED = Tangential stress on Oblique plane
= σt
2θ
length AE = Resultant stress on Oblique plane
C θ
B
σn 2 2
A O D = σt + σn
_
€
+ σ1
σ2
€
€
8. Mohr Stress Circle
Body subjected to two mutually perpendicular principal
stresses + simple shear stress.
σt length AD = Normal stress on oblique plane
= σn
E length ED = Tangential stress on Oblique plane
2θ
= σt
length AE = Resultant stress on Oblique plane
B M σ
n
L C D σ1 2 2
A O = σ +σ
t n
€
σ2
σ1 €
€
9. Theories of failure
Maximum principal stress (Rankine theory)
Maximum principal strain (Saint Venant theory)
Maximum shear stress (Guest theory)
Maximum strain energy (Haigh theory)
Maximum shear strain energy (Mises & Henky
theory)
10. 1. Maximum principal
stress theory
σ1,σ2 ,σ3 =principal stresses in 3 perpendicular
directions
*
max(σ1,σ2 ,σ3 ) ≤ σ
€
Maximum principal stress should be less than the max stress (yield stress) that material
can bear in tension or compression.
*
σ = max tensile or compressive strength of material
€
σ*
max principal stress=
safety _ factor
11. 2. Maximum principal
strain theory
σ1,σ2 ,σ3 =principal stresses in 3 perpendicular
directions
σ1 υσ2 υσ3 σ2 υσ1 υσ3 σ3 υσ1 υσ2
e1 = − − e2 = − − e3 = − −
E E E E E E E E E
* σ*
€ max(e1,e2 ,e3 ) ≤ e *
e =
E
*
σ = max tensile or compressive strength of material
€ Maximum principal strain should be less than the max strain (yield strain) that material
€ €
can bear in tension or compression. €
σ*
€ max principal stress=
safety _ factor
12. 3. Maximum shear stress
theory
max shear stress =half the difference of max and min principal stresses
1
= (σ1 − σ3 )
2 In simple tension the stress
To prevent failure max shear stress should be less that shear is existing in one direction
stress in simple tension at elastic limit
1 * *
= (σt − 0) σt
max shear stress at elastic limit = max tensile of material
€ 2
(σ1 − σ 3 ) ≤ σ *
t
Maximum shear stress should be less than the max shear stress in simple tension (at
elastic limit) that material can bear.
€ €
σ*t
allowable stress =
€ safety _ factor
13. 4. Maximum strain
energy theory
Strain energy per unit volume should be less than the strain energy per unit volume in
simple tension (at elastic limit) that material can bear.
2
[σ 2
1 + σ + σ − 2υ (σ1σ2 + σ1σ3 + σ2σ3 ) ≤ (σ
2
2
2
3 ] *
t )
σ*t
max allowable stress=
safety _ factor
€
€
14. 5. Maximum shear strain
energy theory
Shear strain energy per unit volume should be less than the shear strain energy per unit
volume in simple tension (at elastic limit).
2 2 2 2
(σ1 − σ2 ) + (σ1 − σ3 ) + (σ2 − σ3 ) ≤ 2 * (σ *
t )
σ*t
max allowable stress=
safety _ factor
€
€
15. Important points
Brittle material -> Max principal stress
Brittle material do not fail in shear
Ductile material -> Max shear stress/max shear strain
energy
Ductile material fail in shear because their yield
strength is high.
16. Failure Theory
PROBLEM- The principal stresses at a point in an
elastic material are 200 N/mm2 (tensile), 100 N/
mm2 (tensile) and 50 N/mm2 (compressive). If the
stresses at the elastic limit in simple tension is 200
N/mm2, determine whether the failure of the
material will occur according to different failure
theory. (take Poisson's ratio =0.3)
Max principal strain theory
Max shear stress theory
Max strain energy theory
Max shear strain energy theory