This document contains a question bank for the Strength of Materials course CE 6306 from Anna University. It includes 20 short answer questions (Part A) and 10 long answer numerical problems (Part B) covering topics like stress, strain, Hooke's law, elastic constants, Poisson's ratio, resilience, elastic limit, thermal stress, modulus of elasticity, shear stress, bending moment diagrams, deflection of beams, torsion, springs and columns. The questions assess students' understanding of fundamental concepts and their ability to apply formulas and theories to solve practical engineering problems involving stresses and deformations of structural elements.
This document contains 9 questions related to mechanics of solids problems involving beams. The questions involve selecting beam sections based on allowable stresses, calculating maximum stresses in beams, and determining maximum loads beams can support. Beam cross sections include W, S, T, and inverted T shapes. Beams are subjected to uniformly distributed loads, concentrated loads, and combinations of loads. Calculations require determining maximum bending moments and stresses given beam properties, loads, and stress allowability criteria.
1. The document provides 10 examples of calculating bending stresses and permissible loads for different beam configurations.
2. The beams have various cross-sectional shapes, loads including uniform and concentrated loads, and span configurations such as simple, overhanging, and cantilevered.
3. The examples calculate quantities like maximum bending stress, required beam dimensions, and maximum permissible loads based on given allowable stresses.
This document contains 36 problems related to mechanics of solids dealing with topics like normal stress, shearing stress, axial deformation, shearing deformation, and statically indeterminate members. The problems involve calculating stresses, strains, loads, diameters, thicknesses, and other values using given structural properties and load/force information. Equations related to stress, strain, elasticity, and structural analysis are applied to solve the engineering problems.
This document contains 15 problems related to determining stresses in beams undergoing bending and shearing. The problems involve calculating stresses in beams with various cross-sectional shapes under different loading conditions. The beams are made of materials like steel, wood, and brass. Parameters like moment of inertia, shear force, beam dimensions, and material properties are provided to calculate stresses.
1. The document discusses the design of various welded joints, including butt joints, transverse and parallel fillet joints, and circular fillet joints subjected to torsion. It provides the equations to calculate the permissible load or torque based on the weld material properties and joint geometry.
2. Examples of design calculations are provided for parallel fillet joints subjected to load and transverse fillet joints. Design stresses for welds using bare and covered electrodes are also tabulated.
3. Review questions at the end test the understanding of welded joint design, and examples are worked out for fillet joints subjected to load and a circular fillet joint subjected to torque.
This document discusses various mechanical properties that are important for selecting materials for structural components. It describes different types of mechanical tests like tension, compression, torsion, bending, impact and fatigue tests that are conducted on metal specimens to determine properties like strength, ductility and toughness. Specifically, it outlines the process for a uniaxial tension test including the equipment used, steps to conduct the test, and how to analyze the stress-strain diagram produced. It also discusses factors that influence mechanical properties like temperature, notches, grain size and hardness tests.
Analysis of Multi-storey Building Frames Subjected to Gravity and Seismic Loa...Pralhad Kore
This document summarizes the results of analyzing 3-bay, 5-bay, and 7-bay 9-story reinforced concrete frames with varying geometric properties under gravity and seismic loads. The response of frames was studied when incorporating idealized T-beams between points of contraflexure in beams and providing haunches of varying widths at beam-column joints. Results found that axial forces in columns increased linearly from top to bottom, while bending moments decreased with larger beam-column stiffness ratios. Lateral displacements under seismic loads were reduced by incorporating T-beams and haunches, demonstrating their beneficial effects on structural response.
This document contains 9 questions related to mechanics of solids problems involving beams. The questions involve selecting beam sections based on allowable stresses, calculating maximum stresses in beams, and determining maximum loads beams can support. Beam cross sections include W, S, T, and inverted T shapes. Beams are subjected to uniformly distributed loads, concentrated loads, and combinations of loads. Calculations require determining maximum bending moments and stresses given beam properties, loads, and stress allowability criteria.
1. The document provides 10 examples of calculating bending stresses and permissible loads for different beam configurations.
2. The beams have various cross-sectional shapes, loads including uniform and concentrated loads, and span configurations such as simple, overhanging, and cantilevered.
3. The examples calculate quantities like maximum bending stress, required beam dimensions, and maximum permissible loads based on given allowable stresses.
This document contains 36 problems related to mechanics of solids dealing with topics like normal stress, shearing stress, axial deformation, shearing deformation, and statically indeterminate members. The problems involve calculating stresses, strains, loads, diameters, thicknesses, and other values using given structural properties and load/force information. Equations related to stress, strain, elasticity, and structural analysis are applied to solve the engineering problems.
This document contains 15 problems related to determining stresses in beams undergoing bending and shearing. The problems involve calculating stresses in beams with various cross-sectional shapes under different loading conditions. The beams are made of materials like steel, wood, and brass. Parameters like moment of inertia, shear force, beam dimensions, and material properties are provided to calculate stresses.
1. The document discusses the design of various welded joints, including butt joints, transverse and parallel fillet joints, and circular fillet joints subjected to torsion. It provides the equations to calculate the permissible load or torque based on the weld material properties and joint geometry.
2. Examples of design calculations are provided for parallel fillet joints subjected to load and transverse fillet joints. Design stresses for welds using bare and covered electrodes are also tabulated.
3. Review questions at the end test the understanding of welded joint design, and examples are worked out for fillet joints subjected to load and a circular fillet joint subjected to torque.
This document discusses various mechanical properties that are important for selecting materials for structural components. It describes different types of mechanical tests like tension, compression, torsion, bending, impact and fatigue tests that are conducted on metal specimens to determine properties like strength, ductility and toughness. Specifically, it outlines the process for a uniaxial tension test including the equipment used, steps to conduct the test, and how to analyze the stress-strain diagram produced. It also discusses factors that influence mechanical properties like temperature, notches, grain size and hardness tests.
Analysis of Multi-storey Building Frames Subjected to Gravity and Seismic Loa...Pralhad Kore
This document summarizes the results of analyzing 3-bay, 5-bay, and 7-bay 9-story reinforced concrete frames with varying geometric properties under gravity and seismic loads. The response of frames was studied when incorporating idealized T-beams between points of contraflexure in beams and providing haunches of varying widths at beam-column joints. Results found that axial forces in columns increased linearly from top to bottom, while bending moments decreased with larger beam-column stiffness ratios. Lateral displacements under seismic loads were reduced by incorporating T-beams and haunches, demonstrating their beneficial effects on structural response.
This document contains a tutorial sheet with questions about strength of materials and simple uniaxial stress and strain. It provides the questions, worked answers to the first 7 questions, and poses questions 8 through 12 for students to work on individually. The questions calculate various mechanical properties of materials like Young's modulus, yield stress, ultimate stress, elongation, stress, strain, and modulus of elasticity when given dimensional and loading information for different structural components and materials like steel, brass, aluminum, and wires.
This document provides a weekly course outline for a Strength of Materials class. It lists the topics that will be covered each week over a semester, including simple stress, strain, beams, columns, springs, and combined stresses. It also lists the required textbooks and the assessment breakdown for the course. Sample problems are provided at the end to demonstrate concepts like stress, strain, shear stress, deformation, stress-strain relationships, and beam stresses.
The document summarizes key concepts related to mechanics of solids, including:
1. Definitions of stress, strain, Hooke's law, shear stress, Poisson's ratio, Young's modulus, and strain energy.
2. Methods for analyzing plane trusses and thin cylindrical shells.
3. Types of beams, loading conditions, shear force and bending moment diagrams.
4. Methods for determining deflection, including double integration, moment area, and Macaulay's method.
This document contains 8 questions on the topics of mechanics of solids for a B.Tech exam. Question 1 has two parts asking about (a) finding the size and length of a middle tie bar portion given stress and extension values, and (b) calculating the extension of a rod with a varying width. Question 2 asks to analyze a beam shown in a figure by drawing shear force, bending moment, and thrust diagrams. The remaining questions cover additional topics like simple bending, stresses in beams and cylinders, truss analysis methods, and deflection calculations.
The document discusses various types of loading on structural members including pure bending, eccentric axial loading, and transverse loading. It covers bending deformations, strain and stress due to bending, section properties, and examples of bending stresses in composite and reinforced concrete beams. Plastic deformations in members made of elastic-plastic materials are also examined.
This document discusses short compression members under axial load with uniaxial bending. It describes the behavior of such columns and their three modes of failure: balanced failure, compression failure, and tension failure. Balanced failure occurs when the outermost longitudinal steel yields simultaneously with maximum concrete compression. Compression failure happens with a neutral axis outside the section. Tension failure occurs when the neutral axis is inside the section, developing tensile strains. An interaction diagram plots load versus moment pairs that cause failure. The behavior and failure modes depend on the neutral axis location and load eccentricity.
Stress in Bar of Uniformly Tapering Rectangular Cross Section | Mechanical En...Transweb Global Inc
This document summarizes stress in a bar with a uniformly tapering rectangular cross section. It defines the width of the larger and smaller ends (b1 and b2), length (L), thickness (t), and modulus of elasticity (E). It describes how to calculate the cross-sectional area (A) as a function of position (x), tensile stress (σ), and total elongation or extension (δL) of the bar when an axial pull force P is applied. As an example, it gives values to calculate the extension of a steel plate that tapers from 200mm to 100mm width over 500mm length, under an axial force of 40kN.
This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.
This document provides unit-wise assignment questions for the subject Mechanics of Materials compiled by Hareesha N G, an assistant professor at Dayananda Sagar College of Engineering. It includes questions covering topics in three units: simple stress and strain, stress in composite sections, and compound stresses. The questions are intended to help students learn and practice key concepts in mechanics of materials through problem solving. There are a total of 10 questions listed for each unit, addressing topics such as stress-strain behavior, thermal stresses, principal stresses, and Mohr's circle analysis. The document aims to equip students with practice questions to solidify their understanding of mechanics of materials.
Unit 4 transverse loading on beams and stresses in beamskarthi keyan
This document discusses transverse loading on beams and stresses in beams. It defines a beam as a structural member used to bear different loads and resist vertical loads, shear forces, and bending moments. It describes different types of beams like cantilever beams and types of loads like point loads, uniformly distributed loads, and uniformly varying loads. It explains that shear force is the sum of forces on one side of a beam section, while bending moment is the sum of moments. It then discusses the theory of simple or pure bending, where a beam portion is only subjected to bending moment without shear force.
This document provides an introduction to strength of materials, including concepts of stress, strain, Hooke's law, stress-strain relationships, elastic constants, and factors of safety. It defines key terms like stress, strain, elastic limit, modulus of elasticity, and ductile and brittle material behavior. Examples of stress and strain calculations are provided for basic structural elements like rods, bars, and composite structures. The document also covers compound bars, principle of superposition, and effects of temperature changes.
Numericals on Columns and struts_-_solvedViriSharma
This document contains 7 problems related to calculating the load capacity of steel columns using Euler's theory and Rankine's formula. Problem 1 compares the strength ratio of a solid vs hollow steel column. Problem 2 calculates the safe load for a solid round bar column with different end conditions. Problem 3 finds the strength ratio of a solid vs hollow steel column with the same cross-sectional area. Problem 4 calculates the Euler crushing load and compares it to Rankine's formula. Problems 5-7 involve calculating column load capacities for various steel sections using Euler, Rankine, and IS code methods.
This document discusses the design of compression members in steel structures. It begins by defining compression members as members subjected to compressive stresses, such as columns, struts, and compression flanges. It notes that compression members are more prone to buckling than tension members. The document then discusses factors that influence the buckling strength of compression members, such as the member's length, cross-sectional properties, end conditions, and bracing. It also discusses eccentric loading of columns and the various sections that can be used or built up for compression members.
Vilas Nikam- Mechanics of Structure-Stress in beamNIKAMVN
1. The document discusses stresses in beams when subjected to external loading, specifically bending stress which is the resistance offered by internal stresses to bending.
2. It defines key concepts like neutral axis, section modulus, and presents flexural formulas for calculating bending stress based on moment of inertia, modulus of elasticity, and distance from neutral axis.
3. Various bending stress distributions are shown for different beam sections including rectangular, circular, hollow circular, and unsymmetrical sections for simply supported and cantilever beams. Shear stress distributions are also presented for several standard sections.
The document contains questions from five units related to strength of materials and structural analysis. Unit I covers topics like strain energy, deflection analysis using principles of virtual work and Castigliano's theorem. Unit II focuses on analysis of determinate and indeterminate beams including shear force and bending moment diagrams. Unit III addresses columns and buckling behavior based on Euler's theory. Unit IV discusses stress and failure theories. Unit V covers unsymmetrical bending, shear center and fatigue failure. The questions range from deriving expressions to solving practical problems in bending, shear, torsion and buckling of beams, columns and shells.
This document contains important questions and answers related to the subject of Strength of Materials. It is divided into multiple parts and units. It includes questions related to engineering materials, deformation of metals, geometric properties of sections and thin shells, and theory of torsion and springs. The questions range from definitions and concepts to practical problems involving calculations. The document is intended to serve as a question bank for students studying Strength of Materials.
This document provides an overview of topics related to simple stresses and strains, including:
- Types of stresses and strains such as tensile, compressive, direct stress, and direct strain.
- Hooke's law and how stress is proportional to strain below the material's yield point.
- Stress-strain diagrams and key points such as the elastic region, yield point, and fracture point.
- Definitions of terms like working stress, factor of safety, Poisson's ratio, and elastic moduli.
- Examples of problems calculating stresses, strains, extensions, and deformations of simple structural members under various loads.
This document contains a past exam for a Mechanics of Solids course, including 10 short answer questions covering key concepts (Part A), and 5 longer problems covering 5 course units (Part B).
The questions cover topics such as resilience, volumetric strain, shear force and bending moment diagrams, stresses in composite materials with different coefficients of expansion, derivation of Young's modulus, shear stress in beams and circular shafts, deflection of beams under point loads, and thickness calculations for pressure vessels.
The problems require calculation of stresses, drawing of shear force and bending moment diagrams, derivation of equations, and determination of beam deflections and pressure vessel plate thickness.
This document contains a tutorial sheet with questions about strength of materials and simple uniaxial stress and strain. It provides the questions, worked answers to the first 7 questions, and poses questions 8 through 12 for students to work on individually. The questions calculate various mechanical properties of materials like Young's modulus, yield stress, ultimate stress, elongation, stress, strain, and modulus of elasticity when given dimensional and loading information for different structural components and materials like steel, brass, aluminum, and wires.
This document provides a weekly course outline for a Strength of Materials class. It lists the topics that will be covered each week over a semester, including simple stress, strain, beams, columns, springs, and combined stresses. It also lists the required textbooks and the assessment breakdown for the course. Sample problems are provided at the end to demonstrate concepts like stress, strain, shear stress, deformation, stress-strain relationships, and beam stresses.
The document summarizes key concepts related to mechanics of solids, including:
1. Definitions of stress, strain, Hooke's law, shear stress, Poisson's ratio, Young's modulus, and strain energy.
2. Methods for analyzing plane trusses and thin cylindrical shells.
3. Types of beams, loading conditions, shear force and bending moment diagrams.
4. Methods for determining deflection, including double integration, moment area, and Macaulay's method.
This document contains 8 questions on the topics of mechanics of solids for a B.Tech exam. Question 1 has two parts asking about (a) finding the size and length of a middle tie bar portion given stress and extension values, and (b) calculating the extension of a rod with a varying width. Question 2 asks to analyze a beam shown in a figure by drawing shear force, bending moment, and thrust diagrams. The remaining questions cover additional topics like simple bending, stresses in beams and cylinders, truss analysis methods, and deflection calculations.
The document discusses various types of loading on structural members including pure bending, eccentric axial loading, and transverse loading. It covers bending deformations, strain and stress due to bending, section properties, and examples of bending stresses in composite and reinforced concrete beams. Plastic deformations in members made of elastic-plastic materials are also examined.
This document discusses short compression members under axial load with uniaxial bending. It describes the behavior of such columns and their three modes of failure: balanced failure, compression failure, and tension failure. Balanced failure occurs when the outermost longitudinal steel yields simultaneously with maximum concrete compression. Compression failure happens with a neutral axis outside the section. Tension failure occurs when the neutral axis is inside the section, developing tensile strains. An interaction diagram plots load versus moment pairs that cause failure. The behavior and failure modes depend on the neutral axis location and load eccentricity.
Stress in Bar of Uniformly Tapering Rectangular Cross Section | Mechanical En...Transweb Global Inc
This document summarizes stress in a bar with a uniformly tapering rectangular cross section. It defines the width of the larger and smaller ends (b1 and b2), length (L), thickness (t), and modulus of elasticity (E). It describes how to calculate the cross-sectional area (A) as a function of position (x), tensile stress (σ), and total elongation or extension (δL) of the bar when an axial pull force P is applied. As an example, it gives values to calculate the extension of a steel plate that tapers from 200mm to 100mm width over 500mm length, under an axial force of 40kN.
This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.
This document provides unit-wise assignment questions for the subject Mechanics of Materials compiled by Hareesha N G, an assistant professor at Dayananda Sagar College of Engineering. It includes questions covering topics in three units: simple stress and strain, stress in composite sections, and compound stresses. The questions are intended to help students learn and practice key concepts in mechanics of materials through problem solving. There are a total of 10 questions listed for each unit, addressing topics such as stress-strain behavior, thermal stresses, principal stresses, and Mohr's circle analysis. The document aims to equip students with practice questions to solidify their understanding of mechanics of materials.
Unit 4 transverse loading on beams and stresses in beamskarthi keyan
This document discusses transverse loading on beams and stresses in beams. It defines a beam as a structural member used to bear different loads and resist vertical loads, shear forces, and bending moments. It describes different types of beams like cantilever beams and types of loads like point loads, uniformly distributed loads, and uniformly varying loads. It explains that shear force is the sum of forces on one side of a beam section, while bending moment is the sum of moments. It then discusses the theory of simple or pure bending, where a beam portion is only subjected to bending moment without shear force.
This document provides an introduction to strength of materials, including concepts of stress, strain, Hooke's law, stress-strain relationships, elastic constants, and factors of safety. It defines key terms like stress, strain, elastic limit, modulus of elasticity, and ductile and brittle material behavior. Examples of stress and strain calculations are provided for basic structural elements like rods, bars, and composite structures. The document also covers compound bars, principle of superposition, and effects of temperature changes.
Numericals on Columns and struts_-_solvedViriSharma
This document contains 7 problems related to calculating the load capacity of steel columns using Euler's theory and Rankine's formula. Problem 1 compares the strength ratio of a solid vs hollow steel column. Problem 2 calculates the safe load for a solid round bar column with different end conditions. Problem 3 finds the strength ratio of a solid vs hollow steel column with the same cross-sectional area. Problem 4 calculates the Euler crushing load and compares it to Rankine's formula. Problems 5-7 involve calculating column load capacities for various steel sections using Euler, Rankine, and IS code methods.
This document discusses the design of compression members in steel structures. It begins by defining compression members as members subjected to compressive stresses, such as columns, struts, and compression flanges. It notes that compression members are more prone to buckling than tension members. The document then discusses factors that influence the buckling strength of compression members, such as the member's length, cross-sectional properties, end conditions, and bracing. It also discusses eccentric loading of columns and the various sections that can be used or built up for compression members.
Vilas Nikam- Mechanics of Structure-Stress in beamNIKAMVN
1. The document discusses stresses in beams when subjected to external loading, specifically bending stress which is the resistance offered by internal stresses to bending.
2. It defines key concepts like neutral axis, section modulus, and presents flexural formulas for calculating bending stress based on moment of inertia, modulus of elasticity, and distance from neutral axis.
3. Various bending stress distributions are shown for different beam sections including rectangular, circular, hollow circular, and unsymmetrical sections for simply supported and cantilever beams. Shear stress distributions are also presented for several standard sections.
The document contains questions from five units related to strength of materials and structural analysis. Unit I covers topics like strain energy, deflection analysis using principles of virtual work and Castigliano's theorem. Unit II focuses on analysis of determinate and indeterminate beams including shear force and bending moment diagrams. Unit III addresses columns and buckling behavior based on Euler's theory. Unit IV discusses stress and failure theories. Unit V covers unsymmetrical bending, shear center and fatigue failure. The questions range from deriving expressions to solving practical problems in bending, shear, torsion and buckling of beams, columns and shells.
This document contains important questions and answers related to the subject of Strength of Materials. It is divided into multiple parts and units. It includes questions related to engineering materials, deformation of metals, geometric properties of sections and thin shells, and theory of torsion and springs. The questions range from definitions and concepts to practical problems involving calculations. The document is intended to serve as a question bank for students studying Strength of Materials.
This document provides an overview of topics related to simple stresses and strains, including:
- Types of stresses and strains such as tensile, compressive, direct stress, and direct strain.
- Hooke's law and how stress is proportional to strain below the material's yield point.
- Stress-strain diagrams and key points such as the elastic region, yield point, and fracture point.
- Definitions of terms like working stress, factor of safety, Poisson's ratio, and elastic moduli.
- Examples of problems calculating stresses, strains, extensions, and deformations of simple structural members under various loads.
This document contains a past exam for a Mechanics of Solids course, including 10 short answer questions covering key concepts (Part A), and 5 longer problems covering 5 course units (Part B).
The questions cover topics such as resilience, volumetric strain, shear force and bending moment diagrams, stresses in composite materials with different coefficients of expansion, derivation of Young's modulus, shear stress in beams and circular shafts, deflection of beams under point loads, and thickness calculations for pressure vessels.
The problems require calculation of stresses, drawing of shear force and bending moment diagrams, derivation of equations, and determination of beam deflections and pressure vessel plate thickness.
This document appears to be an exam for a Strength of Materials course, as it contains multiple choice and numerical problems relating to topics in strength of materials. It begins with 10 short answer questions on concepts like Poisson's ratio, volumetric strain, points of contraflexure, assumptions of bending theory, and properties of springs, cylinders, and materials. It then provides 13 multi-part numerical problems calculating stresses, shear forces, bending moments, deflections, spring properties, cylinder dimensions, and more. It concludes with 2 long form problems, one involving drawing shear force and bending moment diagrams and the other calculating slope and deflection of a cantilever beam. The document tests students' understanding of key analytical concepts and calculations in strength of
This document appears to be an exam for a Strength of Materials course, as it contains multiple choice and numerical problems relating to concepts in strength of materials. It begins with 10 short answer questions worth 2 marks each [Part A]. It then lists 5 problems worth 16 marks each [Part B], covering topics such as stresses and strains in rods due to tensile forces, shear force and bending moment diagrams, stresses and deflections in beams, stresses and deflections in springs, stresses and failures in compression members, and principal stresses. The document provides data and asks students to show working to calculate values for stresses, strains, deflections, loads, and other strength of materials variables. It aims to test students' understanding and application of key
This document appears to be an exam for a Strength of Materials course, consisting of multiple choice and free response questions. It includes questions about stress and strain, shear stress and compressive stress calculations, types of beams, shear force and bending moment diagrams, assumptions in bending theory, modulus of elasticity calculations from tensile tests, shear and bending stresses, deflections of beams and shafts, and stresses in helical springs and thin cylindrical shells. The exam has two parts, with Part A containing short answer questions and Part B containing longer free response problems.
ME6503 design of machine elements - question bank.Mohan2405
This document contains questions and problems related to the design of machine elements, specifically regarding shafts and couplings. It includes 20 questions in Part A testing basic recall and understanding, 13 multi-part problems in Part B applying concepts to design scenarios, and 4 complex design problems in Part C. The topics covered include stresses in shafts, hollow vs solid shafts, keys and keyways, rigid and flexible couplings, and the design of shafts and keys based on strength and rigidity considerations.
1. Stress is defined as force per unit area and can be calculated using the formula stress = force/area. The main types of stress are axial/normal stress, shear stress, and bearing stress.
2. Strain is the ratio of deformation to original length and is calculated using the formula strain = change in length/original length. Hooke's law states that stress is proportional to strain within the elastic limit defined by a material's Young's modulus.
3. Additional concepts covered include thin-walled pressure vessels, Poisson's ratio, thermal deformation, and stress-strain diagrams. Worked examples are provided to demonstrate calculating stresses, strains, deformations and other mechanical properties.
M E C H A N I C S O F S O L I D S J N T U M O D E L P A P E R{Wwwguest3f9c6b
This document contains 8 sets of questions for a Mechanics of Solids exam. The questions cover topics like stresses and strains in rods, beams, and shells; shear force and bending moment diagrams; deflection of beams; principal stresses and Mohr's circle of stresses; columns and springs. Set 1 contains 8 questions, Set 2 contains 8 questions, and so on, with each set containing questions of equal marks that students can choose to answer.
1) A bar subjected to torsion experiences twisting about its central axis due to a torque applied at one end. The torsional shear stress at a distance from the center is equal to the torque divided by the polar moment of inertia.
2) Beams experience bending stresses and shear stresses when subjected to forces and couples acting on their cross sections. Under the assumptions of small deflections and uniform properties, the bending stress is proportional to the distance from the neutral axis.
3) The maximum bending stress in a cantilever beam carrying a linearly increasing load can be calculated using the beam's moment of inertia and section modulus.
This document discusses mechanics of structures and simple stresses and strains. It covers the following key points in 3 sentences:
The document introduces mechanical properties of materials like strength, stiffness, elasticity and defines different types of loads, stresses and strains. It explains concepts like axial load, shear load and different types of stresses and strains. Various mechanical properties of materials are defined along with important formulas for calculating stresses, strains, modulus of elasticity and deformation of structures under different loads.
1. The document discusses flexural and shear stresses in beams. It covers the theory of simple bending, assumptions made, derivation of the bending equation, neutral axis, and determination of bending stresses.
2. Formulas are derived for shear stress distribution in beams with different cross sections like rectangular, circular, triangular, I-sections, and T-sections.
3. Examples are provided to calculate stresses induced in beams under different loading conditions using the bending stress formula and section modulus concept. The maximum stress is calculated for beams with various cross-sections subjected to point loads, uniformly distributed loads, and combinations of loads.
This document contains 8 assignment sheets related to mechanical engineering concepts including:
1. Free body diagrams and reactions at supports
2. Internal reaction diagrams for beams
3. Axially loaded bars including stresses and deflections
4. Bending of bars including stresses, deflections, and internal reaction diagrams
5. Torsion of bars including shear stresses and angles of twist
6. Thin walled pressure containers including stress components and allowable pressures
7. Stress transformation including Mohr's circle and principal stresses
8. A problem involving stresses in a thin walled steel pressure container
The assignments cover a range of load cases and ask students to calculate stresses, deflections, reactions and other mechanical properties.
Solution of Chapter- 05 - stresses in beam - Strength of Materials by SingerAshiqur Rahman Ziad
This document discusses stresses in beams, including flexural and shearing stresses. It provides formulas for calculating flexural stress based on the beam's moment of inertia, bending moment, and distance from the neutral axis. Several example problems are worked through applying these formulas. The document also discusses using economic beam sections that optimize the use of material by placing more area on the outer fibers where stresses are highest.
This document discusses static engineering systems and structural members experiencing bending. It covers key concepts such as:
- The bending of structural members and the neutral axis where the length remains unchanged during bending.
- How bending stress varies across a beam's cross-section, with maximum stress occurring on the surfaces furthest from the neutral axis.
- The general bending formula that relates bending moment, stress, elastic modulus, and distance from the neutral axis.
- Other bending concepts like the second moment of area, parallel axis theorem, and position of the neutral axis through the centroid.
Worked examples demonstrate calculating bending stresses, moments, strains, and selecting suitable beam dimensions.
This document contains questions related to several topics in physics including elasticity, quantum physics, surface tension, optics, sound, and crystal physics. It begins with definitions and concepts in each topic and then provides related math problems to solve. For example, in elasticity it asks about Hooke's law, stress-strain diagrams, and relationships between elastic constants. In optics, it asks about wave fronts, interference, diffraction, and polarization. It concludes with 7 math problems related to optics to calculate values like wavelength and diffraction orders.
This document provides an introduction to basic mechanical principles of stress and strain. It defines key terms like stress, strain, modulus of elasticity, shear stress and shear strain. It includes example problems and solutions to illustrate direct stress and strain from tensile or compressive forces. It also covers shear stress and strain, and the modulus of rigidity. The document is intended to provide prerequisite knowledge for engineering exams on mechanics of solids.
Structure design -I (Moment of Resistance)Simran Vats
This document discusses moment of resistance in structural beams. It defines moment of resistance as the moment of the couple set up at a beam section by longitudinal forces caused by the beam's deflection. The document explains that at equilibrium, the moment of resistance of a beam section must equal the bending moment applied. It also describes how stress varies linearly from compression to tension across the beam's cross-section, with the neutral axis experiencing no stress. The moment of resistance of a rectangular beam section is calculated as fbd2/6, where f is the maximum stress, b is the width, and d is the depth.
Online train ticket booking system project.pdfKamal Acharya
Rail transport is one of the important modes of transport in India. Now a days we
see that there are railways that are present for the long as well as short distance
travelling which makes the life of the people easier. When compared to other
means of transport, a railway is the cheapest means of transport. The maintenance
of the railway database also plays a major role in the smooth running of this
system. The Online Train Ticket Management System will help in reserving the
tickets of the railways to travel from a particular source to the destination.
Sachpazis_Consolidation Settlement Calculation Program-The Python Code and th...Dr.Costas Sachpazis
Consolidation Settlement Calculation Program-The Python Code
By Professor Dr. Costas Sachpazis, Civil Engineer & Geologist
This program calculates the consolidation settlement for a foundation based on soil layer properties and foundation data. It allows users to input multiple soil layers and foundation characteristics to determine the total settlement.
This is an overview of my career in Aircraft Design and Structures, which I am still trying to post on LinkedIn. Includes my BAE Systems Structural Test roles/ my BAE Systems key design roles and my current work on academic projects.
Data Communication and Computer Networks Management System Project Report.pdfKamal Acharya
Networking is a telecommunications network that allows computers to exchange data. In
computer networks, networked computing devices pass data to each other along data
connections. Data is transferred in the form of packets. The connections between nodes are
established using either cable media or wireless media.
Covid Management System Project Report.pdfKamal Acharya
CoVID-19 sprang up in Wuhan China in November 2019 and was declared a pandemic by the in January 2020 World Health Organization (WHO). Like the Spanish flu of 1918 that claimed millions of lives, the COVID-19 has caused the demise of thousands with China, Italy, Spain, USA and India having the highest statistics on infection and mortality rates. Regardless of existing sophisticated technologies and medical science, the spread has continued to surge high. With this COVID-19 Management System, organizations can respond virtually to the COVID-19 pandemic and protect, educate and care for citizens in the community in a quick and effective manner. This comprehensive solution not only helps in containing the virus but also proactively empowers both citizens and care providers to minimize the spread of the virus through targeted strategies and education.
1. VIDYARTHIPLUS - ANNA UNIVERSITY ONLINE STUDENTS COMMUNITY
DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK
CE 6306 - STRENGTH OF MATERIALS
UNIT I
STRESS STRAIN DEFORMATION OF SOLIDS
PART- A (2 Marks)
1. What is Hooke’s Law?
2. What are the Elastic Constants?
3. Define Poisson’s Ratio.
4. Define: Resilience
5. Define proof resilience
6. Define modulus of resilience.
7. Define principal planes and principal stresses.
8. Define stress and strain.
9. Define Shear stress and Shear strain.
10. Define elastic limit.
11. Define volumetric strain.
12. Define tensile stress and compressive stress.
13.Define young’s Modulus.
14.What is the use of Mohr’s circle?
15.Define thermal stress.
16. Define Bulk modulus.
17. What is modulus of rigidity?
18. Define factor of safety.
19. State the relationship between young’s modulus and modulus of rigidity..
20. What is compound bar?
PART- B (16 Marks)
1. A Mild steel rod of 20 mm diameter and 300 mm long is enclosed centrally inside a hollow
copper tube of external diameter 30 mm and internal diameter 25 mm. The ends of the rod
and tube are brazed together, and the composite bar is subjected to an axial pull of 40 kN. If
E for steel and copper is 200 GN/m2 and 100 GN/m2 respectively, find the stresses
developed in the rod and the tube also find the extension of the rod.
2. A cast iron flat 300 mm long and 30 mm (thickness) × 60 mm (width) uniform cross section,
is acted upon by the following forces : 30 kN tensile in the direction of the length 360 kN
compression in the direction of the width 240 kN tensile in the direction of the thickness.
Calculate the direct strain, net strain in each direction and change in volume of the flat.
Assume the modulus of elasticity and Poisson’s ratio for cast iron as 140 kN/mm2
and 0.25
respectively.
3. A bar of 30 mm diameter is subjected to a pull of 60 kN. The measured extension on gauge
length of 200 mm is 0.09 mm and the change in diameter is 0.0039 mm. calculate the
Poisson’s ratio and the values of the three moduli.
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2. 4. The bar shown in fig. is subjected to a tensile load of 160 KN. If the stress in the middle
portion is limited to 150 N/mm2
, determine the diameter of the middle portion. Find also the
length of the middle portion if the total elongation of the bar is to be 0.2mm. young’s
modulus is given as equal to 2.1 x 105
N/mm2
.
5. A member ABCD is subjected to point loads P1, P2, P3, P4 as shown in fig. calculate the
force P2 necessary for equilibrium, if P1 = 45 KN, P3 = 450 KN and P4 = 139 KN.
Determine the total elongation of the member, assuming the modulus of elasticity to be 2.1
x 105
N/mm2
.
6. A steel rod of 20mm diameter passes centrally through a copper tube of 50mm external
diameter and 40mm internal diameter. The tube is closed at each end by rigid plates of
negligible thickness. The nuts are tightened lightly home on the projecting parts of the rod. If
the temperature of the assembly is raised by 50˚C, calculate the stress developed in copper
and steel. Take E for steel and copper as 200 GN/m2
and 100 GN/m2
and α for steel and
copper as 12 x 10-6
per ˚C and 18 x 10-6
per ˚C.
7. Two vertical rods one of steel and the other of copper are each rigidly fixed at the top and
50cm apart. Diameters and lengths of each rod are 2cm and 4m respectively. A cross bar
fixed to the rods at the lower ends carries a load of 5000 N such that the cross bar remains
horizontal even after loading. Find the stress in each rod and the position of the load on the
bar. Take E for steel = 2 x 105
N/mm2
and E for copper = 1x 105
N/mm2
.
8. Drive the relationship between modulus of elasticity and modulus of rigidity. Calculate the
modulus of rigidity and bulk modulus of a cylindrical bar of diameter 30 mm and of length
1.5 m if the longitudinal strain in a bar during a tensile stress is four times the lateral strain.
Find the change in volume, when the bar is subjected to a hydrostatic pressure of 10 N/mm2.
Take E = 1X 105
N/mm2
A) what are the different types of machining operations that can be
performed on a lathe? And explain any six in detail.
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3. 9. (A). Find the young’s modulus of a rod of diameter 30mm and of length 300mm which is
subjected to a tensile load of 60 KN and the extension of the rod is equal to 0.4 mm.
(B). The ultimate stress for a hollow steel column which carries an axial load of 2MN is 500
N/mm2
.If the external diameter of the column is 250mm, determine the internal diameter
Take the factor of safety as 4.0
10. The extension in a rectangular steel bar of length 400mm and thickness 3mm is found be
0.21mm .The bar tapers uniformly in width from 20mm to 60mm E for the bar is 2x 105
N/mm2
.Determine the axial load on the bar.
UNIT II
BEAMS – LOADS AND STRESSES
PART- A (2 Marks)
1. State the different types of supports.
2. What is cantilever beam?
3. Write the equation for the simple bending theory.
4. What do you mean by the point of contraflexure?
5. What is mean by positive or sagging BM?
6. Define shear force and bending moment.
7. What is Shear stress diagram?
8. What is Bending moment diagram?
9. What are the different types of loading?
10. Write the assumption in the theory of simple bending.
11. What are the types of beams?
12. When will bending moment is maximum.
13. Write down relations for maximum shear force and bending moment in case of a
cantilever beam subjected to uniformly distributed load running over entire span.
14. Draw the shear force diagram for a cantilever beam of span 4 m and carrying a
point load of 50 KN at mid span.
15. Sketch (a) the bending stress distribution (b) shear stress distribution for a beam of
rectangular cross section.
16. A cantilever beam 3 m long carries a load of 20 KN at its free end. Calculate the
shear force and bending moment at a section 2 m from the free end.
17. Derive the relation between the intensity of load and shear force, in bending
theory.
18. A clockwise moment M is applied at the free end of a cantilever. Draw the SF and
BM diagrams for the cantilever.
19. What is maximum bending moment in a simply supported beam of span ‘L’
subjected to UDL of ‘w’ over entire span?
20. What is mean by negative or hogging BM?
PART- B (16 Marks)
1. Three blanks of each 50 x200 mm timber are built up to a symmetrical I section for a
beam. The maximum shear force over the beam is 4KN. Propose an alternate rectangular
section of the same material so that the maximum shear stress developed is same in both
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4. sections. Assume then width of the section to be 2/3 of the depth.
2. A beam of uniform section 10 m long carries a udl of 2KN/m for the entire length and a
concentrated load of 10 KN at right end. The beam is freely supported at the left end. Find the
position of the second support so that the maximum bending moment in the beam is as
minimum as possible. Also compute the maximum bending moment
3. A beam of size 150 mm wide, 250 mm deep carries a uniformly distributed load of w
kN/m over entire span of 4 m. A concentrated load 1 kN is acting at a distance of 1.2 m from
the left support. If the bending stress at a section 1.8 m from the left support is not to exceed
3.25 N/mm2
find the load w.
4. A cantilever of 2m length carries a point load of 20 KN at 0.8 m from the fixed end and
another point of 5 KN at the free end. In addition, a u.d.l. of 15 KN/m is spread over the
entire length of the cantilever. Draw the S.F.D, and B.M.D.
5. A Simply supported beam of effective span 6 m carries three point loads of 30 KN, 25
KN and 40 KN at 1m, 3m and 4.5m respectively from the left support. Draw the SFD and
BMD. Indicating values at salient points.
6. A Simply supported beam of length 6 metres carries a udl of 20KN/m throughout its
length and a point of 30 KN at 2 metres from the right support. Draw the shear force and
bending moment diagram. Also find the position and magnitude of maximum Bending
moment.
7. A Simply supported beam 6 metre span carries udl of 20 KN/m for left half of span and
two point loads of 25 KN end 35 KN at 4 m and 5 m from left support. Find maximum SF and
BM and their location drawing SF and BM diagrams.
8. A cantilever 1.5m long is loaded with a uniformly distribution load of 2 kN/m run over a
length of 1.25m from the free end it also carries a point load of 3kn at a distance of 0.25m from
the free end. Draw the shear force and bending moment diagram of the cantilever.
9. For the simply supported beam loaded as shown in Fig. , draw the shear force diagram
and bending moment diagram. Also, obtain the maximum bending moment.
10. A cast iron beam is of T-section as shown in Fig. The beam is simply supported on a
span of 6 m. The beam carries a uniformly distributed load of 2kN/m on the entire length
(span). Determine the maximum tensile and maximum compressive stress.
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5. UNIT III
TORSION
PART-A (2 Marks)
1. Define torsional rigidity of the solid circular shaft.
2. Distinguish between closed coil helical spring and open coil helical spring.
3. What is meant by composite shaft?
4. What is called Twisting moment?
5. What is Polar Modulus ?
6. Define: Torsional rigidity of a shaft.
7. What do mean by strength of a shaft?
8. Write down the equation for Wahl factor.
9. Define: Torsional stiffness.
10. What are springs? Name the two important types.
11. How will you find maximum shear stress induced in the wire of a close-coiled helical spring
carrying an axial load?
12. Write the expressions for stiffness of a close coiled helical spring.
13. Find the minimum diameter of shaft required to transmit a torque of 29820 Nm if the
maximum shear stress is not to exceed 45 N/mm2
.
14. Find the torque which a shaft of 50 mm diameter can transmit safely, if the allowable shear
stress is 75 N/mm2
.
15. Differentiate open coiled helical spring from the close coiled helical spring and state the type
of stress induced in each spring due to an axial load.
16. What is spring index (C)?
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6. 17. State any two functions of springs.
18. Write the polar modulus for solid shaft and circular shaft.
19. What are the assumptions made in Torsion equation
20. Write an expression for the angle of twist for a hollow circular shaft with external
diameter D, internal diameter d, length l and rigidity modulus G.
PART- B (16 Marks)
1. Determine the diameter of a solid shaft which will transmit 300 KN at 250 rpm. The
maximum shear stress should not exceed 30 N/mm2 and twist should not be more than 10 in a
shaft length 2m. Take modulus of rigidity = 1 x 105
N/mm2
.
2. The stiffness of the closed coil helical spring at mean diameter 20 cm is made of 3 cm
diameter rod and has 16 turns. A weight of 3 KN is dropped on this spring. Find the height by
which the weight should be dropped before striking the spring so that the spring may be
compressed by 18 cm. Take C= 8x104
N/mm2
.
3. It is required to design a closed coiled helical spring which shall deflect 1mm under an axial
load of 100 N at a shear stress of 90 Mpa. The spring is to be made of round wire having shear
modulus of 0.8 x 105
Mpa. The mean diameter of the coil is 10 times that of the coil wire. Find
the diameter and length of the wire.
4. A steel shaft ABCD having a total length of 2400 mm is contributed by three different sections
as follows. The portion AB is hollow having outside and inside diameters 80 mm and 50 mm
respectively, BC is solid and 80 mm diameter. CD is also solid and 70 mm diameter. If the angle
of twist is same for each section, determine the length of each portion and the total angle of twist.
Maximum permissible shear stress is 50 Mpa and shear modulus 0.82 x 105
MPa
5. The stiffness of close coiled helical spring is 1.5 N/mm of compression under a maximum load
of 60 N. The maximum shear stress in the wire of the spring is 125 N/mm2
. The solid length of
the spring (when the coils are touching) is 50 mm. Find the diameter of coil, diameter of wire
and number of coils. C = 4.5.
6. Calculate the power that can be transmitted at a 300 r.p.m. by a hollow steel shaft of 75 mm
external diameter and 50 mm internal diameter when the permissible shear stress for the steel is
70 N/mm2 and the maximum torque is 1.3 times the mean. Compare the strength of this hollow
shaft with that of an solid shaft. The same material, weight and length of both the shafts are the
same.
7. A solid cylindrical shaft is to transmit 300 kN power at 100 rpm. If the shear stress is not to
exceed 60 N/mm2
, find its diameter. What percent saving in weight would be obtained if this
shaft is replaced by a hollow one whose internal diameter equals to 0.6 of the external diameter,
the length, the material and maximum shear stress being the same.
8. A helical spring of circular cross-section wire 18 mm in diameter is loaded by a force of 500
N. The mean coil diameter of the spring is 125mm. The modulus of rigidity is 80 kN/mm2.
Determine the maximum shear stress in the material of the spring. What number of coils must
the spring have for its deflection to be 6 mm?
9. A close coiled helical spring is to have a stiffness of 1.5 N/mm of compression under a
maximum load of 60 N. the maximum shearing stress produced in the wire of the spring is 125
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7. N/mm2
.The solid length of the spring is 50mm. Find the diameter of coil, diameter of wire and
number of coils .C = 4.5 xl04N/mm2
.
10. A closely coiled helical spring of round steel wire 10 mm in diameter having 10 complete
turns with a mean diameter of 12 cm is subjected to an axial load of 250 N. Determine
I. the deflection of the spring
II. maximum shear stress in the wire and
III. stiffness of the spring and
IV. frequency of vibration. Take C = 0.8 x 105
N/mm2
.
UNIT IV
DEFLECTION OF BEAMS
PART-A (2 Marks)
1. State the condition for the use of Macaulay’s method.
2. What is the maximum deflection in a simply supported beam subjected to uniformly
distributed load over the entire span?
3. What is crippling load? Give the effective length of columns when both ends hinged and
when both ends fixed.
4. Find the critical load of an Euler’s column having 4 m length, 50 mm x 100 mm cross section
and hinged at both the ends E = 200 kn/mm2.
5. Calculate the maximum deflection of a simply supported beam carrying a point load of 100
KN at mid span. Span = 6 m, E= 20000 kn/m2.
6. A cantilever beam of spring 2 m is carrying a point load of 20 kn at its free end. Calculate the
slope at the free end. Assume EI = 12 x 103
KNm2
.
7. Calculate the effective length of a long column, whose actual length is 4 m when : a. Both
ends are fixed b. One end fixed while the other end is free.
8. A cantilever is subjected to a point load W at the free end. What is the slope and deflection at
the free end?
9. What are the methods for finding out the slope and deflection at a section?
10. Why moment area method is more useful, when compared with double integration?
11. Explain the Theorem for conjugate beam method?
12. What are the points to be worth for conjugate beam method?
13. What are the different modes of failures of a column?
14. Write down the Rankine formula for columns.
15. What is effective or equivalent length of column?
16. Define Slenderness Ratio.
17. Define the terms column and strut.
18. What are the advantages of Macaulay method over the double integration method, for finding
the slope and deflections of beams?
19. State the limitations of Euler’s formula
20. A cantilever beam of spring 4 m is carrying a point load of 2x103
Nat its free end. Calculate
the slope at the free end. Assume EI = 2X105
N/mm2
PART-B (16 Marks)
1. A beam AB of length 8 m is simply supported at its ends and carries two point loads of 50 kN
and 40 kN at a distance of 2 m and 5 m respectively from left support A. Determine, deflection
under each load, maximum deflection and the position at which maximum deflection occurs.
Take E = 2 x 105
N/mm2
and I = 8.5 X106
mm4
.
2. A 1.2 m long column has a circular cross section of 45 mm diameter one of the
ends of the column is fixed in direction and position and other ends is free. Taking
factor of safety as 3, calculate the safe load using
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8. (i) Rankine's formula, take yield stress = 560 N/mm2
and a = 1/1600 for pinned ends.
(ii) Euler's formula, Young's modulus for cast iron = 1.2 x 105 N/mm2
.
3. For the cantilever beam shown in Fig.3. Find the deflection and slope at the free end. EI =
10000 kN/m2
.
Fig.3
4.A beam is simply supported at its ends over a span of 10 m and carries two concentrated loads
of 100 kN and 60 kN at a distance of 2 m and 5 m respectively from the left support. Calculate
(i) slope at the left support (ii)slope and deflection under the 100 kN load. Assume EI = 36 x 104
kN-m2
.
5. Find the Euler critical load for a hollow cylindrical cast iron column 150 mm external
diameter, 20 mm wall thickness if it is 6 m long with hinged at both ends. Assume Young's
modulus of cast iron as 80 kN/mm2. Compare this load with that given by Rankine formula.
Using Rankine constants a =1/1600 and 567 N/mm2
.
6.A 3 m long cantilever of uniform rectangular cross–section 150 mm wide and 300 mm deep is
loaded with a point load of 3 kN at the free end and a udl of 2 kN/m over the entire length. Find
the maximum deflection. E = 210 kN/mm2. Use Macaulay’s method.
7. A simply supported beam of span 6 m is subjected to a udl of 2 kN/m over the entire span and
a point load of 3 kN at 4 m from the left support. Find the deflection under the point load in
terms of EI. Use strain energy method.
8.A simply supported beam of uniform flexural rigidity EI and span l, carries two
symmetrically placed loads P at one–third of the span from each end. Find the slope at
the supports and the deflection at mid–span. Use moment area theorems.
9. Derive double integration method for cantilever beam concentrated load at free end.
10. Determine the section of a hollow C.I. cylindrical column 5 m long with ends firmly built in.
The column has to carry an axial compressive load of 588.6 KN. The internal diameter of the
column is 0.75 times the external diameter. Use Rankine’s constants. a = 1 / 1600, σc = 57.58
KN/cm2
and F.O.S = 6.
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9. UNIT V
THIN CYLINDERS, SPHERES AND THICK CYLINDERS
PART-A (2 Marks)
1. A cylindrical pipe of diameter 1.5 m and thickness 1.5 cm is subjected to an internal fluid
pressure of 1.2 N/mm2
. Determine the longitudinal stress developed in the pipe.
2. Find the thickness of the pipe due to an internal pressure of 10 N/mm2
if the permissible
stress is 120 N/mm2
. The diameter of pipe is 750 mm.
3. The principal stress at a point are 100 N/mm2
(tensile) and 50 N/mm2
(compressive)
respectively. Calculate the maximum shear stress at this point.
4. A spherical shell of 1 m diameter is subjected to an internal pressure 0.5N/mm2
. Find the
thickness if the thickness of the shell, if the allowable stress in the material of the shell is 75
N/mm2
.
5. Normal stresses s x and s y and shear stress t act at a point. Find the principal stresses and the
principal planes.
6. Derive an expression for the longitudinal stress in a thin cylinder subjected to an uniform
internal fluid pressure.
7. Distinguish between thick and thin cylinders.
8. What is mean by compressive and tensile force?
9. How will you determine the forces in a member by method of joints?
10. Define thin cylinder?
11. What are types of stress in a thin cylindrical vessel subjected to internal pressure?
12. What is mean by Circumferential stress (or hoop stress) and Longitudinal stress?
13. What are the formula for finding circumferential stress and longitudinal stress?
14. What are maximum shear stresses at any point in a cylinder
15. What are the formula for finding circumferential strain and longitudinal strain?
16. What are the formula for finding change in diameter, change in length and change volume of
a cylindrical shell subjected to internal fluid pressure p?
17. Distinguish between Circumferential stress (or hoop stress) and Longitudinal stress?
18. Find the thickness of the pipe due to an internal pressure of 10 N/mm2
if the permissible
stress is 120 N/mm2
. The diameter of pipe is 750 mm.
19. what do you mean by a thick compound cylinder? how will you determine the hoop stresses
in a thick compound cylinder?
20. what are the different methods of reducing hoop stresses?
PART –B ( 16 MARKS)
1.A thin cylinder 1.5 m internal diameter and 5 m long is subjected to an internal pressure of 2
N/mm2
. If the maximum stress is limited to 160 N/mm2
, find the thickness of the cylinder. E =
200 kN/mm2
and Poisson’s ratio = 0.3. Also find the changes in diameter, length and volume of
the cylinder.
2. At a point in a strained material the horizontal tensile stress is 80 N/mm2
and the vertical
compressive stress is 140 N/mm2
. The shear stress is 40N/mm2
. Find the principal stresses and
the principal planes. Find also the maximum shear stress and its planes.
3. A thin cylindrical shell 3 m long has 1m internal diameter and 15 mm metal thickness.
Calculate the circumferential and longitudinal stresses induced and also the change in the
dimensions of the shell, if it is subjected to an internal pressure of1.5 N/mm2
Take E = 2x105
N/mm2
and poison’s ratio =0.3. Also calculate change in volume.
4. A closed cylindrical vessel made of steel plates 4 mm thick with plane ends, carries fluid
under pressure of 3 N/mm2 The diameter of the cylinder is 25cm and length is75 cm. Calculate
the longitudinal and hoop stresses in the cylinder wall and determine the change in diameter,
length and Volume of the cylinder. Take E=2.1x105
N/mm2
and 1/m = 0.286.
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10. 5. A cylindrical shell 3 m long, 1 m internal diameter and 10 mm thick is subjected to an internal
pressure of 1.5 N/mm2. Calculate the changes in length, diameter and volume of the cylinder. E
= 200 kN/mm2
, Poisson’s ratio = 0.3.
6. A steel cylindrical shell 3 m long which is closed at its ends, had an internal diameter of 1.5 m
and a wall thickness of 20 mm. Calculate the circumferential and longitudinal stress induced and
also the change in dimensions of the shell if it is subjected to an internal pressure of 1.0N/mm2
.
Assume the modulus of elasticity and Poisson's ratio for steel as 200kN/mm2
and 0.3
respectively.
7. A cylindrical shell 3 m long which is closed at the ends has an internal diameter 1m and wall
thickness of 15 mm. Calculate the change in dimensions and change in
volume if the internal pressure is 1.5 N/mm2
,E = 2 x 105
N/min2, μ= 0.3.
8. A cylindrical shell 3 m long which is closed at the ends, has an internal diameter of 1m and a
wall thickness of 20 mm. Calculate the circumferential and longitudinal stresses induced and also
changes in the dimensions of the shell, if it is subjected to an
internal pressure of 2.0 N/mm2
. Take E = 2 X 105
N/mm2
and — 1= 0.3.m
9. A closed cylindrical vessel made of steel plates 5 mm thick with plane ends, carries fluid
under pressure of 6 N/mm2
The diameter of the cylinder is 35cm and length is 85 cm. Calculate
the longitudinal and hoop stresses in the cylinder wall and determine the change in diameter,
length and Volume of the cylinder. Take E=2.1x105
N/mm2
and 1/m = 0.286
10. Determine the maximum hoop stress across the section of a pipe of external diameter 600mm
and internal diameter 440mm. when the pipe is subjected to an internal fluid pressure of
50N/mm2
.
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