This document provides a table of contents for a textbook on structural analysis. It covers topics such as properties of materials, stresses and strains, analysis of trusses, beams, frames, cables, and statically indeterminate structures. The textbook contains 25 chapters and over 660 pages of content on analyzing the strength and behavior of engineering structures and their components.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
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journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Simulation and Experimental Studies on Composite BeamsIJERA Editor
A composite beam a one dimensional structure or a rod all of them are sectional dimensions in which width and height are much smaller in comparison to the structure. In structural applications longer beams are more frequently used. In this work a composite beam is manufactured with glass and epoxy combination. And stress analysis is carried out using derived analytical expressions. This research work carried out will enable to determine the beam strength due to bending loads. The importance of fiber reinforcement in the manufacturing of the beam is studied in terms of bending strength of the beam. Mat lab codes are generated to implement analytical equations of the composite beam. The analytical results are validated by performing experiments on composite beams. In this investigation, two different composite beams have been tested and compared the experimental results with the analytical results.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Simulation and Experimental Studies on Composite BeamsIJERA Editor
A composite beam a one dimensional structure or a rod all of them are sectional dimensions in which width and height are much smaller in comparison to the structure. In structural applications longer beams are more frequently used. In this work a composite beam is manufactured with glass and epoxy combination. And stress analysis is carried out using derived analytical expressions. This research work carried out will enable to determine the beam strength due to bending loads. The importance of fiber reinforcement in the manufacturing of the beam is studied in terms of bending strength of the beam. Mat lab codes are generated to implement analytical equations of the composite beam. The analytical results are validated by performing experiments on composite beams. In this investigation, two different composite beams have been tested and compared the experimental results with the analytical results.
In a multi-storied building, the beam-column joint is one of the most critical regions. Usually the beam-column joint was considered as rigid frames. Various researchers over the past years indicated that the joint is not rigid. Now it is also stated that instead of the failure in beam and column, failure can also occur in joint hence joint must be considered as a structural member. The Indian standards define a joint as the portion of the column within the depth of the deepest beam that frames into the column. In framed structures the bending moment and shear forces are maximum at the junction area. So, beam column joint is one of the failure zones. Among the beam column joints, the exterior joint is more critical. The exterior beam column joint have been a study for about 30 years since now. Still there are many more to be understood. In the present work a building is designed in STAAD. Pro V8i and an exterior beam column joint is considered. This joint is modelled in NX CAD and imported to ANSYS to analyse it to derive the shear stress and the corresponding deformation. Pramod Verma | Prof. Pratiksha Malviya "Exterior Beam Column Joint: An Assessment" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd21589.pdf
Paper URL: https://www.ijtsrd.com/engineering/civil-engineering/21589/exterior-beam-column-joint-an-assessment/pramod-verma
Analysis of Two Way Simply Supported Slabs With Central Sunk Using Finite Ele...IJERA Editor
Majority of the sunken slabs are constructed with supporting beams, which leads to the uneconomy of the structure and difficult in arrangement of the centering work. In this view, it is considered to analyze a two way simply supported slab of different thicknesses with central sunk having one sunk depths.The objective of the paper is to analyze a two way simply supported slab having different thicknesses of 125,150,175,and 200mm with central sunk having depths of 250mm using Finite Element Analysis. This study significantly concludes that, adopting FE analysis using STAAD Pro for analysis of two-way sunken slab is advisable. By using FE analysis using STAAD Pro, we can avoid tedious and lengthy procedure of manual methods. From the chosen sunken slab it was observed that, there is decrease in sagging moments for sunk size of 0.25lx x 0.25ly with respect to two way slab without sunk.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Tensile test of a strand with 2 broken wires artificially damaged and life pr...theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Contact Stress Analysis of Stainless Steel Spur Gears using Finite Element An...IJERA Editor
Gears or toothed wheels form a positive drive for power transmission system in precision machines wherein a definite velocity ratio is needed. Despite having high cost, complicated manufacturing, need of precise alignment of shafts and lubrication, the gear drives are preferred over other power transmission drives. One of the important reasons of preference being that of efficiency which is very high in gear drives, even upto 99 per cent in case of spur gears. Spur gears are the simplest of the gear drives having teeth cut parallel to the axis of the shaft. Herein, we report the contact stress analysis of Stainless Steel spur gears by theoretical method using Hertz equations and by Finite Element Analysis using FEA software ANSYS 14.0 Workbench. The spur gear is sketched and modelled in ANSYS Design Modeller and the contact stress analysis is done in Mechanical ANSYS Multiphysics. When compared, the results of both theoretical method and FEA show a good degree of agreement with each other.
In a multi-storied building, the beam-column joint is one of the most critical regions. Usually the beam-column joint was considered as rigid frames. Various researchers over the past years indicated that the joint is not rigid. Now it is also stated that instead of the failure in beam and column, failure can also occur in joint hence joint must be considered as a structural member. The Indian standards define a joint as the portion of the column within the depth of the deepest beam that frames into the column. In framed structures the bending moment and shear forces are maximum at the junction area. So, beam column joint is one of the failure zones. Among the beam column joints, the exterior joint is more critical. The exterior beam column joint have been a study for about 30 years since now. Still there are many more to be understood. In the present work a building is designed in STAAD. Pro V8i and an exterior beam column joint is considered. This joint is modelled in NX CAD and imported to ANSYS to analyse it to derive the shear stress and the corresponding deformation. Pramod Verma | Prof. Pratiksha Malviya "Exterior Beam Column Joint: An Assessment" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd21589.pdf
Paper URL: https://www.ijtsrd.com/engineering/civil-engineering/21589/exterior-beam-column-joint-an-assessment/pramod-verma
Analysis of Two Way Simply Supported Slabs With Central Sunk Using Finite Ele...IJERA Editor
Majority of the sunken slabs are constructed with supporting beams, which leads to the uneconomy of the structure and difficult in arrangement of the centering work. In this view, it is considered to analyze a two way simply supported slab of different thicknesses with central sunk having one sunk depths.The objective of the paper is to analyze a two way simply supported slab having different thicknesses of 125,150,175,and 200mm with central sunk having depths of 250mm using Finite Element Analysis. This study significantly concludes that, adopting FE analysis using STAAD Pro for analysis of two-way sunken slab is advisable. By using FE analysis using STAAD Pro, we can avoid tedious and lengthy procedure of manual methods. From the chosen sunken slab it was observed that, there is decrease in sagging moments for sunk size of 0.25lx x 0.25ly with respect to two way slab without sunk.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Tensile test of a strand with 2 broken wires artificially damaged and life pr...theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Contact Stress Analysis of Stainless Steel Spur Gears using Finite Element An...IJERA Editor
Gears or toothed wheels form a positive drive for power transmission system in precision machines wherein a definite velocity ratio is needed. Despite having high cost, complicated manufacturing, need of precise alignment of shafts and lubrication, the gear drives are preferred over other power transmission drives. One of the important reasons of preference being that of efficiency which is very high in gear drives, even upto 99 per cent in case of spur gears. Spur gears are the simplest of the gear drives having teeth cut parallel to the axis of the shaft. Herein, we report the contact stress analysis of Stainless Steel spur gears by theoretical method using Hertz equations and by Finite Element Analysis using FEA software ANSYS 14.0 Workbench. The spur gear is sketched and modelled in ANSYS Design Modeller and the contact stress analysis is done in Mechanical ANSYS Multiphysics. When compared, the results of both theoretical method and FEA show a good degree of agreement with each other.
Lecture slides on the evaluation of the shear stresses in solid, thick-walled and thin-walled cross sections, and the determination of the shear centre
Now in its seventh edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for introductory level engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, and full solutions for all 1,600 further questions.
Comparison of Multi-Risers using Stiffness matrix method and Gazetas Semi-Ana...Roshni Ramakrishnan
The most common Superstructure modelling procedure is the fixed base approach which assumes infinite stiffness at the foundation –soil interface. The above assumption is valid only for light structures on very stiff, rocky strata. It is seen that the relative stiffness between the superstructure & foundation is the major influencing factor. The current codes do not specify the provision of Soil-Structure-Interaction effects on the super structure modelling. Literature study showed a large number of case studies of the soil structure interaction effects on the low rise buildings. The S.S.I effect for the low rise buildings is considered to be more severe because of the height as it results in much smaller time period which generally falls in the linearly increasing range in the response spectrum given in IS 1893(Part 1).The linear range gives a higher value of the seismic base shear due to increased period on account of consideration of flexibility of soils. Also the earthquake forces are the predominant dynamic load case for low to medium rise buildings.In the present study, the performance of a set of multi –risers with similar plan, geometric configuration and material properties with variable heights is checked considering the soil structure interaction model with respect to the fixed base model. The assessment of the variation in design due to the soil structure interaction effect is done. For the purpose, the study of various soil structure models was done and the pros and cons of each model were studied and a comparative assessment was done to find the best suitable model for the problem in consideration. The IS code specifications for the dynamic load case analysis of structures were studied to know the assumptions made for the dynamic analysis of structures and also select the best soil structure model. The most common dynamic load analysis methods for . the R.C.C buildings are the equivalent lateral force method and the response spectrum method for the seismic forces and the wind load analysis is done using the static method of application of wind forces calculated from the wind pressure which is dependent on the basic wind speed. Hence the representation of soil medium as static springs whose stiffness values are calculated using a continuum method where the soil is viewed as a continuum with elastic properties and the solution involves rigid body motion equations and the matrix of dynamic influence is solved using various methods like Laplace’s transformations, Fourier transformations etc. The paper “Analysis of Machine foundation vibrations” by George Gazetas has given the various soil models and the different methodologies used in the solutions which was used as reference to compute the spring stiffness. The fixed base analysis was done and an appropriate foundation was arrived at. The direct method of the interaction study in which the soil element represented as static springs using continuum are applied to the structure.
This is a Major Project Report successfully done at DVRCET under the guidance of Mechanical Engineering Department & the Managing Director of NIRAJA TECHNOLOGIES located at Uppal (Hyderabad).
2. 2
STRENGTH OF MATERIALS
and
STRUCTURAL ANALYSIS
(Formerly Elementary Structural Analysis)
Ashok K. Jain
Ph.D. (Michigan), F.I.E.
Professor of Civil Engineering
Indian Institute of Technology Roorkee
Roorkee
Second Edition 2008
Nem Chand & Bros., Roorkee 247 667, India
3. 3
Contents
1. INTRODUCTION 1 - 18
1.1 Introduction 1
1.2 Need of Analysis 2
1.3 Idealization of the Solid 3
1.4 Techniques of Idealization of Civil Engineering Structures 4
1.5 Loads on Structures 12
1.6 Basic Tools of Analysis 13
1.7 Principle of Superposition 17
1.8 Factor of Safety 17
References 18
2. PROPERTIES OF MATERIALS 19 - 30
2.1 Introduction 19
2.2 Stress – Strain Diagram 20
2.3 Hooke’s Law 22
2.4 Idealized Stress – Strain Relations 25
2.5 Compressive Strength 26
2.6 Shear Strength 26
2.7 Fatigue Strength 26
2.8 Impact Strength 27
2.9 Poisson’s Ratio 28
2.10 Composite Materials 28
Problems 30
3. PROPERTIES OF SECTIONS 32 - 45
3.1 Importance of Section Property 32
3.2 Area of the Section and Moment of Areas 33
3.3 Finding the Neutral Axis 34
3.4 Finding the Moment of Inertia 36
3.5 Principal Axes and Principal Moment of Inertia 40
Problems 45
4. AXIAL STRESS AND DEFORMATIONS IN BARS 46 - 76
4.1 Introduction 46
4.2 Axial Deformation 46
4.3 St. Venant’s Principle 48
4.4 Illustrative Examples 48
4.5 Statically Indeterminate Problems 55
4. 4
4.6 Thermal Strains and Deformations 65
Problems 72
vii
viii
5. SHEAR STRESS IN RIVETS AND WELDS 77 - 92
5.1 Introduction 77
5.2 Riveted Connections 77
5.3 Types of Joints 78
5.4 Transmission of Forces through Rivets 79
5.5 Failure of a Riveted Connection 80
5.6 Welded Connections 85
5.7 Design of Butt Weld 87
5.8 Design of Fillet weld 87
Problems 91
6. CONCEPT OF STRESSES 93 - 122
6.1 Definition of Stress 93
6.2 Stress Components 94
6.3 Stresses on Oblique Planes 96
6.4 Principal Stresses 97
6.5 Maximum and Minimum Shear Stresses 99
6.6 State of Pure Shear 100
6.7 The Mohr’s Circle 101
6.8 Illustrative Examples 103
6.9 Stress Transformation in 3-D 113
Problems 120
7. CONCEPT OF STRAINS 123 - 148
7.1 Introduction 123
7.2 Generalized Hooke’s Law for Isotropic Materials 123
7.3 Strains in 2-D 126
Plane Stress Problems
Plane Strain Problems
7.4 Transformation of Strain in 2-D 128
7.5 Principal Strains and Maximum Shearing Strain 130
7.6 Mohr’s Circle for Plane Strain 130
7.7 Strain Rosettes 131
7.8 Illustrative Examples 133
7.9 Strain Transformation in 3-D 136
7.10 Volumetric Strains and Bulk Modulus 138
7.11 Relation Between the Elastic Constants 140
Problems 146
8. THIN AND THICK PRESSURE VESSELS 149 - 168
8.1 Introduction 149
5. 5
8.2 Thin Cylindrical Pressure Vessel 149
8.3 Thick Walled Cylindrical Pressure Vessel 151
8.4 Thin Spherical Pressure Vessel 154
8.5 Illustrative Examples 155
Problems 167
ix
9. TORSION IN SHAFTS 169 - 188
9.1 Introduction 169
9.2 St. Venant’s Torsion 169
9.3 Torsion Formula 170
9.4 Angle of Twist 171
9.5 Membrane Analogy 172
9.6 Illustrative Examples 174
9.7 Close Coiled Helical Springs 185
Problems 188
10. FAILURE THEORIES AND FATIGUE 189 - 207
10.1 Introduction 189
10.2 Maximum Normal Stress Theory 189
10.3 Maximum Strain Theory (St. Venant Theory) 190
10.4 Maximum Shear Stress Theory 192
10.5 Energy of Distortion Theory (Von-Mises Yield Criteria) 193
10.6 Octahedral Shear Stress Theory 195
10.7 Fatigue 196
10.8 S-N Curve 199
10.9 Effect of Mean Stress on Endurance Limit 200
10.10 Illustrative Examples 201
11. PLANE TRUSSES 208 - 248
11.1 Introduction 208
11.2 Arrangement of Members of a Truss 209
11.3 Conventional Types of Roof and Bridge Trusses 210
11.4 Stability and Determinacy 211
11.5 Free Body Diagrams 215
11.6 Notation and Sign Convention 216
11.7 Analysis of Trusses 218
11.8 Illustrative Examples 219
11.9 Equations of Condition 235
11.10 Zero Load Test 236
11.11 Classification of Trusses 239
11.12 Illustrative Examples 240
Problems 244
12. BENDING MOMENT AND SHEAR FORCE – BEAMS 249 - 293
12.1 Introduction 249
12.2 Definitions and Sign Convention 249
12.3 Static Determinacy 251
12.4 Equations of Conditions 251
6. 6
12.5 Stability of Structures 251
12.6 Computation of Axial Force, Shear Force and Bending Moment 253
12.7 Relationship between Load, Shear and Moment 254
12.8 Properties of Shear Force and Bending Moment Diagrams 256
12.9 Illustrative Examples 256
Problems 289
x
13. BENDING MOMENT, SHEAR FORCE AND THRUST –
PLANE FRAMES 294 - 319
13.1 Introduction 294
13.2 Stability and Determinacy 294
13.3 Sign Convention 295
13.4 Illustrative Examples 297
Problems 317
14. STRESSES IN BEAMS 320 - 363
14.1 Introduction 320
14.2 Bending Stresses – Theory of Simple Bending 320
14.3 Assumptions and Limitations in the Flexure Formula 324
14.4 Illustrative Examples 325
14.5 Shear Stresses 341
14.6 Shear Stresses in Common Beams 343
14.7 Illustrative Examples 345
Problems 359
15. COLUMNS AND STRUTS 364 - 396
15.1 Introduction 364
15.2 Euler’s Theory 364
15.3 Strength of a Perfect Column 373
15.4 Eccentric Loading of Columns 375
15.5 Elastic design 376
Rankine Gordon Formula
Straight Line Formula
Johnson’s Parabolic Formula
AISC Parabolic Formula (1989)
Perry Robertson Formula
Secant Formula
Merchant Rankine Formula
Multiple Curves for Steel Columns
15.6 Illustrative Examples 383
Problems 395
16. COMBINED AXIAL AND BENDING STRESSES 397 - 416
16.1 Introduction 397
16.2 Combined Stresses in Beams 397
16.3 Combined Stresses in Columns 401
16.4 Combined Stresses in Walls 410
Problems 414
7. 7
17. UNSYMMETRICAL BENDING AND SHEAR CENTER 417 - 448
17.1 Introduction 417
17.2 Assumptions 418
17.3 Stress at Any Point in a Short Column 419
xi
17.4 Illustrative Examples 420
17.5 Shear in Thin Walled Sections 429
17.6 Locating Shear Center 431
17.7 Shear Flow in Rectangular Section 434
17.8 Illustrative Examples 436
Problems 446
18. DEFLECTION OF BEAMS 449 - 510
18.1 Introduction 449
18.2 Direct Integration Method 450
18.3 Illustrative Examples 452
18.4 The Moment Area Method 468
18.5 Basic Properties of Parabolic Curves 470
18.6 Illustrative Examples 471
18.7 Elastic Load Method 480
18.8 Conjugate Method 482
18.9 Illustrative Examples 485
18.10 Principle of Virtual Work for Rigid Bodies 490
18.11 Unit Load Method 493
18.12 Illustrative Examples 495
18.13 Other Useful Theorems 503
Betti’s Law of Reciprocal Deflections
Maxwell’s Law of Reciprocal Deflections
Castigliano’s Theorems
Problems 507
19. DEFLECTION OF FRAMES 511 - 523
19.1 Introduction 511
19.2 Moment Area Method 511
19.3 Unit Load Method 514
Problems 519
20. DEFLECTION OF TRUSSES 524 - 541
20.1 Introduction 524
20.2 Virtual Work Method 524
20.3 Illustrative Examples 526
20.4 Williot Diagram 533
20.5 Williot Mohr Diagram 535
Problems 538
21. ARCHES 542 - 555
8. 8
21.1 Introduction 542
21.2 Arch vs. Beam 544
21.3 Three Hinged Arch 545
21.4 Illustrative Examples 546
Problems 554
xii
22. INFLUENCE LINES 556 - 602
22.1 Introduction 556
22.2 Moving Loads 556
22.3 Influence Lines 563
22.4 Influence Lines for Beams 564
22.5 Influence Lines for Girders with Floor Beams 576
22.6 Muller – Breslau Principle 580
22.7 Influence Lines for Trusses 583
22.8 Counters in Bridge Trusses 591
22.9 Influence Lines for Arches 592
Problems 599
23. CABLES 603 - 631
23.1 Introduction 603
23.2 Static Determinacy and Stability 604
23.3 General Equation of a Cable 605
23.4 Length of Cable 612
23.5 Graphical Analysis 613
23.6 Deformations of a Parabolic Cable 617
23.7 Illustrative Examples 619
Problems 630
24. SPACE TRUSSES 632 - 644
24.1 Introduction 632
24.2 Analysis of Space Trusses 633
24.3 Illustrative Examples 635
Problems 642
25. APPROXIMATE ANALYSIS OF STATICALLY
INDETERMINATE STRUCTURES 645 - 661
25.1 Introduction 645
25.2 Number of Assumptions Required 645
25.3 Portal Frames 646
25.4 Mill Buildings 647
25.5 Lateral Bracing for Bridges 648
25.6 Building Frames for Vertical Loads 648
25.7 Analysis for Lateral Loads 651
Problems 659
INDEX 662