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STEEL STRUCTURES
Editorial Board
Prof. Ajaya Kumar Nayak, BTech (NIT Rourkela), ME (IISc Bangalore), PhD (University of Southampton, UK)
Course Leader
Assistant Professor (Formerly Reader)
Civil Engineering Department, VSSUT, Burla
Email: [email protected], Ph No: +91-
Prof Leena Sinha, BTech (VSSUT, Burla), MTech (NIT, Rourkela)
Co-Course Leader
Assistant Professor (Formerly Lecturer)
Civil Engineering Department, VSSUT, Burla
Email: [email protected], Ph No: +91-
Prof Bjian Kumar Roy, BTech (BESU, Shibapur), MTech (BESU, Shibapur)
Co-Course Leader
Assistant Professor (Formerly Lecturer)
Civil Engineering Department, VSSUT, Burla
Email: [email protected], Ph No: +91-
Department of Civil Engineering
Veer Surendra Sai University of Technology, Burla, 768018, Odisha, India
DISCLAIMER
These lecture notes are being prepared and printed for the use in training the students and practicing engineers. No commercial use of these notes is permitted and copies of these will not be offered for sale in any manner. Due acknowledgement has been made in the reference sections. The readers are encouraged to provide written feedbacks for improvement of course materials.
Dr Ajaya Kumar Nayak
Mrs Leena Sinha
Mr Bijan Kumar Roy
Module 1 Lecture 1
In this lecture the course outline and the module and lecture wise breakup of the steel structure course are discussed. Also, the list of reference books, conference papers, reports and journals have been given.
Course Outline of BCE 309 Steel Structures (3-1-0) CR-04 (IS 800-2007 and Steel Tables are permitted in the Examination)
Module I: Philosophy, concept and methods of design of steel structures, structural elements, structural steel sections, riveted and welded connections, design of tension members
Module II: Design of compression members, Design of columns, lacing and battening, Column base and foundation
Module III: Design of beams, Plate Girder and Gantry Girder
Module IV: Design of roof trusses.
Course Prerequisites: Structural Analysis, Mechanics of Materials, Engineering Mechanics
References
- Ram Chandra and V. Gehlot, Design of Steel Structures, Scientific Publishers, Jodhpur
- L.S. Negi, Design of Steel Structures, Tata McGraw Hill Book Co.
- B.C. Punmia, A.K. Jain and A.K. Jain, Design of Steel Structures, Laxmi Publishers
- N. Subramanian, Design of Steel Structures, Oxford University Press
- S.K. Duggal, Limit State Design of Steel Structures, Tata McGraw Hill Book Co.
- R. Narayanan and Kalyanraman V, INSDAG Guide for the Structural Use of Steel Work in Buildings, IIT Madras and Institute of Steel Development and Growth
- PH Waarts, ACWM Vrouwenvelder, Stochastic finite element analysis of steel structures, Journal of Constructional Steel Research, 1999, 52, pp. 21-
- IS 800:2007, Indian Standard General Construction in Steel- Code of Practice (Third Revision), Bureau of Indian Standards, New Delhi, Dec 143 pages
- N Subramanian, Code of Practice on Steel Structures- A Review of IS800: 2007, CE & CR 2008. Pp 1-
- IS 800-1984, Indian Standard General Construction in Steel- Code of Practice (Second Revision), Bureau of Indian Standards, New Delhi, Dec 137 pages
- SP (1) 1964, Hand Book For Structural Engineers, 1. Structural Steel Sections, Bureau of Indian Standards
- J.C. McCormac and S.F. Csernak, Structural Steel Design, 5th^ Edition, Prentice Hall, 2011
- T.B. Quimby, A Beginner’s Guide to the Steel Construction Manual, 2008
- W.F. Chen and S. Toma, Advanced Analysis of Steel Frames, CRC Press, 1994
- M.K. Chryssanthopoulos, G.M.E Manzocchi and A.S. Elnashai Probabilistic assessment of ductility for earthquake resistant design of steel members, Joutnal of Constructional Steel Research, 1999, 52, 47-
- Code of Practice for the structural use of steel 2011, Building Department, HongKong
- R.B. Kulkarni and R.S. Jirage, Comparative Study of Steel Angles as Tension Members Designed by Working Stress Method and Limit State Method, International Journal of Scientific and Engineering Research, Volume 2, 10, 2011, 1-
- CAN/CSA-S16-01 Limit States Design of Steel Structures, A National Standard of Canada, 2003
- NORSOK STANDARD, Design of Steel Structures, 1998
- H. Krawinkler, Earthquake Design and Performance of Steel Structures, Bulletin of the New Zealand National Society for Earthquake Engineering, Vol 29, No 4, 1996.
- A Ivan, M Ivan and I Both Comparison of FEA and Experimental Results for a Steel Frame Connection, WSEAS Transactions on Applied and Theoretical Mechanics, 2010, 3(5), 187-196.
- BCSA and SCI, Hand Book of Structural Steel Work,2007, pp. 393,
- LA Pasnur, S.S Patil, Comparative Study of Beam Using IS 800-1984 & IS 800-2007, International Journal of Engineering and Innovative Technology, 2(10), 2013.
- C.W. Roeder, D.E. Lehman and J.H. Yoo, Improved Seismic Design of Steel Frame Connections, Steel Structures, 2005, 5, pp. 143-153.
- S.L.Chan and P.P.T Chui, Nonlinear Static and Cyclic Analysis of Steel Frames With Semi-rigid Connections, Elsevier, 2000
- M. Bill Wong, Plastic Design and Design of Steel Structures, Elsevier, 2009
- S. Leelataviwat, S.C. Goel and S.H. Chao, Plastic versus Elastic Design of Steel Structures, Encyclopedia of Life Support Systems, 2011
- K.M. Ghosh, Practical Design of Steel Structures, CRC Press, 2010
- B. Gorenc, R Tinyou and A Syam, Steel Designers HandBook, UNSW Press,
- Y.C. Wang, Steel and Composite Structures, Behaviour and Design for fire safety, Spon Press, 2002
- C Clifton, M Bruneau, G. MacRae, R Leon and A Fussell, Steel Structures Damage From The Christchurch earthquake 2010 and 2011, Bulletin of the New Zealand and Society for earthquake Engineering, Vol 44, 4, 2011, pp. 1-
- B. Kirkee and I H Al-Jamd, Steel Structures Design Manual to AS 4100, 2004, pp 1- 243
- T.J. MacGimley, Steel Structures Practical Design Studies, E & FN Spon, 2005
- F Wald, L.S. Da Silva, D.B. Moore, T. Lennon, M. Chladna, A Santiago, M Benes, L Borges, Experimental Behaviour of Steel Structure under natural fire, Fire Safety Journal, 41, 2006, pp. 509-
- Kim KD, Large displacement of elasto-plastic analysis of stiffened plate and shell structures, Steel Structures, 2006, 6, 65-69.
- Steel Bridge Design Handbook, Structural Behaviour of Steel, US Department of Transportation, November 2012
- IS 7216-1974 (Reaffirmed 2006) Indian Standard Tolerances for fabrication of steel structures, pp. 1-27.
- Y Gong Ultimate tensile deformation and strength capacities of bolted-angle connections, Journal of Constructional Steel Research, 2014, 100, 50-59.
- DT Phan, JBP Lim, TT Tanyimboh, R Mark Lawson, Y Xu, Effect of serviceability limits on optimal design of steel portal frames, Journal of Constructional Steel Research, 2013, 86, 74-84.
- A EI Hassouni, A Plumier, A Cherrabi Experimental and Numerical analysis of the strain-rate effect on fully welded connections, Journal of Constructional Steel research, 2011, 67, 533-546.
- R Bjorhovde The 2005 American steel structures design code, Journal of Constructional Steel Research, 2006, 62, 1008-1076.
- G Sedlacek, C Muller The European standard family and its basis, Journal of Constructional Steel research, 2006, 62, 1047-1059.
- R Aceti, G Ballio, A Capsoni and L Corradi A Limit analysis study to interpret the ultimate behaviour of bolted joints, Journal of Constructional Steel research, 2004, 60, 1333-1351.
- R Bjorhovde Development and use of high performance steel, Journal of Constructional steel research, 2004, 60, 393-400.
- MT Hanna Failure loads of web panels loaded in pure shear Journal of Constructional Steel research, 2015, 105, 39-48.
- YB Wang, GQ Li, W Cui, SW Chen, FF Sun Experimental investigation and modelling of cyclic behaviour of high strength steel, Journal of Constructional Steel Research, 2015, 104, 37-48.
- JM Ricles, JW Fisher, LW Lu, EJ Kaufmann, Development of improved welded moment connections for earthquake-resistant design, Journal of Constructional Steel research, 2002, 58, 565-604.
- Brockenbrough RL and F.S. Merritt, Structural Steel Designer’s Hand Book, McGRAW-HILL INC, 1999.
- HD Young and RA Freedman, University Physics, Addison Wesley Publishing Company, INC, 1996
- MJ Sienko and RA Plane, Chemistry Principles and Applications, McGRAW-HILL INC, 1979
- RT Morrison and RN Boyd, Organic Chemistry, Prentice Hall of India, Private Limited, New Delhi, 1998.
- E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 1999.
- AD Polyanin and AV Manzhirov, Handbook of Mathematics for Engineers and Scientists, Chapman and Hall, CRC Press, 2007
- SP Timoshenko and JM Lessells, Applied Elasticity, D. Van Nostrand Co. Inc, New York, 1925
- SP Timoshenko and DH Young, Vibration Problems in Engineering, D. Van Nostrand Co. Inc, New York, 1955
- SP Timoshenko, Strength of Materials, Part I. Elementary Theory and Problems, D. Van Nostrand Co. Inc, Princeton New Jersey, 1955
- SP Timoshenko, Strength of Materials, Part II. Advanced Theory and Problems, D. Van Nostrand Co. Inc, Princeton New Jersey, 1956
- SP Timoshenko and JN Goodier, Theory of Elasticity, Mc-Grawhill Book Co, 1951
- SP Timoshenko and GH MacCullough, Elements of strength of materials, D. Van Nostrand Co. Inc, Princeton New Jersey, 1949
- SP Timoshenko and DH Young, Elements of strength of materials, D. Van Nostrand Co. Inc, Princeton New Jersey, 1962
- SP Timoshenko and JM Gere, Theory of Elastic Stability, Mc-Grawhill Book Co, 1961
- SP Timoshenko and DH Young, Engineering Mechanics, Mc-Grawhill Book Co, 1956
- SP Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, Mc- Grawhill Book Co, 1959
- SP Timoshenko and DH Young, Theory of Structures, Mc-Grawhill Book Co, 1965
- SP Timoshenko and DH Young, Advanced Dynamics, Mc-Grawhill Book Co, 1948
- SP Timoshenko, History of strength of materials, Mc-Grawhill Book Co, 1953
- SP Timoshenko, Engineering Education in Russia, Mc-Grawhill Book Co, 1959
- SP Timoshenko, The collected papers of STEPHEN P TIMOSHENKO, Mc-Grawhill Book Co, 1953
- SP Timoshenko, As I Remember, The Autobiography of Stephen P Timoshenko, D. Van Nostrand Co. Inc, Princeton New Jersey, 1968
Detailed Course Plan: (Module Wise/Lecture Wise)
Sl No Module Lecture No
Content
1 1 Introduction
1 Philosophy of design of steel structures 2 2 Concept of design of steel structures 3 3 Methods of Design of steel structures 4 4 Structural Elements 5 5 Structural Steel Sections 6 6 Rivetted Connections 7 7 Welded Connections 8 8 Welded Connections 9 9 Design of Tension Members 10 10 Design of Tension Members
Introduction to Philosophy of design of steel structures
In this lecture the Philosophy of design of steel structures has been briefly discussed.
1.1 Historical Development of Structural Steel in the World
Ancient Hittis were the first users of iron some 3 to 4 millenniums ago. Their language was altered to Indo – European and they were native of Asia Minor. There is archaeological evidence of usage of iron dating back to 1000 BC, when Indus valley, Egyptians and probably the Greeks used iron for structures. Thus, iron industry has a long ancestry.
structures in public buildings, railway stations and bridges, which testifies the growth of steel in the past. The “Rabindra Sethu" Howrah Bridge in Calcutta stands testimony to a marvel in steel. Even after its service life, Howrah Bridge today stands as a monument. The recent example is the Second Hooghly cable stayed bridge at Calcutta, which involves 13, tonnes of steel. Similarly the Jogighopa rail-cum-road bridge across the river Brahmaputra is an example of steel intensive construction, which used 20,000 tonnes of steel. There are numerous bridges, especially for railways built, exclusively using steel.
As far as production of steel in India is concerned, as early as in 1907, Jamsetji Nusserwanji Tata set up the first steel manufacturing plant at Jamshedpur. Also at the same time in 1905, Tata Institute for research and development works was established in Bangalore, Karnataka which was later renamed as Indian Institute of Science, Bangalore. Later Pandit Jawaharlal Nehru realised the potential for the usage of steel in India and authorised the setting up of major steel plants at Bhilai, Rourkela and Durgapur in the first two five year plans. In Karnataka Sir Mokshakundam Visweswarayya established the Bhadravati Steel Plant. The annual production of steel in 1999-2000 has touched about 25 million tonnes and this is slated to grow at a faster rate.
1.2 Stress-strain Behaviour of Steel
The primary characteristics of structural steel include mechanical and chemical properties, metallurgical structures and weldability. In the past structural engineers have tended to focus only on the tensile properties (longitudinal yield stress and ultimate tensile strength), with some attention paid to the deformability as measured by the elongation at fracture of a tension specimen. Since the modulus of elasticity, E, is constant for all practical purposes for all grades of steel, it has rarely been a consideration other than for serviceability issues. Weldability was assumed to be adequate for all such steels. Deformability or ductility was similarly assumed to be satisfactory, in part because the design specification has offered only very limited, specific requirements.
The stress-strain curve for steel is generally obtained from tensile test on standard specimens as shown in Fig.1.1. The details of the specimen and the method of testing is elaborated in IS: 1608 (1995). The important parameters are the gauge length ‘Lc’ and the initial cross section area So. The loads are applied through the threaded or shouldered ends. The initial gauge length is taken as 5.65 (So)1/2 in the case of rectangular specimen and it is five times the diameter in the case of circular specimen. A typical stress-strain curve of the tensile test coupon is shown in Fig.1.2 in which a sharp change in yield point followed by plastic strain is observed. When the specimen undergoes deformation after yielding, Luder’s lines or Luder’s bands are observed on the surface of the specimen as shown in Fig.1.3.
These bands represent the region, which has deformed plastically and as the load is increased, they extend to the full gauge length. This occurs over the Luder’s strain of 1 to 2% for structural mild steel. After a certain amount of the plastic deformation of the material, due to reorientation of the crystal structure an increase in load is observed with increase in strain. This range is called the strain hardening range. After a little increase in load, the specimen eventually fractures. After the failure it is seen that the fractured surface of the two pieces form a cup and cone arrangement. This cup and cone fracture is considered to be an indication of ductile fracture. It is seen from Fig.1.2 that the elastic strain is up to εy followed by a yield plateau between strains εy and εsh and a strain hardening range start at εsh and the specimen fail at εult where εy, εsh and εult are the strains at onset of yielding, strain
hardening and failure respectively. Depending on the steel used, εsh generally varies between 5 to 15 εy, with an average value of 10 εy typically used in many applications. For all structural steels, the modulus of elasticity can be taken as 205,000 MPa and the tangent modus at the onset of strain hardening is roughly 1/30th of that value or approximately 6700 MPa.
Figure 1.1 Standard steel specimen
Figure 1.2 Stress-strain curve for sharp yielding structural steels
Figure 1.3 Luder’s band in steel specimens
and similarly
where ft and fn are the true and nominal stresses respectively and εt and εn are the true and nominal strains respectively.
1.3 Experimental Investigation of a True Stress-True Strain Model
In this section, experimental investigation of a true stress-true strain model is described. A standard uniaxial tensile test, in general, provides the basic mechanical properties of steel required by a structural designer; thus, the mill certificates provide properties such as yield strength Fy , ultimate strength Fu, and strain at fracture εf. The stress parameters are established using the original cross-section area of the specimen, and the average strain within the gauge length is established using the original gauge length. Because of the use of original dimensions in engineering stress-strain calculations, such relations will always show an elastic range, strain hardening range, and a strain softening range. As the load increases and when the specimen begins to fail, the cross-section area at the failure location reduces drastically, which is known as the “necking” of the section. In general, the strain softening is associated with the necking range of the test. Once the specimen begins to neck, the distribution of stresses and strains become complex and the magnitude of such quantities become difficult to establish. Owing to the non-uniform stress strain distributions existing at the neck for high levels of axial deformation, it has long been recognized that the changes in the geometric dimensions of the specimen need to be considered in order to properly describe the material response during the whole deformation process up to the fracture. The true stress-true strain relationship is based on the instantaneous geometric dimensions of the test specimen. Figure 1.6 illustrates the engineering stress-strain relationship and the true stress- true strain relationships for structural steels. These relationships can be divided into five different regions as follows.
Region-I (Linear Elastic Range). During the initial stages of loading, stress varies linearly proportional to strain (up to a proportional limit). The proportional limit stress Fpl is typically established by means of 0.01% strain offset method. Thus, the engineering stress can be related to engineering strain as follows: Fe = Eεe in the range Fe < Fpl and εe < εpl, where E is the initial elastic modulus of steel, which is often taken as 200,000MPa. The corresponding true stress and the true strain, which recognize the deformed geometrics of the section during tests, can be established directly from the engineering stress and the engineering strain based on the concept of uniform stress, small dimensional change, and In compressible material, which is valid for steel. Resulting relations are Ft = Fe (1 + εe) and εt = ln(1 + εe), where Ft and Fe are the true stress and engineering stress and εt and εe are the true strain and the engineering strain, respectively. The difference between true stress and engineering stress at
proportional limit stress may be about 0.2%; thus, the difference is insignificant in this region.
Figure 1.6 The engineering stress-strain relations and the proposed true stress-true strain material model
Region-II (Nonlinear Elastic Range). This range represents a region between the proportional limit and the yield point. The yield point Fy may be conveniently established as 0.2% strain offset method. In this region, the variation of stress-strain relationship can be idealized as Fe = Fpl+Et (εe−εpl), which is valid in the range Fpl < Fe < Fy. Here, Et is the tangent modulus given as Et = (Fy −Fpl)/(εy −εpl). The true stress and true strain can be obtained as in the linear elastic range as follows: Ft = Fe(1 + εe) and εt = ln(1 + εe), where εpl < εe < εy.
Region-III (Yield Plateau). Some steels may exhibit yield plateau. The engineering stress in this region can be assumed as a constant value of Fy , which is valid in the range εy < εe < εsh, where εsh is the strain at the onset of strain hardening. The ratio between εsh and εy is defined here as m = εsh/εy. The value for m must be determined from the uniaxial tension test. The true stress and true strain can be obtained as in the linear elastic range as; Ft = Fy(1+εe) and εt = ln(1+εe), where εy < εe < εsh.
Region-IV (Strain Hardening). At the end of yield plateau, strain hardening begins with a subsequent increase in stress. Region-IV includes the strain hardening range up to ultimate strength when the test specimen may begin to exhibit necking. Though this region involves a nonlinear stress-strain relation, it is postulated that the true stress and the true strain can be obtained using the relations Ft = Fe(1 + εe) and εt = ln(1 + εe). However, a power law is often used to relate the true stress to the true strain in this strain hardening region. A power law of the form Ft = Fut · (εt/εut)n is proposed herein, where Fut and εut are the true stress and true strain associated with the ultimate tensile strength Fu. The value for n must be
different locations within the reduced cross-section of the tensile coupons, and the average thickness and the average width of the test coupons were established. The thickness of the flange coupons was about 9.1mmand thickness of the web coupons was 5.8 mm. The width of the specimens was about 40 mm. The initial gross cross-sectional area of each specimen was calculated based on these average dimensions. Some test specimens, which were used for the validation of the proposed model, had a central hole. The net area at the hole location was established based on measured hole diameter. The specimen ID (identification) used in this investigation is based on net area/gross area ratio of the test specimen. In the specimen ID related to the experimental investigation, A992/350W indicates the steel grade followed by F/W, which indicates the flange/web, followed by the value of net area/gross area ratio. For example, Specimen ID-A992-F-0.8 refers to a coupon cut from the flange of the A992 steel with net area/gross area ratio of 0.8. Three identical flange and web coupons with no holes (shown as F1, W1, etc., in Figure 1.7 and Table 1.1) were used to establish the mechanical characteristics of the steel grades under consideration. Five remaining flange coupons and the three remaining web coupons were used as perforated tension coupons having different diameter holes at the centre of the specimens. Holes with net area/gross area ratios varying from 0.5 to 0.9 in increments of 0.1 were prepared for the flange coupons, whereas holes with net area/gross area ratios varying from 0.5 to 0.9 in increments of 0.2 were considered for the web coupons. The photographic image of the test specimens (solid sample with no holes, and perforated samples) is shown in Figures 1.7(a) and 1.7(b), respectively. The coupons were tension tested in a Tinius Olsen machine with an axial load capacity of 600 kN. Each test specimen was first aligned vertically and centered with respect to the grips of the machine’s loading platforms. Two extensometers having gauge lengths of 200mm and 50mm were attached on either face of the test coupon. The larger extensometer was used to establish the overall engineering stress-strain curve of the coupons, whereas the smaller extensometer, which had a greater sensitivity, allowed a more accurate estimation of the initial modulus (E) and the proportional limit stress (Fpl). Figure 1.8 shows the engineering stress-engineering strain relationships obtained during these tests. As evident from this figure, consistent results were obtained for three identical specimens. Furthermore, the specimens from the web exhibited yield plateau, whereas no such behavior was observed in the specimens taken from the flange. Table 1.1 summarizes the mechanical properties established from the solid coupon tensile tests. The average yield strength Fy and ultimate strength Fu of the A992-flange coupons were calculated to be 444MPa and 577MPa, respectively, resulting in the Fy/Fu ratio of 0.77. The average strains corresponding to the ultimate strength εu and at fracture ε f were measured to be 13.8% and 20.8%, respectively. Note that the above strains were based on 200mm gauge length. The average Fy and Fu values for the A992-web coupons were 409MPa and 573MPa, respectively, resulting in the Fy/Fu ratio of 0.71. These coupons reached the ultimate strength at the strain of 15.6% and fractured at the strain of 21.4%. The 350Wflange coupons had the Fy and Fu values of 427MPa and 578MPa, respectively, resulting in the Fy/Fu ratio of 0.74. The average εu and ε f values associated with these coupons were 13.9% and 22.0%, respectively. The average Fy and Fu values of 350W-web coupons were measured to be 416MPa and 582MPa, respectively, resulting in the Fy/Fu ratio of 0.71. These coupons had average εu and ε f of 15.3% and 19.5%, respectively. The Fy/Fu ratio value for the A992-flange coupon was 4%higher than that of the 350W-flange coupon.
The true stress-true strain model parameters for Regions-I, II, and III were extracted from these results and are shown in Table 1.2. The Region-IV requires the power law parameter n, which was established through linear regression of the test results corresponding to that region. The test results considered for this region is between points C and D in Figure 1.6 and is valid for true stress-true strain region between points C1 and D1 shown in Figure 1.6. Figure 1.9 shows a representative calculation corresponding to 350W web element. The experimental engineering stress and strains were first converted to true stress and strains, and then the strain hardening portion of the relationship was used to obtain a power law fit, which resulted in n = 0.1628 for 350W web element. Complete power law relationships for A992, 350W flange and web elements are given in Table 1.2. The Region-V requires establishment of a weighting constant w, which is found here by trial and error. The task is to match the finite element numerical analysis results with the corresponding experimental results in this region. Here, the tensile test coupon was modeled using the finite element analysis package ADINA. The model used the 4-node shell elements with six degrees of freedom per node. This element can be employed to model thick and thin general shell structures, and it accounts for finite strains by allowing for changes in the element thickness. Also, this shell element can be efficiently used with plastic multilinear material models for large- displacement/large-strain analyses. Each shell element employed 2 × 2 integration points in the mid surface (in r-s plane) and 3 Gauss numerical integration points through thickness (in t-direction). The model also incorporated a geometric imperfection (maximum amplitude of 0.1% of the width—40mm) of a half sine wave along the gauge length in order to cause diffuse necking. The analysis incorporated both geometric and material nonlinearities (von Mises yield criterion and isotropic strain hardening rule). One edge of the model was fully restrained while the other end was subjected to a uniform displacement. For analysis of members with mid-hole, which is presented in the next section, a finer mesh was used for a 50mm length of the middle region, where the strain gradient is expected to be large. The true stress and strain relationship for Regions- I, II, III, and IV used in the analysis model was derived from the engineering stress-strain curve obtained from tension coupon tests as described above and as given in Table 1.2. The material model in Region-V first requires a true fracture strain εft (point E1 shown in Figure 1.6). A Study undertaken previously indicated that the localized fracture strains for structural steel under uni-axial tensile load could vary between 80% and 120%. Therefore, this study considered a true fracture strain of 100% (i.e., εft = 100%.) corresponding to point E1. Figure 1.10 shows a representative FE model used to reproduce the standard coupon test and the associated failure of the model due to necking followed by fracture. This figure also shows the boundary conditions used in the FE model. The weighting constant w for Region-V has to be established in an iterative manner by numerical simulation of tensile tests until a good correlation is achieved between the calculated and the experimental load extension curves. In order to illustrate the influence of the weighting constant, three different values for w = 1.0, 0.6, and 0.4 were considered in the numerical simulations. Figure 1.11 shows the resulting FE predicted responses along with the experimental responses of three identical tension coupons (A992 flange). The weighting factor w = 1.0, which represents the Region-V by a power-law hardening model, results in a numerical response well below the experimental curves. However, for w = 0.4, the numerical curve was slightly above the experimental curve and sustains larger fracture strain. The
Figure 1.8 Experimental engineering stress-engineering strain relationships (over 200mm gauge length).
Figure 1.9 True stress-true strain relationships in region IV—350Wweb
Figure 1.10 Comparison of failure pattern of test sample with FE simulation results.
