 Open Access
 Total Downloads : 17
 Authors : Jyoti, Rachna , Satish Kumar, Jaidutt
 Paper ID : IJERTCONV3IS10011
 Volume & Issue : NCETEMS – 2015 (Volume 3 – Issue 10)
 Published (First Online): 24042018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Ultimate Capacity of Structural Steel Cross Section under Compression, Bending and Combined Loading
Jyoti1, Rachna 2 , Satish Kumar 3, Jaidutt4
1,2,3,4Department of Civil Engineering, Applied college of Management & Engineering,
Palwal Haryana, India
Abstract The Continuous Strength Method (CSM) is a strain based structural steel design approach which allows for the beneficial influence of strain hardening. The method has been previously developed for predicting compression and bending resistances in isolation. This paper describes extension of the method to enable the prediction of the ultimate crosssection resistance of Isections and box sections under combined loading. At the core of the method is a base curve, which relates the deformation capacity of a crosssection to its cross section slenderness. Deformation capacity is defined as the ratio of the maximum strain that a crosssection can endure relative to its yield strain. Knowing this limiting strain and assuming plane sections remain plane, the resistance of a crosssection to combinations of axial load and bending moments can be calculated, by integrating the stresses arising from a suitable strain hardening material model over the area of the crosssection. By considering a range of combinations of applied actions, analytical expressions and numerically derived interaction surfaces have been produced, which were then rationalised into simple expressions for use in design. The resulting CSM design predictions for box sections and I sections have been compared with existing test data, and shown to give additional capacity over current design approaches and a reduction in scatter of the predictions.
Keywords Compression; Bending; Combined loading; Steel structures; Strain hardening; Continuous Strength Method

INTRODUCTION
Design rules for structural steel crosssections often include simplifications that allow quick and conservative estimates of capacity (e.g. the ability to withstand combinations of axial forces, shear forces and bending moments) to be obtained. Some of these simplifications are at the material level, where structural steel is typically assumed to have an elasticplastic or rigidplastic stress strain ( ) response, some are based on equations limited by elastic conditions, while other approximations involve the grouping of similar behaviour, as in the case of cross section classification for the treatment of local buckling.
At the ultimate limit state, a crosssection subjected to flexure is typically designed on the basis of its plastic (Mpl = Wplfy) or elastic moment capacity (Mel = Welfy), where Wpl and Wel are the plastic and elastic section moduli and fy is the material yield stress. The choice between the two is based on the susceptibility of the crosssection to local buckling, which is assessed by considering the width
tothickness ratios of the elements that make up the cross section through a process known as crosssection classification. For slender crosssections, where local buckling occurs prior to the initiation of yielding, reduced moment capacities are assigned. This approach generally results in a step from Mel to Mpl at a particular slenderness limit.

MATERIAL MODEL
The stressstrain ( ) response of structural steel can differ depending on the material grade and how the material has been manufactured, subsequently mechanically worked, and ultimately tested. Hotrolling ( Fig. 1a) or coldforming ( Fig. 1b) can affect the material behaviour by altering the distinctiveness of the yield point, the length of the yield plateau, and the magnitude of the strain hardening slope. Variation in material properties around structural crosssections is also possible, such as in the case of coldformed sections, where higher strength but lower ductility are typically found in the corner regions..
Fig. 1. Schematic stressstrain curves (a) for hotrolled material, (b) coldformed material and (c) the CSM material model.
In Fig. 1, E is the Young's modulus, fy and fu are the yield and ultimate tensile stresses, y = fy/E and u are the strains at the yield and ultimate stress, 0.2 and t,0.2 are the 0.2% offset proof stress and corresponding strain, Esh is the strain hardening slope and fcsm and csm are the CSM limiting stress and strain. Traditionally a bilinear, elasticperfectly plastic material model is used to model structural steel, with the key advantage of being very simple to analyse, but with the potential disadvantage of being overly conservative since no postyield strain hardening is accounted for. Alternatives to the elasticperfectly plastic
model include bilinear (elasticlinear hardening), tri linear, power, Ramberg and Osgood and other stress strain models. In principle, any material law can be used in conjunction with the deformation based CSM. The proposed material model ( Fig. 1c) is an elasticlinear hardening relationship, which consists of an initial linear region with Young's modulus E defining stresses up to the yield stress, followed by a strain hardening region, described by an appropriate strain hardening modulus Esh for the material. A maximum limiting strain is also set at
15 times the yield strain (csm/y = 15), a value which corresponds to the material ductility requirements given in Clause 3.2.2(1) of EN 199311. This material model gives the following stressstrain relationship:
equation(1)
=Eyfy+Eshyy<csm.
The key characteristic to be defined in the adopted material model is the strain hardening modulus Esh, which should be representative of the whole crosssection.

CROSS SECTION SLENDERNESS
Local plate buckling may initiate before or after the onset of material yielding, with the key determining geometric factor being the relative widthtothickness ratios of the plate elements that make up the crosssection. Plate slenderness is commonly defined in the nondimensional form of equation(2)
Â¯p=fycr
where cr is the elastic buckling stress, which is influenced by the boundary and loading conditions of the plate. The plate slenderness values of all the elements that make up the crosssection are evaluated, with the critical and governing element determined as that with the highest value of Â¯p. Since basing the crosssection slenderness upon the most slender constituent plate element does not consider the connectivity between the plates.Crosssection slenderness reduces when element interaction is considered; this reduction is by a factor of between 0.85
1.0 for axial loading, and approximately 0.701.0 for major or minor axis bending for typical hotrolled structural profiles

STRAIN RATIO AND CURVATURE RATIO
The CSM is a deformation based design approach, founded upon a derived relationship between the failure strain of a crosssection and its local slenderness. The results of both stub column and inplane bending tests can be used in the derivation of this relationship. A stub column is defined herein as a column with a global nondimensional slenderness Â¯0.1, where Â¯=Ny/Ncr, Ny being the yield load of the crosssection and Ncr the
elastic buckling load of the member. While meeting the above requirement of Â¯0.1 to avoid any significant influence from global buckling, the test lengths L of stub columns should also ideally be at least three times the larger crosssectional dimension, in order to contain a representative distribution of geometric imperfections and residual stresses and to allow local failure modes to form without a strong influence fromend effects.A typical load endshortening (N ) curve from a stub column test is shown in Fig. 2, where loads above the yield load will be reached if the crosssection slenderness is sufficiently low to allow stresses to enter the strain hardening regime. The endshortening at the ultimate load Nlb (i.e. the peak load Nu achieved in the stub column test), is divided by the length of the specimen to obtain the average failure strain of the crosssection lb. The deformation capacity of the stub column is then defined as csm, which is taken directly as lb for materials that exhibit a distinct yield point and as lb 0.002 for materials with a rounded stressstrain curve. The subtraction of 0.2% strain in the case of rounded stressstrain curves is to ensure compatibility with the chosen material model of Fig. 1c and to avoid over predictions of capacity. The CSM strain is normalised by the yield strain in Eqn. (3), and csm/y is referred to as the strain ratio.
equation(3)
csmy=lbyforhotrolledmaterialswithdistinctyieldpointl b0.002yforcoldformedandnonlinearmaterials.
Fig. 2. Stub column loaddeformation response.
Crosssections that fail at strain ratios greater than unity can exceed their yield loads and mobilise some of their strain hardening potential. Note that, in the present study, when considering test specimens that exhibit a variation in material properties around the crosssection (e.g. enhanced strength at corners due to coldforming), area weighted average values have been used to establish Ny and y. For slender crosssections (defined herein as crosssections with Â¯p>0.68), elastic local buckling is followed by stable postbuckling, which results in increased capacities but with reduced axial stiffness. The consequence of this is that a slender crosssection can have a high deformation capacity (i.e. strain at failure), greater than y, but a peak load still below the yield load. This would result in an overprediction of capacity when using
the CSM. To avoid this, the deformation capacity of slender crosssections is defined by Eqn. (4).
equation(4)
csmy=NuNyforNuNy<1orÂ¯p>0.68.
The value of Â¯p=0.68 has been found by Afshan and Gardner to represent the transition point for which crosssections behave as either slender (achieving peak loads below the yield values Ny and Mel), or as nonslender (achieving peak loads above the yield values). For cross sections in bending, the strain distribution is assumed to be linearlyvarying through the crosssection depth, and a relationship can be made between curvature and outerfibre strains. With the height and width of a crosssection denoted as h and b, the yield curvatures y,y and y,z for the major and minor axes are defined as:
equation(5)
y,y=2yhandy,z=2yb.
These are the curvatures at which a crosssection will reach its major and minor axis elastic moments, Mel,y and Mel,z respectively. Assuming that plane sections remain plane during bending, there is a proportional relationship between the strains at Â±h / 2 and Â±b / 2 and curvature. This permits the equivalence of the strain ratio csm/y to the curvature ratio csm/y, where csm is the curvature when the strain csm is reached in the outermost compressive outer fibre of the crosssection.
equation(6)
in which lb is the curvature at maximum moment Mlb (or Mu). Hence csm is related to lb in a similar manner to the relationship between csm and lb, as defined by Eqn. (6) for the case of the major axis. For slender crosssections Â¯p>0.68) in bending, the definition of curvature ratio, given by Eqn. (6) has been modified for similar reasons to those previously explained for compression:
equation(7)
had been tested to failure,; the majority of the test cross sections were nonslender and had therefore reached axial loads and strains above the yield values, Ny and y. In addition, test data on short or laterally restrained beams in fourpoint bending, and were also collated. These data are plotted in Fig. 3 on a graph of strain ratio versus cross section slenderness, alongside equivalent stainless steel and and aluminium and test data.
Fig. 3. CSM base curve with stub column and bending test data for structural steel, stainless steel and aluminium.
The test data shows a clear trend of increasing deformation capacity with reducing crosssection slenderness (i.e. lower Â¯p), with the strain at peak load sometimes exceeding 25y. For the slender crosssections Â¯p>0.68), the strain ratio drops below the elastic value of csm/y = 1. A nonlinear least squares fit to the collected data set, excluding crosssections where Â¯p>0.68, is given by Eqn. (8), with an upper bound of 15 applied to the strain ratio to avoid excessive strains and to remain within the fracture ductility limits set out in EN 199311. Fig. 3 shows a good match between the collected test data and Eqn. (8). Similar agreement was observed between a slightly modified version of Eqn. (8) by [9] and the numerical results for a range of material models. Hence, Eqn. (8), referred to as the CSM base curve, may be used to predict the CSM failure strain csm from the crosssection slenderness Â¯p.
equation(8)
csmy=0.25Â¯p3.6butcsmy
15
VI. AXIAL AND BENDING RESISTANT
lforMuMel<1orÂ¯p>0.68.
csmy=MuMe

AXIAL RESISTANT
For a column unaffected by global buckling, the strains in
This allows experimental bending data to be plotted on a common deformation capacityslenderness curve with axial test data;


BASE CURVE
The CSM base curve relates normalised crosssection failure strain csm/y to crosssection slenderness Â¯p. Stub column test data were collected for specimens that
the crosssection are assumed to be uniform at A. When A < y, the crosssection is within its elastic material range. However, when A y the crosssection is deforming inelastically and, following the CSM strain hardening material model described in Section 2.1, will reach the CSM limiting stress fcsm. Thus, for csm/y > 1, the CSM axial resistance Ncsm given by Eqn. (9), will be greater than the yield load. In Eqn. (9), M0 is the partial factor for
crosssection resistance, with a recommended value of unity.
equation(9)
For box sections bending about the minor axis, the Ww
modulus in Eqn. (12) is similar to Eqn. (11): equation(12)
Ncsm=Afc
smM0withfcsm=fy+Eshcsmy
B. BENDING CAPACITY
In bending, a crosssection that has a strain ratio equal to unity will have an outerfibre stress equal to the yield stress, and will fail at the elastic moment capacity Mel. For higher strain ratios, the outerfibre CSM stress fcsm will be greater than the yield stress fy, and the crosssection resistance will exceed the elastic moment capacity. This results from the fact that the integrals Mcsm,y = y dA and Mcsm,z = z dA, where stresses are defined from a linear strain distribution and the CSM bilinear material model, and y and z are the distances from the neutral axes, will result in moments greater than Mel. Crosssections with higher csm/y enter further into the strain hardening regime and can achieve Mcsm > Mpl.For the crosssection geometry shown in Fig. 4, an analytical moment resistance expression was presented by [9], which gave the normalised moment capacity of Eqn. (10), where the appropriate section moduli Wpl,y and Wel,y or Wpl,z and Wel,z are used for bending about the yy or zz axes.
equation(10)
McsmMpl
=1+EshEcsmyWelWpl1WwWpl1EshE
Fig. 4. For box and Isections bending about the major axis, the
Ww modulus is defined by Eqn. (11):
equation(11)
Wwtwp12csmy2for1+2tfhwcsmybp12csmy2 btw12hw232hwhcsmyfor1+2tfhw>csmy1.
Ww=twb212csmy2for11twbcsmyhb212csmy2
htw12btw2321twbcsmyfor11twb>csmy1.
Isections perform notably different aout the minor axis and have modulus Ww as:
equation(13)
Ww=hb212csmy2forcsmybtwtw2hw212tw3bcsm y+tfb26csmy2forcsmy<btw.
The analytical equations are exact for the chosen bilinear material model, but are lengthy for practical design due to the Ww term. However, accurate approximations to Eqns. (11), (12) and (13) are achieved using the simpler design expression of Eqn. (14):
Mcsm=WplfyM01+EshEWelWplcsmy11WelWpl/ csmy
where = 2 for Isections bending about the major axis and box sections bending about either axis, and = 1.2 for Isections bending about the minor axis. This CSM design bending equation requires the assignment of three ratios to the crosssection: the ratio of strain hardening modulus to Young's modulus Esh/E, the shape factor reciprocal Wel/Wpl, and the strain ratio csm/y.

COMBINED AXIAL LOAD AND BENDING
Combined loading differs from the basic cases of axial load or uniaxial bending in that stresses and strains depend on both the y and z coordinates (i.e. those in the plane of the crosssection). The proposed CSM model for doubly symmetric crosssections under combined loading is based on orientations of a rotated (due to bending) planar strain surface shifted by a uniform compressive strain A and limited by the CSM strain csm. Examples of such strain planes are shown in Fig. 5, from which the stresses and crosssection resistances to axial forces and bending moments may be derived; this is undertaken by means of a numerical model, as described in Section 4.2.
lower values of B and C). With the strain at each element known, the element stress fi normalised by the yield stress is calculated from Eqn. (16).
equation(16)
Fig. 5. Strain distributions in crosssections under combined
1i>y
fify=iyiy1+EshEiy
axial load and biaxial bending; compression is positive and NA is the neutral axis.
For bending about both axes and with A = 0 (Fig. 5a), the area and distribution of stresses in compression equal those in tension and no net axial force is produced; when A is nonzero a net axial force exists. Failure of the cross section is deemed to occur when the maximum compressive strain reaches the CSM limiting strain csm. With reference to Fig. 5, the maximum compressive strain will occur at y = h/2, z = b/2 for box and Isections. The uniform compressive strain A has the effect of preventing the tensile corner strain (at y = h/2, z = b/2) from reaching csm and accelerating the compressive corner strain reaching csm ( Fig. 5b and Fig.5c).

NUMERICAL MODEL
In this subsection, crosssection capacities under combined loading are determined by means of a numerical model. In the numerical model, the crosssection is divided into i elements each of area Ai, and with element centroids at distances yi and zi from the centroidal axes of the cross section. There are three strain components that must be considered: A, B and C. The strain A is the uniform strain across the whole of the crosssection, associated with axial deformations. The strains B and C describe bending about the major and minor axes respectively. The linearly varying strains are associated with flexural deformations and are defined by 2yiB/h for the major axis and 2ziC/b for the minor axis. The numerical analysis procedure is initiated with a given value of A/csm from between 0 and 1, with A = 0 indicating no axial deformations and A = csm indicating only axial loading. The parameter B/csm is then varied from 0, for no major axis bending, to 1 A/csm for axial load plus major axis bending. This limits the maximum value of the minor axis bending parameter C/csm = 1 A/csm B/csm. The strain i at element i is then given by Eqn. (15), based on the addition of A, B and C, all normalised by csm. equation(15)
icsm=Ac sm+Bcsm2yih+1AcsmBcsm2zib
The failure criterion is based on 2y /h = 2z /b = 1, that is the
The normalised crosssection resistances N (axial force), My (major axis bending) and Mz (minor axis bending) are then:
equation(17)
NNy=1AififyAi equation(18)
MyMpl,y=1Wpl,yififyyiAi equation(19)
MzMpl,z=1Wpl,zififyziAi.
The output from the numerical model is a suite of interaction curves between My and Mz, as displayed in Fig. 6 for an Isection with a strain ratio of 15. This forms an interaction surface that can be used to create design interaction curves for different combinations of axial load and bending moments. The curves and surfaces can be plotted in two or threedimensional space with respect to the plastic resistances Mpl,y, Mpl,z and Ny or, more suitably, with respect to the CSM resistances Mcsm,y, Mcsm,z and Ncsm.
Fig. 6. Typical interaction surface generated from the numerical model for an Isection with a strain ratio csm/y = 15.
The numerically generated surfaces can be used to create interaction curves between major axis and minor axis bending for a given axial load, and for a constant strain
i i ratio. This gives contours of constant axial load by slicing
CSM limiting strain csm being reached at the corner element where yi = h/2, zi = b/2, and A + B + C = csm. As A increases, the strain plane can rotate to a lesser extent before csm is reached and hence the lower the capacity of the crosssection to coexisting bending (corresponding to
through the interaction surface with a series of parallel planes. Examples of these contours with curves normalised by the plastic moment capacities, are displayed in Fig. 7 and Fig. 8 for a typical Isection and box section respectively, both of which have a strain ratio of 15 and are
plotted with and without strain hardening (Esh = E/100 and Esh = 0). curves provide a good representation of the numerically generated results for the case of no strain hardening, though some deviation may be seen in the middle region of the Isection curves. It may also been seen that as the axial load increases, the biaxial bending interaction curves from both the numerical model and EN 199311 contract towards the origin and become more rectangular in shape. The influence of strain hardening, which is essentially to expand the interaction surfaces, may also be clearly seen from the numerical results. In the following subsection, design interaction expressions are developed on the basis of the numerical results.
Fig. 7. Biaxial bending interaction curves for a typical I section at fixed axial load levels n = N/Ny.
MR,csm,z, and map surfaces that conform well to the numerical model surfaces.equation(20)
MyMR,csm,y+MzMR,csm,z1 equation(21)
MR,csm,y=Mcsm,y1nay1byandMR,csm,z=Mcsm,z1naz 1bz
The design equations simplify when the appropriate loading terms are taken as zero. For example, when there is no axial load (n = 0), the reduced moments in Eqn. (21) collapse to the CSM moments and convert Eqn. (20) into a biaxial bending design equation, and when either My or Mz is zero, the equations collapse into the simple axial load and uniaxial bending forms of Mz MR,csm,z and My MR,csm,y respectively.The powers ay, az, by, bz, and are all defined in Table 1. The tabulated powers were found via a nonlinear least squares fitting regime, and are based on the ratio of the crosssection web area to gross area a = Aw/A and the ratio of the major to minor axis plastic section moduli Wr = Wpl,y/Wpl,z. A strain ratio of 5 is required before the convergence of the powers for I sections, compared to that of 3 needed for box sections. The powers ay, az, by, bz, and are all unity when csm/y < 3.
.
Fig. 8.Biaxial bending interaction curves for a typical box section at fixed axial load levels n = N/Ny.
2 1.5n 1
0.8 + 5n2.2
4
2 + 0.15Wr 5n1.5
1.3
0.8 + (15 Wr)n2.2
8
1.75 + Wr(2n2 0.15) 1
.7 + Wr
1.6 + (3.5 1.5Wr)n2 3.
7 Wr

DESIGN INTERACTION CURVE
This subsection introduces the CSM design equation for combined loading, shows comparisons with the numerical model presented in Section 4.2, and defines a goodness of fit by a residual. The proposed design equations for the prediction of the combined axial load and bending capacity of a crosssection, are based on curve fits that rationalise the numerical model surface in the CSM domain. In CSM normalised space, the surfaces are bound to a unit box defined by Mcsm,y, Mcsm,z and Ncsm; this prevents the interaction surfaces from progressively expanding outwards away from the origin as the strain ratio (and hence crosssection capacity) increases.The proposed form of design equations, given by Eqns. (20) and (21), trace bi axial bending interaction curves that are anchored by reduced moments MR,csm,y and MR,csm,z, which are functions of the axial load level n = N/Ncsm. Eqn. (20) contains two reduced moment normalised terms for major and minor axis bending, raised to powers and respectively.The equations provide smooth curves between MR,csm,y and
The CSM design equation for a typical Isection (for strain ratios 515) and box section (for strain ratios 315) are plotted in Fig. 9 and Fig. 10 respectively, together with the corresponding numerical envelopes. For both cross sections, the design equations fit well to the numerical model, providing interaction curves that pass through the middle of the envelopes, or giving predictions on the conservative side. For the Isection, the straight sides of the curves at high axial loads are produced by the larger powers.
Fig. 9. Isection numerical model envelopes (strain ratios 5
15) and the CSM design equation for combined loading.
Fig. 10. Rectangular hollow section numerical model envelopes (strain ratios 315) and the CSM design equation for combined loading.
In order to assess the conformity between the design interaction surfaces and the numerical results, a residual is defined. The selected residual definition is the distance between the design interaction surfaces produced by Eqns. (20) and (21) and an associated point produced by the numerical model, based on a projection from the origin to the surface. The line from the origin to the known numerical data point R, will intersect the trial surface at point S, with the distance from the origin to this intersection as S=cR. The scalar c for every interaction surface point is then found by solving implicitly by a numerical root finding procedure, and the residual is then expressed as 100(1 c) %. A positive value of the residual corresponds to the numerical point lying outside the design interaction surface and therefore a conservative prediction of capacity. For a negative value, the opposite is true.
Fig. 11 and Fig. 12 show shaded surface maps of the residuals for a typical Isection and box section respectively. For the Isection, the magnitudes of the residuals are less than 3.5%, with a negative region appearing towards the centre of the surface, and two smaller concentrations at the Mcsm,y and Ncsm end points. The shaded residual plot is more uniform for the box section and gives residuals of lower magnitude, the highest being approximately 2.5%. A similar residual analysis based on the EN 199311 combined loading equations, but using the CSM axial and moment capacities in place of the yield load and plastic moment capacities, leads to residuals which are on average 12% greater in magnitude than the CSM design equations using the powers.
Fig. 11. Isection residuals (%) between the CSM design equation and the numerical results (strain ratio of 15).
Fig. 12. Rectangular hollow section residuals (%) between the CSM design equation and the numerical results (strain ratio of 15)

CONCLUSION
The Continuous Strength Method (CSM) is a strain based structural design approach that has been previously developed for crosssections under either compression or bending. Herein, the method was extended to the case of combined loading. Analyses have been performed for structural steel Isections and box sections via a strain based numerical model, and rationalised with simple equations suitable for use in design.
A bilinear material model was represented that combined the stressstrain relationships of hotrolled and cold formed structural steel and allowed for the benefits of strain hardening. A maximum strain of 15 times the yield strain was allowed based upon ductility requirements, and a value of Esh = E/100 was selected to represent the strain hardening modulus. A strain ratio and curvature ratio were defined as the strain or curvature at the peak axial load or peak bending moment from tests, and then normalised by the yield values. Higher values of strain ratio indicated greater deformation capacity and hence increased resistance to local buckling. The relationship between the strain ratio and the crosssection slenderness was displayed on a base curve, for which a suitable expression was presented.
Using the two key components of the CSM the base curve and the material model, crosssection resistance expressions for axial compression and bending in isolation were presented. Comparisons with test data revealed that the CSM provides closer and more consistent predictions of capacity than existing design codes, through a rational allowance of strain hardening.
Extension of the strain based design from simple axial and bending resistances to the general case of combined loading was then presented. A numerical method was formulated to generate interaction surfaces for box sections and Isections, by computing all permutations of uniform and linearly varying strains, which when combined did not exceed the CSM limiting strain in compression. From the numerical results, design expressions to describe the interaction surfaces, anchored to the CSM endpoints, were developed, with the key parameters determined by means of nonlinear least squares regression. The accuracy of the fits to the numerical model envelopes was assessed through a residual analysis, which showed excellent agreement with deviations of less than 3.5%. Use of the EN 199311 interaction curves, but with CSM endpoints, also yielded accurate results. Comparisons of the resulting design expressions were then made with tests, which showed similarly good agreement to that observed under the individual load cases.
REFERENCES

EN 199311. Eurocode 3: design of steel structures part 1 1: general rules and rules for buildings European standard, CEN: 196, (2005)

BS 59501. Structural use of steelwork in buildings part 1
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R. Greiner, M. Kettler, A. Lechner, B. Freytag, J. Linder, J.P. Jaspart, et al. Plastic member capacity of semicompact steel sections a more economic design Eur Res Fund Coal Steel (2008)

P. JuhÃ¡sElasticplastic bending loadcarrying capacity of steel members Challenges, opportunities and solutions in structural engineering and construction (2010), pp. 141147

Y. Shifferaw, B.W. Schafer Inelastic bending capacity of cold formed steel members
AUTHOR PROFILE
Jyoti B.Tech., M. Tech. Scholar in Civil Engineering (Structural Design) from Ganga Institute of Technology and Management, Kablana, Jhajjar, Haryana (India) affiliated to Maharshi Dayanand University, Rohtak, Haryana (India).