Second-order inelastic analysis of composite framed structures based on the refined plastic hinge method

Composite steel-concrete structures experience non-linear effects which arise from both instability-related geometric non-linearity and from material non-linearity in all of their component members. Because of this, conventional design procedures cannot capture the true behaviour of a composite frame throughout its full loading range, and so a procedure to account for those non-linearities is much needed. This paper therefore presents a numerical procedure capable of addressing geometric and material non-linearities at the strength limit state based on the refined plastic hinge method. Different material non-linearity for different composite structural components such as T-beams, concrete-filled tubular (CFT) and steel-encased reinforced concrete (SRC) sections can be treated using a routine numerical procedure for their section properties in this plastic hinge approach. Simple and conservative initial and full yield surfaces for general composite sections are proposed in this paper. The refined plastic hinge approach models springs at the ends of the element which are activated when the surface defining the interaction of bending and axial force at first yield is reached; a transition from the first yield interaction surface to the fully plastic interaction surface is postulated based on a proposed refined spring stiffness, which formulates the load-displacement relation for material non-linearity under the interaction of bending and axial actions. This produces a benign method for a beam-column composite element under general loading cases. Another main feature of this paper is that, for members containing a point of contraflexure, its location is determined with a simple application of the method herein and a node is then located at this position to reproduce the real flexural behaviour and associated material non-linearity of the member. Recourse is made to an updated Lagrangian formulation to consider geometric non-linear behaviour and to develop a non-linear solution strategy. The formulation with the refined plastic hinge approach is efficacious and robust, and so a full frame analysis incorporating geometric and material non-linearity is tractable. By way of contrast, the plastic zone approach possesses the drawback of strain-based procedures which rely on determining plastic zones within a cross-section and which require lengthwise integration. Following development of the theory, its application is illustrated with a number of varied examples.

Effects of cold weather on durability of CFRP strengthened circular hollow steel members

Tubular members have become progressively more popular due to excellent structural properties, aesthetic appearance, corrosion and fire protection capability. However, a large number of such structures are found structurally deficient due to reduction of strength when they expose to severe environmental conditions such as marine environment, cold and hot weather. Hence strengthening and retrofitting of structural members are in high demands. In recent times Carbon Fibre Reinforced Polymers (CFRP) composites appears to be an excellent solution to enhance the load carrying capacity and serviceability of steel structures because of its superior physical and mechanical properties. However, the durability of such strengthening system under cold environmental condition has not yet been well documented to guide the engineers. This paper presents the findings of a study conducted to enhance the bond durability of CFRP strengthened steel tubular members by treating steel surface using epoxy based adhesion promoter under cold weather subjected to bending. The experimental program consisted of six number of CFRP strengthened specimens and one bare specimen. The sand blasted surface of the three specimens to be strengthened was pre-treated with MBrace primer and other three were remained untreated and then cured under ambient temperature and cold weather (3oC) for three and six months period of time. The beams were then loaded to failure under four point bending. The structural response of each specimen was predicted in terms of failure mode, failure load and mid-span deflection. The research findings show that the cold weather immersion had an adverse effect on durability of CFRP strengthened structures. Moreover, the epoxy based adhesion promoter was found to enhance the bond durability in elastic range.

The molecular structure of the vanadate mineral mottramite [PbCu(VO4)(OH)] from Tsumeb, Namibia – a vibrational spectroscopic study

We have studied a mineral sample of mottramite PbCu(VO4)(OH) from Tsumeb, Namibia using a combination of scanning electron microscopy with EDX, Raman and infrared spectroscopy. Chemical analysis shows principally the elements V, Pb and Cu. Ca occurs as partial substitution of Pb as well as P and As in substitution to V. Minor amounts of Si and Cr were also observed. The Raman band of mottramite at 829 cm-1, is assigned to the ν1 symmetric (VO-4) ) stretching mode. The complexity of the spectra is attributed to the chemical composition of the Tsumeb mottramite. The ν3 antisymmetric vibrational mode of mottramite is observed as very low intensity bands at 716 and 747 cm-1. The series of Raman bands at 411, 439, 451 cm-1 and probably also the band at 500 cm-1 are assigned to the (VO-4) ν2 bending mode. The series of Raman bands at 293, 333 and 366 cm-1 are attributed to the (VO-4) ) ν4 bending modes. The ν3, ν3 and ν4 regions are complex for both minerals and this is attributed to symmetry reduction of the vanadate unit from Td to Cs.

Raman spectroscopy of the arsenate minerals maxwellite and in comparison with tilasite

Maxwellite NaFe3+(AsO4)F is an arsenate mineral containing fluoride and forms a continuous series with tilasite CaMg(AsO4)F. Both maxwellite and tilasite form a continuous series with durangite NaAl3+(AsO4)-F. We have used the combination of scanning electron microscopy with EDS and vibrational spectroscopy to chemically analyse the mineral maxwellite and make an assessment of the molecular structure. Chemical analysis shows that maxwellite is composed of Fe, Na and Ca with minor amounts of Mn and Al. Raman bands for tilasite at 851 and 831 cm�1 are assigned to the Raman active m1 symmetric stretching vibration (A1) and the Raman active triply degenerate m3 antisymmetric stretching vibration (F2). The Raman band of maxwellite at 871 cm�1 is assigned to the m1 symmetric stretching vibration and the Raman band at 812 cm�1 is assigned to the m3 antisymmetric stretching vibration. The intense Raman band of tilasite at 467 cm�1 is assigned to the Raman active triply degenerate m4 bending vibration (F2). Raman band at 331 cm�1 for tilasite is assigned to the Raman active doubly degenerate m2 symmetric bending vibration (E). Both Raman and infrared spectroscopy do not identify any bands in the hydroxyl stretching region as is expected.

A vibrational spectroscopic study of a hydrated hydroxy-phosphate mineral fluellite, Al2(PO4)F2(OH)·7H2O

Raman and infrared spectra of two well-defined fluellite samples, Al2(PO4)F2(OH)�7H2O, from the Krásno near Horní Slavkov (Czech Republic) and Kapunda, South Australia (Australia) were studied and tentatively interpreted. Observed bands were assigned to the stretching and bending vibrations of phosphate tetrahedra, aluminum oxide/hydroxide/fluoride octahedra, water molecules and hydroxyl ions. Approximate O–H���O hydrogen bond lengths were inferred from the Raman and infrared spectra.

A vibrational spectroscopic study of the phosphate mineral lulzacite Sr2Fe2+(Fe2+,Mg)2Al4(PO4)4(OH)10

The mineral lulzacite from Saint-Aubin des Chateaux mine, France, with theoretical formula Sr2Fe2+(Fe2+,Mg)2Al4(PO4)4(OH)10 has been studied using a combination of electron microscopy with EDX and vibrational spectroscopic techniques. Chemical analysis shows a Sr, Fe, Al phosphate with minor amounts of Ga, Ba and Mg. Raman spectroscopy identifies an intense band at 990 cm�1 with an additional band at 1011 cm�1. These bands are attributed to the PO3� 4 m1 symmetric stretching mode. The m3 antisymmetric stretching modes are observed by a large number of Raman bands. The Raman bands at 1034, 1051, 1058, 1069 and 1084 together with the Raman bands at 1098, 1116, 1133, 1155 and 1174 cm�1 are assigned to the m3 antisymmetric stretching vibrations of PO3� 4 and the HOPO2� 3 units. The observation of these multiple Raman bands in the symmetric and antisymmetric stretching region gives credence to the concept that both phosphate and hydrogen phosphate units exist in the structure of lulzacite. The series of Raman bands at 567, 582, 601, 644, 661, 673 and 687 cm�1 are assigned to the PO3� 4 m2 bending modes. The series of Raman bands at 437, 468, 478, 491, 503 cm�1 are attributed to the PO3� 4 and HOPO2� 3 m4 bending modes. No Raman bands of lulzacite which could be attributed to the hydroxyl stretching unit were observed. Infrared bands at 3511 and 3359 cm�1 are ascribed to the OH stretching vibration of the OH units. Very broad bands at 3022 and 3299 cm�1 are attributed to the OH stretching vibrations of water. Vibrational spectroscopy offers insights into the molecular structure of the phosphate mineral lulzacite.

Vibrational spectroscopic study of the sulphate mineral glaucocerinite (Zn,Cu)10Al6(SO4)3(OH)32⋅18H2O – a natural layered double hydroxide

We have studied the molecular structure of the mineral glaucocerinite (Zn,Cu)5Al3(SO4)1.5(OH)16�9(H2O) using a combination of Raman and infrared spectroscopy. The mineral is one of the hydrotalcite supergroup of natural layered double hydroxides. The Raman spectrum is characterised by an intense Raman band at 982 cm�1 with a low intensity band at 1083 cm�1. These bands are attributed to the sulphate symmetric and antisymmetric stretching mode. The infrared spectrum is quite broad with a peak at 1020 cm�1. A series of Raman bands at 546, 584, 602, 625 and 651 cm�1 are assigned to the m4 (SO4)2� bending modes. The observation of multiple bands provides evidence for the reduction in symmetry of the sulphate anion from Td to C2v or even lower symmetry. The Raman band at 762 cm�1 is attributed to a hydroxyl deformation mode associated with AlOH units. Vibrational spectroscopy enables aspects of the molecular structure of glaucocerinite to be determined.

A vibrational spectroscopic study of the phosphate mineral churchite (REE)(PO4)⋅2H2O

Vibrational spectroscopy has been used to study the rare earth mineral churchite of formula (REE)(PO4)-⋅2H2O. The mineral contains a range of rare earth metals including yttrium depending on the locality. The Raman spectra of churchite-(REE) are characterized by an intense sharp band at 984 cm-1 assigned to the v1 (PO¾-) symmetric stretching mode. A lower intensity band observed at around 1067 cm-1 is attributed to the v3 (PO¾-) antisymmetric stretching mode. The (PO¾-) bending modes are observed at 497 cm-1 (v2) and 565 cm-1(v4). Raman bands at 649 and 681 cm-1 are assigned to water librational modes. Vibrational spectroscopy enables aspects of the structure of churchite to be ascertained.

A vibrational spectroscopic study of the silicate mineral inesite Ca2(Mn,Fe)₇Si10O28(OH)⋅5H2O

We have studied the hydrated hydroxyl silicate mineral inesite of formula Ca2(Mn,Fe)7Si10O28(OH)⋅5H2O using a combination of scanning electron microscopy with EDX and Raman and infrared spectroscopy. SEM analysis shows the mineral to be a pure monomineral with no impurities. Semiquantitative analysis shows a homogeneous phase, composed by Ca, Mn2+, Si and P, with minor amounts of Mg and Fe. Raman spectrum shows well resolved component bands at 997, 1031, 1051, and 1067 cm-1 attributed to a range of SiO symmetric stretching vibrations of [Si10O28] units. Infrared bands found at 896, 928, 959 and 985 cm-1 are attributed to the OSiO antisymmetric stretching vibrations. An intense broad band at 653 cm-1 with shoulder bands at 608, 631 and 684 cm-1 are associated with the bending modes of the OSiO units of the 6- and 8-membered rings of the [Si10O28] units. The sharp band at 3642 cm-1 with shoulder bands at 3612 and 3662 cm-1 are assigned to the OH stretching vibrations of the hydroxyl units. The broad Raman band at 3420 cm-1 with shoulder bands at 3362 and 3496 cm-1 are assigned to the water stretching vibrations. The application of vibrational spectroscopy has enabled an assessment of the molecular structure of inesite to be undertaken.

The molecular structure of the borate mineral rhodizite (K, Cs)Al4Be4(B, Be)12O28 – A vibrational spectroscopic study

We have studied the borate mineral rhodizite (K, Cs)Al4Be4(B, Be)12O28 using a combination of DEM with EDX and vibrational spectroscopic techniques. The mineral occurs as colorless, gray, yellow to white crystals in the triclinic crystal system. The studied sample is from the Antandrokomby Mine, Sahatany valley, Madagascar. The mineral is prized as a semi-precious jewel. Semi-quantitative chemical composition shows a Al, Ca, borate with minor amounts of K, Mg and Cs. The mineral has a characteristic borate Raman spectrum and bands are assigned to the stretching and bending modes of B, Be and Al. No Raman bands in the OH stretching region were observed.

The molecular structure of the phosphate mineral beraunite Fe2+Fe⅗+(PO4)4(OH)5⋅4H2O– A vibrational spectroscopic study

The mineral beraunite from Boca Rica pegmatite in Minas Gerais with theoretical formula Fe2+Fe5 3+(PO4)4(OH)5⋅4H2O has been studied using a combination of electron microscopy with EDX and vibrational spectroscopic techniques. Raman spectroscopy identifies an intense band at 990 cm-1 and 1011 cm-1. These bands are attributed to the PO4 3- v, symmetric stretching mode. The m3 antisymmetric stretching modes are observed by a large number of Raman bands. The Raman bands at 1034, 1051, 1058, 1069 and 1084 together with the Raman bands at 1098, 1116, 1133, 1155 and 1174 cm-1 are assigned to the m3 antisymmetric stretching vibrations of PO4 3- and the HOPO3 2- units. The observation of these multiple Raman bands in the symmetric and antisymmetric stretching region gives credence to the concept that both phosphate and hydrogen phosphate units exist in the structure of beraunite. The series of Raman bands at 567, 582,601, 644, 661, 673, and 687 cm-1 are assigned to the PO4 3- v2 bending modes. The series of Raman bands at 437, 468, 478, 491, 503 cm-1 are attributed to the PO4 3- and OPO3 2- v4 bending modes. No Raman bands of beraunite which could be attributed to the hydroxyl stretching unit were observed. Infrared bands at 3511 and 3359 cm-1 are ascribed to the OH stretching vibration of the OH units. Very broad bands at 3022 and 3299 cm-1 are attributed to the OH stretching vibrations of water. Vibrational spectroscopy offers insights into the molecular structure of the phosphate mineral beraunite.

Infrared and Raman spectroscopic characterization of the Borate mineral Vonsenite

There are a large number of boron-containing minerals, of which vonsenite is one. Some discussion about the molecular structure of vonsenite exists in the literature. Whether water is involved in the structure is ill-determined. The molecular structure of vonsenite has been assessed by the combination of Raman and infrared spectroscopy. The Raman spectrum is characterized by two intense broad bands at 997 and 1059 cm−1 assigned to the BO stretching vibrational mode. A series of Raman bands in the 1200–1500 cm−1 spectral range are attributed to BO antisymmetric stretching modes and in-plane bending modes. The infrared spectrum shows complexity in this spectral range. No Raman spectrum of water in the OH stretching region could be obtained. The infrared spectrum shows a series of overlapping bands with bands identified at 3037, 3245, 3443, 3556, and 3614 cm−1. It is important to understand the structure of vonsenite in order to form nanomaterials based on its structure. Vibrational spectroscopy enables a better understanding of the structure of vonsenite.

Vibrational spectroscopy of the copper (II) disodium sulphate dihydrate mineral kröhnkite Na2Cu(SO4)2 · 2H2O

A natural single-crystal specimen of the kröhnkite from Chuquicamata, Chile, with the general formula Na2Cu(SO4)2 · 2H2O, was investigated by Raman and infrared spectroscopy. The mineral kröhnkite is found in many parts of the world's arid areas. Kröhnkite crystallizes in the monoclinic crystal system with point group 2/m and space group P21/c. It is an uncommon secondary mineral formed in the oxidized zone of copper deposits, typically in very arid climates. The Raman spectrum of kröhnkite dominated by a very sharp intense band at 992 cm−1 is assigned to the ν1 symmetric stretching mode and Raman bands at 1046, 1049, 1138, 1164, and 1177 cm−1 are assigned to the ν3 antisymmetric stretching vibrations. The infrared spectrum shows an intense band at 992 cm−1. The Raman bands at 569, 582, 612, 634, 642, 655, and 660 cm−1 are assigned to the ν4 bending modes. Three Raman bands observed at 429, 445, and 463 cm−1 are attributed to the ν2 bending modes. The observation that three or four bands are seen in the ν4 region of kröhnkite is attributed to the reduction of symmetry to C2v or less.

Web crippling tests of hollow flange channel beams – end one flange and interior one flange load cases

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. The LSBs were commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Due to the unique geometry of LSBs, as well as its unique residual stress characteristics and initial geometric imperfections resultant of manufacturing processes, much of the existing research for common cold-formed steel sections is not directly applicable to LSBs. Many research studies have been carried out to evaluate the behaviour and design of LSBs subject to pure bending actions, predominant shear and combined actions. However, to date, no investigation has been conducted into the web crippling behaviour and strength of LSB sections. Hence detailed experimental studies were conducted to investigate the web crippling behaviour and strengths of LSBs under EOF (End One Flange) and IOF (Interior One Flange) load cases. A total of 26 web crippling tests was conducted and the results were compared with current AS/NZS 4600 design rules. This comparison showed that AS/NZS 4600 (SA, 2005) design rules are very conservative for LSB sections under EOF and IOF load cases. Suitable design equations have been proposed to determine the web crippling capacity of LSBs based on experimental results. This paper presents the details of this experimental study on the web crippling behaviour and strengths of LiteSteel beams under EOF and IOF load cases.

Numerical modelling and design of lipped channel beams subject to shear

Cold-formed steel members are increasingly used as primary structural elements in buildings due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. Many research studies have been carried out to evaluate the behaviour and design of LCBs subject to pure bending actions. However, limited research has been undertaken on the shear behaviour and strength of LCBs. Hence a numerical study was undertaken to investigate the shear behaviour and strength of LCBs. Finite element models of simply supported LCBs with aspect ratios of 1.0 and 1.5 were considered under a mid-span load. They were then validated by comparing their results with test results and used in a detailed parametric study based on the validated finite element models. Numerical studies were conducted to investigate the shear buckling and post-buckling behaviour of LCBs. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs. Improved design equations were therefore proposed for the shear strength of LCBs. This paper presents the details of this numerical study of LCBs and the results.