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<p>Composite plate shear walls – concrete-filled (C-PSW/CF) are a new innovative lateral force resisting system intended for high-rise buildings. The walls consist of parallel steel faceplates connected with tie bars and filled with concrete. This dissertation introduces the C-PSW/CF </p> <p>system and coupled C-PSW/CFs consisting of C-PSW/CF walls and composite coupling beams. Three studies are presented herein covering seismic design parameters for C-PSW/CFs, non-linear modeling techniques for composite coupling beams, and the design philosophy for coupled C-PSW/CFs.</p> <p> </p> <p>The first study summarizes the results of a recent FEMA P695 study completed to verify seismic design parameters for uncoupled C-PSW/CFs with rectangular flange plate boundary elements. Seven archetype structures were: (i) designed, (ii) modeled using a benchmarked fiber-based finite element analysis approach, (iii) subjected to nonlinear pushover analysis, (iv) subjected to incremental nonlinear dynamic analysis to failure for 22-sets of scaled ground motions, and (v) the results were statistically analyzed to assess performance. These structures ranged from three (3) to twenty-two (22) stories and included both planar and C-shaped wall configurations. As part of this design process, recommendations for stiffness approximations for linear analysis of C-PSW/CFs</p> <p>were developed. Additionally, these nonlinear incremental dynamic analysis results were post-processed to determine the rotation and strain demands at the base of these structures at the design basis, maximum considered, and failure level earthquakes. These results showed that the rotation and strain demand at failure level earthquakes were comparable regardless of the ground motion. Ultimately, this FEMA P695 approach verified the R factor of 6.5, C_d factor of 5.5, and Ω₀ of 2.5 for C-PSW/CFs with boundary elements. </p> <p><br></p> <p>The second study proposes modeling approaches for composite coupling beams used in combination with C-PSW/CFs. Capturing the behavior of these components is critical to understanding the system behavior of coupled C-PSW/CFs, as the coupling beam components undergo yielding, plastification, and fracture prior to collapse of coupled C-PSW/CF walls. Although steel-concrete composite walls have been a known structural system for decades, only recently have coupled C-PSW/CF systems been investigated and implemented as a seismic force resisting system. As the interest in coupled C-PSW/CF systems increases, the necessity of reliable nonlinear modeling techniques for pushover, cyclic, and seismic analysis has become apparent. This paper presents fiber-based options for modeling composite coupling beam components of coupled C-PSW/CF walls for use in nonlinear and seismic response analyses. Recommendations include effective steel and concrete stress-strain curves, modeling parameters for fiber-based </p> <p>materials, and concentrated plasticity options for additional computational efficiency. These recommendations are then implemented for a full-scale coupling beam section. </p> <p><br></p> <p>In the final study, a capacity design principle is used to establish a basis for the seismic design of coupled composite plate shear walls – concrete filled (CC-PSW/CF) systems. This design philosophy implements a strong wall-weak coupling beam approach, where flexural yielding in coupling beams occurs before flexural yielding at the base of walls. The coupling beams are sized </p> <p>to resist the calculated seismic lateral force level. The walls are sized to resist an amplified seismic lateral force corresponding to the overall plastic mechanism for the structure, while accounting for the capacity-limited forces from the coupling beams and the coupling action between the walls. Based on this philosophy, recommendations and requirements for appropriate sizing of coupling beams and C-PSW/CFs are presented. These recommendations are used to design four example (8-22 story) structures and evaluate their seismic behavior. The structures were modeled using 2D finite element models and fiber-based models subjected to monotonic and time history analysis. </p> <p>The nonlinear inelastic behavior and seismic responses of the example structures were in accordance with the capacity limited design philosophy (strong wall-weak beam), thus confirming the philosophy’s  efficacy. </p>

In this Thesis, the problem of the Free Vibrations Analysis of Doubly Stiffened Composite, Orthotropic and/or Isotropic, Base Plates or Panels (with Orthotropic Stiffening Plate Strips) is investigated. The composite plate or panel system is made of an Orthotropic and/or Isotropic Base Plate stiffened or reinforced by adhesively bonded Upper and Lower Orthotropic Stiffening Plate Strips. The plates are assumed to be the Mindlin Plates connected by relatively very thin adhesive layers. The general problem under study is considered in terms of three problems, namely Main PROBLEM I Main PROBLEM II and Main PROBLEM III. The theoretical formulation of the Main PROBLEMS is based on a First Order Shear Deformation Plate Theory (FSDPT) that is, in this case, the Mindlin Plate Theory. The entire composite system is assumed to have simple supports along the two opposite edges so that the Classical Levy&#039 / s Solutions can be applied in that direction. Thus, the transverse shear deformations and the rotary moments of inertia of plates are included in the formulation. The very thin, yet elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The sets of the systems of equations of the Mindlin Plate Theory are reduced to a set of the Governing System of First Order Ordinary Differential Equations in the state vector form. The sets of the Governing System for each Main PROBLEM constitute a Two-Point Boundary Value Problem in the y-direction which is taken along the length of the plates. Then, the system is solved by the Modified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials)which is a relatively semi-analytical and numerical technique. The numerical results and important parametric studies of the natural modes and the corresponding frequencies of the composite system are presented.

The diploma thesis deals with the structure design of steel frame of a storeyed building housing a shopping and administration centre in the area near Rokycany. The building consists of a truss cylinder tower structure with 11.165 m in diameter, nine storeys and the height of 33.3 m, connected to a rectangle part by means of a steel bridge structure 3.6 m long. The frame of the rectangular part, 26.8 m wide and 45 metres long, has three altitude levels with flat roofs, suitable and non-suitable for walking. The interior of the building is divided into two parts, connected at the outskirts, by a covered atrium. The design height is 3.7 m. The structure is designed of steel S235. The thesis contains the technical report, static calculation, outputs of a program, the record of the material and design documentation. Two versions were considered; the more convenient one is further processed.

Composite structures are extremely useful for aerospace, automotive, marine and civil applications due to their very high specific structural properties. These structures are subjected to severe dynamic loading in their service life. Repeated exposure to these severe loading conditions can induce structural damage which ultimately may precipitate a catastrophic failure. Therefore, an interest in the continuous inspection and maintenance of engineering structures has grown tremendously in recent years. Sensitive aerospace applications can have small design margins and any inadequacy in knowledge of the system may cause design failure. Structures made from composite materials posses complicated failure mechanism as compared to those made from conventional metallic materials. In composite structural design, it is hence very important to properly model geometric intricacies and various imperfections such as delaminations and cracks. Two important issues are addressed in this thesis: (1) structural modeling of nonlinear delamination and uncertainty propagation in nonlinear characteristics of composite plate structures and (2) development of a model based damage detection system to handle uncertainty issues. An earlier proposed shear deformable C0 composite plate finite element is modified to alleviate modeling uncertainty issues associated with a damage detection problem. Parabolic variation of transverse shear stresses across the plate thickness is incorporated into the modified formulation using mixed shear interpolation technique. Validity of the proposed modification is established through available literature. Correction of the transverse shear stress term in the formulation results in about 2 percent higher solution accuracy than the earlier model. It is found that the transverse shear effect increases with higher modes of the plate deformation. Transverse shear effects are more prominent in sandwich plates. This refined composite plate finite element is used for large deformation dynamic analysis of delaminated composite plates. The inter-laminar contact at the delaminated region in composite plates is modeled with the augmented Lagrangian approach. Numerical simulations are carried out to investigate the effect of delamination on the nonlinear transient behavior of composite plates. Results obtained from these studies show that widely used unconditionally stable β-Newmark method presents numerical instability problems in the transient simulation of delaminated composite plate structures with large deformation. To overcome this instability issue, an energy and momentum conserving composite implicit time integration scheme presented by Bathe and Baig is used for the nonlinear dynamic analysis. It is also found that a proper selection of the penalty parameter is very crucial in the simulation of contact condition. It is shown that an improper selection of penalty parameter in the augmented Lagrangian formulation may lead to erroneous prediction of dynamic response of composite delaminated plates. Uncertainties associated with the mathematical characterization of a structure can lead to unreliable damage detection. Composite structures also show considerable scatter in their structural response due to large uncertainties associated with their material properties. Probabilistic analysis is carried out to estimate material uncertainty effects in the nonlinear frequencies of composite plates. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also revealed in eigenvalue sensitivity analysis. For fault isolation, variations in natural frequencies, modal curvatures and curvature damage factors due to damage are investigated. Effects of various physical uncertainties like, material and geometric uncertainties on the success of damage detection is studied. A robust structural damage detection system is developed based on the statistical information available from the probabilistic analysis carried out on beam type structures. A new fault isolation technique called sliding window defuzzifier is proposed to maximize the success rate of a Fuzzy Logic System (FLS) in damage detection. Using the changes in structural measurements between the damaged and undamaged state, a fuzzy system is generated and the rule-base and membership functions are generated using probabilistic informations. The FLS is demonstrated using frequency and mode shape based measurements for various beam type structures such as uniform cantilever beam, tapered beam in single as well as in multiple damage conditions. The robustness of the FLS is demonstrated with respect to the highly uncertain input information called measurement deltas (MDs). It is said, if uncertainty level is larger than or close to the changes in damage indicator due to damage, the true information would be submerged in the noise. Then the actual damaged members may not be identified accurately and/or the healthy members may be wrongly detected as damaged giving false warning. However, this being the case, the proposed FLS with new fault isolation technique tested with these noisy data having large variation and overlaps shows excellent robustness. It is observed that the FLS accurately predicts and isolates the damage levels up-to considerable uncertainty and noise levels in single as well as multiple damage conditions. The robustness of the FLS is also demonstrated for delamination detection in composite plates having very high material property uncertainty. Effects of epistemic uncertainty on damage detection in composite plates is addressed. The effectiveness of the proposed refined Reddy type shear deformable composite plate element is demonstrated for reducing the modeling or epistemic uncertainty in delamination detection.

Cette thèse porte sur le développement d'un traducteur ultrasonore multi-élément capacitif à couplage air (MEACUT) et son utilisation dans le domaine du contrôle non destructif (CND) de matériaux. Un modèle est employé pour simuler numériquement ce traducteur, et pour optimiser sa conception. Un prototype est ensuite fabriqué, puis caractérisé expérimentalement pour quantifier ses performances. Son originalité réside dans le fait qu'il possède une large bande passante en fréquence, tout en offrant la possibilité d'une focalisation variable. Ce prototype est alors employé pour la détection d'un endommagement causé par impact, dans une plaque composite. Il est clairement constaté que la résolution spatiale du procédé d'inspection employé (C-scan) est fortement améliorée grâce aux performances techniques du MEACUT. Enfin, un modèle hybride 3D est développé pour simuler, rapidement et intégralement, ce procédé de CND. Le très bon accord obtenu entre prédictions numériques et mesures expérimentales laisse présager que cet outil de simulation pourra servir à mettre au point d'autres expérimentations de CND, qui pourront à leur tour exploiter les performances du MEACUT. / This thesis focuses on the development of a Multi-Element Air-coupled Capacitive Ultrasonic Transducer (MEACUT) and its use in the field of non-destructive testing (NDT) of materials. A numerical model is used to simulate the translator, and to optimize its design. A prototype is then built and experimentally characterized to quantify its performance. Its originality lies in the fact that it has a broad frequency bandwidth while offering the possibility of a dynamic focusing. This prototype is then used for the detection of damage caused by impact, in a composite plate. It is clearly found that the spatial resolution of the inspection process employed (C-scan) is greatly improved thanks to the technical performance MEACUT. Finally, a 3D hybrid model is developed to simulate quickly and fully, the process of NDT. The good agreement obtained between numerical predictions and experimental measurements suggests that this simulation tool can be used to develop other NDT experiments, which may in turn exploit the performance of MEACUT.

Dans le cadre linéaire, les modèles de Mindlin-Reissner pour les plaques épaisses et de Naghdi pour les coques épaisses sont les plus utilisés. Il est connu que la discrétisation par éléments finis de ces modèles conduit à un phénomène de verrouillage numérique quand l’épaisseur tend vers zéro. Il s’agit du verrouillage en cisaillement dans le cas des plaques et du verrouillage en cisaillement et en membrane dans le cas des coques. Il existe quelques éléments finis qui permettent d’éviter ces difficultés ou du moins de les réduire. L’élément DKMQ pour les plaques et sa version DKMQ24 pour les coques, sont des éléments de bas ordre, basés sur une formulation mixte, qui ont été proposés il y a quelques années afin d’éviter ces phénomènes de verrouillage. Dans cette thèse, on s’est attaché à évaluer numériquement les performances de ces éléments. Outre les cas tests classiques, on s’est focalisé sur l’analyse de la condition inf-sup discrète pour l’élément DKMQ. Nous avons étudié également le test de la s-norme proposé par Bathe, pour l’élément DKMQ24. Enfin, nous avons effectué une analyse d’erreur a posteriori pour les éléments DKMQ et DKMQ24, en utilisant l’estimateur d’erreur Z2 (dû à Zienkiewicz et Zhu), associé aux techniques de recouvrement de la moyenne, de projection ou encore SPR. Les résultats obtenus ont permis de quantifier les performances de ces deux éléments finis pour les problèmes de verrouillage, et d’en dégager les limites. Deux applications importantes de ces éléments DKMQ et DKMQ24 ont été ensuite présentées, la première concerne la simulation des poutres à parois minces à section ouverte et la seconde le calcul des plaques composites. / In the linear case, the Mindlin-Reissner model for thick plates and the Naghdi model for thick shells are commonly used. The finite element discretization of these models leads to numerical locking phenomenon when the thickness approaches zero : shear locking for plates and both shear and membrane locking for shells. There are some finite elements that could reduce or even eliminate this phenomenon. DKMQ element for plates or DKMQ24 element for shells, are low-order elements, based on a mixed formulation, introduced a few years ago to prevent the numerical locking phenomenon. In this thesis, we concentrated on numerical evaluation of the performance of these elements. Besides the classical benchmark tests, we also focused on the analysis of discrete inf-sup condition for DKMQ element. We studied the s-norm test proposed by Bathe for DKMQ24 element. Finally, we performed a posteriori error estimation for DKMQ and DKMQ24 elements, using the error estimator Z2 (proposed by Zienkiewicz and Zhu), associated with the averaging, projection or SPR recovery methods. The results obtained have enabled us to quantify the performance of these two finite elements for locking problems, and to identify their limits. Two important applications of these elements DKMQ and DKMQ24 were then presented ; the first one concerns thin-walled beams with open cross-section and the second one composite plates.

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Composite laminated structures are prone to delamination. Rotorcraft flexbeams, apart from many other aerospace primary load carrying members are made up of composite laminated structures. A delaminated primary load carrying member can lead to catastrophic failure of the system of which it is a part. Delamination modeling and detection in composite laminated structures are challenging areas of ongoing research worldwide. Existing literature falls short of addressing effects of widthwise partial delamination on the modal characteristics of beams. To address this issue, a new partial delamination model for composite beams is proposed and implemented using the finite element method. Homogenized cross-sectional stiffness of the delaminated beam is obtained by the proposed analytical technique, including extension-bending, extension-twist and torsion-bending coupling terms, and hence can be used with an existing finite element method. A two-noded C1-type Timoshenko beam element with four degrees of freedom per node for dynamic analysis of beams is implemented. The results for different delamination scenarios and beams subjected to different boundary conditions are validated with available experimental results in the literature and/or with a 3-D finite element simulation using COMSOL. Results of the first torsional mode frequency for the partially delaminated beam are validated with the COMSOL results. The key point of the current work is that even partial delamination in long structures can be analyzed using a 1-D beam model, rather than using computationally more demanding 3-D or 2-D models. Rotor craft flexbeams are prone to delaminations, which in most realistic situations are partial along both the length and the width. However, the effect of partial delamination on the modal characteristics of the beam is not studied by researchers to the best of the author’s knowledge. Addressing this issue, a rotorcraft flexbeam is analysed here in the presence of delamination. A set of nonlinear governing equations for the rotating flexbeam are developed in hybrid basis. The flexbeam model developed has axial stretch, transverse displacement and flexural rotation in flapwise direction and twist as its degrees of freedom. The nonlinear governing differential equations are linearised and solved for eigenvalues and eigenvectors using a finite element method. The effects of angular speed and delamination size and location on the flexbeam modes are analysed. The results obtained using the proposed model are validated with the COMSOL 3-D finite element simulations. Next, the issue of delamination detection in beams is addressed. Mode shape curvature and Katz fractal dimension are used to detect the presence of partial delaminations in a beam. The effects of boundary conditions and location of delamination on the fractal dimension curve are studied. Usage of higher mode shape data for detection of delamination in beams is evaluated. Limitations of the Katz fractal dimension curve for delamination detection are enumerated. It is shown that fractal dimension measure and mode shape curvature can be used to detect the presence of partial delamination in beams. It is found that the torsional mode shape is best suited for partial delamination detection in beams. Apart from beams, Shell-and plate-like structures are also extensively used in aerospace structures. The modeling of multilayered plates is introduced herein with the intention to model delaminations in 2D. Carrera Unified Formulation(CUF)plate model, developed using variational formulations, is used to derive the stiffness matrices and to apply, the Principle of Virtual Displacement(PVD) and the Reissner Mixed Variational Theorem (RMVT). It is known that FEM implementation for plates leads to the phenomenon of numerical locking: the so-called membrane and shear locking effects. A well-known remedy for addressing locking is the use of the Mixed Interpolated Tensorial Components(MITC) technique. A strategy similar to MITC approach in the RMVT formulation is used to construct an advanced locking-free finite element to treat the multilayered plates. Composite laminated plates are prone to delamination. Implementation of delamination in the CUF frame work using nine-noded quadrilateral MITC9 elements is discussed. MITC9 elements are devoid of shear locking and membrane locking. Delaminated structures, as well as the corresponding healthy structures, are analysed for free vibration modes. The results from the present work are compared with those from available experimental or/and theoretical research articles or/and the 3-D finite element simulations. The effects of different kinds and different percentages of interfacial area of delaminations on the first three natural frequencies of the structure are discussed. The presence of the open-mode or breathing mode delamination mode shape for large delaminations within the first three natural frequencies is discussed. Also, the switching of the places between the second bending mode and the first torsional mode frequencies is discussed. Results obtained from different ordered theories are compared in the presence of delamination. Advantage of layer wise theory as compared to equivalent single layer theories for very large delaminations is stated. The effects of different kinds of delamination and its effect on the second bending and first torsional mode shapes are discussed.

<p>Composite Plate Shear Walls - Concrete Filled (C-PSW/CF), also known as SpeedCore walls, are increasingly used in commercial buildings. C-PSW/CF offer the advantages of modularization and expedited construction time. The performance of C-PSW/CF under wind and seismic loading has been extensively studied. As such, building codes permit the use of these walls in non-seismic and seismic regions. In addition to these lateral loads, C-PSW/CF may be exposed to fire loading during their service life. Elevated temperatures resulting from the fire loading subject structural components to a set of forces and deformations. These elevated temperatures result in the significant degradation of the material properties. Thus, fire loading may lead to the failure of structural components during fire incidents within the buildings.</p> <p>This dissertation describes (i) experimental, numerical, and analytical studies conducted to evaluate the performance of C-PSW/CF and (ii) the development of design guidelines for C-PSW/CF subjected to fire and gravity loading. The results from prior experimental investigations were compiled, and five additional fire tests were conducted to address gaps in the experimental data. The fire tests were conducted on laboratory-scale specimens subjected to axial compressive loading and simulated standard fire loading (heating). The parameters considered in the tests were axial compressive loading (21% – 30% of section compressive strength, <em>Ag f’c</em>), steel plate slenderness (24 – 48, tie spacing-to-steel plate thickness ratio), and uniformity of heating (all-sided versus three-sided heating).</p> <p>Numerical and analytical studies were conducted using two independent methods namely Finite Element (FE) and Finite Difference (FD) methods. The developed models were benchmarked to test data, and the benchmarked models were used to conduct parametric studies to expand the database. The thermal and structural material properties recommended by Eurocode standards were applied in these models. The parameters considered were the wall thickness (200 mm – 600 mm), wall slenderness (story height-to-concrete thickness ratio, <em>H/tc</em>= 5 – 25), axial load ratio (<em>Pu</em> ≤ 30% section concrete strength, <em>Ac f’c</em>), heating uniformity (uniform versus non-uniform heating), boundary conditions (pinned versus fixed), cross-sectional steel plate reinforcement ratio (<em>As/Ag</em> =1.3% – 5.3%), steel plate slenderness ratio (<em>stie/tp</em> = 20 – 75), tie bar spacing-to-wall concrete thickness ratio (<em>stie/tc</em> = 0.5 – 1.0), and concrete compressive strength (<em>f’c</em> = 40 MPa – 55 MPa).</p> <p>Symmetric nonlinear thermal gradients were developed through wall thickness for the walls exposed to uniform fire loading. Due to the low thermal conductivity of concrete, the temperature decreased nonlinearly through the wall thickness towards the mid-thickness of the walls. For the non-uniform fire exposure, temperatures through the wall thickness decreased nonlinearly towards the unexposed surface of the walls. A consistent trend was observed in the axial displacements of C-PSW/CF under combined fire and gravity loading. The observed trend consisted of several steps including (i) thermal expansion, (ii) gradual axial shortening, (iii) fast axial shortening, and (iv) failure.</p> <p>Local buckling of steel plates between tie bars was observed in all walls. However, this phenomenon did not cause any significant degradation in structural performance or failure of the walls. The results from parametric studies indicated that wall slenderness ratio (story height-to-wall thickness ratio), wall thickness, applied axial load ratio, and end boundary conditions have a significant influence on the fire resistance of C-PSW/CF. Higher wall slenderness ratios and load ratios had a detrimental effect on the fire resistance of walls. Global buckling was the dominant failure mode for the walls with high slenderness ratios (e.g., <em>H</em>/<em>tc </em>³ 15). In thicker walls, the lower temperatures in the middle regions of the concrete helped to maintain the axial compressive capacity of walls under fire loading. Limiting the steel plate slenderness ratio could slightly improve the fire resistance of unprotected walls by arresting the extent of local buckling between tie bars.</p> <p>The results from the parametric studies have been used to develop an approach for designing C-PSW/CF subjected to combined fire and gravity loading. The total (linear) length of the wall was discretized into unit width columns, where each unit width column corresponded to a length of wall equal to the tie bar spacing (<em>stie</em>). Thus, each unit is like a column with steel plates on two opposite surfaces, concrete infill, and tie bars distributed uniformly along the height. The axial load capacity of C-PSW/CF can be estimated as the axial load capacity of the unit width column, calculated using the developed approach, multiplied by the linear length of the wall divided by the unit width (tie bar spacing). For this approach, the wall slenderness ratio (<em>H/tw</em>), has a limiting value of 20. Walls with wall slenderness ratios greater than 20 should be fire protected. The expansion of the material on the exposed surface of walls generated moments through the wall cross-section in non-uniform fire scenarios. This phenomenon caused the early failure of walls (~40 minutes) with wall slenderness ratios greater than 20. An approach was developed to conservatively estimate the fire-resistance rating (in hours) of unprotected C-PSW/CF exposed to the standard fire time-temperature curve. The fire-resistance rating of C-PSW/CF depends directly on the applied axial load ratio, wall slenderness ratio, and wall thickness.</p> <p>The temperature profile through the wall thickness can be calculated by discretizing the section into fibers (or elements). Since the temperature of the elements is uniform along the height and length of walls, 1D thermal analysis (through wall thickness) can be performed using heat transfer equations or the fiber-based program developed in the study.</p> <p>Vent holes are recommended to relieve the buildup steam pressure as the moisture content of concrete evaporates at temperatures exceeding the boiling point of water. A rational method was developed to design the vent holes as a function of the maximum temperature and thermal gradient through the wall thickness, heating duration, moisture content, and the acceptable level of pressure buildup on the steel plates. However, in typical cases, unprotected C-PSW/CF walls can be provided with 25 mm diameter vent holes spaced at a distance equal to story height or 3.6 m (maximum) in the horizontal and vertical directions to relieve the buildup of steam or water vapor pressure.</p> <p>This research study also led to the development and validation of a computer program that can be used instead of the design equations to more accurately model and calculate the thermal and structural performance of composite C-PSW/CF. This program is based on a fiber-based section and member analysis method that can be used to evaluate the performance and axial (gravity) load capacity of unprotected and protected C-PSW/CF subjected to uniform or non-uniform heating. The analysis can be conducted by implementing standard (ISO 834 or ASTM E119), Eurocode parametric, or user input gas (or surface) time-temperature curves.</p> <p>The proposed equations and the recommendations in this study can be used to develop design guidelines and specifications for fire resistance design of C-PSW/CF under combined fire and gravity loading. A code change proposal will be proposed to AISC <em>Specification</em> - Appendix 4 (Structural Design for Fire Condition).</p>