Inelastic Large Deflection Modeling of Beam-Columns

Wind resistant size optimization of geometrically nonlinear lattice structures using a modified optimality criterion method

To extend previous research on obtaining designs that rely on a second-order inelastic hinge analysis to demonstrate that a structure is adequate in resisting the effects of factored loads, this paper presents a study of a series of two-story planar steel frames where all columns are subjected to combinations of axial force and minor-axis bending. Inelastic designs, which are prepared to satisfy both strength and serviceability limit states requirements, are compared to designs obtained using a conventional second-order elastic analysis in conjunction with the AISC LRFD Specification. The degree of accuracy and reliability of using a concentrated plasticity analysis to model system behavior is also established. The study indicates that for a majority of the frames investigated, a second-order inelastic hinge analysis can be used effectively to design steel structures. It is also shown that in some cases a distributed plasticity analysis may be required.

Chapter 3 - Second-order elastic analysis by the newton-raphson method

This research presents a comprehensive investigation of the global stability of cellular steel columns, beam-columns, and frames. For the cellular steel columns, the existing equation for predicting the elastic buckling load is improved to account for the local bending deformation of the web posts. Subsequently, the column strength equation is analytically developed from the energy approach. The second-order inelastic analysis is performed using 3D finite element (FE) models and validated against the experimental results. The validated FE models are then employed to assess the developed column strength curve and examine the influence of initial imperfections on the critical strength of the columns. Equivalent geometric imperfection amplitudes are determined to implicitly incorporate the effect of residual stresses on the flexural buckling strength of cellular steel columns. The developed equation provides a conservative prediction of the strong-axis flexural buckling strength, with a mean prediction-to-FE critical strength ratio of 0.97. For the cellular steel beam-columns, the energy approach is also used to develop the axial-bending (P-M) strength interaction diagrams. Overall, the developed equation yields accurate predictions of the strength of cellular steel beam-columns, with a mean prediction-to-FE critical strength ratio of 0.98. In addition, the strength of cellular steel and its parent hot-rolled steel shapes is compared to establish the criterion for the effective utilization of cellular steel beam-columns, ensuring that the selected cellular steel shape offers greater strength compared to its parent shape (larger P-M envelope). Finally, stability analysis methods for the cellular steel members and frames are proposed based on the current AISC-LRFD specification. The equivalent cross-sectional properties of cellular steel members are derived and utilized for the beam elements to represent the global responses of cellular steel members in the second-order elastic analysis. The proposed methods using beam elements are verified with the second-order inelastic analysis using shell elements. These methods can be used to predict the strength of cellular steel members and frames within the provided limitations.

An inelastic analysis program for three-dimensional structures subjected to static/gravity loads and (or) dynamic loads in the form of three translational and orthogonal components of base motions is described. Using incremental integration technique, the program computes structural response as a function of time. Deformation history of elements within the structure can be traced and pertinent information obtained via user element subroutines. Each node can possess up to six displacement degrees of freedom and can accommodate user elements with any specified nodes and degrees of freedom per node. The program is very flexible for modelling different structural configurations, and components like beam column elements, shear wall elements, slab elements, semirigid connection elements, and inelastic spring elements can be easily added to the base program. Key words: inelastic analysis, three-dimensional structures, earthquake, computer program, dynamic, stiffness matrix, base accelerations, unbalanced forces, element subroutines.

Matrix method for stability and second-order analysis of Timoshenko beam-column structures with semi-rigid connections

The advantage of second-order nonlinear analysis lies on its capacity to model actual structural response instead of making assumption on the structural behavior such as the arbitrary assumption of effective length factor. Considering the construction process of a structure, it may become a sway frame from a non-sway frame when a story is added or, on the contrary, to convert to a non-sway frame from a sway frame when bracings or infill walls are constructed and this makes the first-order linear analysis extremely inconvenient to use. Further, the deformation and load distributions of the structures considering the construction sequence can be much different from those obtained by assuming all structural elements share loads simultaneously. This paper proposes an advanced simulation-based design using an improved second-order analysis for structures accounting for both local and global imperfections, sequential loads and construction process. The technique for such an analysis is described and the error for ignoring the effects of sequential loads and construction procedure is quantified. Both the elastic and the plastic second-order analyses are used for comparison.

Experimental and parametric investigation of castellated steel beam-column in various expansion ratios, lengths and loading conditions

An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

When a scaffold system that is free to sway is tested to demonstrate its strength and stiffness, serious errors can occur if the load is applied by jacks with tiebars or cables. Experiments with techniques permitted by some specifications showed that strength was overestimated by amounts up to 63 percent, and second-order elastic analyses were consistent with that result. The current practice of using recovery of deflection as an indication of distress in a test scaffold is criticized because it has been shown to be inappropriate when the test structure is relatively stiff. This is so because it is likely that a higher proportion of its deflection consists of nonsystematic components. It is also misleading when the response of the structure comprises competing nonlinear modes.

This paper explores an all-steel design philosophy for flexural bracing requirements in cold-formed steel stud walls that employ mechanical bridging alone without sheathing. The current cold-formed steel design specification requires the brace for a single compression member to have stiffness equal to twice the ideal brace stiffness, but related proposals for braces in multiple stud walls, including brace force accumulation and minimum brace stiffness, have not yet been adopted. Bracing strength and stiffness demands in cold-formed steel-framed walls must be adequate to ensure safety but not overly conservative so that the requirements cannot be practically met. Elastic critical load and second-order elastic analyses are conducted herein to determine an adequate level of stiffness for a single braced compression member and relationships between strength and stiffness for braced multiple studs to that of a single stud. Statistics of measured member imperfections are incorporated to provide an equiv...

Buckling assessment of steel members through overall imperfection method

Optimal design of trusses with geometric imperfections: Accounting for global instability

The warping effects may predominate in geometrically nonlinear analysis of open cross-section members. The formulation of conventional beam-column elements incorporating the warping effects is cumbersome due to the method considering the inconsistency between the shear center and centroid. To develop a concise warping element formulation, this paper presents a transformation matrix to integrate the inconsistent effects into the element stiffness matrix. The co-rotational (CR) method used to establish the element equilibrium conditions in the geometrically nonlinear analysis is adopted to simplify the element formulation and improve the efficiency of nonlinear analysis. A new beam-column element explicitly considering the warping deformation and the Wagner effects is derived based on the CR method and the Euler–Bernoulli beam theory. A detailed kinematic description is provided for considering large deflections and rigid body motions. Based on the mechanical characteristic, the coordinate and the rigid body motion transformation matrices are given. The secant relationship is developed to evaluate the element internal forces accurately and effectively in each iteration. Several verification examples are provided to validate the proposed method’s reliability and robustness. The verifications demonstrate that the proposed element leads to considerable computational advantages. The results of this paper are useful for future upgrading of frame analysis software with warping degrees-of-freedom (DOFs).

Corrosion-induced deterioration of steel RC highway bridges is one of the major distress types that can render a structurally deficient bridge before reaching the design life. One feasible solution to the problem is to replace the conventional steel reinforcement with noncorrosive carbon fiber–reinforced polymer (CFRP) reinforcements. However, the CFRP reinforcement as an internal reinforcement has not been explored in AASHTO-type prestressed concrete beam bridges. AASHTO-type beams have an I-type cross section with a bottom flange, and on integration of the deck slab, the final shape is a bulb-T section. This paper discusses the experimental investigation of a precast prestressed AASHTO control beam and a bridge model. A 12.5-m-long one-third scale AASHTO-type control beam was experimentally investigated for its flexural behavior when reinforced and prestressed with CFRP. Subsequently, a one-third scale bridge model made of five such beams was constructed, instrumented, and tested under both service and ultimate load conditions. As anticipated, the control beam and the bridge model failures were initiated by rupturing of the prestressing CFRP tendons at the bottom layer. The observed flexural response of the bridge model was in close agreement with that of the control beam. As expected, the failure mode was progressive, with extensive cracking of the bridge model, which gives significant warning prior to the ultimate collapse, overcoming issues related to the otherwise brittle behavior of the CFRP-reinforced structures. It is therefore highly recommended to provide the CFRP tendons in different layers along the depth of the beams to effectively address the issues related to brittle failure exhibited by CFRP reinforcements.