A new damage index for plane steel frames exhibiting strength and stiffness degradation under seismic motion

A new damage index for plane steel frames under earthquake ground motion is proposed. This index is defined at a section of a steel member and takes into account the interaction between the axial force N and bending moment M acting there. This interaction is defined by two curves in the N-. M plane. The first curve is the limit between elastic and inelastic material behavior, where damage is zero, while the second one is the limit between inelastic behavior and complete failure, where damage is equal to one. The damage index is defined by assuming a linear variation of damage between the two abovementioned curves. Thus, for a given N-. M combination at a member section, obtained with the aid of a two dimensional finite element program, one easily defines the damage index of that section. Material nonlinearities are taken into account by a stress-strain bilinear model including cyclic strength and stiffness degradation in the framework of lumped plasticity (plastic hinge model), while geometrical nonlinearities are modeled by including large deflection effects. The increase of damage related to strength reduction due to low-cycle fatigue is also taken into account. Several illustrative examples serve to demonstrate the use of the proposed damage index and to compare it with other well known damage indices. © 2012

Direct damage-controlled design of plane steel moment-resisting frames using static inelastic analysis

A new direct damage-controlled design method for plane steel frames under static loading is presented. Seismic loading can be handled statically in the framework of a push-over analysis. This method, in contrast to existing steel design methods, is capable of directly controlling damage, both local and global, by incorporating continuum damage mechanics for ductile materials in the analysis. The design process is accomplished with the aid of a two-dimensional finite element program, which takes into account material and geometric nonlinearities by using a nonlinear stress-strain relation through the beam-column fiber modeling and including P-δ and P-Δ effects, respectively. Simple expressions relating damage to the plastic hinge rotation of member sections and the interstorey drift ratio for three performance limit states are derived by conducting extensive parametric studies involving plane steel moment-resisting frames under static loading. Thus, a quantitative damage scale for design purposes is established. Using the proposed design method one can either determine damage for a given structure and loading, or dimension a structure for a target damage and given loading, or determine the maximum loading for a given structure and a target damage level. Several numerical examples serve to illustrate the proposed design method and demonstrate its advantages in practical applications

Direct damage controlled seismic design of plane steel degrading frames

A new method for seismic design of plane steel moment resisting framed structures is developed. This method is able to control damage at all levels of performance in a direct manner. More specifically, the method: (a) can determine damage in any member or the whole of a designed structure under any given seismic load, (b) can dimension a structure for a given seismic load and desired level of damage and (c) can determine the maximum seismic load a designed structure can sustain in order to exhibit a desired level of damage. In order to accomplish these things, an appropriate seismic damage index is used that takes into account the interaction between axial force and bending moment at a section, strength and stiffness degradation as well as low cycle fatigue. Then, damage scales are constructed on the basis of extensive parametric studies involving a large number of frames exhibiting cyclic strength and stiffness degradation and a large number of seismic motions and using the above damage index for damage determination. Some numerical examples are presented to illustrate the proposed method and demonstrate its advantages against other methods of seismic design. © 2014, Springer Science+Business Media Dordrecht

Seismic damage estimation of in-plane regular steel moment resisting and x-braced frames

Simple empirical expressions to estimate maximum seismic damage on the basis of five well known damage indices for planar regular moment resisting and x-braced steel frames are presented. They are based on the results of extensive parametric studies concerning the inelastic response of a large number of these frames to a large number of ground motions. Thousands of nonlinear dynamic analyses are performed by scaling the seismic records to different intensities in order to drive the structures to different levels of inelastic deformation and finally to collapse. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, stiffness ratio, capacity factor (for moment resisting frames), brace slenderness ratio and column stiffness (for x-braced frames) and characteristics of the ground motion, such as characteristic period and spectral acceleration, strongly influence damage. Nonlinear regression analysis is employed in order to derive simple formulae, which reflect the influence of the aforementioned parameters and offer a direct estimation of the damage indices used in this study. More specifically, given the characteristics of the structure and the ground motion, one can calculate the maximum damage observed in column bases and beams (for moment resisting frames) or in braces (for x-braced frames). Finally, two examples serve to illustrate the use of the proposed expressions and demonstrate their accuracy and efficiency. © 2012 Springer Science+Business Media Dordrecht

Simple formulae for damage estimation of composite steel/concrete moment resisting frames

Simple empirical expressions to estimate maximum seismic damage on the basis of three well known damage indices for planar regular steel/concrete composite moment resisting frames are presented. They are based on the results of extensive parametric studies concerning the inelastic response of a large number of frames to a large number of ordinary far-field type ground motions. Thousands of nonlinear dynamic analyses are performed by scaling the seismic records to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, beam strength ratio, material strength and the ground motion characteristics affect structural damage. Nonlinear regression analysis is employed in order to derive simple formulae, which offer a direct estimation of the damage indices used in this study. More specifically, given the characteristics of the structure and the ground motion, one can calculate the maximum damage observed in column bases and beams. Finally, one example serves to illustrate the use of the proposed expressions and demonstrates their efficiency and accuracy