C V R Murty

Soft or extreme soft storeys in multi-storied buildings cause localized damage (and even collapse) during strong earthquake shaking. The presence of such soft or extremely soft storey is identified through provisions of vertical stiffness irregularity in seismic design codes. Identification of the irregularity in a building requires estimation of lateral translational stiffness of each storey. Estimation of lateral translational stiffness can be an arduous task. A simple procedure is presented to estimate storey stiffness using only properties of fundamental lateral translational mode of oscillation (namely natural period and associated mode shape), which are readily available to designers at the end of analysis stage. In addition, simplified analytical expressions are provided towards identifying stiffness irregularity. Results of linear elastic time-history analyses indicate that the proposed procedure captures the irregularity in storey stiffness in both low- and mid-rise buildings.

A simple hand calculation based method is presented to develop axial flexure design P-M interaction curves of rectangular reinforced concrete sections. The proposed method uses basic principles of mechanics satisfying compatibility of strains, equilibrium of forces and constitutive relations of constituent materials. Simple step-wise calculation is enough to develop the interaction curve; it does not require any iterations. Accuracy of the method is demonstrated by comparing the results of two RC sections with the interaction curves of the sections obtained using SP:16. Step-wise calculations are presented of the two RC sections to illustrate the use of this method for generating design P-M interaction curves.

A quantitative approach is required to ensure desired global ductile behaviour with at least a guaranteed level of deformation capacity of buildings. This paper quantifies the required column-to-beam strength ratio, and insufficiency of the current code prescribed values of strength ratio to achieve a ductile mechanism. Column-to-beam strength ratio is varied by varying column size and reinforcement in the columns; beam size and reinforcement are kept constant. Nonlinear static pushover analyses of designed RC buildings with different column-to-beam strength ratios show different collapse mechanisms, lateral strengths and energy dissipation characteristics. Column-to-beam strength ratio alone does not result in the desired global ductile behaviour and do not guarantee the desired deformability. Further, the required column-to-beam strength ratio is same, depending on the design, for different hazard levels (reflected by the design seismic coefficient). An appropriate value of minimum column-to-beam strength ratio to achieve a ductile mechanism is presented along with pointers to ensure large deformability of buildings.

The paper reviews seismic behaviour and performance of reinforced concrete (RC) deep vertical members, particularly bridge piers and structural walls. The provisions of the relevant Indian codes of practice, concerning shear strength and shear demand in these members, are reviewed in light of the provisions of international codes of practice. The deficiencies are identified in the seismic shear design philosophy, prescribed by Indian codes.

An analytical method is presented to estimate lateral shear strength (and identify likely mode and location of failure) in reinforced concrete (RC) cantilever columns of rectangular cross-section under combined axial force, shear force and bending moment. Change in shear capacity of concrete with flexural demand at a section is captured explicitly and the shear resistance offered by concrete estimated; this is combined with shear resistance offered by transverse and longitudinal reinforcement bars to estimate the overall shear capacity of RC columns. Shear–moment (V-M) interaction capacity diagram of an RC column, viewed alongside the demand diagram, identifies the lateral shear strength and failure mode. These analytical estimates compare well with test data of 107 RC columns published in literature; the test data corresponds to different axial loads, transverse reinforcement ratios, longitudinal reinforcement ratios, shear span to depth ratios, and loading conditions. Also, the analytical estimates are compared with those obtained using other analytical methods reported in literature; in all cases, the proposed method gives reasonable accuracy when estimating shear capacity of RC columns. In addition, the method provides insights into the shear resistance mechanism in RC columns under the combined action of P-V-M, and it is simple to use.

Capacity design precludes brittle actions thereby maximising energy dissipation capacity of moment resisting frame buildings through flexural yielding in beams before possible yielding in columns during strong earthquake shaking. The flexural strength of columns is required to be more than that of beams framing into it. Seismic design codes stipulate guidelines for design and detailing of members to achieve desired ductile behaviour of buildings. This paper examines seismic behaviour of RC moment frame buildings in seismic Zone V and IV designed as per the column-to-beam strength ratio (CBSR) requirements of the draft IS 13920, and its adequacy along with the detailing requirements. The CBSR of 1.4 specified in the draft code is not sufficient for buildings in seismic Zone V.

This paper presents an externally reinforced I-beam-to-box-column seismic connection. An inclined rib-plated collar-plated configuration with web plates is used to ensure planar continuity between I-beam and box-column webs; the rib plates, inclined in plan between the beam web and the two column web planes, along with collar-plates encircling the box-column at beam flange levels and web plates in plane with the rib plates at the beam web level constitute the new configuration. This connection configuration relieves stresses on box-column flanges and helps in force transfer to the box-column webs. Performance evaluation of the proposed connection configuration shows that sufficient inelasticity is mobilized in the beam away from the column face with connection elements and welds remaining elastic. The seismic performance of the proposed connection is also found to be better than two state-of-the-art connection schemes in terms of higher strength, stiffness, and higher reserve strength of the welds under cyclic displacement loading. © 2010 ASCE.

Earthquake Resistant Design Philosophy seeks (a) no damage, (b) no significant structural damage, and (c) significant structural damage but no collapse of normal buildings, under minor, moderate and severe levels of earthquake shaking, respectively. A procedure is proposed for seismic design of low-rise reinforced concrete special moment frame buildings, which is consistent with this philosophy; buildings are designed to be ductile through appropriate sizing and reinforcement detailing, such that they resist severe level of earthquake shaking without collapse. Nonlinear analyses of study buildings are used to determine quantitatively (a) ranges of design parameters required to assure the required deformability in normal buildings to resist the severe level of earthquake shaking, (b) four specific limit states that represent the start of different structural damage states, and (c) levels of minor and moderate earthquake shakings stated in the philosophy along with an extreme level of earthquake shaking associated with the structural damage state of no collapse. The four limits of structural damage states and the three levels of earthquake shaking identified are shown to be consistent with the performance-based design guidelines available in literature. Finally, nonlinear analyses results are used to confirm the efficacy of the proposed procedure.

A seismic design method is proposed for RC frame buildings, with focus on two of the seven virtues of earthquake resistant buildings, namely deformation capacity and desirable collapse mechanism. Fundamental lateral translation mode of the building and plastic rotation capacity of beams are included as input to estimate lateral force demand. Guidelines are provided to proportion beam and column cross-sections through: (a) closed-form expressions of flexural rigidities to maximize participation of the fundamental mode, and (b) relative achievable plastic rotation capacity using current design and detailing practice. This method is seen to surpass two prominent displacement-based design methods reported in literature. Results of nonlinear static pushover and nonlinear time history analyses of buildings of three different heights designed by this and the said two methods are used to make a case for the proposed method; the proposed method is able to control plastic rotation demand in beams and provide at least 20% more lateral deformation capacity than the said methods.

A simple approach is presented to derive limiting strain-based bilinear overstrength moment-curvature response curves of reinforced concrete sections. These curves are obtained by simple hand calculations proposed in the paper. Implications of use of these idealized curves are examined on estimating seismic behaviour of RC frame buildings by nonlinear static pushover analyses. The use of idealized moment-curvature curves and its properties, as proposed, offers a consistent and non- empirical approach compatible with actual section properties.