ISSN 2075-5309 www.mdpi.com/journal/buildings/ Article
An Introduction to the Methodology of Earthquake Resistant Structures of Uniform Response Mark Grigorian 1,* and Carl E. Grigorian 2
MGA Structural Engineering Inc., 111 N. Jackson Street Glendale, CA 91206, USA URS Corporation, 915 Wilshire Blvd., Los Angeles, CA 90017, USA; E-Mail: Carl.Grigorian@urs.com
* Author to whom correspondence should be addressed; E-Mail: email@example.com. Received: 9 December 2011; in revised form: 22 March 2012 / Accepted: 24 April 2012 / Published: 2 May 2012
Abstract: Structures of Uniform Response are special earthquake resistant frames in which members of similar groups such as beams, columns and braces of similar nature share the same demand-capacity ratios regardless of their location within the group. The fundamental idea behind this presentation is that seismic structural response is largely a function of design and construction, rather than analysis. Both strength and stiffness are induced rather than investigated. Failure mechanisms and stability conditions are enforced rather than tested. Structures of Uniform Response are expected to sustain relatively large inelastic displacements during major earthquakes. A simple technique has been proposed to control and address the gradual softening of such structures due to local/partial instabilities and formation of plastic hinges. In structures of uniform response, the magnitude and shape of distribution of lateral forces affects the distribution of story stiffness in proportion with story moments, therefore affecting the dynamic behavior of the system as a whole. Simple closed form formulae describing the nonlinear behavior of moment frames of uniform response have been proposed. While the scope of this contribution is limited to moment frames, the proposed method can successfully be extended to all types of recognized earthquake resisting systems. Keywords: earthquake resistant frames; structural instability; plastic analysis; stiffness degradation; sequential hinging; energy equivalency; drift control; period analysis
Buildings 2012, 2 Notation f i, j h h m n s C E F magnification factor integer coordinates story height height from base number of stories number of bays order of occurrence numerical constant modulus of elasticity external force H I J K L M N P MP NP total building height beam moment of inertia column moment of inertia sub frame stiffness span length beam moment column moment joint load beam plastic moment column plastic moment T U V W Q period of vibration internal energy shear force sub frame weight total weight local displacement total displacement drift ratio joint rotation
Indexes, superscripts and the remaining symbols are defined, as they first appear in the text.
1. Introduction The purpose of this paper is to introduce the performance of Structures of Uniform Response (SUR) under lateral loading. SUR are special frameworks in which members of similar groups such as beams, columns and braces of similar physical characteristics e.g., length, end conditions etc., share the same demand-capacity ratios regardless of their location and numbers within the group. In other words, selected groups of members develop identical levels of stress and strain under similar loading conditions. Results of inelastic static, push-over and dynamic time-history analyses [1,2], have shown that Performance Based Plastic Design methods can successfully be applied to almost all types of code recognized earthquake resisting systems. The performance of SUR as earthquake resisting systems is directly supported by these findings. In introducing SUR the paper also presents a new analytic Performance-Based Elastic-Plastic Design method for earthquake resisting moment frames, with the ability to control their response during all phases of seismic...