Int. Journal of Applied Sciences and Engineering Research, Vol. 1, No. 2, 2012 www.ijaser.com © 2012 by the authors – Licensee IJASER- Under Creative Commons License 3.0 editorial@ijaser.com Research article ISSN 2277 – 9442 1 *Corresponding author (e-mail: pravin7717@rediffmail.com) Received on Jan., 2012; Accepted on Feb. 16, 2012; Published on Feb. 26, 2012 Response spectrum analysis of a shear frame structure by using MATLAB Pravin B. Waghmare, P.S.Pajgade, N. M. Kanhe doi: 10.6088/ijaser.0020101001 Abstract: A shear frame may be defined as a structure in which there is no rotation of a horizontal section at the level of the floor. In this respect the deflected frame will have many of the features of a cantilever beam that is deflected by shear forces, Hence the name Shear frame is given to those frames. To accomplish such deflection in frame, it is assume that: (1) the total mass of the structure is concentrated at the levels of the floors; (2) the beams on the floor are infinitely rigid as compared to the columns; and (3) the deformation of the structure is independent of the axial forces present in the columns. These assumptions transform the problem from a structure with an infinite number of degree of freedom (due to the distributed mass) to a structure which has only as many degrees as it has lumped masses at the floor levels. This paper is concerned with the response spectrum analysis of six stories shear frame with six degrees of freedom i.e. six horizontal displacement at the floor levels. From the analysis it concluded that, the first mode shape is most important one, because 86.96%, of Mass will respond to ground motion, when only 8.91% of mass will respond in the second. Mode shape, also the only first-two mode shapes will be adequate to insure that more than 90% of the mass will vibrate responding to ground motion Keywords: Spectrum analysis, Shear frame, Portal frame, MATLAB 1. Determination of lumped mass matrix For shear structure; the mass matrix is a diagonal matrix (the nonzero elements are only in the main diagonal) whereas each one of these elements represents the total equivalent entire mass of the story as a concentrated lumped mass at the level of this story with understanding that only horizontal displacement of this mass is possible. Therefore the lumped mass matrix is given by: M 1 0 0 0 0 0 0 M 2 0 0 0 0 0 0 M 3 0 0 0 0 0 0 M 4 0 0 0 0 0 0 M 5 0 0 0 0 0 0 M 6 2. Determination of stiffness matrix The stiffness matrix of shear frame can be determined by applying a unit displacement to each story alternatively and evaluating the resulting story forces. Because the beams are infinitely rigid compare to columns; then the story forces can easily be determined by adding the side-sway stiffness of the appropriates stories which equal to the total sum of columns stiffness of that stories. In shear frame as defined previously the stiffness of column with two ends fixed against rotation is given by M =