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# m12l30 - Module 12 Yield Line Analysis for Slabs Version 2...

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Module 12 Yield Line Analysis for Slabs Version 2 CE IIT, Kharagpur

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Lesson 30 Basic Principles, Theory and One-way Slabs Version 2 CE IIT, Kharagpur
Instructional Objectives: At the end of this lesson, the student should be able to: state the limitations of elastic analysis of reinforced concrete slabs, explain the meaning of yield lines, explain the basic principle of yield line theory, state the assumptions of yield line analysis, state the rules for predicting yield patterns and locating the axes of rotation of slabs with different plan forms and boundaries, state the upper and lower bound theorems, explain the two methods i.e., (i) method of segmental equilibrium and (ii) method of virtual work, explain if the yield line analysis is a lower or upper bound method, analyse one-way slab problems to determine the location of yield lines and determine the collapse load applying the theoretical formulations of (i) method of segmental equilibrium and (ii) method of virtual work. 12.30.1 Introduction The limit state of collapse method of design of beams and slabs considers the actual inelastic behaviour of slabs when subjected to the factored loads. Accordingly, it is desirable that the structural analysis of beams and slabs has to be done taking the inelastic behaviour into account. Though the coefficients in Annex D-1 of IS 456 to determine the bending moments for the design of two- way slabs are based on inelastic analysis, the code also recommends the use of linear elastic theory for the structural analysis in cl. 22.1. Moreover, IS 456 further stipulates the use of coefficients of moments and shears for continuous beams given in Tables 12 and 13 of cl. 22.5 in lieu of rigorous elastic analysis. These coefficients of beams are also applicable for the design of one-way slabs, based on linear elastic theory. Thus, there are inconsistencies between the methods of analysis and design. Version 2 CE IIT, Kharagpur

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The above discussion clearly indicates the need of adopting the inelastic analysis or collapse limit state analysis for all structures. However, there are sufficient justifications for adopting the inelastic analysis for slabs as evident from the following limitations of the elastic analysis of slabs: (i) Slab panels are square or rectangular. (ii) One-way slab panels must be supported along two opposite sides only; the other two edges remain unsupported. (iii) Two-way slab panels must be supported along two pairs of opposite sides, supports remaining unyielding. (iv) Applied loads must be uniformly distributed. (v) Slab panels must not have large opening. Version 2 CE IIT, Kharagpur
Therefore, for slabs of triangular, circular and other plan forms, for loads other than uniformly distributed, for support conditions other than those specified above and for slabs with large openings (Figs.12.30.1a to d); the collapse limit state analysis has been found to be a powerful and versatile method.

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m12l30 - Module 12 Yield Line Analysis for Slabs Version 2...

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