m13l34 - Module 13 Working Stress Method Version 2 CE IIT,...

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Module 13 Working Stress Method Version 2 CE IIT, Kharagpur
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Lesson 34 Rectangular Beams under Flexure Version 2 CE IIT, Kharagpur
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Instructional Objectives: At the end of this lesson, the student should be able to: explain the philosophy of the design by working stress method, explain the concepts of permissible stresses in concrete and steel and the factors of safety in this method, state the limit of increase of permissible stresses under specific loading considerations, state the assumptions for the design of flexural members employing working stress method, explain the concept of modular ratio, derive the governing equations of rectangular, balanced and under-reinforced (singly-reinforced) sections, name the two types of problems for the designer, write down the steps separately for the two types of problems in the working stress method, justify the need for doubly-reinforced beams, and derive the governing equations of the doubly-reinforced rectangular flexural members. 13.34.1 Introduction Design of reinforced concrete structures started in the beginning of this century following purely empirical approach. Thereafter came the so called rigorous elastic theory where it is assumed that concrete is elastic and reinforcing steel bars and concrete act together elastically. The load-deflection relation is linear and both concrete and steel obey Hooke’s law. The method is designated as working stress method as the loads for the design of structures are the service loads or the working loads. The failure of the structure will occur at a much higher load. The ratio of the failure loads to the working loads is the factor of safety. Accordingly, the stresses of concrete and steel in a structure designed by the working stress method are not allowed to exceed some specified values of stresses known as permissible stresses. The Version 2 CE IIT, Kharagpur
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permissible stresses are determined dividing the characteristic strength f ck of the material by the respective factor of safety. The values of the factor of safety depend on the grade of the material and the type of stress. Thus, for concrete in bending compression, the permissible stress of grade M 20 is 7 N/mm 2 , which is obtained by dividing the characteristic strength f ck of M 20 concrete by a number 3 and then rationalising the value to 7. This permissible stress is designated by σ cbc , the symbol stands for permissible stress and the letters c , b and c mean concrete in bending compression, respectively. 13.34.2 Permissible Stresses in Concrete The permissible stress of concrete in direct tension is denoted by td . The values of td for member in direct tension for different grades of concrete are given in cl. B-2.1.1 of IS 456. However, for members in tension, full tension is to be taken by the reinforcement alone. Though full tension is taken by the reinforcement only, the actual tensile stress of concrete f td in such members shall not exceed the respective permissible values of td to prevent any crack. Table 13.1 presents the values of
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This note was uploaded on 03/17/2012 for the course CENG 3012 taught by Professor Prof.j.n.bandopadhyay during the Summer '01 term at Indian Institute of Technology, Kharagpur.

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m13l34 - Module 13 Working Stress Method Version 2 CE IIT,...

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