Lesson 34 Rectangular Beams under FlexureVersion 2 CE IIT, Kharagpur
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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