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Unformatted text preview: Module 13 Working Stress Method Version 2 CE IIT, Kharagpur Lesson 35 Numerical Problems Version 2 CE IIT, Kharagpur Instructional Objectives: At the end of this lesson, the student should be able to: • employ the equations established for the analysis and design of singly and doublyreinforced rectangular beams, • use tables of SP16 for the analysis and design of singly and doubly reinforced rectangular beams, • understand the economy in the design by limit state of collapse. 13.35.1 Introduction Lesson 34 explains the equations for the analysis and design of singly and doublyreinforced rectangular beams. The applications of the equations are illustrated in this lesson through the solutions of several numerical problems. Direct computation method and use of tables of SP16 are the two approaches for the analysis and design of singly and doublyreinforced rectangular beams. In direct computation method, the derived equations are employed directly, while the use of tables of SP16 gives the results quickly with several alternatives avoiding tedious calculations. Some of the numerical problems are solved using both methods. Problems having the same width and effective depth but of different grades of steel are solved to compare the results. Moreover, problems of singly and doublyreinforced rectangular beams, solved earlier by limit state of collapse method are also taken up here to compare the results. It is shown that the beams designed by limit state of collapse method are economical. In addition to illustrative examples, practice and test problems are also given in this lesson. Understanding the solved numerical examples and solving the practice and test problems will help in following the applications of the equations and the use of tables of SP16 in analysing and designing singly and doublyreinforced rectangular beams. Version 2 CE IIT, Kharagpur 13.35.2 Numerical Problems Problem 1. (a) Determine the moment of resistance of the rectangular beam of Fig. 13.35.1 having b = 350 mm, d = 600 mm, D = 650 mm, A st = 804 mm 2 (4 16T), σ cbc = 7 N/mm 2 and σ st = 230 N/mm 2 . (b) Determine the balanced moment of resistance of the beam and the balanced area of tension steel. (c) Determine the actual compressive stress of concrete f cbc and tensile stress of steel f st when 60 kNm is applied on the beam. Use direct computation method for all three parts. Solution 1. 1 (a): Given data are: b = 350 mm, d = 600 mm, A st = 804 mm 2 , σ cbc = 7 N/mm 2 and σ st = 230 N/mm 2 . We have: p t = A st (100) / bd = 80400 / (350) (600) = 0.383 per cent and m = 93.33 / σ cbc = 93.33 /7 = 13.33. We determine the value of k from Eq. 13.16. k =  ( p t m / 100) + {( p t m /100) 2 + ( p t m/ 50)} 1/2 (13.16) =  0.051 + 0.323 = 0.272 j = 1 k /3 = 0.909 Equation 13.17 gives the moment of resistance of the beam as, M = ( p t / 100) σ st (1 – k /3) bd 2 (13.17) Version 2 CE IIT, Kharagpur = (0.383/100) (230) (0.909) (350) (600) (600) = 100.89 kNm....
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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.
 Summer '01
 Prof.J.N.Bandopadhyay

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