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# m5l11 - Module 5 Flanged Beams Theory and Numerical...

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Module 5 Flanged Beams – Theory and Numerical Problems Version 2 CE IIT, Kharagpur

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Lesson 11 Flanged Beams – Numerical Problems Version 2 CE IIT, Kharagpur
Instructional Objectives: At the end of this lesson, the student should be able to: identify the two types of numerical problems – analysis and design types, apply the formulations to analyse the capacity of a flanged beam, determine the limiting moment of resistance quickly with the help of tables of SP-16. 5.11.1 Introduction Lesson 10 illustrates the governing equations of flanged beams. It is now necessary to apply them for the solution of numerical problems. Two types of numerical problems are possible: (i) Analysis and (ii) Design types. This lesson explains the application of the theory of flanged beams for the analysis type of problems. Moreover, use of tables of SP-16 has been illustrated to determine the limiting moment of resistance of sections quickly for the three grades of steel. Besides mentioning the different steps of the solution, numerical examples are also taken up to explain their step-by-step solutions. 5.11.2 Analysis Type of Problems The dimensions of the beam b f , b w , D f , d , D , grades of concrete and steel and the amount of steel A st are given. It is required to determine the moment of resistance of the beam. Step 1: To determine the depth of the neutral axis x u The depth of the neutral axis is determined from the equation of equilibrium C = T . However, the expression of C depends on the location of neutral axis, D f / d and D f / x u parameters. Therefore, it is required to assume first that the x u is in the flange. If this is not the case, the next step is to assume x u in the web and the computed value of x u will indicate if the beam is under- reinforced, balanced or over-reinforced. Version 2 CE IIT, Kharagpur

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Other steps: After knowing if the section is under-reinforced, balanced or over- reinforced, the respective parameter D f / d or D f / x u is computed for the under- reinforced, balanced or over-reinforced beam. The respective expressions of C , T and M u , as established in Lesson 10, are then employed to determine their values. Figure 5.11.1 illustrates the steps to be followed. Version 2 CE IIT, Kharagpur
5.11.3 Numerical Problems (Analysis Type) Ex.1: Determine the moment of resistance of the T -beam of Fig. 5.11.2. Given data: b f = 1000 mm, D f = 100 mm, b w = 300 mm, cover = 50 mm, d = 450 mm and A st = 1963 mm 2 (4- 25 T). Use M 20 and Fe 415. Step 1: To determine the depth of the neutral axis x u Assuming x u in the flange and equating total compressive and tensile forces from the expressions of C and T (Eq. 3.16 of Lesson 5) as the T -beam can be treated as rectangular beam of width b f and effective depth d , we get: mm 100 mm 98.44 (20) (1000) 0.36 (1963) (415) 0.87 36 . 0 0.87 < = = = ck f st y u f b A f x So, the assumption of x u in the flange is correct.

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m5l11 - Module 5 Flanged Beams Theory and Numerical...

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