m5l12 - 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 12 Flanged Beams – Numerical Problems (Continued) Version 2 CE IIT, Kharagpur
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Instructional Objectives: At the end of this lesson, the student should be able to: identify the two types of problems – analysis and design types, apply the formulations to design the flanged beams. 5.12.1 Introduction Lesson 10 illustrates the governing equations of flanged beams and Lesson 11 explains their applications for the solution of analysis type of numerical problems. It is now necessary to apply them for the solution of design type, the second type of the numerical problems. This lesson mentions the different steps of the solution and solves several numerical examples to explain their step-by-step solutions. 5.12.2 Design Type of Problems We need to assume some preliminary dimensions of width and depth of flanged beams, spacing of the beams and span for performing the structural analysis before the design. Thus, the assumed data known for the design are: D f , b w , D , effective span, effective depth, grades of concrete and steel and imposed loads. There are four equations: (i) expressions of compressive force C , (ii) expression of the tension force T , (iii) C = T and (iv) expression of M u in terms of C or T and the lever arm { M = ( C or T ) (lever arm)}. However, the relative dimensions of D f , D and x u and the amount of steel (under-reinforced, balanced or over-reinforced) influence the expressions. Accordingly, the respective equations are to be employed assuming a particular situation and, if necessary, they need to be changed if the assumed parameters are found to be not satisfactory. The steps of the design problems are as given below. Step 1: To determine the factored bending moment M u Step 2: To determine the M u , lim of the given or the assumed section The beam shall be designed as under-reinforced, balanced or doubly reinforced if the value of M u is less than, equal to or more than M u , lim . The design of over-reinforced beam is to be avoided as it does not increase the bending moment carrying capacity beyond M u , lim either by increasing the depth or designing a doubly reinforced beam. Version 2 CE IIT, Kharagpur
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Step 3: To determine x u , the distance of the neutral axis, from the expression of M u Here, it is necessary to assume first that x u is in the flange. Later on, it may be necessary to calculate x u if the value is found to be more than D f . This is to be done assuming first that D f / x u < 0.43 and then D f / x u > 0.43 separately. Step 4: To determine the area(s) of steel For doubly reinforced beams A st = A st , lim + A st2 and A sc are to be obtained, while only A st is required to be computed for under-reinforced and balanced beams. These are calculated employing C = T (for A st and A st , lim ) and the expression of M u2 to calculate A st2 and A sc .
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m5l12 - Module 5 Flanged Beams Theory and Numerical...

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