m3l6 - Module 3 Limit State of Collapse Flexure(Theories...

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Module 3 Limit State of Collapse - Flexure (Theories and Examples) Version 2 CE IIT, Kharagpur
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Lesson 6 Numerical Problems on Singly Reinforced Rectangular Beams 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 main two types of problems of singly reinforced rectangular sections, name the inputs and outputs of the two types of problems, state the specific guidelines of assuming the breadth, depths, area of steel reinforcement, diameter of the bars, grade of concrete and grade of steel, determine the depth of the neutral axis for specific dimensions of beam (breadth and depth) and amount of reinforcement, identify the beam with known dimensions and area of steel if it is under- reinforced or over-reinforced, apply the principles to design a beam. 3.6.1 Types of Problems Two types of problems are possible: (i) design type and (ii) analysis type. In the design type of problems, the designer has to determine the dimensions b , d , D , A st (Fig. 3.6.1) and other detailing of reinforcement, grades of concrete and steel from the given design moment of the beam. In the analysis type of the problems, all the above data will be known and the designer has to find out the moment of resistance of the beam. Both the types of problems are taken up for illustration in the following two lessons. Version 2 CE IIT, Kharagpur
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3.6.2 Design Type of Problems The designer has to make preliminary plan lay out including location of the beam, its span and spacing, estimate the imposed and other loads from the given functional requirement of the structure. The dead loads of the beam are estimated assuming the dimensions b and d initially. The bending moment, shear force and axial thrust are determined after estimating the different loads. In this illustrative problem, let us assume that the imposed and other loads are given. Therefore, the problem is such that the designer has to start with some initial dimensions and subsequently revise them, if needed. The following guidelines are helpful to assume the design parameters initially. 3.6.2.1 Selection of breadth of the beam b Normally, the breadth of the beam b is governed by: (i) proper housing of reinforcing bars and (ii) architectural considerations. It is desirable that the width of the beam should be less than or equal to the width of its supporting structure like column width, or width of the wall etc. Practical aspects should also be kept in mind. It has been found that most of the requirements are satisfied with b as 150, 200, 230, 250 and 300 mm. Again, width to overall depth ratio is normally kept between 0.5 and 0.67. 3.6.2.2 Selection of depths of the beam d and D The effective depth has the major role to play in satisfying (i) the strength requirements of bending moment and shear force, and (ii) deflection of the beam.
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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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m3l6 - Module 3 Limit State of Collapse Flexure(Theories...

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