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Unformatted text preview: Module 10 Compression Members Version 2 CE IIT, Kharagpur Lesson 23 Short Compression Members under Axial Load with Uniaxial Bending Version 2 CE IIT, Kharagpur Instructional Objectives: At the end of this lesson, the student should be able to: • draw the strain profiles for different locations of the depth of the neutral axis, • explain the behaviour of such columns for any one of the strain profiles, • name and identify the three modes of failure of such columns, • explain the interaction diagram and divide into the three regions indicating three modes of failure, • identify the three modes of failure from the depth of neutral axis, • identify the three modes of failure from the eccentricity of the axial load, • determine the area of compressive stress block, distance of the centroid of the area of the compressive stress block from the highly compressed edge when the neutral axis is within and outside the crosssection of the column, • determine the compressive stress of concrete and tensile/compressive stress of longitudinal steel for any location of the neutral axis within or outside the crosssection of the column, • write the two equations of equilibrium, • explain the need to recast the equations in nondimensional form for their use in the design of such columns. 10.23.1 Introduction Short reinforced concrete columns under axial load with uniaxial bending behave in a different manner than when it is subjected to axial load, though columns subjected to axial load can also carry some moment that may appear during construction or otherwise. The behaviour of such columns and the three modes of failure are illustrated in this lesson. It is explained that the moment M , equivalent to the load P with eccentricity e (= M/P ), will act in an interactive manner. A particular column with specific amount of longitudinal steel, therefore, can carry either a purely axial load P o (when M = 0), a purely moment M o (when P = 0) or several pairs of P and M in an interactive manner. Hence, the needed interaction diagram of columns, which is a plot of P versus M , is explained Version 2 CE IIT, Kharagpur discussing different positions of neutral axis, either outside or within the cross section of the column. Depending on the position of the neutral axis, the column may or may not have tensile stress to be taken by longitudinal steel. In the compression region however, longitudinal steel will carry the compression load along with the concrete as in the case of axially loaded column. 10.23.2 Behaviour of Short Columns under Axial Load and Uniaxial Moment Normally, the side columns of a grid of beams and columns are subjected to axial load P and uniaxial moment M x causing bending about the major axis xx, hereafter will be written as M . The moment M can be made equivalent to the axial load P acting at an eccentricity of e (= M/P ). Let us consider a symmetrically reinforced short rectangular column subjected to axial load P u at an eccentricity...
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 Summer '01
 Prof.J.N.Bandopadhyay
 neutral axis, Kharagpur

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