m10l26 - Module 10 Compression Members Version 2 CE IIT...

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Unformatted text preview: Module 10 Compression Members Version 2 CE IIT, Kharagpur Lesson 26 Short Compression Members under Axial Load with Biaxial Bending Version 2 CE IIT, Kharagpur Instructional Objectives: At the end of this lesson, the student should be able to: • understand the behaviour of short columns under axial load and biaxial bending, • understand the concept of interaction surface, • identify the load contour and interaction curves of P u-M u in a interaction surface, • mention the limitation of direct application of the interaction surface in solving the problems, • explain the simplified method of design and analysis of short columns under axial load and biaxial bending, • apply the IS code method in designing and analysing the reinforced concrete short columns under axial load and biaxial bending. 10.26.1 Introduction Beams and girders transfer their end moments into the corner columns of a building frame in two perpendicular planes. Interior columns may also have biaxial moments if the layout of the columns is irregular. Accordingly, such columns are designed considering axial load with biaxial bending. This lesson presents a brief theoretical analysis of these columns and explains the difficulties to apply the theory for the design. Thereafter, simplified method, as recommended by IS 456, has been explained with the help of illustrative examples in this lesson. Version 2 CE IIT, Kharagpur 10.26.2 Biaxial Bending Figures 10.26.1a and b present column section under axial load and uniaxial bending about the principal axes x and y , respectively. Figure 10.26.1c Version 2 CE IIT, Kharagpur presents the column section under axial load and biaxial bending. The eccentricities e x and e y of Fig.10.26.1c are the same as those of Fig.10.26.1a (for e x ) and Fig.10.26.1b (for e y ), respectively. Thus, the biaxial bending case (case c) is the resultant of two uniaxial bending cases a and b. The resultant eccentricity e , therefore, can be written as (see Fig.10.26.1c): (10.55) 2 / 1 2 2 ) ( y x e e e + = Designating the moments of cases a, b and c by M ux , M uy and M u , respectively, we can write: (10.56) 2 / 1 2 2 ) ( uy ux u M M M + = and the resultant M u is acting about an inclined axis, so that tan θ = e x /e y = M uy /M ux (10.57) the angle of inclination θ is measured from y axis. This inclined resultant axis shall also be the principal axis if the column section including the reinforcing bars is axisymmetric. In such a situation, the biaxial bending can be simplified to a uniaxial bending with the neutral axis parallel to the resultant axis of bending. The reinforced concrete column cross-sections are, in general, non- axisymmetric with reference to the longitudinal axis and, therefore, the neutral axis is not parallel to the resultant axis of bending ( θ is not equal to λ in Fig.10.26.1c). Moreover, it is extremely laborious to find the location of the neutral axis with successive trials. However, failure strain profile and stress block neutral axis with successive trials....
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m10l26 - Module 10 Compression Members Version 2 CE IIT...

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