Procedure for using of Non-dimensional Interaction Diagrams as Design Aids to find steel
Size of column, Grade of concrete, Grade of steel (otherwise assume suitably) Factored load and Factored moment
Assume arrangement of reinforcement: On two sides or on four sides
Assume moment due to minimum eccentricity to be less than the actual moment Assume suitable axis of bending based on the given moment (xx or yy) Assuming suitable diameter of longitudinal bars and suitable nominal cover
1. Find d1/D from effective cover d1
2. Find non dimensional parameters Pu/fckbD and Mu/fckbD2
3. Referring to appropriate chart from S-16, find p/fck and hence the percentage of reinforcement, p
4. Find steel from, As = p bD/100
5. Provide proper number and arrangement for steel
6. Design suitable transverse steel
7. Provide neat sketch
Members Subjected to Combined Axial Load and Biaxial Bending
The resistance of a member subjected to axial force and biaxial bending shall be obtained on the basis of assumptions given in IS:456 with neutral axis so chosen as to satisfy the equilibrium of load and moments about two axes. Alternatively such members may be designed by the following equation:
[Mux/Mux1]?n + [Muy/Muy1]?n ? 1, where
Mux and My = moments about x and y axes due to design loads,
Mux1 and My1 = maximum uni-axial moment capacity for an axial load of Pu bending about x and y axes respectively, and ?n is related to Pu /Puz, where Puz = 0.45 fck .Ac + 0.75 fy Asc
For values of Pu /Puz = 0.2 to 0.8, the values of ?n vary linearly from 1 .0 to 2.0. For values less than 0.2 and greater than 0.8, it is taken as 1 and 2 respectively
NOTE -The design of member subject to combined axial load and uniaxial bending will involve lengthy calculation by trial and error. In order to overcome these difficulties interaction diagrams may be used. These have been prepared and published by BIS in SP:16 titled Design aids for reinforced concrete to IS 456-2000.
IS:456-2000 Code Procedure
1. Given Pu, Mux, Muy, grade of concrete and steel
2. Verify that the eccentricities ex = Mux/Pu and ey = Muy/Pu are not less than the corresponding minimum eccentricities as per IS:456-2000
Assume a trial section for the column (square, rectangle or circular).
4. Determine Mux1 and Muy1, corresponding to the given Pu (using appropriate curve from SP-16 design aids)
5. Ensure that Mux1 and Muy1 are significantly greater than Mux and Muy respectively; otherwise, suitably redesign the section.
6. Determine Puz and hence ?n
7. Check the adequacy of the section using interaction equation. If necessary, redesign the section and check again.
Slender Compression Members: The design of slender compression members shall be based on the forces and the moments determined from an analysis of the structure, including the effect of deflections on moments and forces. When the effects of deflections are not taken into account in the analysis, additional moment given in 39.7.1 shall be taken into account in the appropriate direction.
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