Procedure for using of Non dimensional Interaction Diagrams as Design Aids to find steel

Procedure for using of Non-dimensional Interaction Diagrams as Design Aids to find steel

Given:

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 P_u/f_ckbD and M_u/f_ckbD²

3.    Referring to appropriate chart from S-16, find p/f_ck and hence the percentage of reinforcement, p

4.    Find steel from, A_s = 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:

[M_ux/M_ux1]^?n + [M_uy/M_uy1]^?n ? 1,  where

M_ux and M_y = moments about x and y axes due to design loads,

M_ux1 and M_y1 = maximum uni-axial moment capacity for an axial load of P_u bending about x and y axes respectively, and ?n is related to P_u /P_uz, where P_uz = 0.45 f_ck .A_c + 0.75 f_y A_sc

For values of P_u /P_uz = 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 P_u, M_ux, M_uy, grade of concrete and steel

2.    Verify that the eccentricities e_x = M_ux/P_u and e_y = M_uy/P_u 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 M_ux1 and M_uy1, corresponding to the given P_u (using appropriate curve from SP-16 design aids)

5.    Ensure that M_ux1 and M_uy1 are significantly greater than M_ux and M_uy respectively; otherwise, suitably redesign the section.

6.    Determine P_uz    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.