Size of column, Grade of concrete, Grade of steel (otherwise assume suitably) Factored load and Factored moment
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 d^{1}/D
from effective cover d^{1}
2. Find non
dimensional parameters P_{u}/f_{ck}bD and M_{u}/f_{ck}bD^{2}
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_{ux}_{1} and M_{uy}_{1},
corresponding to the given P_{u} (using appropriate curve from
SP-16 design aids)
5. Ensure
that M_{ux}_{1} and M_{uy}_{1}
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.