 # D8.A.2.7 Combined Interaction Check

Members subjected to various forces – axial, shear, moment, torsion - are checked against combined interaction check.

## Limit State Method

This interaction check is done taking care of two aspects:

• Section strength

• Overall member strength

Section strength interaction ratio is calculated as per sec. 9.3.1 of the code.

Overall Member Strength interaction ratio is calculated as per sec. 9.3.2, taking care of the design parameters PSI, CMX, CMY, and CMZ

## Working Stress Method

The following interactions are considered:

1. Combined Bending and Shear — No reduction in allowable stresses for the interaction of bending and shear is considered.

2. Combined Axial Compression and Bending — The following formulas are intended to require member stability:

 fc/facy + 0.6·Ky(Cmyfbcy/fabcy) + KLTfbcz/fabcz ≤ 1.0

 fc/facz + 0.6·Ky(Cmyfbcy/fabcy) + Kzfbcz/fabcz ≤ 1.0

 fc/(0.6fy) + fbcy/fabcy + fbcz/fabcz ≤ 1.0

where
 fc = Actual axial compressive stress. facy, facz = Allowable compressive stress, governed by buckling, about the local Y and Z axis, respectively. fbcy, fbcz = Actual bending compressive stress about minor and major axes, respectively. fabcy, fabcz = Allowable bending compressive stress about minor and major axes, respectively.

 Ky = 1 + (λy - 0.2)·ny ≤ 1 + 0.8·ny

 Kz = 1 + (λz - 0.2)·nz ≤ 1 + 0.8·nz

 KLT = 1 - 0.1·λLT·ny/(CmLT - 0.25) ≥ 0.1·ny/(CmLT - 0.25)

3. Combined Axial Tension and Bending — The following formulas are intended to require member stability:

 ft/fat + fbty/fabty + fbtz/fabtz ≤ 1.0

where
 ft = Actual axial tensile stress. fat = Allowable axial tensile stress. fbty, fbtz = Actual bending tensile stress about minor and major axes, respectively. fabty, fabtz = Allowable bending tensile stress about minor and major axes, respectively.

## Solid Rod Design

The ɑ1 and ɑ2 values are not explicitly available for circular rod section in the IS800:2007 specification. However, there is a design note mentioned for Eq6-41 in the EN 1993-1-1:2005 specification regarding this. Thus, these values are taken as 1.0 by the program.

The IS800:2007 does not provide guidance for the Mndy and Mndz calculation for circular solid rod section. The formula mentioned in the CL 9.3.1.2(e) has been followed by the program for solid circular sections.