In your opinion, if the storey stability index is less than 0.05, can cracking coefficients of 0.5 for beams and 1 for columns be used for designing members?
Some people believe that without a shear wall, even if the stability index is less than 0.05, coefficients of 0.5 and 1 cannot be used except for short buildings with high stiffness frames.
Please give your opinion on this matter.
According to ACI318-14, the definition for nonsway frames is as follows:
6.6.4.3 It shall be permitted to analyze columns and stories in structures as nonsway frames if (a) or (b) is satisfied:
(a) The increase in column end moments due to second-order effects does not exceed 5 percent of the first-order
end moments
(b) Q in accordance with 6.6.4.4.1 does not exceed 0.05
6.6.4.4 Stability properties
6.6.4.4.1 The stability index for a story, Q, shall be calculated by:
Q=(ΣP∆/Vh)
where ∑P and V are the total factored vertical load and horizontal story shear, respectively, in the story being evaluated, and ∆ is the first-order relative lateral deflection between the top and the bottom of that story due to V.
In table 6.6.3.1.1(a) of the same regulations, cracking coefficients are given for beams 0.35Ig, for columns 0.7Ig, uncracked walls 0.7Ig, cracked walls 0.35Ig regardless of whether the frame is restrained or not. In Table 6.6.3.1.1(b), another method for calculating the cracking coefficient is proposed, which depends on the forces of the element. Also, according to the following paragraph, to analyze the structure in order to control its deformations, the cracking coefficients can be considered to be 1.4 of the values given above.
6.6.3.2.2 It shall be permitted to calculate immediate lateral deflections using a moment of inertia of 1.4 times I defined in 6.6.3.1, or using a more detailed analysis, but the value shall not exceed Ig.
R6.6.3.2.2 Analyzes of deflections, vibrations, and building periods are needed at various service (unfactored) load levels (Grossman 1987, 1990) to determine the performance of the structure in service. The moments of inertia of the structural members in the service load analyzes should be representative of the degree of cracking at the various service load levels investigated. Unless a more accurate estimate of the degree of cracking at service load level is available, it is satisfactory to use 1.0/0.70 = 1.4 times the moments of inertia provided in 6.6.3.1, not to exceed Ig, for service load analyses.
On the other hand, in another paragraph of ACI, we have:
R6.3—Modeling assumptions
for braced frames, relative values of stiffness are important. A common assumption is to use 0.5 Ig for beams and Ig for columns.
For sway frames, a realistic estimate of I is desirable and should be used if second-order analyzes are performed. Guidance for the choice of I for this case is given in 6.6.3.1.
As it can be seen, for the restrained frame (frame with shear wall), the moment of inertia values of the beam sections are allowed to be 0.5 and 1.0 for the columns. But for the said frames with lateral movement, the values of table 6.6.3.1 should be used. Of course, a structure that has a shear wall is not necessarily free of lateral movement, and its stability index should be controlled.
The ninth topic in paragraph 9-16-3-2 also states that for short buildings up to 4 floors, if the total lateral stiffness of the walls is more than six times the total lateral stiffness of the columns of the floor, that floor can be considered as lateral restraint.
(Question and answer from Dr. Alirezaei)
This post is written by AminNajafgholizadeh