ACI Section Thanks for all your help everyone. RE: ACI If a strut and tie model STM like this is possible, it will likely be the stiffest load path available.
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Observations on Section Section This is not a topic that is easy to convey but I believe ACI has made a great stride in clarifying their intent for the engineer in the latest edition of the code. As a developer of concrete design software I must convert the instructions given in ACI to automated computer processes. The process of implementing a new design code within software is a good litmus test for the clarity of the code content. The way I like to think of this is "what happens when you consider equilibrium on the deformed structure rather than the undeformed structure, and what you need to do if there is a significant difference between the two".
Considering equilibrium on the deformed structure known as second-order analysis will, in general, produce greater member moments and curvatures than for the equivalent first-order situation. Second-order analysis is a more physically accurate representation of the structure. All structures feel second-order effects, no matter how lightly loaded. Conveniently, in many circumstances the additional response induced from second-order effects is small enough to be neglected.
Types of Second-Order Effects There are two types of second-order effects that prevail in buildings: those resulting from story drift and those resulting from member curvature. A diagram of each is given below. The latter option has the benefit that the solution is mathematically linear, and thus not as computationally rigorous as an iterative solution. The latter option also allows the additive combination of results from multiple load cases. Thus, obtaining results for the combined loads is simply a matter of scaling each of the load case results by the respective load factor and summing.
This is not possible with an iterative solution. The iterative solution has the advantage that it can produce the theoretically exact result, even when displacements become large. A discussion of each is given below. Nonlinear second-order analysis, described in Section The most apparent benefit of using this approach is that the member stresses, forces, and deflections that are obtained from the analysis need no manipulation to be used for design purposes.
Second-order effects and material nonlinearity are accounted for directly in the analysis. If performing an inelastic second-order analysis, Section That is, moment magnification, variable stiffness multipliers to account for cracking, and identifying frames as sway or non-sway are all unnecessary. Elastic second-order analysis, described in Section This requires less computation time than inelastic analysis. The drawback is that material nonlinearity must be accounted for by scaling the elastic stiffness of members in some way.
This is an inexact approach. Strictly speaking, the stiffness multiplier used for a member applies only to a single load condition. If you remove load from the structure less cracking will occur. If you load the structure at the same magnitude in a different direction, the member forces will change and thus so will the distribution of cracking in each member. Similarly, service-level conditions dictate different stiffness multipliers than ultimate-level conditions.
This effect is captured automatically in one model when performing an inelastic analysis. With an elastic second-order analysis, as with inelastic second order analysis, moment magnification and the identification of stories as sway or non-sway is unnecessary. However, unlike inelastic second-order analysis, stiffness multipliers must be assigned to members to simulate the effects of member cracking.
The moment magnification procedure, described in Section The benefit of this method is that it requires only a first-order elastic analysis of the structure. The stresses, forces, and deflections from this analysis are then scaled according to code-mandated procedures to account for second-order effects.
There is a good deal of book-keeping that goes along with this procedure. To conduct this analysis such that an economical design is attained without making too many simplifying assumptions , it is a good idea to utilize a software package that handles all the ACI slenderness calculations.
This procedure requires the identification of stories and frames as sway or non-sway. Putting it into Practice So which of these procedures should be utilized? That is a question I am hoping practicing engineers reading this article will answer. The decision will likely depend on the type of building under consideration, as well as the loads to which the structure is subjected. As developers of engineering software, we here at Bentley face the challenge of accommodating a wide range of structural configurations within our analysis and design routines.
However, what works for a twenty-story cast-in-place office structure will likely not suffice for a single story precast warehouse, and vice-versa. It is through feedback from and interaction with our clients that we hope to identify the best means of implementing the intent of ACI within our software. I encourage anyone involved in the design of concrete building structures to post a follow-up to this article with his or her own opinions and conclusions.
ACI 318 Building Code Portal
Observations on Section 10.10 in ACI 318-08