The mode shapes, while useful alone as indicators of the behavior of the structure, are important in dynamic analyses such as modal superposition and response spectra. Figure 1. Figure 2. Ground Level Definition. Analysis Criteria Items. Most FE-based analysis tools assume default values for a number of general criteria items used in the analysis process. In most programs, these default values are set by the user during installation.
While deformation in these zones has been ignored by many engineers in the past, studies supported by observation of building behavior suggest that there is very significant amount of shear deformations in these zones. Axial loads acting through lateral displacements of a structure cause additional displacements and forces.
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These effects commonly known as second-order effects, or alternatively as P-Delta effects, could produce significant loads and deformations that need to be considered in the design of building structures. Moment-frame and braced-frame buildings are typically sensitive to P-Delta effects and the consideration of these effects is required by almost all modern building codes for both static and dynamic analyses.
This factor multiplies the effect of the weight of the floor that causes the P-Delta effects. The mass dead load is the total dead load weight that is supported by a floor diaphragm.
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The same scale factor can also be modified to account for factored load effects if LRFD code is used. Both static and dynamic analyses consider lateral displacement of stories above this level only. Diaphragm Constraints. The in-plane stiffness of the floor systems of most building structures are extremely high compared to the stiffness of framing members.
As a result, the in-plane deformations of beams can often be neglected, and columns, braces and walls connected to a given diaphragm will be constrained to move as one single unit in the lateral directions. This property is widely used in structural analysis to reduce the size of the system equations of buildings with such rigid floor types. The equations that govern the transformation of the in-plane lateral displacements of each member to that of the lateral displacements at the center of mass are:.
See Figure 4 for details. Figure 4. Buildings with multiple wings, light metal deck floors [usually used at roof levels], short shear-wall buildings are some of the examples where the floors cannot be assumed rigid diaphragms. Research has shown, for example, in the case of short shear-wall buildings such an assumption could give erroneous results because the walls have a comparable lateral stiffness to that of the floor diaphragms [Rutenberg, , Boppana and Naiem, ].
On the other hand, the use of this important and realistic analysis assumption could give results that are sometimes not obvious. For example, the lateral and torsional displacement of unsymmetrical buildings subjected to gravity loads causes a significant redistribution of axial loads in columns and braces. The same assumption is also the reason why walls subjected to gravity loads might experience significant shear and bending moments. This is caused by differential vertical settlement which in turn forces the diaphragm to displace in the vertical and rotational direction resulting in redistribution of both vertical and horizontal loads.
Another class of structures where the choice of this assumption has a significant bearing on the response of a numerical model of a structure is building or industrial structures with trusses. In the modeling of truss systems in a building or industrial structures, some engineers prefer disconnecting the interior nodes from the diaphragm in order to be able to evaluate the chord forces in the system. Experience has shown that the selection of nodes to be disconnected from a diaphragm has a strong bearing on the magnitude of chord forces evaluated. Disconnecting interior nodes and nodes at one or more supports allows the system to deflect more like a truss.
On the other hand disconnecting only the interior nodes but leaving the supports connected to a diaphragm results in the truss system being rigidly suspended from the diaphragms. The axial forces in the top and bottom chords for these two systems could be drastically different. Figures 5. Figure 5. Truss with Only Interior Nodes Disconnected. Another common example where the choice of nodes to be disconnected from a diaphragm has a bearing on the magnitude of member forces is the case of beams in braced frames.
Figure 6. Since both ends of the beam are disconnected from the diaphragm, any lateral load applied to the diaphragm at that level will not be transmitted to the beam. The additional load of 2P will be picked up by other members connected to the diaphragm, if there are any. If there are no members in the model, the program used may totally discard the load without even warning the user. However, if one of the ends of the beam is connected back to the diaphragm, this particular beam will pick additional axial loads as shown in Figure 6.
It is important, therefore, to recognize that the design of these beams for collector forces depends strongly on the selection of these disconnected nodes. While the proliferation of powerful structural analysis software has empowered engineers and architects to automate most of their analysis and design routines, the need for understanding the basic assumptions and theories used in these programs has also increased.
It is only when users understand these basic principles and assumptions that they can arrive at a numerical model of their structure that very well approximates the real world external loads and the response of the structure itself. This course trains users of such programs with this in mind.
3D Structural Modeling & Analysis of Buildings and Structures
References and Further Readings. Bathe, K. Boppana, R. Reddy, J. Wilson, E.
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Fenves, N. Perrone, A. Robinson, and W. Schnobrich, Academic Press, NY, pp. Kassegne, S.
Proceedings of the Institution of Civil Engineers - Structures and Buildings
Once you finish studying the above course content , you need to take a quiz to obtain the PDH credits. The materials are for general information only. Author Affiliations. Key: Open access content Subscribed content Free content Trial content. Full Text References. Related content. Full-scale tests on composite concrete T-beams subjected to cyclic and monotonic loading. Ranking water transfer projects using fuzzy methods.
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