09-05-2012, 12:25 PM
STABILITY ANALYSIS OF FRAME TUBE TALL BUILDINGS
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Introduction:
In the past, designers had no need to accommodate for terror attacks from the
air, but now that this threat is a reality; designers have to look for sensible ways to
defend our high-rises
All the evidence so far points that a combination of the impact and the fires
triggered the collapse of the World Trade Center buildings; we must now ask,
what we can do in the future to prevent another failure like this one. Some
believe that nothing can, or should, be done. While some opine that "nothing is
designed or will be designed to withstand that [kind of] fire.” Numbers of
theories have evolved to explain exact reason for the collapse of the Twin towers;
some believe the impact alone was the actual cause of the failure by providing
evidence that the structure failed quicker than the time required for the
fireproofed steel to fail while some argue that the fires where to blame, the steeltube
construction of the towers could not resist the intensity of the fires resulting
from the energy released by the 2400 gallons jet fuel that brought the fires to
higher than normal temperatures, as high as 2000 degrees Fahrenheit. But
combination of these two appears to be logical explanation to the tragedy on
9/11. Bottom line is one or combination of them may have caused the structure
to fail, from now on it would be necessary to do a thorough stability check of tall
buildings for all possible circumstances.
In “Limit state design”, buildings are designed for limit state of strength and limit
state of serviceability, leaving the structure with minimum reserve energy. If it is
the design case of a low-rise structure subjected to low horizontal loads,
deflections are small with insignificant change in geometry of the structure. Thus
the reserve energy of the building is sufficient to bring back the structure to
equilibrium state after the load is removed, rendering stability to the structure as a
whole. There by first order analysis of structures to satisfy the equilibrium
conditions is sufficient to verify the design. In case of tall buildings about 40 to
50 story’s high horizontal loads cause huge deflection of the building and a
significant change in the geometry of the structure. The large deformation and
low reserve energy can prove to be cataclysmic if this small energy in the
structure fails to resist loads. Thus failing to satisfy the equilibrium conditions the
structure could become highly unstable. To predict the exact behavior of the
structure a second order analysis of the structure has to be conducted. In this
thesis I have devolved a program to do first order, second order analysis and also
to calculate the elastic critical buckling loads of planar framed structures.
Objectives
The main objective of the thesis work is to develop software to check the stability
of structures and also to do a second order analysis of the 40 story Frame-Tube
Buildings. Matrix approach is used in the analysis. It is realized that the fulfillment
of the following sub-objectives would in turn fulfill the main objective.
1. To understand the concepts of Matrix analysis of structure.
2. To study the behavior of Frame tube buildings.
3. To study various technique in nonlinear analysis of frame-tube buildings.
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4. To develop a Mat Lab program using the principles of Matrix/Finite
Element approach for both Linear and Nonlinear analysis. To develop
modular structured program versatile and should be able to analyze a
wide variety of problem.
5. Run the program for Non Linear analysis of Frame Tube building and
verify its structural stability as a whole and to compare these results with
commercial software called Mastan2 for accuracy.
Scope:
Focus of the work is on planar frames with the following characteristics.
1. The behavior of the structure is elastic.
2. Structure may behave like a truss or frame depending on the element
node connection. In frame element for example all member are
considered beam column elements.
3. The structures are considered to be an assembly of planar elements.
Different frames may interact through common columns and through
the floor diaphragms, which are considered to be rigid in their plane. If
the structure contains shear wall or cores it has to be idealized as a single
isolated column.
4. Static gravity loads and horizontal wind loads are applied as nodal forces.
5. During second order analysis geometric non-linearity due to large
member deformation is the main focus and material non-linearity due to
change in material property is not considered.
6. Connections are considered either fixed or hinged and it does not
account for partial fixity.
The program is based on Matrix analysis of structure. Each structural member is
idealized, i.e. is the depth, the width and elemental length are conventionally
reduced to line elements. The material property are represented by area (A),
young’s modulus of elasticity (E), torsion constant (J) and poisons ratio (n). For
second order analysis simple step method has been employed
Previous work:
Refs (10 & 12) have introduced the topic of high-rise structure building by
introducing the different structural forms, with the main intention of explaining
the different approximate methods for analysis.