Structural Analysis
Vasthu sasthra is the mother of structural
analysis, but it is misinterpreted. The basic principles are not studied well.
Now it has ceased to make scientific sense. Several centuries ago big temples,
palaces, stupas have been built. Scientific analysis had been done behind these
wonders. The pyramids of Egypt, Qutab minar in India Colossus, the ancient
engineers who had designed this analyzed the forces transferred, loads and the
concept stresses. They had known how to span lengths and cover areas.
Before sizing the elements of a structure
we must study, due to the application of the load which part of the structure
is more stressed. The element can be a column, beam, a slab, a truss. For
stability, we are analyzing the geometry.
Strength and Stability
With the principles of mechanics, we analyze
the structure to determine reactions, internal forces, deformations,
deflections etc. Our structure must be strong otherwise it may brake, if it is
not stable it may slide or rotate. If foundation soil is not strong it may sink,
support also must be good.
Strength is another criterion of the good
structure. It is decided by examining the stress at failure.
Buckling is classified as instability. It will occur in a compression member. If the member is too slender it may buckle. The beam will bend about an axis about which the radius of gyration is least. Good practice is known also other than theory.
Serviceability
A good structure must be serviceable or it
has no use. It does not have cracks, will not deflect excessively. The structure
with cracks and excessive deflection will cause tension. If a building is poor
in thermal and acoustic insulation it is not serviceable.
The structural analysis must be the first
tool the Engineer is mastered. Theory and practice are different we must
observe built structures before going to design one.
Architects have to study history of
architecture and structures. Practice is something different than theory.
Determinate structures and Indeterminate structures
Determinate structures
1)
It can be analyzed with three
conditions of statics there can be only three unknowns
2)
Reactions are independent of
member properties
3)
No temperature stresses
4)
Lack of fit is not a problem
5)
If one of the members fail the
structure would collapse
Indeterminate structures
1)
3 equations of statics is not
sufficient to analyze the structure
2)
Dependent on member properties
like E A I etc
3)
Lack of fit would produce
internal stresses
4)
Redundancy makes additional
safety
5)
Temperature stresses do
Types of analysis
Stiffness methods
1)
Moment distribution
2)
Slope deflection
3)
Matrix stiffness
4)
Kanis method
Flexibility method
1)
Energy methods
2)
Matrix flexibility method
3)
Column analogy method
Linearity
A linear structure is that the resulting
displacements are proportional to applied loads. A structure would behave
linearly when
1) The material is linear, elastic all over
2) Displacements are small
Analysis software
Structural analysis software makes the life
of the engineer soft and easy. With thumb rules decide dimensions, analyze the
structure with software. But dead load is a problem, live load is taken as equal
dead load.
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