reinforced concrete design 2: frame analysis
DESCRIPTION
Reinforced Concrete Design 2: Frame AnalysisTRANSCRIPT
The structure is three dimensional (3D),
comprising floor slabs, beams, columns and
footings, which monolithically connected and
act integrally to resist vertical loads and lateral
loads.
3D view of reinforced concrete building structure
Idealized as 3D frame which consist of slabs, beams and column.
In many cases the slabs are analyzed separately (analyses frame consist only beams and columns)
3D frame of building structure
Analysis of 3D frame represent the real behavior
of the structure but it is quite complicated since
the structure is highly indeterminate
The analysis normally carried out by computer
since the manual calculation is unfeasible
In order to simplify the analysis, the 3D structure
is generally divided into a series of independent
parallel two dimensional plane frames (2D).
2D frame of building
structure
Simplified frame into substitude frames (sub-
frame) or continuous beams
Braced Frame ◦ Frames that not contribute to
the overall stability of the
structure
◦ None of the lateral actions,
including wind, are transmitted
to the columns and beams but
carries by bracing members
such as shear wall
◦ Support vertical actions only
Unbraced Frame
◦ Frame that not contribute to
the overall stability of the
structure
◦ All lateral actions, including
wind, are transmitted to the
columns and beams since
there are no bracing
members such as shear wall
are provided.
◦ Support vertical and lateral
actions
Primary objective - to obtain a set of internal
forces and moments throughout the structure
that are in equilibrium with the design loads for
the required loading combinations.
General provisions to analysis are set out in EN
1992-1-1 section 5.
One-level sub-frame ◦ Each sub-frame mat be taken to consist of the beams at one level
together with the columns above and below.
◦ The ends of the columns remote from the beams may generally
be assumed to be fixed unless the assumption of a pinned end is
clearly more reasonable
Sub-frame for analysis of beams and columns
Two-points sub-frame ◦ The moments and forces in certain individual beam may be found
by considering a simplified sub-frame consisting only of the beam,
the columns attached to the end of that beam and the beams on
either side is any.
◦ The column and beam ends remote from the beam under
consideration may generally be assumed to be fixed unless the
assumption of pinned is clearly more reasonable
Sub-frame for analysis of individual beam
The stiffness of the beams on either side of the beam considered should be taken as half their actual values if they are taken to be fixed at their outer ends
Continuous beam and one-point sub-frame
◦ The moments and forces in the beams at one level may also be obtained by considering the beams as a continuous beam over supports providing no restraint to rotation
Continuous beam for analysis of beams
One-point sub-frames for analysis of columns
The ultimate moments for column may be calculated by simple moment distribution procedure
assumption that the column and beam ends remote from the junction under consideration are fixed and that the beams posses half their actual stiffness
The arrangement of the design ultimate variable loads should be such as to cause the maximum moment the column
Action on buildings is due to permanent (dead load),
variable (imposed, wind, dynamic, seismic loads)
and accidential load
Mostly multistiry buildings for office or residential
purpose are design for dead, imposed and wind
loads
Separate actions must be applied to the structure in
appropiate directions and various tyoes of actions
combined with partial safety factors selscted to
cause the most severe design condition.
The framing plans for a
multistory building are shown
in Fig E9.1. The main
dimensions structural features,
loads, material, etc. are also
set out in the figure. Analyze
sub frame 3/A-D, Level 1 to
determine shear forces and
bending moments of
corresponding beams and
columns. Use all the three
methods of analysis that
discussed before
Building frames are subjected to lateral loads as
well as vertical loads.
Building must not only have sufficient lateral
resistance to prevent failure but also must have
sufficient resistance to deflection to prevent
damage to their various part.
Portal method ◦ The frame theoretically divided into independent portals.
◦ The shear in each storey is assumed to be divided between the
bays in proportion to their span.
◦ Shear in each bay is then divided equally between columns.
◦ The column end moments are the column shear multiplied by
one-half the column height
◦ Beam moment balance the column moments
◦ The external column only resist axial load which is found by
dividing the overturning moment at any level by the width of the
building
Cantilever method
◦ The axial loads in column are assumed to be
proportional to the distance from the center of
gravity of the frame
◦ Assume that all the column in a storey are of
equal cross-section area and the point of
contraflexures are located at the mid-points of
all column and beams.
Wind forces- variable loads which act directly on
the internal and external surfaces of structures.
The intensity is related to the square of the wind
velocity and the dimension of the members that are
resisting the wind.
Wind velocity-dependent on geographical location,
the height of the structure, the topography of the
area and the roughness of the surrounding terrain.
The response of a structure to the variable
action of wind can be separated into two
components
Background component ◦ Involves static deflection of the structure under the wind pressure
Resonant component ◦ involves dynamic vibration of the structure in response to
changes in wind pressure
Wind
◦ creates pressure on the windwards side of a building
and suction on its other three sides
◦ Produces suction on flat roofs, on the leeward side of
sloping roofs, and even on the windwards side of roofs
with a pitch less than 30°
Simplified procedure ◦ Limited in application to building of rectangular in
plan and not greater than 15.0 m high
Analytical procedure
◦ Limited to regular building that are not more
than 200m high and structure with roof span
less than 100 m
Wind tunnel procedure
◦ Used for complex buildings