### Rigid Frame Structures

```CE 636 - Design of Multi-Story Structures
T. B. Quimby
UAA School of Engineering
Resistance to horizontal loading provided by
flexural stiffness of the girders, columns, and
connections.
 Opens up the floor space allowing freedom in
space utilization.
 Economical for buildings up to about 25 stories.
 Well suited for reinforced concrete construction
due to the inherent continuity in the joints.
 Design of floor system cannot be repetitive since
the beams forces are a function of the shear at
the level in addition to the normal gravity loads.
 Gravity loads also resisted by frame action.
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Approximate gravity load analysis and design
 Estimate gravity loads and use approximate analysis to
determine member forces. (2 cycle moment dist.)
 Select beam and column sizes using gravity forces and an
allowance for additional member forces due to lateral
loads.
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Approximate lateral load analysis
 Cantilever or Portal method
Check drift.
Resize members based on lateral load analysis and
drift analysis.
 Detailed computer analysis and resize members as
appropriate.
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Accumulated story shear above a given story is
resisted by shear in the columns at that story.
Points of contraflexure are located an midheight
of columns and beams since both types of
elements are in double curvature.
Deflected shape is predominately in a shear
configuration with concavity being upwind.
A Flexural component in the deflection results
from chord action (axial forces in column).
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Note the bending in the typical beam,
column, and joint.
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Continuity at joints tends to create negative
moments at supports and Positive moments
at midspan of girders.
 There are two points of inflection on each girder.
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Each span is effected by the loading of other
spans in the structure.
Determination of maximum moments and
shears must account for probability of
uneven Live Load distribution.
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The influence line
for a reaction or
internal stress is,
to some scale,
the elastic curve
of the structure
when deflected
by an action
similar to the
reaction of stress.
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Entire spans are loaded, no partial span
loading.
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Code recommended values (See ACI 318
section 8.3, UBC has also adopted these)
 Limited to spans of approximately equal stiffness
and a constant magnitude of uniformly
distributed load.
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Two-cycle moment distribution.
Multiple elastic analyses using all the
potential load patterns.
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More accurate than code coefficients.
May use many different types of loading.
Method is quick and easy to implement.
Can obtain midspan moments and column
forces as well as end moments on beams.
See the worked problem in the text.
The Portland Cement Association publishes
the original paper as a pamphlet entitled
“Continuity in concrete building frames”
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Loads are distributed in relation to the
relative rigidity of each bent.
Must include torsional effects, if any.
Text method allows you to compute the point
load on each level of each bent. To has a
translational and rotational component.
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Best used on shorter, wider frames.
 Building whose deflection is primarily racking.
 height to width ratio not greater than 4:1
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Highly indeterminate frame is reduced to a
statically determinate system by the following
assumptions:
 The points of contraflexure are located at the middle
of columns and beams. (locations of zero moment)
 Horizontal shear at midstory levels is shared between
the columns in proportion of the width of aisle each
column supports.
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Used in structures for which the flexural
component of deflection is more prominent.
 Up to 35 stories
 Height to width ratios up to 5:1
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Highly indeterminate frame is reduced to a
statically determinate system by the following
assumptions:
 The points of contraflexure are located at the middle
of columns and beams. (locations of zero moment)
 The AXIAL STRESS in a column is in proportion to its
distance from the centroid of the column areas.
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Need to consider the effects of:
 Joint rotation due to girder flexibility
 Column flexibility
 Overall bending
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Need to make some changes to equations at
the first level because foundation
connections are considered to be either fully
rigid or fully pinned.
Joint rotation due to girder flexibility is normally
the predominate component of drift.
Increasing girder stiffness will reduce this
component.
 Column flexibility is the next most predominate
component. Increasing column stiffness will
reduce this component.
 A look at the contributions of each component
of drift can help decide whether to stiffen the
girders or the columns.
 The text proposes a more analytical method for
making decisions.
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(GA) corresponds to the shear rigidity of an
analogous shear cantilever of sectional area A
and Modulus of rigidity G. (See text figure
7.15)
(GA) = Qh/d = Q/f
For the drift calculations, the shear stiffness
of a story is given in the text's equation 7.28.
If the effective shear rigidity (GA) is known for
a particular level, finding the story drift is
found by the text's equation 7.29
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Newer computer programs (such as ETABS)
have made hand methods virtually obsolete.
The stiffness based programs inherently take
into account the relative stiffnesses of
frames when determining bent forces.
Member forces are more accurate than from
the approximate methods.
Deflection outputs simplify the drift analysis.
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Lumped Girder Frames
 Can be used for repetitive floors
 Do not lump roof level
 Do not lump lower few floors
 See text for equivalent girder and column
properties.
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Single-Bay Frames
 Good for estimating deflections for stability.
 Good for dynamic analyses where member forces
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are not required.
Can use for a two stage analysis
Ige = 1*S(Ig/L)i
(Ice)i = .5*S(Ic)i
(Ace)i = (2/l2)*S(Acc2)i
```