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CE 636 - Design of Multi-Story Structures T. B. Quimby UAA School of Engineering.

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Presentation on theme: "CE 636 - Design of Multi-Story Structures T. B. Quimby UAA School of Engineering."— Presentation transcript:

1 CE Design of Multi-Story Structures T. B. Quimby UAA School of Engineering

2  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.

3  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.  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.

4  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).

5  Note the bending in the typical beam, column, and joint.

6  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.  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.

7  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.

8  Entire spans are loaded, no partial span loading.

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10  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.  Two-cycle moment distribution.  Multiple elastic analyses using all the potential load patterns.

11  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”

12  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.

13  Best used on shorter, wider frames.  Building whose deflection is primarily racking.  height to width ratio not greater than 4:1  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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15  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  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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17  Need to consider the effects of:  Joint rotation due to girder flexibility  Column flexibility  Overall bending  Need to make some changes to equations at the first level because foundation connections are considered to be either fully rigid or fully pinned.

18  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.

19  (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/  = Q/   For the drift calculations, the shear stiffness of a story is given in the text's equation  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

20  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.

21  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.

22  Single-Bay Frames  Good for estimating deflections for stability.  Good for dynamic analyses where member forces are not required.  Can use for a two stage analysis  I ge = 1*  (Ig/L)i  (Ice)i =.5*  (Ic)i  (Ace)i = (2/l 2 )*  (Acc 2 )i


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