5 ce elec2 earthquake approximate analysis

8/2/2019 5 CE ELEC2 Earthquake Approximate Analysis

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APPROXIMATE ANALYSIS

Preliminary design of indeterminate structures are usually based on the

results of approximate analysis.

Approximate analysis proves to be quite convenient to use in the planning

phase of projects, when several alternative designs of the structure are

usually evaluated for economy.

Approximate analysis is sometimes used to roughly check the results of

exact analysis, which due to its complexity is prone to errors.

Many structures prior to 1960, including high rise buildings were designed

solely on the basis of approximate analysis, so a knowledge andunderstanding of approximate methods used by the original designers is

usually helpful in a renovation undertaking.


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In order to determine the reactions and internal forces of an

indeterminate structure, the equilibrium equations must be supplemented

by additional equations whose number must equal the degree of

indeterminacy of the structure.

In an approximate analysis, these equations are established by using

engineering judgment to make simplifying assumptions about the responseof the structure.

The equations based on the simplifying assumptions are then solved in

conjunction with the equilibrium equations of the structure to determine the

approximate values of its reactions and internal forces.

Assumptions


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In this first approach, a qualitative deflected shape of the indeterminate

structure is sketched and used to assume the location of the points of

inflection-that is, the points where the curvature of the elastic curve changes

signs, or becomes zero.

Assumption About the Location of Points of Inflection


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Since the bending moments must be zero at the points of inflection,

internal hinges are inserted in the indeterminate structure at the assumed

locations of inflection points to obtain a simplified determinate structure.



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Each of the internal hinges provides one equation of condition, so the

number of inflection points assumed should be equal to the degree of

indeterminacy of the structure.

The inflection points should be selected such that the resulting determinate

structure must be statically and geometrically stable.



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The simplified determinate structure is the analyzed to determine the

approximate values of the reactions and internal forces of the original

indeterminate structure.



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The portal frame below can alternatively be analyzed by assuming that the

horizontal reactions Ax and Bx are equal.

Assumptions About the Distribution of Forces Among

Members and/or Reactions


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The portal method was initially developed by A. Smith and is generally

considered to be appropriate for the approximate analysis of relatively low

building frames.

Portal Method

1. An inflection point is located at the middle of each member of the frame.

2. On each story of the frame, interior columns carry twice as much shear as the

exterior columns.

Assumptions


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APPROXIMATE ANALYSISPortal Method


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Determine the approximate axial forces, shears, and moments for all the

members of the frame shown below by using the portal method.


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The cantilever method was initially developed by

A. C. Wilson in 1908 and is generally considered to be

appropriate for the approximate analysis of relatively

tall building frames.

The method is based on the assumption that

under lateral loads, the building frames behave like a

cantilever beam.

Cantilever Method


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APPROXIMATE ANALYSISCantilever Method

1. An inflection point is located at the midpoint of each

member of the frame.

2. On each story of the frame, the axial forces in columns are

linearly proportional to their distances from the

centroid of the cross-sectional areas of the columns onthat story.

Assumptions


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Determine the approximate axial forces, shears, and moments for all the

members of the frame shown below by using the cantilever method.


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Cantilever Method Portal Method

Comparison


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Thank You!

5 ce elec2 earthquake approximate analysis

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