ram frame drift control

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RAM Structural System

V8i(SELECTseries 6)

Drift Control

Last Updated: October 09, 2013


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RAM Structural System 3 Drift Control
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Table of Contents

Chapter 1: Introduction .......................................................................................................9

1.1 Results ..............................................................................................................................................................................................9

Chapter 2: Using the RAM Frame Drift Control Module ..................................................... 11

2.1 Creating Virtual Load Cases .................................................. ........................................................ ....................................... 11

2.2 Drift Control Analysis .................................................... ........................................................ ................................................. 11

2.2.1 Load Pairs ............................. ........................................................ ......................................................... ...................12

2.2.2 View/Update ...........................................................................................................................................................12

2.2.3 Output Reports ............................................... ........................................................ .................................................12

2.2.4 Exiting Drift Control Module .................................................. ........................................................ ..................13

Chapter 3: Technical Notes on Virtual Work Theory .......................................................... 153.1 Example Problem ....................................................................... ........................................................ ...................................... 16

Chapter 4: References .........................................................................................................19



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Introduction 1

The RAM Frame Drift Control module provides a great functionality to study and control the drift

behavior of buildings. Drift, related to the axial, shear, flexural, torsional and beam-connection behavior

of each member of a building structure, is an important design consideration. The total drift at a point

can be considered as the sum of all governing displacement components from each member such as

joint , axial, shear, flexure, torsion and beam-connections related displacements. To this end, RAM

Frame Drift Control module helps users identify which member contributes the most to the drift at a

point. The break-down of a member contribution to the drift constitutes displacement components such

as joint, axial, shear, flexure, torsion and beam-connection and this information helps the user identify

what sectional properties of a member to change to arrive at an optimized size. The joint displacement

represents the deformation in the rigid-end zones (panel-zones).

The module is based on the well-known Castiglianos Energy Theorem where a fictitious or virtualload is applied in the direction of the drift under investigation. A special acknowledgement is given here

to Dr. Finley A. Charney, President, Advanced Structural Concepts Inc., for his prior work in this area,

particularly the virtual work based concepts as implemented it in the computer programs DISPAR and

PANELS, published by Advanced Structural Concepts, Inc., Golden, Colorado.

Energy methods, such as Castiglianos, help determine the deflection of a structure at a given point due

to an external load by pairing it with what is commonly called a virtual load. The loads are referred

to as fictitious or virtual interchangeably only because they do not represent any real-world load

cases. The module helps users quantify the contribution of each frame member to the flexibility of the

building under investigation. This information can then be used to modify the sizes and topology of the

frames to arrive at a building design optimized for drift considerations.

The steps required in using the module are explained in detail in Chapter 2. The chapter describes how

to set up nodal and story load cases that are required to calculate the so-called displacementparticipation factors that help quantify the contribution of a member to the building flexibility. The

chapter also discusses the graphical and report outputs for the module. Chapter 3 covers the theoretical

basis for the Drift Control module.

1.1 ResultsThe Process Resultscommand allows the user to visually observe, through normalized color-coding,

the contribution of each member to overall building flexibility. These quantities are called

Displacement Participation Factors[DPF]or alternatively PF, for short. The following DPF are

available for color-coded display:

Total Displacement

Participation Factor

This represents the total member contribution (which is the sum of axial,

shear, flexure, torsion, joint and beam connection displacements) and is

the default used in the module whenever Drift Control analysis is carried

out.



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Total Displacement/

Volume Participation

Factor

The total DPF divided by the member volume gives critical information

for a minimum weight (or volume) design. Information on Total DPF per

volume helps identify members whose size can be modified to arrive at

the most weight/volume optimized design. Total DPF/Volume is also

called the Sensitivity Index (SI). SI can also be viewed as a measure of the

participation of each member per unit volume.

Axial Displacement


This represents the contribution of members through axial deflection.

Shear Displacement


This represents the contribution of members through major and minor

shear deflection.

Flexural Displacement


This represents the contribution of members through major and minor

flexural deflection.

Joint Displacement


This represents the contribution of members through deflections in the

rigid end zone. In centerline analysis, the joint DPFs are all zero.

Beam Connection

DisplacementParticipation Factor

This represents the contribution of connections assigned to beams.

Member Volume This represents the volume of the member under consideration.

The currently selected load pair can be changed through the load pair drop-down box. The quantities

of interest can also be changed

IntroductionResults



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Using the RAM Frame Drift Control Module 2

This chapter explains the basics of the Drift Control module. This includes how to set up nodal and story

load cases and how to pair them as load pairs and carry out a Drift Control analysis. The chapter also

discusses the graphical and report outputs for the module.

2.1 Creating Virtual Load CasesA virtual work or optimization operation requires the application of fictitious load(s) in the direction of

the displacement under investigation. Such fictitious loads are grouped in the RAM Structural System as

Virtual Load Cases. Both nodal loads and story loads are available in the Virtual Load cases. The nodal

virtual load cases are defined in the Modeler while the story virtual load cases are defined in RAM

Frame Analysis Load Cases Mode.

The nodal virtual load cases are created just like any other nodal load case as described in the RAM

Modeler manual.

Virtual story loads are created in RAM Frame using the Loads Load Casescommand while in Analysis

Load Cases Mode. Virtual loads have their own type: Virtual Load. The loads are entered by

specifying their magnitude, their direction and point of application.

The magnitude of the virtual load is not an absolute number. A load of any magnitude is theoretically

possible. The only practical requirement is that the load be of a magnitude that produces reasonable

(not very high or very low) participation factors (PF). The participation factor of an element is defined

as the measure of a members contribution to the quantity under investigation, such as roofdisplacement. A good rule of thumb is to pick the magnitude as somewhere between 20 to 50% of the

estimated seismic or wind load base shear in the building.

The direction of the virtual load should be in the direction of the drift under investigation. For example,

for studying the behavior of the building in the global X-direction, both the virtual and real (wind,

seismic or other) load case should be oriented along the global X-Axis. For studying the rotational

characteristics of a building, the user should enter a small virtual load at a large eccentricity. This will

essentially produce virtually a twisting moment that can be paired with the real load that is producing

rotations in the building.

After both the real and virtual load cases are created and defined, they should be included in the list of

load cases that are to be analyzed using the Process Analyzecommand in Analysis Load Cases

Mode.



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2.2 Drift Control AnalysisOnce the analysis of the building is completed, the user needs to go to the Drift Control Mode, by

selecting Drift Control from the Mode menu. It is in this module that the load pairs are defined and

the actual Drift Control analysis carried out.

2.2.1 Load Pairs

In the Drift Control Module, the Virtual Load cases created and analyzed in RAM Frame are paired

with a corresponding real load cases. The pairing of loads is an important feature of energy methods

and care should be taken in identifying what virtual and real load cases to pair. For example, for

studying Drift Control in the global X-direction, a virtual load case applied in the X-direction should be

paired with a real load case in the same direction. These load pairs could be single load pairs or

multiple load-pairs. While single pairing is what is commonly used, multiple pairing may be necessary

to study drifts in a none-orthogonal direction. The load pairs are defined using the Loads - Load Pairscommand in the Drift Control Module, which lists both the analyzed virtual and real load cases. Pairing

is done by specifying the virtual and real components of the pair and the factor that multiplies them. The

factor is usually taken as 1.0.

Once load pairs are defined, the user needs to select the Process-Analyze command to perform the

Drift Control analysis. The module then evaluates the participation factors (PF) of each member and

color-codes the elements according to their contribution to the flexibility of the building.

For example, if the user is interested in reducing the roof story drift due to an earthquake load, an

earthquake load case is selected as the real-load component of a load pair. The virtual component of

the load pair will then be a virtual load that has lateral forces only at the roof level even though the real

displacement is caused by a distributed earthquake load. The structure is then displayed with the PF

that elements are experiencing from the stresses induced by the earthquake load case.

2.2.2 View/Update

The Process - View/Updatecommand lets the user pick a particular member and view the different

components of its participation factor (such as flexural, shear, joint , axial and connections for beams).

For example doing a View/Update on a beam will display the beam properties (size, Fy etc) and also its

axial, joint, shear, flexural and beam connection displacement participation factors that contribute to the

total drift of the building.

The user can also modify the member size and material properties in this dialog box. Once sizes and

material properties are changed, the Drift Control Module automatically recalculates the member PFs

based on the new data. However, note that the elastic stiffness analysis results remain the same until a

re-analysis is invoked from the Analysis mode.

Using the RAM Frame Drift Control ModuleDrift Control Analysis



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2.2.3 Output Reports

The module provides features for printing three outputs that are accessed through the Reports

command.

Reports - Displacement

Participation Single

A comprehensive summary of participation factors for each

lateral member for each load pair.

Reports - Participation Summary A summary of member volume and participation factor/volume

for each lateral member for each load pair.

Reports - Displacement/Volume

Summary

A summarized output for a single member.

2.2.4 Exiting Drift Control Module

The user may exit the Drift Control Mode through the Mode drop-down list box right below the tool

bar. Once a Drift Control analysis is done, if any sizes are changed it is recommended to re-check the

validity of the design for strength considerations by going to the steel post-processors.




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Technical Notes on Virtual Work Theory 3

Energy methods such as Virtual Work method have traditionally been used to calculate deflections in

determinate and indeterminate truss structures. The principle of Virtual Work states that the external

work done in a physical domain should be equal to the internal work done.

This principle is further used in such theories as the Castiglianos theorem that states that the work

done by virtual loads going through real displacements is the same as the internal work done by real

loads causing virtual displacements. This can be expressed as follows:

DPFi =(iv)Ti

rd V Equation 3-1

where

DPFi = the displacement participation factor for member i

dV = the volume of the member i

iv = the stresses in member i due to a virtual load

ir = the strains member i due to real loads

The virtual stresses and real strains are computed during analysis in RAM Frame due to real and virtual

load cases, considering element properties and structural configurations.

In its most general form, the contributions to displacements could be expanded through its component

stresses and strains as:

Fvirreal =h /2h /2 (xx

vxx

r+yy

vyy

r+zz

vzz

r+xz

vxz

r+yz

vyz

r+xy

vxy

r )d z d A Equation 3-2

As can be seen from the above equation, the contribution to the component participation is made of

strain energy due to in-plane, transverse shear and transverse normal stresses and strains.

This breakdown of contribution helps to identify which behavior is dominant and what sectional or

material property needs to be modified to arrive at acceptable and desired response.

The same principles are extended here to a case of civil engineering structures to get a useful

quantitative assessment of contribution of member flexibility to structural responses such as roof

displacement (or drift) and fundamental periods. Furthermore, the methodology also helps evaluate the

contribution of each energy component, i.e., shear, flexure, axial and joint deformation to the structures

response under consideration thereby indicating the member properties that need to be modified for an

optimized design.

By multiplying the contribution of both a virtual load case and a real load to each of the energy

components (i.e., shear, flexure, axial and torsion), the contribution of each member in the structure to

drift is evaluated. The elemental contribution (also called DPF - displacement participation factor) to

drift (or frequency, as the case maybe) is further broken down to each of the components such as shear,flexure, axial, joint and torsion displacements.

This breakdown of contribution helps to identify which behavior is dominant and what sectional or

material property needs to be modified to arrive at acceptable and desired responses. For instance,

to reduce drift or frequency, members with large participation factors should be made stiffer

and contributing members with very small participation factors could be made smaller.

Furthermore, an important piece of information is the per volume contribution(or participation) of



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each structural element, which is also referred to as Sensitivity Index (SI). It is obtained by dividing

the element participation factor by its volume. From a weight optimization point of view, the

Sensitivity Index provide valuable information as summarized below:

1. When adding material to a structure to reduce displacement, the material should be added to the

member (s) with the largest sensitivity index.

2. When removing material from a structure to improve economy, the material should be removed

from member (s) with the smallest SI values. [1]

The reader is referred to References [1] - [3] for further reading on Virtual Work optimization.

3.1 Example ProblemA simple 2-Dimensional braced-frame structure is used here to demonstrate the use of the Drift Control

module in generating useful information in controlling drift with minimum weight/volume

considerations. The following figure shows problem definitions and loadings on the frame. The frame is

subjected to lateral loads of 100 Kips, 75 Kips and 50 Kips at the roof, the second and the first floors,

respectively. A virtual load of 100 Kips is applied at the roof.

The member sizes are given in the following table. As shown in the table, columns and braces contribute

most to the flexibility of the frame, particularly Columns 5 and 6 at first floor and braces 2 and 3 at

second and first floor, respectively, which is an expected behavior. To decrease the roof drift, the

column sizes at the first floor and the braces need to be increased. The breakdown into components

suggests that columns of higher axial area are needed to reduce drift since it is the axial contribution

that is very significant. A column with higher Ixx and Iyy will not necessarily reduce drift as much as

expected.

The beams could be made much smaller because they account for less than 5% of the whole

deformation. From a weight optimization point of view, an increase or decrease in brace sizes will

produce the most change in drift. In other words, the braces have the highest sensitivity index. Toreduce drift, increasing the brace sizes (i.e., area) produces an efficient system. This exercise results in

maximum stiffness with a minimum volume of material.

On the other hand, if the need arises to allow more drift, then member sizes could be reduced. The

tabulated results indicate that beam and column sizes could be safely reduced without introducing a

significant increase in drift. The only practical limit on the sizes of the beams and columns will be

gravity load designs. However, since the braces have the highest SI (Sensitivity Index), then reducing

their sizes even slightly (particularly cross-sectional area) will result in large increase in drift. This

reduction in brace sizes is therefore very much limited, compared to beams and columns.

Technical Notes on Virtual Work TheoryExample Problem



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Figure 1: A simple Braced-Frame

Table 1: Distribution of Displacement Participation Factors Element-by-Element

Member Size Axial PF Shear PF Flexure PF Joint PF Total PF Total PF /

Volume

Beam 1 W21x166 0.0 0.0970 0.3265 0.1122 0.535 0.00

Beam 2 W21x166 0.0 0.4221 1.4202 0.4881 2.33 0.01

Beam 3 W21x166 0.0 0.661 2.2253 0.7649 3.65 0.02

Col 1 W16x89 1.9311 0.1650 0.8922 0.4398 3.42 0.03

Col 2 W16x89 0.0265 0.1650 0.8922 0.4398 1.52 0.01

Col 3 W16x89 11.5828 0.2572 1.3924 0.7050 13.93 0.13

Col 4 W16x89 2.9996 0.2572 1.3924 0.7050 5.35 0.05

Col 5 W16x89 31.6713 0.5447 4.1813 0.2819 36.67 0.35

Col 6 W16x89 14.7126 0.5447 4.1813 0.2819 19.72 0.19

Brace 1 HSS4X4X1

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17.5384 0.00 0.00 0.00 17.5384 0.49

Brace 2 HSS4X4X1

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31.5886 0.00 0.00 0.00 31.5886 0.87

Brace 3 HSS4X4X1

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36.1335 0.00 0.00 0.00 36.1335 1.00




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References4

1. Charney, F.A., The Use of Displacement Participation Factors in the Optimization of Wind Drift

Controlled Buildings, Proceedings of the Second Conference on Tall Buildings in Seismic Regions,

Council on Tall Buildings and Urban Habitat, Los Angeles, 1991.

2. Charney, F.A., Economy of Steel Framed Buildings through Identification of Structural Behavior,

Proceedings of the National Steel Construction Conference, AISC, Orlando, FL 1993.

3. Velivasakis, E.E., and DeScenza, R., Design Optimization of Lateral Load Resisting Frameworks,

Proceedings of the Eights Conference on Electronic Computation, ASCE, Houston, Texas, 1983.



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References




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Index

Ddrift control

analysis 11

Drift Control control module

using 11

drift control module

exiting 13

IIntroduction 9

Lload pairs 12

Rreferences 19

reports

output 12

results 9

Uupdating 12

Vviewing 12

virtual load cases

creating 11

virtual work theory

example problem 16

technical notes on 15



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ram frame drift control

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