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MODELLING HIGH RISESTRUCTURES

USINGMICROSTRAN

INTRODUCTION

High rise structures, by their very nature, can require many number of nodes and a large number of members. The problemwith acomputer analysis is the size of the model generated plus the ease of either adding or deleting members during theanalytical process and the simplicity of being able to quickly find resuits (moments, shears, etc.) for any particular member orgroup of members.

The version of Microstran currently being usedmaximum node number and member number limitation of 32,000.nodes and 6,1 00 members.

is by definition "unlimited". However, there is aEven the full model of Grollo Tower only requires 3,100

With the advent of the modern desktop personal computers, size of model, in terms of running time, is not an issue. Themain problem is one of "housekeeping", therefore by maintaining simple systems to ensure any member group results can beobtained quickly is important.

The system described in this paper achieves this, and can be used for any multi-level structure and, with some modification,most other structures.

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PLAN ON TYPICAL FLOOR

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Floor to floor height ~ 3,200 Footing - Levell5,000 Levell - Level 23,600 Level 2- Levell 0

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PLAN ON TYPICAL FLOOR SHOWING EXACT POSITIONS OF NODES

Node numbers shown 5Member numbers shown ®

Node 15 is centre of bUilding and used for positioning wind or earthquake loads. (Note, no column need be placed at thisposition).

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PLAN ON TYPICAL FLOOR SHOWING POSITIONS OF BEAMS AFTER RIGID OFFSETS HAVEBEEN INCLUDED

For obvious reasons, rigid offsets must be included for beams joining core. However, column rigid offsets are not entirelynecessary and could be ignored by placing nodes at more convenient positions, e.g.: Column NO.1

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The primary purpose of this node and member number system is to allow the designer to number the structure on a typicalfloor plan and be able to recognise instantly where any member in the total structure can be found in the final print-out of thecomputer analysis.

To achieve this, the following rules apply:

1} Node numbers have position and level as:

0001 to 1001

LL.-J LLJLevel Position Level Position

Hence the node at position 1. as:

X y Z

0001 0.0 21.0 0.00101 0.0 21.0 3.20201 0.0 21.0 8.20301 0.0 21.0 11.8

( 0401 0.0 21.0 15.40501 0.0 21.0 19.00601 0.0 21.0 22.60701 0.0 21.0 26.20801 0.0 21.0 29.80901 0.0 21.0 33.41001 0.0 21.0 37.0

2) Member numbers also have position and level as:

0101 to 0110

LL.-J LLJMember Level Member Level

Hence the member of node 1 has the following:

First Nod. last Node

( 101 1 101102 101 201103 201 301104 301 401105 401 501106 501 601107 601 701108 701 801109 801 901110 901 1001

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and the member 50 has:

First Node Last Node

5001 101 1025002 201 2025003 301 3025004 401 4025005 501 5025006 601 6025007 701 7025008 801 8025009 901 9025010 1001 1002

It can be seen, therefore, every beam (or column) can be clearly identified by number and level instantly by itsnumber.

1001 SOlO '002 5111) '00' 5210 1004

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TYPICAL ELEVATION SHOWN ON GRID 1SHOWING NODE AND MEMBER NUMBERS

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LIMITATIONS

Microstran has a limitation of maximum node and member number being 32,000. Therefore, for a 99 storey building with thissystem of numbering, there is a limitation of 319 being the maximum total number of beams and columns.

Taller buildings with less than 319 beams and columns or shorter buildings with more than 319 beams and columns can behandled, however care must be taken in the numbering of the system.

CO-ORDINATE SYSTEMS

By maintaining the same co-ordinate system for all models, a base set of parameters will remain constant.

Any system can be adopted, however the one used in this example provides the following:

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1) Beams

Although not required, it is good practice tei give all beam elements a directional reference axis of Z. This willprovide easy reference on checking input and produces the following criteria:

v

Iz=i±F=z

I X

Iv

Local Axes for Beams with Reference Axis of Z

2) Columns

Again, give columns a reference direction. Square or circular columns require no specific rules as properties for Y­Yand Z-Z axes are the same. Shaped columns require reference and the system adopted uses direction referencein the same line as the longer portion of the column, i.e.:

y

Direction ofColumn Reference

And:

Direction ofColumn Reference

y

,LxGlobal Axes

y

.. x L XZ

Global Axes

y

2 --,.t-:;-x--2

y

Local Axes of Columnswith Reference Y

2

y ---1::=+:=1-- y

2

Local Axes of Columnwith Reference X

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You will note the above reference criteria produces the larger (or important) stiffness of all members to be I..

SECTIONAL PROPERTIES

1) Beams

In high rise structures, it is usual to assume the floor slab will act as a diaphram and there is no axial shortening orlateral movement between all members on each different level.

When using units of metres, i.e. m, m2, m' and m', the value of 100 can be assumed to be infinite.

Hence, the properties of floor beams can be taken as:

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A" = 100A" =rea I va lueAn = 100

J=OI" = 100I" = real value

The above is v.ery general and real values must be used if:

i) beams are part of chords for trusses; or

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ii) large openings are required within the diaphram floor and shear flow cannot be transferred betweenelements.

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2) Columns

All properties for column elements are required and are actual values. The exception is J. which should be treatedas zero.

Refer to Appendix A for properties for arange of different shapes.

The torsional stiffness of cores is·generally taken as zero, unless this additional stiffness is considered necessary.For methods of treating this stiffness, refer later section.

SUPPORTS

Column and wall supports are normally treated as fixed for movement and moment, in all directions. However, largemoments at the footing level may occur and foundations will require design for these moments. If moments cannot becatered for, then release should be used for the RYand RX directions, i.e.:

111111 for fully fixed111 100 for pinned

MASTER-SLAVE CONSTRAINTS

With the use of beam properties A = 100 and I" = 100 the need for master-slave constraints is not entirely necessary.However, if used, the programme will solve the matrix faster because a number of unknowns will not be calculated. Theprint-out of results will be clearer also, as axial loads and moments in the diaphram direction will be zero. The centre of loadnode (Node 15 in example) will also act as part of the diaphram and not require unrelated members joining it to theremainder of the structure.

Any node in the structure at each floor level one can be assumed as the "master" node and all remaining nodes slaved to itfor specific displacements and rotations.

Hence, for convenience of generation node, 1 on each floor is normally treated as the master and all nodes slaved to it.Displacements in Xand Ydirection plus rotation ebout the Zdirection, e.g.: .

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x Y Z RX RY RZ

102 101 101 101103 101 101 101104 101 101 101105 101 101 101106 101 101 101107 101 101 101108 101 101 101109 101 101 101110 101 101 101111 101 101 101112 101 101 101113 101 101 101114 101 101 101115 101 101 101202 201 201 201203 201 201 201204 201 201 201205 201 201 201206 201 201 201207 201 201 201208 201 201 201209 201 201 201210 201 201 201211 201 201 201212 201 201 201 (213 201 201 201214 201 201 201215 201 201 201

etc.

Note

The same rules apply for truss chords and open spaces, as explained in the "section properties" notes above, i.e. constraintscan not be given for these specific nodes.