hrs project report

MBRH

Sy

MelbBuilRepHigh R

yed Sibga

CV

bouldin

port ise St

atul Ahsa

VEN

urneng P

ructur

an

N9

e CBProje

res

5165

00

BD ect

547

24

CVEN90024 High Rise Structures

Contents

1. Introduction......................................................................................................................................... 1

2. Executive Summary ............................................................................................................................. 1

3. Core system and lateral load distribution ............................................................................................. 2

3.1. Objective ................................................................................................................................................ 2

3.2. Proportion of wind load distributed to each core cell ......................................................................... 2

3.2.1 Find the centroid of each core cell relative to the origin .............................................................. 3

3.2.2 Find moments of inertia Ixx and Iii ................................................................................................. 3

3.2.3 Find centre of stiffness of the building ......................................................................................... 5

3.2.4 Find torsional stiffness Kθθ ............................................................. Error! Bookmark not defined.

3.2.5 Calculate the proportion of lateral load wind load distributed to each core cell ......................... 6

4. Wind load ............................................................................................................................................ 7

4.1. Objective ................................................................................................................................................ 7

4.2. Results ................................................................................................................................................... 7

4.2.1 Site Wind Speed ............................................................................................................................ 7

4.2.2 Design Wind Speed ..................................................................................................................... 12

4.2.3 Design Wind Pressure ................................................................................................................. 13

4.2.4 Calculation of Cdyn ....................................................................................................................... 14

4.2.5 Lateral Along‐Wind Loads & Base Overturning Moments .......................................................... 17

5. Seismic load ....................................................................................................................................... 18

5.1. Objective .............................................................................................................................................. 18

5.2. Results ................................................................................................................................................. 18

5.2.1 Vertical distribution of VB ............................................................................................................ 19

6. SpaceGass model and analysis ........................................................................................................... 21

6.1. Objective .............................................................................................................................................. 21

6.2. Methodology ....................................................................................................................................... 21

6.3. Results ................................................................................................................................................. 23

6.3.1. Model A ..................................................................................................................................... 23

6.3.1.1. Deflection at the top of the building .............................................................................. 23

6.3.1.2. Percentage distribution of wind load moments to cores .............................................. 24

6.3.2. Model B...................................................................................................................................... 26

6.3.2.1. Deflection at the top of the building .............................................................................. 26

6.3.2.2. Percentage distribution of wind load moments to cores and header beams ................ 27

6.4. Discussion ............................................................................................................................................ 29

6.4.1. Deflection at the top of the building .......................................................................................... 29

6.4.2. Percentage distribution of wind load moments to cores and header beams ............................ 30

7. Conclusion ......................................................................................................................................... 30

8. Reference List .................................................................................................................................... 31

9. Appendix ........................................................................................................................................... 32

of 30

1. Introduction

This report provides an analysis and evaluation of the impacts of vertical (gravity) and lateral (wind

and seismic) loads on a high‐rise building situated within the Melbourne CBD. Methods that were

used in determining these impacts include Gravity Load Analysis through a lateral load resisting

structural system, Dynamic Analysis Method for wind load impacts and Equivalent Static Analysis

Method for seismic impacts. Many assumptions were made throughout the report to obtain

accurate estimates and understanding of high‐rise behaviour under these imposed loads and

concluding remarks regarding design for structural effectiveness of high‐rise buildings in minimising

the impacts of external loading.

2. Executive Summary

This report focuses on the impact of lateral load applications on high‐rise structures. Through our

analyses, we have obtained essential findings that can benefit future high‐rise structural safety

design in terms of lateral load application resistance and serviceability limitations. The following are

our main outcomes from our analyses:

Proportion of lateral load distribution varies according to point of load application

Base overturning moments are higher for wind loads than seismic loads

Header beams provide additional stiffness, load transfer and deflection absorption

Our research was conducted through conventional theories of structural analyses and the usage of a

structural analysis modelling software, Space Gass.

Discussion of header beams is also within this report, identifying its importance in addressing our

main outcomes as listed above; resisting lateral loading through transfer and limiting overall

deflection of the high‐rise.

3.

3.1. Obj

To deter

below),

Our mai

total win

the wind

total wid

eccentri

applied

calculati

3.2. Prop

To deter

needs to

1.

2.

3.

4.

5.

Core system

jective

rmine, manu

assuming th

n assumptio

nd load appl

d load applic

dth East from

city. Therefo

relative to (0

ing centroids

portion of w

rmine the pr

o be underta

Find the cen

Find momen

Find centre

Find torsion

Calculate th

m and lateral

ually, the % o

at there are

Figure 1

on for this pa

ied on the b

cation is from

m the centre

ore, 9500mm

0, 0) on the x

s).

wind load dis

roportion of

aken:

ntroid of each

nts of inertia

of stiffness o

al stiffness K

e proportion

load distrib

of wind load

no header b

: Core layou

rt of the rep

uilding to sim

m the South o

of the build

m (centre) + 9

x‐y axis (bott

tributed to e

wind load di

h core cell re

Ixx and Iyy

of the buildin

Kθθ

n of lateral w

1

2

bution

resisted by e

beams in the

t of the Mel

port is that th

mplify calcula

of the buildin

ding (or centr

950mm = 10

tom left corn

each core ce

istributed to

elative to the

ng

wind load dist

3

4

each of the 6

e core system

bourne CBD

he core syste

ations. We a

ng and is app

re of mass) ‐

0450mm East

ner of the bu

ell

each core ce

e origin (cent

tributed to e

5

6

6 core cells (s

m.

D building

em is designe

lso idealised

plied at ecce

i.e. 19000*5

t is where th

ilding diff

ell, the follow

tre of mass o

each core cel

Pag

shown in Fig

ed to resist t

d a scenario w

ntricity 5% o

5% = 950mm

he wind load

ferent to orig

wing proced

of the buildin

ll

e 2 of 40

gure 1

the full

where

of the

m

will be

gin in

ure

ng)

of 40

3.2.1. Find the centroid of each core cell relative to the origin

We use the following formula to determine the centroid of each core cell:

Centroidx = ∗

Centroidy = ∗

Although calculations can be found in the Appendix, we will conduct calculation of the centroid for

Core 1 for demonstrative purposes.

Centroidx1 = . ∗ . . . ∗ . . . ∗ . . . ∗ . .

. ∗ . . ∗ . . ∗ . . ∗ .

7.990

Centroidy1 = . ∗ . . . ∗ . . . ∗ . . . ∗ . .

. ∗ . . ∗ . . ∗ . . ∗ .

5.590

Hence, the centroid of Core 1 is situated at the point (‐7.990m, 5.590m) relative to the centre of the

building (or centre of mass) (0, 0).

Through similar calculations, the centroids for each of the 6 core cells are found in Table 1 below.

Table 1: Summary of centroids for each of the 6 core cells

Core Centroidrelativetoorigin(0,0)1 (‐7.990m, 5.590m)

2 (‐7.990m, ‐5.590m)

3 (0.000m, 5.983m)

4 (0.000m, ‐5.983m)

5 (7.990m, 5.590m)

6 (7.990m, ‐5.590m)

3.2.2. Find moments of inertia Ixx and Iyy

We are now to determine the moments of inertia for each of the 6 core cells. As this requires a

substantial amount of calculations, only one example will be showing which will be for Core 1 –

shown diagrammatically below (the remaining calculations can be found on the Appendix).

3

1 2

4

of 40

Essentially, we are trying to obtain the parameters for the following equation to determine our

moments of inertia Ixx and Iyy:

The parameters required for the above equations are found in Table 2 and Table 3

Table 2: Parameters required for moment of inertia Ixx calculation

i Ai(m2) yi(m) Aiyi (m3) (m4) dyi (yi ‐ )(m) Aidyi2 (m4)1 3.20 5.45 17.44 17.06700 ‐0.14 0.06272

2 2.40 5.45 13.08 12.80000 ‐0.14 0.04704

3 1.04 9.30 9.67 0.01387 3.71 14.31466

4 0.78 1.65 1.29 0.00585 ‐3.94 12.10841

SUM 7.42 41.48 29.88672 26.53283

.

.5.590m

Hence,

29.88672 26.53283 56.41955m4

Table 3: Parameters required for moment of inertia Iyy calculation

i Ai(m2) xi(m) Aixi (m3) (m4) dxi (xi ‐ )(m) Aidxi2 (m4)

1 3.20 ‐9.30 ‐29.76 0.04267 ‐1.31 5.49152

2 2.40 ‐6.35 ‐15.24 0.01800 1.64 6.45504

3 1.04 ‐7.85 ‐8.16 0.58590 0.14 0.02038

4 0.78 ‐7.85 ‐6.12 0.43940 0.14 0.01529

SUM 7.42 ‐59.29 1.08597 11.98223

Note: Full calculations can be found on the Appendix

.

.‐7.990m

Hence,

1.08597 11.98223 13.06820m4

Through similar calculations, the moments of inertia Ixx and Iyy for each of the 6 core cells are found

in Table 4 below.

of 40

Table 4: Summary of moments of inertia Ixx and Iyy for each of the 6 core cells

Core Ixx (m4) Iyy(m4)1 56.41955 13.06820

2 56.41955 13.06820

3 92.60461 64.63975

4 92.60461 64.63975

5 56.41955 13.06820

6 56.41955 13.06820

3.2.3. Find centre of stiffness of the building

Now, we estimate the coordinates for the centre of stiffness of the building by taking into account

the centroids and moments of inertia Ixx for each of the 6 core cells and inputting it into the

following equations:

∑ ,

∑ ,

∑ ,

∑ ,

We calculate the two equations as follows:

∑ ,

∑ ,

: . ∗ . : . ∗ . : . ∗ . : . ∗ . : . ∗ . : . ∗ .. .

.

∑ ,

∑ ,

: . ∗ . : . ∗ . : . ∗ . : . ∗ . : . ∗ . : . ∗ .. .

.

Hence, the centre of stiffness relative to the origin (0, 0) is a translation of (0.000m, 0.000m) which

means the location for the centre of stiffness is the same as the centre of mass of the building as no

translation occurs (it can also be told simply by observing that the building is symmetrical in both the

x and y direction). It should also be mentioned that the centre of stiffness is now the new reference

point for our system even if it has not changed from the original reference point.

3.2.4. Find torsional stiffness Kθθ

We can now calculate the torsional stiffness Kθθ which is crucial in calculating our final wind load

proportion distributions to each of the 6 core cells.

, ,

of 40

We calculate the torsional stiffness as follows:

56.42 ∗ 7.990 56.42 ∗ 7.990 92.60 ∗ 0.000 92.60 ∗ 0.000

56.42 ∗ 7.990

56.42 ∗ 7.990 4 13.07 ∗ 5.590 2 64.64 ∗ 5.980 20664.18895

3.2.5. Calculate the proportion of lateral wind load distributed to each core cell

We can finally calculate the proportion of lateral wind load that is distributed to each core cell. This

is done by using the following expression:

, ∆ ∆

,,

As mentioned before, the point of application of the load shall be offset from the centroid of the

projected surface by 5% of the total width of the projected area towards the East.

The eccentricity is now measured from the centre of stiffness:

ex = ((0.05*19000) + 0.00) = +0.95m positive sign indicates that the load is located to the east of

the centre of stiffness

We will also make two further simplifications to make calculations of the wind load proportions

more feasible:

, . . .

0.00243380

.

.4.5973 ∗ 10

Now, we can simply plug in everything we have calculated so far back into the formula mentioned

above to about our wind load proportions distributed to each of the 6 core cells.

56.42 0.00243380 7.990 ∗ 4.5973 ∗ 10 0.117

56.42 0.00243380 7.990 ∗ 4.5973 ∗ 10 0.117

92.60 0.00243380 0.000 ∗ 4.5973 ∗ 10 0.225

92.60 0.00243380 0.000 ∗ 4.5973 ∗ 10 0.225

56.42 0.00243380 7.990 ∗ 4.5973 ∗ 10 0.158

56.42 0.00243380 7.990 ∗ 4.5973 ∗ 10 0.158

of 40

Table 5: Summary of proportions of lateral wind load distributed to each of the 6 core cells

Core ProportionofVydistributed1 0.117

2 0.117

3 0.225

4 0.225

5 0.158

6 0.158

4. Wind load

4.1. Objective

To determine the lateral along‐wind loads for the northerly wind application on the Melbourne CBD

building through Dynamic Analysis Methods.

Table 1: Basic information of the building project

Information Type

Location Region A5, non‐cyclonic

Wind direction Northerly

Terrain Assume suburban terrain in all directions – Terrain Category 3 Zone

Shielding No surrounding buildings provide shielding

Topography Assume ground slope less than 1 in 20 for greater than 5km in all directions

Building dimensions 50m wide, 35m deep, 184m high

4.2. Results

Note: All results were obtained using AS/NZS1170.2‐2011 and the resulting wind speed calculated is

assumed to be in all directions.

4.2.1. Site Wind Speed

The following formula is used to determine maximum Site Wind Speed for the design of the

structural system, where Vsit,β = maximum site wind speed:

, ,

Where

= Regional wind speed for all directions

= Wind direction multiplier

, = Terrain/height multiplier

= Shielding multiplier

= Topographic multiplier

is det

project.

paramet

servicea

We need

1.

2.

1.

From Ta

Building

termined ba

The use of R

ter is the inv

ability limit st

d to determi

Importance

Design Even

able B1.2a, w

gs or structur

sed on 3‐sec

R, average re

verse of the a

tates.

ine two facto

Levels of Bu

nts for Safety

we see that t

res that are d

cond gust wi

ecurrence int

annual proba

Table 2: R

ors before w

ildings and S

y

he building p

designed to c

nd speed de

terval, may b

ability of exc

Regional Win

we can identif

Structures

project most

contain a lar

epending on t

be required w

ceedance of t

nd Speeds

fy a value of

t closely iden

rge number o

the region of

where R exce

the wind spe

VR:

ntifies to Imp

of people.

Pag

f the buildin

eeds 5 years

eed for ultim

portance Lev

e 8 of 40

g

. The

mate or

el 3:

2.

From Ta

Non‐cyc

Now tha

correspo

Wind dir

wind on

1.00 (sh

,

The terr

terrain i

able B1.2b, w

clonic, leadin

at we are aw

onding regio

rection mult

ly we have t

own in Table

rain/height m

s determine

we see that t

g to the ann

ware that the

onal wind spe

tiplier for 8 c

he required

e 3).

Ta

multiplier bas

d from the fo

he building p

ual probabil

building pro

eed for all dir

ardinal direc

factors of Ca

able 3: Wind

sed on the te

ollowing fou

project most

lity of exceed

oject is situat

rections is 46

ctions in this

ardinal Direc

d Direction M

errain over w

ur categories

t closely iden

dance equall

ted within an

6 m/s.

situation. Si

ction N and R

Multiplier (M

which wind f

:

ntifies to Imp

ing to 1:1000

n A5 Region

nce this incl

Region A5 he

Md)

lows toward

Pag

portance Lev

0.

and is V1000,

udes the nor

ence our Md

ds a structure

e 9 of 40

vel 3 and

the

rtherly

value is

e. The

The tall

heart of

is select

Now tha

we can

184m by

simply fo

as well).

Table 4

Note: Re

Append

office build

f the Melbou

ed.

at we have t

select Mz,cat

y linear inte

ound from li

.

4: Terrain/he

limit state d

emaining

ix

ing is to be

urne CBD and

he required

to be equal

erpolation). T

inear interpo

eight multipl

design – all r

, values w

situated in

d is surround

factors of Te

to: 1.21 + (1

The remainin

olations with

lies for gust

regions and u

were obtaine

Melbourne,

ded by obstr

errain catego

1.24‐1.21) /(

ng Mz,cat valu

h Table 4 (Cl

wind speeds

ultimate lim

ed through li

an office/re

ructions 3m

ory 3 and the

(200‐150) x (

ues for the c

. 4.2.2) value

s in fully dev

mit state – reg

near interpo

esidential are

to 5m high n

e height of t

(184‐150) =

correspondin

es below (wi

veloped terra

gions A1 to A

olation and a

Page

ea situated

nearby so Ca

the building

1.2304 (for

ng lower he

ill be shown

rains – servic

A7, W and B

re found in t

10 of 40

near the

ategory 3

of 184m,

height at

ights are

on Excel

ceability

B

the

Note: Re

An assum

shielding

The topo

Option (

and opti

The buil

all direct

since Mt

Table

Heigh

efer to Excel

mption of su

g multiplier,

ographic mu

(b)(i) is select

ion (b)(ii) cor

ding project

tions which c

t = Mh, the va

e 5: Summar

ht of Sector(

184

160

140

120

100

80

60

40

20

0

sheet for

urrounding b

is 1.0.

ultiplier is det

ted because

rresponds to

is assumed

corresponds

alue of Mt =

ry of , v

m)

, at each

uildings not

termined fro

option (a) c

o lee zones w

to attribute

s to <0.05 in t

1.0 as well.

values for co

h storey (4m

providing sh

om the follow

orresponds t

which have n

a ground slo

the table be

orresponding

adjacents)

hield is made

wing options

to New Zeala

ot been iden

ope less than

low, giving a

g heights of

,

1.2304

1.2160

1.2000

1.1800

1.1600

1.1280

1.0900

1.0400

0.9400

0.8300

e and so the v

s:

and sites onl

ntified in Aus

n 1 in 20 for g

a value of 1.0

Page

sector

value of Ms,

ly (not applic

stralia.

greater than

0 for Mh. Hen

11 of 40

the

cable)

5km in

nce,

We can

using th

The calc

Note: Re

4.2.2. De

For the p

which is

peak of

Table

now calculat

e following f

culations can

Table

Heigh

efer to Excel

esign Wind S

purposes of

to be equal

the building

e 6: Hill‐Shap

te Vsit,N for M

formula:

be found in

e 7: Summa

ht of Sector(

184

160

140

120

100

80

60

40

20

0

sheet for Vs

Speed

our analysis,

to the maxim

(184m) and

pe Multiplier

Melbourne, t

,

the Append

ary of Vsit,N va

m)

sit,N at all stor

, we will assu

mum northe

so, we will t

r at Crest (x=

the northerly

,

dix and the re

alues for cor

reys (4m adj

ume a conse

erly site wind

take , =

=0), z=0 (for g

y site wind sp

esults are sh

rresponding

acents)

ervative value

d speed value

= 56.5984 m/

gust wind sp

peeds at diff

own below i

heights of s

Vsit,N (m/s

56.5984

56.2120

55.6600

54.7400

53.8200

52.6240

51.0600

49.2200

46.0000

38.1800

e for Design

e. This maxim

/s.

Page

peeds)

ferent sector

in Table 7.

sector

s)

4

0

0

0

0

0

0

0

0

0

Wind Speed

mum occurs

12 of 40

r heights,

d ( ,

at the

of 40

4.2.3. Design Wind Pressure

Design wind pressure can be calculated using the following formula:

0.5 ,

Where

= 1.2 kg/m3

, = Design wind speed

= Aerodynamic shape factor

= Dynamic response factor

We will assume that all wind pressures are considered external in these scenarios and hence, we can

expand from the aerodynamic shape factor, , in the above equation to

, , ,

Where

, = External pressure coefficient

= Area reduction factor

, = Combination factor applied to external pressures

= Local pressure factor

= Porous cladding reduction factor

Now, we have two orientations to consider in determining maximum wind pressures on the building

sides:

For (a):

Now, from Table 5.2(A) and Table 5.2(B) of the AS/NZS1170.2‐2011, we find that the External

Pressure Coefficient ( , ) equates to 0.8 for the Windward Wall and ‐0.5 for the Leeward Wall as

d/b < 1 where d = 35m and b = 50m.

For (b):

Now, from Table 5.2(A) and Table 5.2(B) of the AS/NZS1170.2‐2011, we find that the External

Pressure Coefficient ( , ) equates to 0.8 for the Windward Wall and ‐0.41 for the Leeward Wall as

d/b = 50/35 = 1.43 > 1 and then using linear interpolation to obtain that value.

50m

35m

WIND WIND

35m

50m

(a) Normal to 50m wall (b) Normal to 35m wall

Windward

Windward

Leeward Leeward

The follo

below.

Hence, w

(a):

Windwa

Leeward

(b):

Windwa

Leeward

4.2.4. Ca

The dyn

Before w

through

1.

2.

Hence, t

We can

natural f

shown b

owing param

Paramet

,

we can now

ard Wall:

d Wall: ,

ard Wall:

d Wall: ,

alculation of

amic respon

we proceed w

the followin

∗

0

the high rise

now also de

frequency of

below (as 0.2

meters remai

Table 6:

ter

calculate the

, 0.80 ∗

0.50 ∗

, 0.80 ∗

0.41 ∗

f

nse factor (

with analysis

ng two check

5.257 5 (a

0.25 1

building is w

termine the

f the structu

2 Hz < 0.25 H

n constant fo

Parameter v

e correspond

1.0 ∗ 0.9 ∗ 1

1.0 ∗ 0.9 ∗ 1

1.0 ∗ 0.9 ∗ 1

1.0 ∗ 0.9 ∗ 1

) can be c

1

s, we should

ks:

assuming 4m

1

wind sensitive

applicable c

ral element:

Hz < 1.0 Hz).

or both scen

values and co

Value

ding , va

1.0 ∗ 1.0 0

1.0 ∗ 1.0

1.0 ∗ 1.0 0

1.0 ∗ 1.0

calculated us

2

1 2

determine if

m inter‐store

e.

clause for cal

0.25 Hz. The

nario (a) and

orrespondin

1

0.9

1

1

1

alue for each

0.72

0.45

0.72

0.37

sing the follo

f the structu

y height)

lculating

e applicable

(b) and are s

g sources

Table 5.4

Table 5.5

Clause 5.6

Clause 5.7

Clause 6.1

h scenario:

owing formul

ral element

as we have

clause is Cl.

Page

shown in the

Source

la:

is wind sens

e the value o

6.1.(b)(i)(B)

14 of 40

e table

sitive

of

as

Now, we

Turbulen

linear in

Terrain C

Peak fac

Backgro

fluctuati

(Equatio

Where

s = heigh

h = heig

= the

= inte

Now, we

found in

is the

e will determ

nce intensity

terpolation,

Category 3. T

ctor for the u

und factor, w

ing response

on 6.2(2)):

ht of the leve

ht to the top

e average br

egral turbule

e obtain v

n the Append

e height fact

mine each ind

y, , is deter

we can obta

The value ob

upwind veloc

which is a me

e, caused by

el at which a

p of a tower

readth of the

ence length s

values for sce

dix.

or for the re

dividual para

rmined from

ain a single v

btained throu

Table 7:

city fluctuatio

easure of the

low‐frequen

ction effects

e structure b

scale at heigh

enarios (a), 0

sonant respo

ameter of the

m Table 7 (Cl.

value of turb

ugh linear in

Turbulence

ons and will

e slowly vary

ncy wind spe

.

s are calculat

between heig

ht h in metre

0.638, and (b

onse which e

e equa

6.1) from th

ulence inten

terpolation w

Intensity

be taken as

ying backgro

ed variation

.

ted for a stru

ghts s and h

es = 85(h/10

b), 0.645, wh

equals 1 + (s

tion.

he Wind Stan

nsity for the 1

was 0.14252

3.7 (Cl. 6.2.2

und compon

s, will be calc

ucture

)0.25

here both cal

s/h)2 = 1 + 0 =

Page

ndards and t

184m tall bu

2.

2).

nent of the

culated as fo

lculations ca

= 1 (Cl. 6.2.2

15 of 40

hrough

ilding in

ollows

n be

2)

of 40

is the peak factor for resonant response (10 minute period) given by:

2 600 2 600 0.25 3.17 (Cl 6.2.2)

Where

= first mode natural frequency of vibration of a structure in the along‐wind direction in hertz

is the size reduction factor which can be calculated through the following formula:

.

, ,

(Equation 6.2(5))

Now, we obtain values for scenarios (a), 0.110, and (b), 0.133, where both calculations can be

found in the Appendix.

(π/4) times the spectrum of turbulence in the approaching wind stream, given as follows:

.

.

. .0.080(Equation 6.2(4))

Where

Reduced frequency, ,

. . . .

.1.188

is the ratio of structural damping to critical damping and is given as 0.05 (Table 6.2)

Now that we have all the required parameters, we can calculate for scenarios (a) and (b).

(a) = 0.95

(b) = 1.01

of 40

4.2.5. Lateral Along‐Wind Loads & Base Overturning Moments

Through all our previous analyses, we can now finally calculate the lateral along‐wind loads at each

of the 46 storeys of the building and consequently, determine the base overturning moments for

scenarios (a) and (b). The summary of the results are shown below in Table 8.

Table 8: Summary of Lateral Along‐Wind Loads & Base Overturning Moments at different heights

(z)

Height of Sector (m)

Wind normal to 50m wall Wind normal to 35m wall

Windward(kN) Leeward(kN) Moment (MNm)

Windward(kN) Leeward(kN) Moment (MNm)

184 2679.0 ‐980.4 673.3 1993.7 ‐602.4 477.7

160 2232.5 ‐817.0 487.9 1626.1 ‐502.0 340.5

140 2128.0 ‐817.0 412.3 1583.7 ‐502.0 292.0

120 2061.5 ‐817.0 345.4 1534.2 ‐502.0 244.3

100 1985.5 ‐817.0 280.3 1477.6 ‐502.0 198.0

80 1881.0 ‐817.0 215.8 1399.9 ‐502.0 152.2

60 1757.5 ‐817.0 154.5 1308.0 ‐502.0 108.6

40 1596.0 ‐817.0 96.5 1187.8 ‐502.0 67.6

20 1301.5 ‐817.0 42.4 968.6 ‐502.0 29.4

0 1016.5 ‐817.0 0 756.5 ‐502.0 0

SUM ~2469 ~1743

Note: Full calculations of windward/leeward forces and overturning moments can be found in the

Appendix

As seen from above, the lateral along‐wind loads tend to decrease as the height of the sector

decreases. This is due to the increasing surface roughness from the base as we descend down the

building, providing additional resistance to the external wind load application. This also proves that

lateral loads increasingly dominate the structural form with increasing height; a major obstacle as to

why high rises are much more complex to design.

We also observed that the north‐south base overturning moment for scenario (a) is 2469 MNm and

for scenario (b), it is 1743 MNm. This shows that wind load application along longer walls tend to

produce more overturning moment causing more structural complexities so preferably, a structural

engineer would want to orient the building in a manner where the shorter face of the building faces

the cardinal direction which provides the maximum site wind speed at the location.

of 40

5. Seismic load

5.1. Objective

To determine the lateral north south design earthquake load up the height of the building in the

Melbourne CBD through Equivalent Static Analysis Method.

5.2. Results

We are essentially trying to determine the value of lateral seismic loads along the height of the

building which can be calculated through the following expression:

for T > 2.5 sec*

Where

= Design Base Shear Force

= Mass of floor i

= Height of floor i

*This formula is used because the natural period of the building exceeds 2.5 seconds:

T(secs) = 1.25(0.05)H0.75 for ‘other’ structures (ultimate)

= 1.25(0.05)(184)0.75

= 3.122 seconds > 2.5 seconds (hence use the above expression)

We now have to calculate the Design Base Shear Force to proceed with the above equation, which

can be calculated as follows:

Where

= Elastic Response Spectral Acceleration

= Probability factor for the annual probability of exceedance

= Structural Response Factor

= Total Seismic Weight of the structure

The following assumptions/calculations were used in determining the required parameters

mentioned above:

Design for 500 years return period

Hence, = 1.0

Natural period of the building (from above) = 3.122 seconds

Site factor S = 1.0 (given rock sites, class Be)

Hazard factor Z = 0.08 m/s2 (building situated in Melbourne, VIC)

= 1.32ZS/T2 for T (3.122 seconds) > 1.5 seconds

= 1.32(0.08)(1.0)/(3.1222)

= 0.01083

Assume the density of the building = 250 kg/m3

of 40

Uniformly distributed loads (UDL) are based on floor type:

‐ UDL1 = 12 kN/m2 (typical floors)

‐ UDL2 = 17 kN/m2 (plant‐room floors levels 15, 30 and 40)

‐ UDL3 = 9 kN/m2 (top floor (roof) level 46)

Uniformly distributed load application area = 50m * 35m = 1750m2

Total Seismic Weight on the building

= (12 kN/m2 * 42 typical floors) + (17 kN/m2 * 3 plant‐room floors)

+ (9 kN/m2 * 1 top floor (roof))

= 987000 kN

Structural Response Factor = 2.6 assuming limited ductile shear wall

(“ordinary moment‐resisting frames (limited ductile)”)

Now, we are able to calculate the value of the Design Base Shear Force ( ):

0.01083 1.02.6

987000

4111

5.2.1. Vertical distribution of

The building will be divided into 47 nodes (inter‐storey height of 4m) assuming uniform distribution

of mass.

We can use the lateral seismic load equation (mentioned above) now to obtain seismic load

magnitudes at each floor of the building.

Note:

‐ at the roof ( ) and at the base ( are calculated as follows:

& 0.25 tonne/m3 (density of building) * [50m*35m] (area of building) * 2m (tributary height)

= 875 kg

‐ at all other floors are calculated as follows:

0.25 tonne/m3 (density of building) * [50m*35m] (area of building) * 4m (tributary height)

= 1750 kg

The summarized results from these calculations are shown below in Table 9 (where only 10 nodes

will be used for illustrative purposes).

of 40

Table 9: Summary of Lateral Seismic Loads & Base Overturning Moments at different nodes

Nodes mi (kg) hi (m) mihi2 (kgm

2) Fi (kN) Bending Moment (kNm)

0 875 0 0 0 0

1 1750 20 700000 16.7 333.8

2 1750 40 2800000 66.8 2670.3

3 1750 60 6300000 150.2 9012.4

4 1750 80 11200000 267.0 21362.8

5 1750 100 17500000 417.2 41724.2

6 1750 120 25200000 600.8 72099.4

7 1750 140 34300000 817.8 114491.1

8 1750 160 44800000 1068.1 170902.2

9 875 184 29624000 706.3 129960.5

SUM 172424000 4111 ~567452*

Note: Full calculations of lateral seismic loads and overturning moments can be found in the

Appendix

As seen from above, the seismic loads tend to increase as the height of the structure increases. This

is due to the decreasing surface roughness from the base as we ascend up the building, providing

additional resistance to the external seismic load application. This also proves that lateral loads

increasingly dominate the structural form with increasing height; a major obstacle as to why high

rises are much more complex to design.

We also observed that the north‐south base overturning moment for our seismic load application is

567.5 MNm. This value is significantly lower than the base overturning moments found in the Wind

section, which were 2469 MNm normal to the 50m wall and 1743 MNm normal to the 35m wall.

This proves that in this building case scenario, wind load application safety carries precedence in

structural design. This may also suggest that the seismic uniformly distributed loads imposed on the

structure may be represented by an earthquake with a ‘low’ magnitude. Hence, our conclusion is for

the structural engineers of the building to focus on wind loading management more as seismic loads

are not as significant.

6.

6.1. Obj

To deter

through

calculati

6.2. Met

Our ana

represen

eccentri

will be o

‐

‐

Before w

Space G

Analysis

Building

The buil

modelle

5.6

‐5.6

SpaceGass m

jective

rmine the im

the structu

ions from th

thodology

alytical resul

nt each of t

c load (0.95m

observed in t

Model A: N

‘dummy col

the 6th colum

each level.

Model B: W

columns are

stiffness of t

(discussed la

we begin loo

ass modellin

s.

g Cross‐Sectio

lding cross‐s

ed on Space G

628m

628m

model and a

mpact of hea

ral analysis

e previous se

lts will be b

the 6 core

m East from

two different

o header be

umn’ at the

mn using the

With header b

e being use

the real bea

ater).

oking into the

ng approach

on

section that

Gass through

Figur

‐7

Core 1

Core 2

nalysis

der beams o

program Spa

ection.

based on a

cells and al

the centre o

t models:

eams – 6 co

location of t

e master slav

beams – 6 c

ed, the head

ms linking e

e analyses of

that has to

was used to

h the followi

re 2: Space G

7.962m

‐5.716m

5.716m

on lateral wi

ace Gass an

configuratio

lso an addit

of mass/stiff

lumns simpl

the load poin

ves option (d

columns link

der beam s

ach of the c

f both our m

be taken be

o model 3D

ng:

Gass ‘6 colum

Core

Core

0.95

nd load ana

d comparing

n of 6 ‘colu

tional ‘dumm

fness) that w

ly going up t

nt. 5 of the c

discussed lat

ed by heade

stiffness will

olumns. This

models, we w

fore being a

column diag

mns’ Model S

7.962m

Z

X

e 3

e 4

0m

Dummy

lysis in the n

g the accura

umns’ drawn

my column’

will be applied

the height o

columns will

ter) to repre

er beams at

be equival

s is done by

will first go th

ble to proce

gram was 19

Setup

X

Column

Page

north south

cy of values

n in the pro

to characte

d to the syst

of the buildi

need to be

esent the rigi

each level. A

lent to the

utilising rigi

hrough the n

eed with Line

9m by 19m.

5.628m

‐5.628m

Core 5

Core 6

21 of 40

direction

s to hand

ogram to

erise the

tem. This

ng and a

linked to

id slab at

As single

physical

d offsets

necessary

ear Static

This was

The core

origin (s

from th

properti

load.

Master a

Figur

The mas

and 6) w

connect

the dum

Load Ap

As show

0.95m to

diamond

height o

Beams o

The follo

beams b

BeamsbetweenCores6‐11‐22‐33‐44‐55‐6

e‐to‐core dis

shown by X i

he beginning

ies that are e

and slave co

re 3: Master

ster and slav

were linked t

ed to Core 2

mmy column)

pplication

wn in Figure 2

o the East of

d shape abo

of the structu

offset (for M

owing adjust

between the

Table 1

n Dx

stances show

in the diagra

g of the re

extremely lo

nstraints

r slave const

e constraints

o the maste

2 too for add

) have Fixed

2 above, the

f the centre

ve on the fig

ure at that ‘d

odel B)

tments were

core cells, id

0: Summary

at A

‐1.338

1.762

3.400

1.338

‐1.762

‐3.400

wn above are

am above). T

port while

ow to avoid t

raints showi

m

s were chose

r node/colum

itional meas

supports at t

e lateral wind

of mass of t

gure, located

dummy colum

e made to o

dealising the

y of Beam Of

BeDy at A

‐0.350

‐0.350

‐0.350

‐0.350

‐0.350

‐0.350

e based on t

The shapes o

the dummy

the column f

ing connecti

master node

en in a mann

mn Core 2 as

sures. It shou

the base of e

d load applic

the building

d 0.950m Ea

mn’ location

offset the be

e system:

ffsets for cor

eamOffsetDz at A

‐4.172

‐3.672

‐3.584

4.172

3.572

3.584

the centroids

of the cores

y column ha

from carryin

ion of 5 colu

10

ner that five

s shown abo

uld also be no

each of those

cation was to

(from Sectio

ast to the ce

.

eams in the c

rresponding

ParameterDx at B

2 ‐1.3

2 ‐3.4

4 ‐1.7

2 1.3

2 3.4

4 1.7

s of each cor

are modelle

as no shape

g any of the

mns + dumm

of the colum

ve. The dum

oted that all

e columns.

o be applied

on 4.) and th

ntre and app

correct direc

inter‐core lo

r(m)B Dy a

338 ‐

400 ‐

762 ‐

338 ‐

400 ‐

762 ‐

Page

re cell relativ

ed based on

e and has

e applied late

my column t

mns (Cores 1,

mmy column

columns (in

d at an eccen

is is modelle

plied throug

ction, transla

ocations

at B D

‐0.350

‐0.350

‐0.350

‐0.350

‐0.350

‐0.350

22 of 40

ve to the

Figure 1

sectional

eral wind

to the

, 3, 4, 5

was also

cluding

ntricity of

ed by the

ghout the

ating the

Dz at B

4.172

‐3.584

‐3.672

‐4.172

3.584

3.672

6.3. Res

6.3.1.

As state

core cel

applicat

effective

‐

‐

6.3.1.1.

As we c

which oc

ults

Model A

Figure 4:

ed above, M

lls) going up

ion on the

eness of hea

Deflection a

Percentage

Deflection a

an see from

ccur in Cores

: Space Gass

Model A corr

p the height

building. O

der beams in

t the top of t

distribution

t the top of t

Figure

m the diagram

s 5 and 6.

Modelled d

esponds to

of the buil

Our analysis

n resisting la

the building

of wind load

the building

5: Deflectio

m above, ma

diagram of M

a simple mo

ding with an

s will be sp

ateral wind lo

d moments t

on values at t

aximum defl

Model A ‐ Gro

odel charact

nother dum

plit into tw

oads:

o cores (and

the top of M

ection at th

ound Floor &

terising 6 co

my column

wo sections

header bea

Model A

e top of Mo

Page

& 1st Floor

olumns (repr

to address

in determi

ms)

odel A is 121

23 of 40

resenting

the load

ning the

11.32mm

6.3.1.2

Before w

‐

‐

‐

‐

‐

‐

a) Sum o

Total(B

Compar

overturn

values b

Percentage

Ta

we continue,

Node 1 corr

Node 2 corr

Node 3 corr

Node 4 corr

Node 5 corr

Node 6 corr

of Moments

Table

Baseovertu

ing the base

ning momen

but not very s

distribution

able 11: Tab

, it should be

esponds to C

esponds to C

esponds to C

esponds to C

esponds to C

esponds to C

in the Z dire

e 12: Summa

Core123456

urningmom

e overturning

nt of 2487 M

significant.

of wind load

ulated Core

e noted that:

Core 1;

Core 3;

Core 5;

Core 2;

Core 4; and

Core 6

ection (North

ary of X‐Axis

ment)

g moment fr

MNm in this

d moments to

Force and M

:

h South direc

s Moment V

rom Wind no

case, we n

o cores

Moment valu

ction)

alues at corr

X‐AxisM

ormal to 50m

otice a sligh

ues in Model

responding C

MomentVa

m wall of 246

ht discrepanc

Page

l A

Cores

alue(MNm)335

335

563

563

343

343

2486

69 MNm to

cy between

24 of 40

)5.869969

5.869969

3.516938

3.516938

3.899062

3.899062

6.571938

the base

the two

of 40

b) Sum of Moments in the X direction (East West direction)

Table 13: Summary of Z‐Axis Moment Values at corresponding Cores

Core Z‐AxisMomentValue(kNm)1 348.206

2 ‐348.206

3 ‐3299.479

4 3299.479

5 ‐1688.619

6 1688.619

Total(Baseoverturningmoment) 0

As we can see from above, there is no base overturning moment for the East West direction.

c) Percentage distribution of wind load to cores

Table 14: Summary of percentage distribution of wind load to Cores

Core X‐AxisMomentValue(MNm)

%distributed Section4.comparison

1 335.869969 13.507 11.700

2 335.869969 13.507 11.700

3 563.516938 22.662 22.500

4 563.516938 22.662 22.500

5 343.899062 13.830 15.800

6 343.899062 13.830 15.800

Total(Baseoverturningmoment)

2486.571938 100.000 100.000

As we see from above, the difference in percentage distributions between the two are minor. Cores

3 and 4 tend to show the most similarity whereas Cores 1 and 2 have a relative increase to Section 4.

and Cores 5 and 6 have a relative decrease to Section 4.

6.3.2.

As state

(represe

the load

effective

‐

‐

6.3.2.1.

As we c

which oc

Model B

Figure 6:

ed above, Mo

enting core c

d application

eness of hea

Deflection a

Percentage

Deflection a

can see from

ccur in Cores

: Space Gass

odel B corre

cells) going u

n on the buil

der beams in

t the top of t

distribution

t the top of t

Figure

m the diagram

s 1 and 2.

Modelled d

esponds to a

up the height

lding. Our an

n resisting la

the building

of wind load

the building

7: Deflectio

m above, m

diagram of M

a member‐lin

t of the build

nalysis will b

ateral wind lo

d moments t

on values at t

aximum def

Model B ‐ Gro

nked simple

ding with an

be split into

oads:

o cores (and

the top of M

flection at th

ound Floor &

model char

other dumm

two section

header bea

Model A

he top of M

Page

& 1st Floor

racterising 6

my column to

ns in determ

ms)

Model B is 32

26 of 40

columns

o address

ining the

22.09mm

6.3.2.2.

a) Sum o

Total(B

Total(B

Hence, B

Compar

significa

Percentage

Ta

of Moments

Table

Baseovertu

Table

Baseovertu

Base overtur

ing this value

nt.

distribution

able 15: Tab

in the Z dire

e 16: Summa

Core123456

urningmom

e 17: Summa

Core123456

urningmom

rning momen

e of 2502 MN

of wind load

ulated Core

ection (North

ary of X‐Axis

ment)

ry of X‐Axis

ment)

nt = 1010.566

Nm to 2469

d moments to

Force and M

h South direc

s Moment V

Moments d

6876 MNm +

MNm origin

o cores and h

Moment valu

ction)

alues at corr

X‐AxisM

ue to Axial L

X‐AxisM

+ 1491.06249

ally found, t

header beam

ues in Model

responding C

MomentVa

Loads in each

MomentVa

96 MNm = 2

he discrepan

Page

ms

l B

Cores

alue(MNm)135

135

228

228

140

140

1010

h Core

alue(MNm)229

229

244

244

270

270

1491

2501.629372

ncy is not too

27 of 40

)5.595219

5.595219

8.730375

8.730375

0.957844

0.957844

0.566876

)9.676766

9.676766

4.955681

4.955681

0.898801

0.898801

1.062496

MNm.

o

of 40

b) Sum of Moments in the X direction (East West direction)

Table 18: Summary of Z‐Axis Moment Values at corresponding Cores


2 ‐49.163

3 ‐2286.595

4 2286.595

5 ‐952.474

6 952.474


Table 19: Summary of Z‐Axis Moments due to Axial Loads in each Core


2 ‐7.95005

3 0.00000

4 0.00000

5 1211.87526

6 ‐1211.87526


As we can see from above, there is no base overturning moment for the East West direction.

c) Percentage distribution of wind load to individual moments and coupling actions

Table 20: Summary of percentage distribution of wind load to Cores and Header Beams

Core X‐AxisMomentValue(MNm)

%distributed Section4comparison

1individual 135.595219 5.420 11.700

2individual 135.595219 5.420 11.700

3individual 228.730375 9.143 22.500

4individual 228.730375 9.143 22.500

5individual 140.957844 5.635 15.800

6individual 140.957844 5.635 15.800

1coupling 229.676766 9.181 ‐

2coupling 229.676766 9.181 ‐

3coupling 244.955681 9.792 ‐

4coupling 244.955681 9.792 ‐

5coupling 270.898801 10.829 ‐

6coupling 270.898801 10.829 ‐

Total(Baseoverturningmoment)

2501.629372 100.000 100.000

6.4. Disc

6.4.1.

The max

was 322

impleme

As seen

coupling

this in tu

between

beams, w

lateral w

1 DiagramProfessor

cussion

Deflection a

ximum defle

2.09mm, whi

entation of h

in Figure 8, t

g system wit

urn creates a

n one wall (o

which essen

wind load, lim

m from Laterar Priyan Mend

t the top of t

ction at the t

ch proves th

header beam

Figure 8: H

the presence

hin the walls

a couple prov

or core in thi

tially means

miting deflec

al Load Resistindis, Melbourne

the building

top of the bu

hat Model B

ms in restricti

Header Beam

e of header b

s. As we have

viding additi

s case) to an

they withsta

tion of the o

ng Structural e School of En

uilding for M

had a lower

ing maximum

m function o

beams withi

e constant te

onal stiffnes

nother, a tran

and a portio

overall system

System (LLRSSngineering

Model A was

deflection th

m deflection.

n cantilever

n the structu

ension and c

ss to the wall

nsfer of load

n of the load

m (Model B)

S) for High‐Ris

1211.32mm

han Model A

.

high rises1

ural system i

ompression

ls of the syst

occurs thro

ding and defl

.

se Buildings by

Page

and for Mo

A explained b

ntroduces a

in opposite

tem. As a ‘br

ugh these he

lection effec

by

29 of 40

del B, it

by the

walls,

idge’

eader

ts of the

of 40

6.4.2. Percentage distribution of wind load moments to cores and header beams

Table 21: Percentage distribution comparison between Model A and Model B

Core %distributed (A) %distributed(B)1 13.507 5.420

2 13.507 5.420

3 22.662 9.143

4 22.662 9.143

5 13.830 5.635

6 13.830 5.635

We see from the above that the % distribution from Model A to Model B has decreased by more

than half in each of the cores. This is explained by the usage of header beams which was mentioned

just before – the header beams act as an ‘additional’ structural element, transferring loads between

cores laterally, essentially sustaining a portion of lateral wind loading that would otherwise be solely

absorbed by a core if these header beams were absent (which can be seen to be a very significant

portion as % distribution has decreased by more than half).

7. Conclusion

From our experimental analyses on a 184m high‐rise structure, we have achieved the following three

main objectives:

To determine, manually, the % of wind load resisted by core cells in a 19m by 19m core

system

To determine the resulting forces and moments on a cantilever high‐rise under lateral load

applications

To model a high‐rise structure through software analysis tools and observing the impact of

lateral load applications using these models

From our analyses, we were able to determine the different in impact of different lateral loads

where wind loads tend to have higher force and moment impacts (higher base overturning moment)

than seismic loads but that is not to say that high‐rises should only be design for wind safety as the

two lateral loads behave in very different manners.

We also reassured the importance of implementing additional structural system into high‐rise

design, such as header beams, as they are able to significantly minimise loading and deflection

impacts on the high‐rise, particularly the loading proportions absorbed by the core.

Our findings have shown accurate and valid results that may be used to design for structural safety,

in regards to high‐rise design, under lateral loads such as wind or seismic impacts and further

analyses need to be conducted to observe micro (cracking, creep, etc.) impacts of these lateral loads

on the high‐rise structure.

of 40

Reference List

1. Standards Australia, Australian/New Zealand StandardTM, Structural design actions, Part 2:

Wind actions, AS/NZS 1170.2:2011, March 2011.

2. Mendis. P, 2014, Lateral Load Resisting Structural System (LLRSS) for High‐Rise Buildings,

Melbourne School of Engineering, The University of Melbourne

Append

Part A

ix

Figure AA1: Core cell centroids annd Ixx/Iyy calcculations

Page 32 of 40

Fiigure A2: Core cell centr

roids and Ixx//Iyy calculatioon correction

Page

ns

33 of 40

Fiigure A3: Core cell centr

roids and Ixx//Iyy calculatioon correction

Page

ns

34 of 40

Figure A4: Centre of stiffness, torsi

ional stiffness and load proportion c

Page

calculations

35 of 40

of 40

WIND

, linear interpolation calculations:

@184: 1.21 + (1.24‐1.21)/(200‐150) x (184‐150) = 1.2304

@160: 1.21 + (1.24‐1.21)/(200‐150) x (160‐150) = 1.2160

@140: 1.16 + (1.21‐1.16)/(150‐100) x (140‐100) = 1.2000

@120: 1.16 + (1.21‐1.16)/(150‐100) x (120‐100) = 1.1800

@100: 1.16 + (1.21‐1.16)/(150‐100) x (100‐100) = 1.1600

@80: 1.12 + (1.16‐1.12)/(100‐75) x (80‐75) = 1.1280

@60: 1.07 + (1.12‐1.07)/(75‐50) x (60‐50) = 1.0900

@40: 1.04 + (1.07‐1.04)/(50‐40) x (40‐40) = 1.0400

@20: 0.94 + (1.00‐0.94)/(30‐20) x (20‐20) = 0.9400

@0 = 0.8300

Northerly site wind speed calculations

, ,

, , 46 ∗ 1.0 1.2304 ∗ 1.0 ∗ 1.0 56.5984 /

, , 46 ∗ 1.0 1.2160 ∗ 1.0 ∗ 1.0 56.2120 /

, , 46 ∗ 1.0 1.2000 ∗ 1.0 ∗ 1.0 55.6600 /

, , 46 ∗ 1.0 1.1800 ∗ 1.0 ∗ 1.0 54.7400 /

, , 46 ∗ 1.0 1.1600 ∗ 1.0 ∗ 1.0 53.8200 /

, , 46 ∗ 1.0 1.1280 ∗ 1.0 ∗ 1.0 52.6240 /

, , 46 ∗ 1.0 1.0900 ∗ 1.0 ∗ 1.0 51.0600 /

, , 46 ∗ 1.0 1.0400 ∗ 1.0 ∗ 1.0 49.2200 /

, , 46 ∗ 1.0 0.9400 ∗ 1.0 ∗ 1.0 46.0000 /

, , 46 ∗ 1.0 0.8300 ∗ 1.0 ∗ 1.0 38.1800 /

linear interpolation calculation:

0.150 + (0.139‐0.150)/(200‐150) x (184‐150) = 0.14252

calculations for scenario (a) and (b):

8518410

.

176.04

(a): For b = 50m, s = 0m (for base bending moment)

. ..

0.638

of 40

(b): For b = 35m, s = 0m (for base bending moment)

. ..

0.645


(a): For b = 50m

. . . ..

. . ..

. .0.110

(b): For b = 35m

. . . ..

. . ..

. .0.133


(a): For b = 50m

. . .. . .

.

. .0.95

(b): For b = 35m

. . .. . .

.

. .1.01

of 40

Lateral along‐wind and base overturning moment Excel worksheet for scenario (a):

Vsit, at height h of building 56.5984 m/s

0.72

0.95

Wind Normal to 50 m wall

Windward wall Cfig,e

Leeward wall Cfig,e

Cdyn

‐0.45

Height of

sector Mz,cat

Moment

contribution

qz qz.Cfig qz.Cfig.Cdyn.A qh qh.Cfig qh.Cfig.Cdyn.A

m kPa kPa kN kPa kPa kN MNm

184 1.2304 3.27 2.35 447 1.92 ‐0.86 ‐164 113

180 1.228 3.26 2.35 446 1.92 ‐0.86 ‐164 110

176 1.2256 3.24 2.34 444 1.92 ‐0.86 ‐164 107

172 1.2232 3.23 2.33 442 1.92 ‐0.86 ‐164 104

168 1.2208 3.22 2.32 440 1.92 ‐0.86 ‐164 102

164 1.2184 3.21 2.31 439 1.92 ‐0.86 ‐164 99

160 1.216 3.19 2.30 437 1.92 ‐0.86 ‐164 96

156 1.2136 3.18 2.29 435 1.92 ‐0.86 ‐164 94

152 1.2112 3.17 2.28 433 1.92 ‐0.86 ‐164 91

148 1.208 3.15 2.27 431 1.92 ‐0.86 ‐164 88

144 1.204 3.13 2.25 428 1.92 ‐0.86 ‐164 85

140 1.2 3.11 2.24 426 1.92 ‐0.86 ‐164 83

136 1.196 3.09 2.22 423 1.92 ‐0.86 ‐164 80

132 1.192 3.07 2.21 420 1.92 ‐0.86 ‐164 77

128 1.188 3.05 2.19 417 1.92 ‐0.86 ‐164 74

124 1.184 3.03 2.18 414 1.92 ‐0.86 ‐164 72

120 1.18 3.01 2.17 411 1.92 ‐0.86 ‐164 69

116 1.176 2.99 2.15 409 1.92 ‐0.86 ‐164 66

112 1.172 2.97 2.14 406 1.92 ‐0.86 ‐164 64

108 1.168 2.95 2.12 403 1.92 ‐0.86 ‐164 61

104 1.164 2.93 2.11 400 1.92 ‐0.86 ‐164 59

100 1.16 2.91 2.09 398 1.92 ‐0.86 ‐164 56

96 1.1536 2.87 2.07 393 1.92 ‐0.86 ‐164 54

92 1.1472 2.84 2.05 389 1.92 ‐0.86 ‐164 51

88 1.1408 2.81 2.02 385 1.92 ‐0.86 ‐164 48

84 1.1344 2.78 2.00 380 1.92 ‐0.86 ‐164 46

80 1.128 2.75 1.98 376 1.92 ‐0.86 ‐164 43

76 1.1216 2.72 1.96 372 1.92 ‐0.86 ‐164 41

72 1.114 2.68 1.93 367 1.92 ‐0.86 ‐164 38

68 1.106 2.64 1.90 361 1.92 ‐0.86 ‐164 36

64 1.098 2.60 1.87 356 1.92 ‐0.86 ‐164 33

60 1.09 2.57 1.85 351 1.92 ‐0.86 ‐164 31

56 1.082 2.53 1.82 346 1.92 ‐0.86 ‐164 29

52 1.074 2.49 1.79 341 1.92 ‐0.86 ‐164 26

48 1.064 2.45 1.76 335 1.92 ‐0.86 ‐164 24

44 1.052 2.39 1.72 327 1.92 ‐0.86 ‐164 22

40 1.04 2.34 1.68 320 1.92 ‐0.86 ‐164 19

36 1.024 2.26 1.63 310 1.92 ‐0.86 ‐164 17

32 1.008 2.19 1.58 300 1.92 ‐0.86 ‐164 15

28 0.988 2.11 1.52 288 1.92 ‐0.86 ‐164 13

24 0.964 2.01 1.45 275 1.92 ‐0.86 ‐164 11

20 0.94 1.91 1.37 261 1.92 ‐0.86 ‐164 9

16 0.9 1.75 1.26 239 1.92 ‐0.86 ‐164 6

12 0.854 1.58 1.13 216 1.92 ‐0.86 ‐164 5

8 0.83 1.49 1.07 204 1.92 ‐0.86 ‐164 3

4 0.83 1.49 1.07 204 1.92 ‐0.86 ‐164 1

0 0.83 1.49 1.07 204 1.92 ‐0.86 ‐164 0

Base Moment 2469

windward leeward

(unlike conventional method at middle of storey) to make comparsion with seismic loads viable

Height of sector is at 4m adjacents as each floor is located at these partitions;

where wind load is applied

***Note: ‐ Wind load application is assumed to be at the floor of each storey

of 40

Lateral along‐wind and base overturning moment Excel worksheet for scenario (b):

56.5984 m/s

Cdyn

‐0.37

1.01

Wind Normal to 35 m wall

Windward wall Cfig,e 0.72

Leeward wall Cfig,e

Vsit, at height h of building

Height of

sector Mz,cat

Moment

contribution

qz qz.Cfig qz.Cfig.Cdyn.A qh qh.Cfig qh.Cfig.Cdyn.A

m kPa kPa kN kPa kPa kN MNm

184 1.2304 3.27 2.35 333 1.92 ‐0.71 ‐101 80

180 1.228 3.26 2.35 332 1.92 ‐0.71 ‐101 78

176 1.2256 3.24 2.34 330 1.92 ‐0.71 ‐101 76

172 1.2232 3.23 2.33 329 1.92 ‐0.71 ‐101 74

168 1.2208 3.22 2.32 328 1.92 ‐0.71 ‐101 72

164 1.2184 3.21 2.31 326 1.92 ‐0.71 ‐101 70

160 1.216 3.19 2.30 325 1.92 ‐0.71 ‐101 68

156 1.2136 3.18 2.29 324 1.92 ‐0.71 ‐101 66

152 1.2112 3.17 2.28 323 1.92 ‐0.71 ‐101 64

148 1.208 3.15 2.27 321 1.92 ‐0.71 ‐101 62

144 1.204 3.13 2.25 319 1.92 ‐0.71 ‐101 60

140 1.2 3.11 2.24 317 1.92 ‐0.71 ‐101 58

136 1.196 3.09 2.22 315 1.92 ‐0.71 ‐101 56

132 1.192 3.07 2.21 312 1.92 ‐0.71 ‐101 55

128 1.188 3.05 2.19 310 1.92 ‐0.71 ‐101 53

124 1.184 3.03 2.18 308 1.92 ‐0.71 ‐101 51

120 1.18 3.01 2.17 306 1.92 ‐0.71 ‐101 49

116 1.176 2.99 2.15 304 1.92 ‐0.71 ‐101 47

112 1.172 2.97 2.14 302 1.92 ‐0.71 ‐101 45

108 1.168 2.95 2.12 300 1.92 ‐0.71 ‐101 43

104 1.164 2.93 2.11 298 1.92 ‐0.71 ‐101 41

100 1.16 2.91 2.09 296 1.92 ‐0.71 ‐101 40

96 1.1536 2.87 2.07 293 1.92 ‐0.71 ‐101 38

92 1.1472 2.84 2.05 289 1.92 ‐0.71 ‐101 36

88 1.1408 2.81 2.02 286 1.92 ‐0.71 ‐101 34

84 1.1344 2.78 2.00 283 1.92 ‐0.71 ‐101 32

80 1.128 2.75 1.98 280 1.92 ‐0.71 ‐101 30

76 1.1216 2.72 1.96 277 1.92 ‐0.71 ‐101 29

72 1.114 2.68 1.93 273 1.92 ‐0.71 ‐101 27

68 1.106 2.64 1.90 269 1.92 ‐0.71 ‐101 25

64 1.098 2.60 1.87 265 1.92 ‐0.71 ‐101 23

60 1.09 2.57 1.85 261 1.92 ‐0.71 ‐101 22

56 1.082 2.53 1.82 257 1.92 ‐0.71 ‐101 20

52 1.074 2.49 1.79 254 1.92 ‐0.71 ‐101 18

48 1.064 2.45 1.76 249 1.92 ‐0.71 ‐101 17

44 1.052 2.39 1.72 243 1.92 ‐0.71 ‐101 15

40 1.04 2.34 1.68 238 1.92 ‐0.71 ‐101 14

36 1.024 2.26 1.63 231 1.92 ‐0.71 ‐101 12

32 1.008 2.19 1.58 223 1.92 ‐0.71 ‐101 10

28 0.988 2.11 1.52 215 1.92 ‐0.71 ‐101 9

24 0.964 2.01 1.45 204 1.92 ‐0.71 ‐101 7

20 0.94 1.91 1.37 194 1.92 ‐0.71 ‐101 6

16 0.9 1.75 1.26 178 1.92 ‐0.71 ‐101 4

12 0.854 1.58 1.13 160 1.92 ‐0.71 ‐101 3

8 0.83 1.49 1.07 151 1.92 ‐0.71 ‐101 2

4 0.83 1.49 1.07 151 1.92 ‐0.71 ‐101 1

0 0.83 1.49 1.07 151 1.92 ‐0.71 ‐101 0

Base Moment 1743

windward leeward

of 40

EARTHQUAKE

Lateral seismic loads and base overturning moment Excel worksheet:

Kp 1

T 3.12 secs

Z 0.08 m/s^2

S 1

C 0.01083

Area 1750 m^2

W 987000 kN

Rf 2.6 Limited ductile shear wall

VB 4111 kN

Return Period

Static Analysis (Based on AS1170.4 (2007))

500 years

>1.5s

(Melbourne, VIC)

Rock Sites, Class Be

1.32ZS/T^2 as T >1.5s

50m by 35m

Nodes mi (kg) hi (m) mihi^2 (kgm^2) Fi (kN)

46 875 184 29624000 134.022679 24660.17

45 1750 180 56700000 256.5178874 46173.22

44 1750 176 54208000 245.2437679 43162.9

43 1750 172 51772000 234.2229994 40286.36

42 1750 168 49392000 223.4555819 37540.54

41 1750 164 47068000 212.9415154 34922.41

40 1750 160 44800000 202.6807999 32428.93

39 1750 156 42588000 192.6734354 30057.06

38 1750 152 40432000 182.9194219 27803.75

37 1750 148 38332000 173.4187594 25665.98

36 1750 144 36288000 164.1714479 23640.69

35 1750 140 34300000 155.1774874 21724.85

34 1750 136 32368000 146.4368779 19915.42

33 1750 132 30492000 137.9496194 18209.35

32 1750 128 28672000 129.715712 16603.61

31 1750 124 26908000 121.7351555 15095.16

30 1750 120 25200000 114.00795 13680.95

29 1750 116 23548000 106.5340955 12357.96

28 1750 112 21952000 99.31359196 11123.12

27 1750 108 20412000 92.34643947 9973.415

26 1750 104 18928000 85.63263797 8905.794

25 1750 100 17500000 79.17218747 7917.219

24 1750 96 16128000 72.96508797 7004.648

23 1750 92 14812000 67.01133948 6165.043

22 1750 88 13552000 61.31094198 5395.363

21 1750 84 12348000 55.86389548 4692.567

20 1750 80 11200000 50.67019998 4053.616

19 1750 76 10108000 45.72985548 3475.469

18 1750 72 9072000 41.04286199 2955.086

17 1750 68 8092000 36.60921949 2489.427

16 1750 64 7168000 32.42892799 2075.451

15 1750 60 6300000 28.50198749 1710.119

14 1750 56 5488000 24.82839799 1390.39

13 1750 52 4732000 21.40815949 1113.224

12 1750 48 4032000 18.24127199 875.5811

11 1750 44 3388000 15.32773549 674.4204

10 1750 40 2800000 12.66755 506.702

9 1750 36 2268000 10.2607155 369.3858

8 1750 32 1792000 8.107231997 259.4314

7 1750 28 1372000 6.207099498 173.7988

6 1750 24 1008000 4.560317998 109.4476

5 1750 20 700000 3.166887499 63.33775

4 1750 16 448000 2.026807999 32.42893

3 1750 12 252000 1.1400795 13.68095

2 1750 8 112000 0.506702 4.053616

1 1750 4 28000 0.1266755 0.506702

0 875 0 0 0 0

908684000 4111 567452

Base Overturning

Moment

Bending Moment (kNm)

hrs project report

Documents