HRS Project Report
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Transcript of 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
Page 1 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)
Page 3 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
Page 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.
Page 5 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.
, ,
Page 6 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
Page 7 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
Page 13 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)
Page 16 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
Page 17 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.
Page 18 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
Page 19 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).
Page 20 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
Page 25 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
Page 28 of 40
b) Sum of Moments in the X direction (East West direction)
Table 18: Summary of Z‐Axis Moment Values at corresponding Cores
Core Z‐AxisMomentValue(kNm)1 49.163
2 ‐49.163
3 ‐2286.595
4 2286.595
5 ‐952.474
6 952.474
Total(Baseoverturningmoment) 0
Table 19: Summary of Z‐Axis Moments due to Axial Loads in each Core
Core Z‐AxisMomentValue(kNm)1 7.95005
2 ‐7.95005
3 0.00000
4 0.00000
5 1211.87526
6 ‐1211.87526
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 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
Page 30 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.
Page 31 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
Page 36 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
Page 37 of 40
(b): For b = 35m, s = 0m (for base bending moment)
. ..
0.645
calculations for scenario (a) and (b):
(a): For b = 50m
. . . ..
. . ..
. .0.110
(b): For b = 35m
. . . ..
. . ..
. .0.133
calculations for scenario (a) and (b):
(a): For b = 50m
. . .. . .
.
. .0.95
(b): For b = 35m
. . .. . .
.
. .1.01
Page 38 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
Page 39 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
Page 40 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)