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1 Billboard Design and Analysis Calculation Note
Calculation Notes for Billboard Foundation and Steel Structure
2 Billboard Design and Analysis Calculation Note
1. General
This Document is Included Structural calculation notes for Analysis & Design of Foundation and steel structure of Billboard. This Billboard is Located near the mehrabad Airport. Dimension and General view of billboard shown in following figure.
2. Codes and Standards ‐ “Iranian Code for Seismic Resistant Design of building” STD‐2800(3rd
Edition) ‐ American Welding Society, AWS ‐ Specification for structural Joints Using ASTM A325 or A490 Bolts. ‐ 519 Iranians Codes. ‐ Iranian Concrete Design Code. (ABA Code) ‐ 9th topic of Iranians’ National Building Codes. ‐ ACI 318‐05. ‐ ACI 351.2R‐94/99
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3. Materials 3.1. Reinforcing Bars
Deformed high tensile strength Steel bars, with minimum yield strength of 4200 kg/cm3 in accordance with ASTM A 615 or approved equivalent.
3.2. Concrete Two Types of concrete are considered for the design of structures.
In analyses and Design, / is minimum compressive characteristic strength at 28 days on cylinder Specimen.
/ 250 2
/ 80 2
/ 2.4 3
4. Soil Parameter This assumption is used in this project, According to Soil Report.
34
0 2
20 3
4 2
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5. Input Data 5.1. Vendor Data
Contractor estimate of projector weight was 50Kg. Structural calculation and Model used this assumption. Estimate location of projectors shown in following figure.
6. Loading 6.1. lateral loadings calculate as follow: 6.1.1 Wind Load Calculation:
According To 519 Iranian Code
20.005e qP C C q
q v
=
=
Ce = combined height, exposure and gust factor coefficient
Cq = pressure coefficient for the structure or portion of structure
Under consideration
P = design wind pressure.
v= wind stagnation pressure
5 Billboard Design and Analysis Calculation Note
100 Tehran stationKmv hr=
0.16
0.16
2( ) 210
5 2.2 0.5 7.77.72( ) 1.92 210
1.5
e
e e
q
zC
Z
C C
C
= ≥
= + + =
= = ⇒ =
=
220.005 100 50 Kgq m= × =
22 1.5 50 150e qKgP C C q P m= ⇒ = × × =
Force : 150 (10 5 2.2 0.6) 7698 Moment : M (150 10 5 4.7) (150 2.2 0.6 1.1) 35467.8 .
Wind F P A KgWind Kg m
= × = × × + × == × × × + × × × =
35.47 .7.7
wind
wind
M Ton mV Ton
==
6 Billboard Design and Analysis Calculation Note
6.1.2 Earthquake Load Calculation:
Design base shear: The total design base shear in a given direction shall be determined from the following formula According to 2800 Iranian Code
20 32.5( ) 2.5
V C WA B IC
RA B IV W
RTBT
= ×× ×
=
× ×= ×
= ≤
I = Importance factor
g = Acceleration due to gravity.
R = numerical coefficient representative of the inherent Over strength and
global ductility capacity of lateral force‐Resisting systems
V = Total design lateral force or shear at the base
W = Total Weight
A I R B 0T h g c 0.35 1.4 5 2.5 0.7 7.7 9.81 0.245
0.245V W= ×
Pr0.245 ( )
0.245 (5700) 1396.5 1.4earthquake Plate Light ojector Structure
earthquake
V C W W W W
V Kg Ton
= × = × + +
= × =
6.2 Gravity Load
6.2.1 Dead Load
Total Dead Load includes of steel Structure weight, thin steel plate with 1.5mm thickness and projectors with 150 kg weight.
7 Billboard Design and Analysis Calculation Note
6.2.2 Live Load
The Live Load include of hand rail and access path of billboard. This load assumed 50 Kg/m.
7. Load Combination : 7.1. Load Combination Using Allowable Stress Design.
This load combination used for checking foundation stability and Designing steel structure.
1.4
0.91.4
0.75 ( or 1.4
DeadDead Live Snow
EarthquakeDead Wind
EarthquakeDead
EarthquakeDead Live Wind
+ +
+ +
±
⎡ ⎤+ +⎢ ⎥⎣ ⎦
7.2. Load Combination using strength Design.
1.41.2 1.6 0.51.2 1.6 0.81.2 1.3 0.51.20.9 ( or 1.3 )
DeadDead Live SnowDead Snow WindDead Wind Live SnowDead Earthquake LiveDead Earthquake Wind
+ ++ ++ + ++ ++
8 Billboard Design and Analysis Calculation Note
8. Stability Check
Stability must be checked in two separate cases, first in wind case and second in Earthquake case. This Structure has light weight and wide surface, so the wind case will be critical. (The Overturning and Resisting moment calculated at “A” point)
2 2
2 2
Total Dead Load Foundation Weight + Structure Weight + Projector weightFoundation Weight = (2 tan(22.5)) (2 3.5 tan 22.5) 0.8 2.4 19.5
Pedestal=(2 tan(22.5)) (2 1.2 tan 22.5) 1.8 2f f c
p p c
D h Ton
D h
γ
γ
=
× × = × × × × =
× × = × × × ×2 2
.4 5.15
Soil Weight =(2 tan(22.5) (2 tan(22.5))) =30.44 Ton
Total Dead Load 19.5 5.15 30.44 5.7 60.79Overturning Moment (Wind Case) = 35.47Ton.mOverturning Moment (Earthquake Case) =7.2
f p s s
Ton
D D h
Ton
γ
=
− × ×
= + + + =
8Ton.mResisting Moment = 106.38Ton.m
Resisting Moment 106.38Safe Factor (Wind Case) = = =3 1.75 OkOverturning Moment (Wind Case) 35.47
Resisting MomentSafe Factor (Wind Case) = Overturning Moment (Earthq
≥
96.41 14.6 1.75 Okuake Case) 7.28
= = ≥
9 Billboard Design and Analysis Calculation Note
9. Design And Analysis of Billboard steel Structure 9.1. Modeling Software
Sap 2000 version 11.0.0 is used for Analyses purpose in this project.
9.2. Structural Geometry And Coding The Billboard structure modeling in Sap 2000 Program.
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Loading the Structure
9.2.1. Dead Load
Dead Loads are including steel plate, handrail, access path and projector load. Dead Load Apply to structure as follow.
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9.2.2. Live Load
Live Load is including the load of person who standing and walking on access path. Live Load Apply to structure as follow.
9.2.3. Earthquake Load
Calculated earthquake loads in each direction Applied to structure directly. Earthquake Load Apply to structure as follow.
12 Billboard Design and Analysis Calculation Note
9.2.4. Wind Load
Calculated Wind load applied only in one direction on Structure, and ignored other direction load. Wind Load Apply to structure as follow.
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9.3. Designing of Steel Structure
Sap2000 program Analysis and Designing the Steel Structure. After designing, Program shows this ratio for beams and column.
Ratio of Beam and column must be under 1, in whole of Beam and column Ratio in this structure under 1, so this structure Designing safe and commercial.
14 Billboard Design and Analysis Calculation Note
10. Design And Analysis of Billboard Foundation 10.1. General
In this project foundation of billboard designed as octagonal shape. Octagonal foundation is commercial than square foundation and has beautiful view.
10.2. Foundation Designing procedure
10.2.1. Sectional properties of foundation
Diameter of foundation is 3.5 meter
Depth of foundation (foundation thickness) is 80 cm
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10.2.2. Loading Data
Load Case Load Type Symbol Foundation Dead
Weight Multiplier Billboard Loads
P (KN) V (KN) M (KN.m) Dead Gravity D 1.00 57.0 Wind Lateral WL 77.0 354.7 Earthquake Lateral EQ 14.0 73.0
10.2.3. Load Combination for checking of soil bearing pressure
Load Combination Load Factors
Dead Dead Dead WL EQ Dead 1.00 Dead +WL 1.00 1.00 Dead +EQ 1.00 1.00 Dead+0.2WL 1.00 0.20 Dead+0.28EQ 1.00 0.28
10.2.4. Allowable soil pressure increase factor and stability factors.
Load Combination Soil Pressure Increase Factor
Vertical Load Min. Safety Factor Against Reduction Factor
(Rf) Overturning Sliding
Dead 1.00 1.00 3.00 1.50 Dead +WL 1.33 1.00 1.75 1.50 Dead 1.00 1.00 3.00 1.50 Dead +WL 1.33 1.00 1.75 1.50 Dead +EQ 1.33 1.00 1.75 1.50 Dead 1.20 1.00 3.00 1.50 Dead +0.2WL 1.33 1.00 1.75 1.50 Dead +0.28EQ 1.33 1.00 1.75 1.50
16 Billboard Design and Analysis Calculation Note
10.2.5. Load combination for foundation design.
Load Combination Load Factors
Dead Dead Dead WL EQ 1.4Dead 1.40 1.2 Dead +1.3WL 1.20 1.30 0.9 Dead +1.3WL 0.90 1.30 1.2Dead +1.3WL 1.20 1.30 0.9Dead +1.3WL 0.90 1.30 1.2Dead +1.4EQ 1.20 1.40 0.9Dead +1.4EQ 0.90 1.40 1.2Dead +0.33WL 1.20 0.33 0.9Dead +0.33WL 0.90 0.33
10.2.6. Sectional properties of pedestal and foundation
10.2.7. Service Load and Eccentricity
Ap 2Dp2 tan 22.5( )⋅=
Af 2Df 2 tan 22.5( )⋅=
If Ifnn Ifmm 0.6381 0.5412Df( )4=
Load Combination Ps(KN) Vs(KN) Ms(KN.m)
Dead 623.1 Dead +WL 623.1 77.0 554.9 0.891 0.254 Dead +EQ 623.1 14.0 109.4 0.176 0.050 Dead +0.2WL 623.1 15.4 111.0 0.178 0.051 Dead +0.28EQ 623.1 3.9 30.6 0.049 0.014
e m( )MsPs
:=eDf
17 Billboard Design and Analysis Calculation Note
10.2.8. Check for soil bearing pressure and soil separation
Load Combination Qnn Qmm Qall
Knn Kmm Pss Moment due to Service Loads "Mc" (KN.m) Check
(KPa) (KPa) (KPa) Dead 61.4 61.4 400.0 0.0% 0.0% 50.0% 4.7 OK. Dead +WL 211.0 223.8 532.0 37.5% 41.4% 50.0% 85.1 OK. OP+WL 211.0 223.8 532.0 37.5% 41.4% 50.0% 85.1 OK. Dead +EQ 85.0 86.9 532.0 0.0% 0.0% 50.0% 17.9 OK. Dead +0.2WL 85.4 87.3 532.0 0.0% 0.0% 50.0% 18.1 OK. Dead +0.28EQ 68.1 68.9 532.0 0.0% 0.0% 50.0% 8.4 OK.
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10.2.9. Foundation design
Qcs hf Gc⋅ hs Gs⋅+=
Lpe Ap=
QmaxL P⋅Af
=
QminPAf
MDf2
⋅
If− K 0if
0 otherwise
=
Qm1 QmaxDf Lpe−
2Qmax Qmin−
1 K−( ) Df⋅⋅−=
Qm2 QminDf Lpe−
2K Df⋅−
⎛⎜⎝
⎞⎟⎠
Qmax Qmin−
1 K−( ) Df⋅⋅+
Df Lpe−
2K Df⋅≥if
0 otherwise
=
Qs QmaxDf Lpe−
2db−
⎛⎜⎝
⎞⎟⎠
Qmax Qmin−
1 K−( ) Df⋅⋅−=
MbuQm1
2Df Lpe−
2⎛⎜⎝
⎞⎟⎠
2⋅
Df Lpe−
2⎛⎜⎝
⎞⎟⎠
2 Qmax Qm1−
3⋅+
Qcs2
Df Lpe−
2⎛⎜⎝
⎞⎟⎠
2⋅−=
19 Billboard Design and Analysis Calculation Note
10.2.10. Section forces
Load Combination
Due to "Gravity + Lateral" Loads (1)
Due to "Gravity" Loads (2)
Due to "Lateral" Loads (3) = (1) -(2)
Msb Mst Vs vps Msb Vs vps Msb Mst Vs vps
(KN.m/m) (KN.m/m) (KN/m) KPa (KN.m/m) (KN/m) KPa (KN.m/m) (KN.m/m) (KN/m) KPa
1.4 Dead 4.71 0.00 3.27 109.57 4.71 3.27 109.57 0.00 0.00 0.00 0.00 1.2Dead+1.3WL 85.11 39.78 66.44 176.78 4.71 3.27 109.57 80.40 39.78 63.16 67.21 0.9Dead+1.3WL 85.11 39.78 66.44 176.78 4.71 3.27 109.57 80.40 39.78 63.16 67.21 1.2Dead+1.4EQ 17.95 8.28 13.49 123.59 4.71 3.27 109.57 13.24 8.28 10.21 14.02 0.9Dead+1.4EQ 17.95 8.28 13.49 123.59 4.71 3.27 109.57 13.24 8.28 10.21 14.02 1.2Dead+0.33WL 85.11 39.78 66.44 176.78 4.71 3.27 109.57 80.40 39.78 63.16 67.21 0.9Dead+0.33WL 85.11 39.78 66.44 176.78 4.71 3.27 109.57 80.40 39.78 63.16 67.21
10.2.11. Factored section forces for foundation design
Load Combination Design Load Factors Factored Design Loads (4) x (2) + (5) x (3)
Gravity Loads (4)
Lateral Loads (5)
Mub (KN.m/m)
Mut (KN.m/m) Vu (KN/m) vpu (KPa)
1.4Dead 1.40 0.00 6.6 0.0 4.6 153.4
1.2Dead+1.3WL 1.20 1.30 110.2 51.7 86.0 218.9
0.9Dead+1.3WL 0.90 1.30 108.8 51.7 85.1 186.0
1.2Dead+1.4EQ 1.20 1.40 24.2 11.6 18.2 151.1
0.9Daed+1.4EQ 0.90 1.40 22.8 11.6 17.2 118.2
1.2Dead+0.33WL 1.20 0.33 31.8 12.9 24.5 153.3
0.9Dead+0.33WL 0.90 0.33 30.4 12.9 23.5 120.5
10.2.12. Required reinforcement for 1m width of Foundation
Vu QsDf Lpe−
2db−
⎛⎜⎝
⎞⎟⎠
⋅Df Lpe−
2db−
⎛⎜⎝
⎞⎟⎠
Qmax Qs−
2⋅+ Qcs
Df Lpe−
2db−
⎛⎜⎝
⎞⎟⎠
⋅−=
MtuQmin
2Df Lpe−
2⎛⎜⎝
⎞⎟⎠
2⋅
Qm2 Qmin−
6Df Lpe−
2K Df⋅−
⎛⎜⎝
⎞⎟⎠
2⋅+
Qcs2
Df Lpe−
2⎛⎜⎝
⎞⎟⎠
2⋅−=
RnMumax
φt b⋅ d2⋅=
ρ0.85F'c
Fy1 1
2Rn0.85F'c
−−⎛⎜⎝
⎞⎟⎠
⋅=
20 Billboard Design and Analysis Calculation Note
Item Bottom Top
Mumax : Maximum factored moment at foundation section for 1.0 m width (KN.m) 110.2 51.7
c : Concrete cover to foundation rebars center (mm) 100 100
d : Effective depth of section (mm) 700 700
Rn : 250 117
ρ : 0.0006 0.0003
As : Reinforcing bar area for 1m width of foundation (mm2) : 437 205
Asmin Final Formula : 1.33·ρ·b·d 1.33·ρ·b·d
Asmin : Minimum reinforcing bar area for 1m width of foundation (mm2) : 582 273
Asreq : Required reinforcing bar area for 1m width of foundation (mm2) : 582 273
db : Bar diameter (mm) 18 12
Ase : Existing area of rebars for 1.0 m width of foundation (mm2) : 1272 565
ρe : Existing steel ratio of foundation 0.0018 0.0008
Use : Ф18 @ 200 Ф12 @ 200
10.2.13. Check reinforcing bar spacing to control cracking
st = 200 mm ≤ smax = 450
sb = 200 mm ≤ smax = 450
10.2.14. Check beam shear
Vumax = 86.0 KN ≤ φs·Vc = 1411 KN OK.
K 2 ρ e n⋅ ρ e n⋅( )2+ ρ e n⋅−=
J 1K3
−=
fsmaxMcmax
Ase J⋅ d⋅=
cmax c 0.5db−=
smax min 380280
fsmax
⎛⎜⎝
⎞⎟⎠
⋅ 2.5 cmax⋅− 3hf, 450,⎡⎢⎣
⎤⎥⎦
=
φs Vc⋅ φs 0.17⋅ F'c b⋅ d⋅=
21 Billboard Design and Analysis Calculation Note
10.2.15. Check punching Shear
Vc1 = 40465.8
Vc2 = 38893.2
Qp1 QmaxDf Lpe−
2db2
−⎛⎜⎝
⎞⎟⎠
Qmax Qmin−
1 K−( ) Df⋅⋅−=
Qp2 QmaxDf Lpe−
2Lpe+
db2
+⎛⎜⎝
⎞⎟⎠
Qmax Qmin−
1 K−( ) Df⋅⋅−=
bo 4 Lpe db+( )⋅=
Ac bo db⋅=
γf1
123
Lpe db+
Lpe db+⋅+
=
γv 1 γf−=
Jcdb Lpe db+( )3⋅
6db3 Lpe db+( )⋅
6+
db Lpe db+( )3⋅
2+=
vpP R−
Ac
γv M⋅Lpe db+
2⋅
Jc+=
β 1=
Vc1 0.17 12β
+⎛⎜⎝
⎞⎟⎠
⋅ F'c⋅ bo⋅ d⋅=
Vc2 0.083αs db⋅
bo2+
⎛⎜⎝
⎞⎟⎠
⋅ F'c⋅ bo⋅ d⋅=
Vc3 0.33 F'c⋅ bo⋅ d⋅=
φs Vc⋅ φs min Vc1 Vc2, Vc3,( )⋅=
22 Billboard Design and Analysis Calculation Note
vpumax = 218.9 KPa ≤ φs·vc = 5812.8 KPa OK.
10.3. Base plate and anchor bolt design
2
5.35.47 .
7.7
( ) 3700
35.47 6.225.7
u
P TonM Ton mV Ton
KgF Anchorbolt cmMe mP
==
=
=
= = =
In order to determined base plate as initial assumption, considering following dimension and anchor bolt.
( )
3 21 2 3
1
2
3 2
3 2
0803 ( ) 3 (622 ) 17462 2
6 6 10 69.27( ) (32.5 622) 34002.9180
( ) 34002.91 40 32.5 2465211.062
1746 34002.91 2465211.06 0After Solving The Equation : 28.
s
x k x k x kHk e
nAk g eB
Hk k g
x x xx
+ + + =
= × − = × − =
× ×= + = × + =
= − × + = − × + = −
+ + − == 9cm
Calculating maximum stress between foundation and base plate.
φs vc⋅ φsVc
bo d⋅=
2anchorboltusing 5 42 as Anchorbolt A 69.27
assumed Baseplate dimension 80cm 80cm 35.47 6225.7
801032.580
cm
Me cmPh cmngB cm
φ ⇒ =×
= = =
====
23 Billboard Design and Analysis Calculation Note
22 ( ) 2 5700 (622 32.5) 7461300 51.33
80 28.9 145355.44( ) 28.9 80 32.52 3 2 3
pP e g Kgf H x cmxB g
+ × × += = = =
⎛ ⎞+ − × × + −⎜ ⎟⎝ ⎠
Anchor bolt tensile Force (T)
28.9 80622 33723103 2 3 2 5700 53.6480 28.9 62.7832.52 3 2 3
x BeT P TonB xg
+ − + −= × = × = =
+ − + −
Allowable compression stress
/ /2
1
2 /2 2 2 2
2 2
0.35 0.7
5500.35 250 601.56 0.7 175 17580
51.33 175
p c c
p c p
p p
AF f fA
Kg Kg KgF f Fcm cm cmKg Kg f F Okcm cm
= ≤
= × × = ≥ = ⇒ =
≤ ⇒ ≤
Anchor Bolt Tensile stress
2
2
53639 774.3669.27
7700 55.582 2 69.27
ts
vs
T Kgf cmAV Kgf cmA
= = =
= = =×
2
2 2
p
0.43 1.8 0.33
0.43 4000 1.8 55.58 1609.71 0.33 1320 1320
774.36 1320
80 50 152
51.332 2 15 4.39 with using Stiffener t =3.5cm 2400
t u v u
t u t
t t t t
pp
v
F F f FKgF F F cm
Kg Kgf F f F Okcm cm
n m cm
ft n cm
F
= − ≤
= × − × = ≥ = ⇒ =
= ≤ = ⇒ ≤
−⎛ ⎞= = =⎜ ⎟⎝ ⎠
= = × × = ⇒ ⇒
24 Billboard Design and Analysis Calculation Note