calculation note rev1

1 Billboard Design and Analysis Calculation Note

Calculation Notes for Billboard Foundation and Steel Structure


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


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


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


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

==


6.1.2 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.


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. 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. 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.


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.


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.


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.


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.


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


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


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


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.


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⋅−=


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

−−⎛⎜⎝

⎞⎟⎠

⋅=


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⋅=


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,( )⋅=


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 ⇒ =×

= = =

====


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

= − ≤

= × − × = ≥ = ⇒ =

= ≤ = ⇒ ≤

−⎛ ⎞= = =⎜ ⎟⎝ ⎠

= = × × = ⇒ ⇒

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