Led display base date：

Led display size：2560mm(8.54ft)*1280mm(4.26ft)

Led display with cabinet size：L 2560mm(8.54ft)*W 1280mm(4.26ft)* D 400mm(1.34ft)

Pillar size：(D)120mm*(T)5mm*(L)1780mm  to Inch: (D)4.73 inch*(T)0.2inch*(L)1495mm70inch

Basic plate size：L 400mm*W 400mm*T 20mm

Ground cage：Ｌ400mm* W 400mm * D 1300mm,Ground size：1200mm*1200mm*1600mm

Permanent load：

Led display weight：mg=280*9.8=2744(N)

Pillar weight：7.8*3.14*(6*6-5.5*5.5).178*9.8/1000=245(N)

Total weight：（Take permanent load calculation coefficient 1.20）

Ｇ＝1.2*（2744+245）＝3587（Ｎ）

Wind load：

Typhoon category 15，V=50.9meter/s，

Gust factor  βz=1.0　　(Reference:Total heigth≤20meter)

Wind load shape coefficient  Us=1.6　　Reference『建筑结构荷载规范 GB50009-2012』

Height variation factor of wind pressure   Uz=0.88　led display height(m) ≤10m

Windward area：Af  unite㎡

Ｗo= Wp(Basic wind pressure)

由　Ｗp=V/1600 ==> Wo=50.9*50.9/1600=1.62 KN/㎡

Led display Standard value of wind load：　Ｗk1=βz*Us*Uz*Wo*Af=1*1.6*0.88*1.62*2.56*1.28＝7.48 KN

Pillar Standard value of wind load：　      Ｗk2=βz*Us*Uz*Wo*Af=1*1.6*0.88*1.62*0.12*1.78＝0.49 KN

Strength checking：

Pillar external diameter 120mm,thickness 5mm,Ａ＝1.8*10^-3(㎡),

area moment of inertia：I＝7.22*10^-6（m⁴）

Section bending modulus：W=9.967*10^-5 (m³)

Bending moment at column root caused by wind load：

Ｍ＝Ｗk1*Hb+Ｗk2*Hp=7.48*2.24+0.49*0.8＝17.16KN*m)

Shear force at column root caused by wind load：

F=Wk1+Wk2=7.48+0.49=7.97(KN)

Checking calculation of maximum direct stress

Pillar material:Q235, maximum tension：235MPa, Maximum shear force :117.5Mpa

Maximum stress at column root caused by wind load：

σmax=M/W=17.16*10^3/9.967*10^-５=172(MPa)<( σd,235 MPa)

Checking calculation of maximum shear force

Maximum shear force at column root caused by wind load：

Ｔmax＝2*F/A=2*7.97/1.8*10^3=8.86Mpa<(Td,117.5Mpa)

Stress checking calculation of dangerous points

For the section of cylindrical column, the normal stress and shear stress are large at the intersection of the straight line whose center is 45 degrees from the x-x axis and the section centerline, and the complex stress state. The stress state analysis should be carried out at this point

Location of dangerous points：X=y=(D-0.05)/2*sin(兀/4)=0.0408(M)

Sx（Static moment of dangerous point section of column）＝1.948*10^ -5

direct stress at dangerous point：σ=My/I=17.16*0.0408/7.22*10^-６=96.97(Mpa)

Shear force at dangerous point:　T=F*Sx/(I*2*t)=7970*1.948*10^-5/(7.22*10^-６*2*5)=2.15(Mpa)

According to the fourth strength theory：

σ4＝（σ²+3*Ｔ²）^1/2＝（96.97²+3*2.15²）^1/2 =97Mpa(σd,235 MPa)，fulfill a request．

Checking calculation of pillar deformation

This sign includes a display screen. The wind load on it is regarded as the concentrated load acting on the geometric centroid, and the wind load on the column clamped between the display screen and the foundation is regarded as the uniformly distributed load．

Deflection due to concentrated load：

Fb=[P*H²/(6*E*I)]*(3*L-H)＝5342.9*2.24² /(6*206*10⁹*7.22*10^-6)*(3*1.6-2.24)=0.0077(m)

Deflection due to uniformly distributed load：

F1=q*h⁴/(8*E*I)=(1/2*ρ* c*V²）*W*1.6⁴/(8*206*10⁹*7.22*10^-6)=0.0001(m)

Corner caused by uniformly distributed load：

Θ＝q*h³/(6*E*I)= (1/2*ρ* c*V²）*W*1.5³/(6*206*10⁹*7.22*10^-6)= 0.0000729°

To sum up, the total deformation deflection at the top of the column is calculated：

F=Fb+F1+tanΘ(Lp-h)=0.0077+0.0001+tan(0.0000721)*(2.88-1.6) ≈0.0078m

F/L=0.0055/2.88=0.0019<0.01, fulfill a request．

Checking calculation of column base strength

External load on column base：

Vertical force：　Ｇ＝Ｙ⁰*Y^Ｇ*Ｇ＝1.0*1.0*3587＝3587（Ｎ）

Horizontal force：　Ｆ＝7.97(KN)

Bending moment caused by wind load：Ｍ＝17.16(KN*m)

eccentric distance：　　 e=M/G=17160/3587=4.784(m)

Base plate geometry：L 400mm*W 400mm*T 20mm

The anchor bolt is proposed to adopt 8M22 specification, the number of anchor bolts on the tension side is n = 3, and the total effective area is:：

Ae=3*3.03=9.09(Cm²)=9.09*10^-4(m²)

length of pressure Xn:It is solved by trial calculation according to the following formula：

(Ｘn)³+3*(e-L/2)*(Xn)²-[6*n*Ae*(e+L/2-Lt)*(L-Lt-Xn)]/W=0

(Ｘn)³+13.752*(Xn)²-2030.5*10^-4* (0.038-Xn)=0

(Ｘn)³+13.752*(Xn)²+0.2(Xn)-0.077=0

Ｘn=0.068(m)

Maximum compressive stress of concrete：

σ_C=2*G(e+L/2-Lt)/[B*Xn*(L-Lt-Xn/3)]

  =2*3587*(4.784+0.4/2-0.02)/[0.4*0.068*(0.4-0.02-0.068/3)]

 ≈3.67(Mpa)< Fcc*βc=[(1.2*1.2)/(0.4*0.4)] ^^0.5*9.6=28.8(Mpa)，，fulfill a request．

Checking calculation of anchor bolt strength：

T_a=G*(e-L/2+Xn/3)/ (L-tt-Xn/3)

  =3587*(4.784-0.4/2+0.068/3)/(0.4-0.02-0.068/3)

   ≈46.3(KN)<n.T₀ =3*55.2=165.6(KN),, fulfill a request．

Verification of horizontal shear force：

Ｖ_fb=K*(G+ T_a) =0.4*(3.587+46.3)=19.95(KN)>17.16KN (Shear force at pillar root caused by wind load)

Checking pill of pillar Basic plate thickness：

The influence coefficient of concrete strength is that the number of flange ribs is 4, and the support conditions of flange on the compression side are considered as two adjacent support plates．

Ｍ＝α*σ_C*(a2) ²=0.089*3670000*0.12*0.12=4703N*m/m)

Basic plate thickness：

t=(6*Mamx/fb1) ^^0.5=(6*4703/210*10⁶) ^^0.5＝0.014(m)=11.6mm<20mm,fulfill a request．

Tension side Basic plate thickness：

T1=｛6*Ma*D(basic)/[ (D(bolt)+sin45*D(basic)+ D(basic)*210*10⁶]) ^^0.5=8.9mm<20mm，fulfill a request．

Foundation checking calculation

The thickness of thebasic plate at the tension side shall be set as the foundation:

Ｗf=1.5m,Ｈf=1.6m,Ｌf=1.5m,

Weight of foundation concrete:r=24KN/m³

Base allowable stress:fa=100KPa.

Load on base

The total vertical load：Ｎ＝Ｇ+rV=3.587+24*(1.5*1.5*1.6)=90(KN)

horizontal load: Ｈ＝7.97(KN)

Bending moment caused by wind load：

M=Ｗk1*(h1+Hf)+Wk2*(h2+Hf)=7.48 *(2.28+1.6)+0.49*(1.6+1.6)=30.57(KN.m)

Stress checking calculation of base

Average base stress calculated under axial compression：

Ｐk=N/A=90/[(1.5)*(1.5)]=40 (Kpa)<fa=100(KPa), fulfill a request．

Maximum base stress:

σmax=N/A+M/W=90/1.5*1.5+30.57/(1/6*1.5*（1.5)²) =94.35(KPa)<1.2fa=120(KPa), fulfill a request．

Minimum base stress:

σmin=N/A-M/W=90/(1.5*1.5)-29/ [1/6*1.5*(1.5)²])=-14.35KPa)

The base appears in negative stress, and the distribution width of negative stress：

Lx＝IσminI*Lf/(IσminI+:σamx)=14.35*1.5/（14.35+94.35）＝0.198 Standard value Lf/4＝0.3．

Checking calculation of anti overturning stability of basement：

K0=Lf/(2*e)=1.5/(2*e)=2.2 ＞ Greater thans tandard value 1.10

Base sliding stability coefficient：

Kc=n*N/F＝0.3*90/7.97=3.38＞Greater than standard value 1.20