Design the stand of a gas station price board that is 42 in

Design the stand of a gas station price board that is 4×2 in size and has a mass of 600kg. The board should be installed at a height of 20m.
Need to consider about
1.Buckling
2.Fatigue
3.Bending Stress
4.Torsional Stress
5.Axial stress

Solution

solution:

we will support price board on single circular column of diametr d mm and designa s follows

1)here it is found that compressive stresses are lesser than bending stresses in heavy wind condition hence we choose material,which is ductile and that is alloy steel and it has properties as follows

Sut=1882 MPa

Syt=758 MPa

endurance strength=Se=.5*Sut=941 MPa

modulus of elasticity=E=210 GPa

2)here design for bending stresses as follows

wind speed for V=100 km/hr or 27.77 m/s

air density=1.22

hence pressure

on board is=P2=Patm+V^2*.5density=1.01325*10^5+(27.77^2*.5*1.22)

P2=1.0179*10^5 N/m2

hence force on board,A=4*2=8 m2

F=P2*A=814365.4321 N

bending moment =M=F*l=F*20000=16287308.64*10^3 N mm

where bending stresses is givenby

Sb=32*M/pi*d^3=165901163.5*10^3/d^3

here for Sb=Syt=758 MPa

we get d=602.64 mm

2)here compressive stress on column

Sc=W/A=600*9.81*4/pi*602.64^2=.02063 MPa

3)as both side of price board will be subjected wind presusre hence there will no torsion about y axis and if occure it posses certain shear stress t==16T/pi*d^3=.5Syt=379 MPa

4)here for fatigue design due to wind load

resulatnt stress=Sr=(Sc^2-Sc*Sb+Sb^2)^.5=757.98 MPa

and for infinite life

Se=941 MPa

here factor safety=Nf=Se/Sr=1.24 hence design safe against fatigue loading

5)buckling load is given by

Pe=euler load=Pe=.25*pi^2*E*pi*d^4/16*L^2=33547.546 KN

compressive load=Pc=Syt*A=216209611.2 N

hence rankine load=(1/Pcr)=(1/Pe)+(1/Pc)

Pcr=29041.41 KN

as our load W=600*9.81=5886 N

as Pc>W,hence it is safe against buckling too.