Those flat roof which face a problem of water accumulation require stability analysis under ponding conditions. For checking the stability we need to see the following equations, if both of these are fulfilled
Cp+0.9Cs<= 0.25
Id>=25S4/106
Where
C p= 32 Ls L4p/107Ip
Cs=32Ls4/107Is
Lp= Length of primarymember or girder in ft (m)
Ls= Length of secondary member or purlin ft (m)
S= Spacing of secondary members ft (m)
Ip= Moment of inertia of primary member in in4 mm4
Is= Moment of inertia of secondary member in in4 mm4
I d= Moment of inertia of steel deck supported on secondary members, in4/ft (mm4/m)
Id>=25S4/106
Where
C p= 32 Ls L4p/107Ip
Cs=32Ls4/107Is
Lp= Length of primarymember or girder in ft (m)
Ls= Length of secondary member or purlin ft (m)
S= Spacing of secondary members ft (m)
Ip= Moment of inertia of primary member in in4 mm4
Is= Moment of inertia of secondary member in in4 mm4
I d= Moment of inertia of steel deck supported on secondary members, in4/ft (mm4/m)
It should be noted that Is should be decreased by 15% for trusses and other open-web members. Also the value of the total bending stress due to ponding , dead loads and live loads should not exceed 0.80Fy(the minimum specified yield stress for the steel)
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