Ponding9 --- Aisc 9th Ed. Ponding Analysis Program
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"PONDING9" --- AISC 9th ED. PONDING ANALYSIS PROGRAM Program Description: "PONDING9" is a spreadsheet program written in MS-Excel for the purpose of analysis for pond or flat roof systems in structural steel per the AISC 9th Edition (ASD) Code, pages 5-83 to Specifically, simplified checks are performed for the steel members as well as the steel dec whether actually required or not, is also performed for the steel members. This program is a workbook consisting of two (2) worksheets, described as follows: Worksheet Name Description Doc This documentation sheet Ponding Ponding analysis per AISC 9th Edition (ASD) Manual Program Assumptions and Limitations: 1. This program utilizes the equations in AISC Code Sect. K2 to perform a simplified check secondary members, as well as the steel roof deck. 2. This program also performs a rigorous analysis on the primary and secondary members util in AISC Code Commentary Sect. C-K2. 3. This program contains numerous “comment boxes” which contain a wide variety of informati explanations of input or output items, equations used, data tables, etc. (Note: prese is denoted by a “red triangle” in the upper right-hand corner of a cell. Merely move t desired cell to view the contents of that particular "comment box".)
Conclusion: Roof Members are O.K.Roof Deck is O.K.
as =
Dw = ap*Do*(1+p/4*as+p/4*r*(1+as))/(1-p/4*ap*as) (Eq. C-K2-1)where: ap = Cp/(1-Cp) , as = Cs/(1-Cs) , r = do/Do = Cs/Cp
Up = Dw/Do = (0.80*Fy-fo)/fo (Eq. C-K2-4)use: Cs =
as =
dw = as*do*(1+p^3/32*ap+p^2/(8*r)*(1+ap)+0.185*as*ap)/(1-p/4*ap*as) (Eq. C-K2-2)where: ap = Cp/(1-Cp) , as = Cs/(1-Cs) , r = do/Do = Cs/Cp
Us = dw/do = (0.80*Fy-fo)/fo (Eq. C-K2-5)
ap =
A7
Low slope roofs are generally considered as roofs with a slope less than 1/4" per foot.
D11
Note: If roof decking is the secondary system, directly supported by the primary members (i.e., no secondary beams, joists, etc. ), it should be handled with Eq. K2-1 using a spacing, S = 1.0 ft.
D12
If primary members are joist girders, their moment of inertia (Ip) may be approximately calculated by the following: Ip = 0.027*N*P*L*d (in.^4) where: N = number of panels in joist girder P = concentrated (point) load at panel points (kips) L = joist girder span (ft.) d = joist girder depth (in.) Reference: SMI Joist Catalog (per Steel Joist Institute)
D13
If secondary members are joists, their moment of inertia (Is) may be approximately calculated by the following: Is = 26.767*(WLL)*L^3*10^(-6) (in.^4) where: WLL = allowable distributed live load/ft. of joist for a deflection of 1/360 of the span (WLL = "red" figures in joist load tables) L = clear span of joist + 0.67 (ft.) Reference: SMI Joist Catalog (per Steel Joist Institute) Note: If steel joists are used as secondary members, this program automatically reduces the 'Is' value input by 15% per AISC Code.
D14
Note: If steel joists are used as secondary members, this program automatically reduces the 'Is' value input by 15% per AISC Code.
D15
Moment of Inertia (Id) for Commonly Used Steel Roof Deck For 1-1/2" Deep For 1-1/2" Deep For 1-1/2" Deep Type "B" (wide rib) Deck Type "F" (intermediate rib) Deck Type "A" (narrow rib) Deck Gage Id (in.^4/ft.) Gage Id (in.^4/ft.) Gage Id (in.^4/ft.) 24 0.121 --- ------- --- ------- 22 0.169 22 0.121 22 0.112 21 0.192 21 0.137 21 0.127 20 0.212 20 0.151 20 0.140 19 0.253 19 0.180 19 0.167 18 0.292 18 0.207 18 0.192 16 0.373 --- ------- --- ------- Note: Above information is taken from Vulcraft Corporation Steel Deck Catalog.
D16
Steel Yield Stress, 'Fy', applies to both primary and secondary members.
D17
Primary member stress, 'fo', is the bending stress in the primary member due to the supported loading, neglecting ponding.
D18
Secondary member stress, 'fo', is the bending stress in the secondary member due to the supported loading, neglecting ponding.
G21
The roof system shall be considered stable and not require further investigation if the following two conditional checks are BOTH met.
F22
Eq. K2-1 results in an approximate "stress index" during ponding, and is limited to a maximum value of 0.25 in the check. To illustrate the concept of "stress index", if the stress in a member increases from 0.60*Fy to 0.80*Fy, the stress index, 'U', is: U = (0.80*Fy-0.60*Fy)/(0.60*Fy) = 0.33
D23
'Cp' is the Flexibility Constant for primary members.
D24
'Cs' is the Flexibility Constant for secondary members.
D36
The Stress Index for primary members, 'Up', is calculated as follows: Up = (0.80*Fy-fo)/fo (Eq. C-K2-4) where: Fy = steel yield stress (ksi) fo = stress in primary member prior to ponding (ksi) Note: The total bending stress due to dead loads, gravity live loads (if any) and ponding shall not exceed 0.80*Fy for primary and secondary members. This results is a Safety Factor = 1.25. Stresses due to wind or seismic forces need not be included in a ponding analysis.
D39
The Primary Member Flexibility Constant, 'Cp', is calculated from Eq. C-K2-1 as follows: Dw = ap*Do*(1+p/4*as+p/4*r*(1+as))/(1-p/4*ap*as) where: Dw = ponding deflection for primary members (in.) Do = primary member deflection prior to ponding (in.) ap = Cp/(1-Cp) as = Cs/(1-Cs) r = Cs/Cp = do/Do Therefore, substituting in the following known values: Up = Dw/Do = (0.80*Fy-fo)/fo Cs = 32*S*Ls^4/(10^7*Is) , and thus 'as' and 'r ' and inserting 'as' in terms of 'Cs', the value of 'Cp' is solved for. Note: The results of Eq. C-K2-1 are depicted graphically in AISC Fig. C-K2-1 on page 5-178.
F39
To prevent against ponding, the Flexiblity Constant, 'Cp', calculated from Eq. C-K2-1 should be more than the value of 'Cp' calculated for the given primary member from the simplified check; if not, a stiffer primary or secondary beam, or combination of both is required.
D44
The Stress Index for secondary members, 'Us', is calculated as follows: Us = (0.80*Fy-fo)/fo (Eq. C-K2-5) where: Fy = steel yield stress (ksi) fo = stress in secondary member prior to ponding (ksi) Note: The total bending stress due to dead loads, gravity live loads (if any) and ponding shall not exceed 0.80*Fy for primary and secondary members. This results is a Safety Factor = 1.25. Stresses due to wind or seismic forces need not be included in a ponding analysis.
D47
The Secondary Member Flexibility Constant, 'Cs', is calculated from Eq. C-K2-2 as follows: dw = as*do*(1+p^3/32*ap+p^2/(8*r)*(1+ap)+0.185*as*ap)/(1-p/4*ap*as) where: dw = ponding deflection for secondary members (in.) do = secondary member deflection prior to ponding (in.) ap = Cp/(1-Cp) as = Cs/(1-Cs) r = Cs/Cp = do/Do Therefore, substituting in the following known values: Us = dw/do = (0.80*Fy-fo)/fo Cp = 32*Ls*Lp^4/(10^7*Ip) , and thus 'ap' and 'r ' and inserting 'ap' in terms of 'Cp', the value of 'Cs' is solved for. Note: The results of Eq. C-K2-2 are depicted graphically in AISC Fig. C-K2-2 on page 5-179.
F47
To prevent against ponding, the Flexiblity Constant, 'Cs', calculated from Eq. C-K2-2 should be more than the value of 'Cs' calculated for the given secondary member from the simplified check; if not, a stiffer secondary or primary beam, or combination of both is required.
