Comparing LRFD & ASD Results

Comparing LRFD & ASD Results Last Revised: 11/04/2014

LRFD and ASD loads are not directly comparable because they are used dierently dierently by the desi!n desi!n codes" LRFD loads are are !enerally !enerally compared to member or component S#R$%&#' (hereas ASD loads are compared to member or component allo(able values that are less than the )ull stren!th stren!th o) the member or or component" *n order to to determine (hich desi!n philosophy is more or less demandin! +i"e" results in lar!er members,members,- it is necessary to .un)actor. the load combinations usin! the material specic stren!th and allo(able stress reuirements" Also- there are times (hen you (ill no( the capacity o) a member relative to a limit state and (ant to no( (hat actual loads you can put on it" *n order to accomplish this tas you need to .turn around. around. the load combination euations and compute D- L- etc" #o accomplish this tas- you (ill need to no( the relative ma!nitudes o) the service load +i"e" actual applied ma!nitudes, ma!nitudes, components" #his tends to !et !et etraordinarily etraordinarily di3cult di3cult i) your member member has multiple load sources +i"e" a uni)orm load- a point load- etc",ho(ever i) you have a sin!le load source the tas is mana!eable" mana!eable" #his tet uses uses a service level level euivalent loadload- s-euiv +or s-e,- )or comparison o) LRFD LRFD and ASD loads" loads" #he euivalent euivalent service load is is taen to be the sum o) all service level load components etracted )rom a particular load combination euation" euation" #he net net section illustrates this concept usin! the reuirements o) the 15th edition o) the A*S6 Steel 6onstruction 7anual"

Converting Load Combinations to a Comparable Equivalent Load #he typical stren!th stren!th based limit state statement statement taes taes the )orm: )orm: LRFD

ASD

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u 8 φn

a 8 n/ Ω

9here u and a are values o) desi!n loads that have been computed usin! the load combination euations and the terms on the ri!ht side o) each euation represent represent the capacity o) the member" For eampleeample- let us assume that (e no( the aial )orce capacity o) a tension member and that the applied dead load euals the live load and the seismic seismic load is t(ice the dead dead load" *n other (ords(ords- the load consists o) one part dead load- one part live load- and t(o parts seismic load For this situation- (e introduce the uantity s-euiv (hich is the sum o) the service level level load components" components" For our our eample: eample: s-euiv  D ; L ; $ 9here • D  1/4  s-euiv  0"2< s-euiv • L  1/4  s-euiv  0"2< s-euiv • $  2/4 s-euiv  0"<0 s-euiv

#he uantities u and a can be related to s-euiv by a composite load factor (CLF) that is derived )rom the load combination euations and the relative values o) the individual load components" LRFD

ASD

u  6LFLRFD=s-euiv

a  6LFASD=s-euiv

#he composite load )actor is then then computed )or each each load case" #he lar!est 6LF (ill be )rom the controllin! load case"





2" u  1"2+0"2<  s-euiv, ; 1">+0"2<  s-euiv, 0"?0  s-euiv 5" u  1"2+0"2<  s-euiv, ; 0"<+0"2<  s-euiv, 0"42< s-euiv 4" u  1"2+0"2<  s-euiv, ; 0"<+0"2<  s-euiv, 0"42< s-euiv <" u  1"2+0"2<  s-euiv, ; 1"0+0"<0  s-euiv, ; 0"<+0"2<  s-euiv, 0"@2< s-euiv >" u  0"@+0"2<  s-euiv, ; 1"0+0"<0  s-euiv, 0"?2< s-euiv #he controllin! controllin! 6LFLRFD in this case is )rom LRFD L6< and is 0"@2<" 9ith the 6LFLRFD (e can no( nd the allo(able ma!nitudes o) D- Land $" 7aimum u  0"@2<  s-euiv 8 φn s-euiv 8 +φn,/0"@2< From this (e can compute the service level ma!nitudes )or D- L- and $- by substitutin! +φn,/0"@2




?" a  0">0+0"2<  s-euiv,  0">0 s-euiv C" a  0">0+0"2<  s-euiv, ; 0"?0+0"<0  s-euiv,  0"<0  s-euiv

#he controllin! controllin! 6LFASD in this case is )rom ASD L6> and is 0"?0" 9ith the 6LFASD (e can no( nd the allo(able ma!nitudes o) D- L- and $" 0"?0 s-euiv 8 n/ Ω s-euiv 8 +n/ Ω,/0"?0 From this (e can compute the service level ma!nitudes )or D- L- and $: D 8 0"2< +n/ Ω,/0"?0 L 8 0"2< + n/ Ω,/0"?0 $ 8 0"<0 + n/ Ω,/0"?0 #he controllin! controllin! composite load )actor- 6LFASD- can be easily computed usin! the same spreadsheet spreadsheet you (ould use )or computin! all the load combinations simply by puttin! in the th e coe3cients )or the various load types in a sin!le load source column"

Comparing ASD vs LRFD Loads 6onsider a steel tension member that has a nominal aial capacityn- and is subected subected to a combination combination o) dead and live loads" 9e (ill use φ  0"@ and Ω  1">? )or no(" #he LRFD and ASD )actored )actored loads are are not directly directly comparable comparable as the combination euations euations use dierent dierent load )actors )actors in each case" 9e can compare them at service levels by computin! an euivalent service load )rom each combination"





ASD

#he controllin! controllin! ASD load combination combination euation euation in this case is ASDE ASDE L62: a  1"0=D ;1"0=L  1"0=+D;L,  1"0= s-euiv 9e can no( determine the euivalent total load allo(ed by ASD by usin! the desi!n ineuality: s-euiv 8 n/Ω s-euiv 8 n/1">?  0">0  n

!s"equiv # !n $ %%

LRFD

#he controllin! controllin! LRFD load combination euation euation in this case is LRFDE LRFDE L62: u  1"2D ;1">L 9e mae the )ollo(in! denitions: D  +G,s-euiv L  +1EG,s-euiv 9here  is the percenta!e o)  s-euiv that is dead dead load" Substitutin! these denitions into the load combination euation you !et: u  1"2+, s-euiv;1">+1E,s-euiv  1"> E 0"4Bs-euiv





Similar .composite load )actors. can be developed )or other load combination euations" Substitutin! the above epression epression into the LRFD version o) the desi!n ineuality- (e !et u 8 φn 1"> E 0"4B s-euiv 8 φn s-euiv 8 φn / 1"> E 0"4B s-euiv 8 0"@0 n / 1"> E 0"4B

!s"equiv # !n $ %'% #  * %+,-

6omparison 9e can no( compare the results by !raphin! the resultin! euations )or s-euiv/ n" Fi!ure 2"5"1 sho(s the compared load limits based on percenta!e dead load" From Fi!ure 2"5"1 you can see that- )or this case- (henever the total service load is 2






%ote that the use o) other load combination euations (ill yield dierent results"

Figure ./ Comparison of LRFD & ASD Results

Comparing LRFD & ASD Results

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