Performance Ratios

 

Allowable Stress Design (ASD) performance ratios represent service stress over allowable stress.

 

Load Factor Design (LFD) and Load and Resistance factor Design (LRFD) performance ratios for flexure are obtained by a comparison of factored strengths with factored loads.  It is shown below that the elastic factored strength of a given cross section is given by the expression:

 

             S = F x SG x (DM1+DM2+LM)/(DM1+DM2xSG/SC3+LMxSG/SC)

 

             where:

 

             S                            = factored bending strength

             F                            = allowable stress (factored for LFD and LRFD)

             DM1                       = factored bending moment from noncomposite dead load

             DM2                       = factored bending moment from composite dead load

             LM                          = factored live load bending moment

             SG                         = section modulus of steel shape only

             SC                          = short term section modulus of composite shape

             SC3                        = long term section modulus of composite shape

 

Factored strengths for bending are checked at the top of the slab (if in a composite region), top flange, and bottom flange.  The strength check also includes the rebars, if the option to use rebars compositely in negative moment regions is selected.  The governing value is reported in the strength table comparing factored strength to factor loads.

 

Derivation of Strength Expression:

 

         S   = DM1 + DM2 + LM

 

             = F/F(DM1 + DM2 + LM)

 

 

Since F = (DM1/SG) + (DM2/SC3) + (LM/SC),

 

          S  = F (DM1 + DM2 + LM) / [(DM1/SG) + (DM2/SC3) + (LM/SC)]

 

             = F SG (DM1 + DM2 + LM) / [(DM1) + (DM2)(SG/SC3) + (LM)(SG/SC)]