Strength 1 Limit State

1. Flexural Strength (These calculations are for midspan section)
   $RF=\frac{{\phi }_c{\phi }_s\phi R_n-{\gamma }_{DC}DC-{\gamma }_{DW}DW}{{\gamma }_{LL}(LL+I)}$
   Where:

   • Evaluation factors

     Evaluation Factors
     Resistance Factor	Ψ	Flexure	1.0
     		Shear	0.9
     Condition Factor	Ψ	1.0 - no deterioration
     System Factor	Ψ	1.0

   • ΨM_n is already computed in Precast/Prestressed Girder in the Ultimate Moment report,

     (M_u-prvd) = 6245.2 k. ft and Ψ= 1.0 for flexural members

   • Ψ_DC, Ψ_DW, Ψ_LL+IM are given in the following table:

     Load	Inventory	Operating
     ΨDC	1.25	1.25
     ΨDW	1.50	1.50
     ΨLL+IM	1.75	1.35

   • Dead Load (DC and DW)

     The dead load values can be selected from File > Print Shear/Moment Envelope for Service I. In the following table we list the dead load moment values at midspan location.

     Dead loads (k.ft) at midspan
     DC	Self-Weight	657.5
     	Deck & Haunch	739.2
     	Diaphragms	120.0
     	Concrete Barriers (Comp DC)	200.0
     	TOTAL	1716.7
     DW	Future Wearing Surface (Comp DW)	162.0

   • Live Load

     We obtain the live load moment value (with impact and distribution factor) from Precast/Prestressed Girder output.

     Live Loads (k.ft) at midspan
     LL + I	1486.0

     By introducing the above data in the general load-rating equation:

     For Inventory Level:

     ${RF}_{INV}=\frac{{\phi }_c{\phi }_s\phi R_n-{\gamma }_{DC}DC-{\gamma }_{DW}DW}{{\gamma }_{LL}(LL+I)}=\frac{1\times 1\times 1\times 6245.2-1.25\times 1716.7-1.5\times 162.0}{1.75\times 1486.0}=1.48$

     For Operating Level:

     ${RF}_{OP}=\frac{{\phi }_c{\phi }_s\phi M_n-{\gamma }_{DC}DC-{\gamma }_{DW}DW}{{\gamma }_{LL}(LL+I)}=\frac{1\times 1\times 1\times 6245.2-1.25\times 1716.7-1.5\times 162.0}{1.35\times 1486.0}=1.92$

2. Shear Strength

   These calculations are for the critical section near left support.

   $RF=\frac{{\phi }_c{\phi }_s\phi V_n-{\gamma }_{DC}DC-{\gamma }_{DW}DW}{{\gamma }_{LL}(LL+I)}$
   • Evaluation Factors

     Evaluation Factors
     Resistance Factor	ϕ	Flexure	1.0
     		Shear	0.9
     Condition Factor	ϕ	1.0 - no deterioration
     System Factor	ϕ	1.0

   • ϕV_n

     For critical location, we use 2 legs US#4(M13) @ 9in:

     $V_{s-provid}=\frac{A_v\times f_y\times d_v\times \cot \theta }{s}=\frac{0.400\times 60\times 58.7\times \cot 22.4}{9}=379.77kft$

     V_p= 0 kft

     V_c-com= – 99.8 kft

     $\mathrm{\Phi }{V}_n=0.9\times (V_{s-provd}+V_p+V_{c-com})=0.9\times (279.77+0+99.8)=431.6kft$
   • ϕDC, ϕDW, ϕLL+I are given in the following table:

     Load	Inventory	Operating
     ϕDC	1.25	1.25
     ϕDW	1.50	1.50
     ϕLL+I	1.75	1.35

   • Dead Load (DC and DW) Shears

     These values are obtained from File > Print Shear/Moment Envelope. The values for shear at critical section were obtained by linear interpolation of the values from Bearing and 0.1L

     location. Please notice that the critical location differs for each truck -- for Design Truck the critical location is 6.35 feet. In the following table, we list the Dead Load shear values at critical location.

     Dead loads (k.ft) at midspan
     DC	Self-Weight	28.09
     	Deck & Haunch	31.58
     	Diaphragms	3.0
     	Concrete Barriers (Comp DC)	8.55
     	TOTAL	71.22
     DW	Future Wearing Surface(Comp DW)	6.96

   • Live Load

     We obtain the live load shear value (with impact and distribution factor) from Precast/Prestressed Girder output.

     Live Load (kips) at critical section near left support
     LL+IM	85.36

By introducing the above data in the general load-rating equation:

For Inventory Level:

For Operating Level: