Legal Load Rating

Since the Inventory Design Load Rating RF > 1.0, the legal load ratings do not need to be performed. However, Precast/Prestressed Girder will compute and display the ratings for legal and permit even if RF is larger than 1.

Note: The Inventory Design Load Rating produced rating factors greater than 1.0. This indicates that the bridge has adequate load capacity to carry all legal loads within the LRFD exclusion limits and need not be subject to Legal Load Ratings.

The legal live loads used in this example are Type 3, Type 3S2 and Type 3-3.

To help in the verification of results, we run Precast/Prestressed Girder three times with the following loads added under the Loads tab. We obtain the following values at midspan to moment:

	Type 3	Type 3S2	Type 3-3
M_LL(k.ft)	846	962	940

Distribution Factor for moment (2+ lane): (DFM) for beam 2, is 0.723167

Dynamic Load Allowance: IM

The dynamic load allowance is given in the following table (Table C6.4.4.3-1) based on the riding surfaces conditions:

Riding Surface Conditions	IM
Smooth riding surface at approaches, bridge deck and expansion joints	10%
Minor surface deviations or depressions	10%
Conservative Condition	33%

We assumed in our example that we have minor surface deviations or depressions, therefore IM = 0.2.

The unfactored live moments per beam due to legal load trucks are:

M_ll + IM = (DFM) (1 + IM) (M_ll)

	Type 3	Type 3S2	Type 3-3
M_LL+IM(k.ft)	734.16	834.82	815.73

A similar calculation is required for shear. For shear, we compute rating factors in critical section near left supports and the values are obtained by linear interpolation from the values from bearing and 0.1L location. To help in the verification of results, we run Precast/Prestressed Girder three times (individually) with the following loads added under the Loads tab.

	Type 3	Type 3S2	Type 3-3
V_LL(kips)	41.06	49.15	49.33

Distribution Factor for shear (2+ lane) (DFV): 0.86104

IM = 0.2

The unfactored live shear per beam due to legal load trucks are:

V_LL + IM = (DFM) (1+ IM) (V_LL)

	Type 3	Type 3S2	Type 3-3
V_LL+IM(kips)	42.43	50.78	50.97

Strength 1 Limit State

V_DC, V_DW are listed in the following table:

Load Type	Value
γ_DC	1.25
γ_DW	1.50

Generalized Vll Live-load Factors are specified in the following table:

ADTT (Average Daily Truck Traffic)	Equivalent Factor in Precast/Prestressed Girder	Generalized Live-Load Factor For Legal Loads
ADTT Š 5000	1.00	1.80
100>ADTT<5000	(0.90; 1)	1.65
ADTT≤100	(0.50; 0.90)	1.40

In the example, the Equivalent Factor is 1.00, therefore γ_LL=1.80

Flexural Strength

These calculations are for Midspan location. All the rest of the values were already computed in the previous Design Load Rating section.

Therefore:

R F = \frac{φ_{c} \times φ_{S} \times φ \times M_{n} - γ_{D C} \times D C - γ_{D W} \times D W}{γ_{L} \times M_{L L + I M}} = \frac{1 \times 1 \times 1 \times 6245.2 - 1.25 \times 1716.7 - 1.5 \times 162.0}{1.8 \times M_{L L + I M}} = \frac{2142.347}{M_{L L + I M}}

Therefore, for each legal load, we have the following Rating Factors:

	Type 3	Type 3S2	Type 3-3
M_LL+IM (k.ft)	734.16	834.83	815.73
RF	2.92	2.57	2.63
Weight (Tons)	25	36	40
Safe Load Capacity (Tons)	73	92.52	105.2

Shear Strength

These calculations are for critical section near left support.

Since the critical location is different for each truck, we need to interpolate the results for each truck to obtain the Dead Load Shears.

Dead Loads (kips) at critical section		Type 3	Type 3S2	Type 3-3
DC	Self-Weight	27.5	27.48	27.58
	Deck & Haunch	30.92	30.89	30.96
	Diaphragms	3.00	3.00	3.00
	Concrete Barriers (Comp DC)	8.37	8.37	8.37
	Total	69.79	69.90	69.91
DW	Future Wearing Surface (Comp DW)	6.87	6.79	6.79

Also, V_n differs in critical location. The values are:

	Type 3	Type 3S2	Type 3-3
V_n(kips)	496.38	478.41	477.73

Therefore:

For Type 3 we have:
$R F = \frac{φ_{c} \times φ_{S} \times φ \times M_{n} - γ_{D C} \times D C - γ_{D W} \times D W}{γ_{L} \times M_{L L + I M}} = \frac{1 \times 1 \times 1 \times 496.38 - 1.25 \times 69.79 - 1.5 \times 6.79}{1.8 \times 42.43} = 5.23$
For Type 3S2 we have:
$R F = \frac{φ_{c} \times φ_{S} \times φ \times M_{n} - γ_{D C} \times D C - γ_{D W} \times D W}{γ_{L} \times M_{L L + I M}} = \frac{1 \times 1 \times 1 \times 478.41 - 1.25 \times 69.90 - 1.5 \times 6.79}{1.8 \times 50.78} = 4.17$
For Type 3-3 we have:
$R F = \frac{φ_{c} \times φ_{S} \times φ \times M_{n} - γ_{D C} \times D C - γ_{D W} \times D W}{γ_{L} \times M_{L L + I M}} = \frac{1 \times 1 \times 1 \times 490.99 - 1.25 \times 69.91 - 1.5 \times 6.79}{1.8 \times 50.97} = 4.15$

Therefore, for each legal load we have the following RFs:

	Type 3	Type 3S2	Type 3-3
RF	5.23	4.17	4.15
Weight (Tons)	25	36	40
Safe Load Capacity (Tons)	130.75	150.12	166

Service Limit States

These calculations are for midspan location. Because we have total moment greater than 0, we have compression at top and tension at bottom. For both cases, we will compute the RFs.

Compression at top (Compression Stress RFs are for Service I Limit State):
${R F}_{C O M P}^{T O P} = \frac{f_{r}^{t o p} - γ_{D} f_{D}^{t o p}}{γ_{L} f_{L L + I}^{t o p}}$

We have the values from File > Print Positive Envelope Stresses. In the following table, we have results for stresses from dead load values at midspan location at the top.

f_R - flexural resistance at top

f_R = f_pb + allowable tensile stress at top

f_pb = stress due to effective prestress: -0.856 ksi

Allowable compression stress - 0.6 x 5 = 3.30 ksi

Therefore, f_R = 3.00 ksi - (- 0.856 ksi) = 3.856 ksi

γ_L=1.00; γ_D=1.00;

$R F = \frac{f_{R} - γ_{D} \times f_{D}}{γ_{L} \times (f_{L L + I M)}} = \frac{3.856 - 1.00 \times 2.115}{1.00 \times f_{L L + I M}} = \frac{1.741}{f_{L L + I M}}$

Now we need to compute f_LL+IM for each legal load type. For this example, S_tc is 61012.22 in₃

The Live Load Moments for each type of load should be converted to kip.in as shown below:

Type 3 Type 3S2 Type 3-3

M_LL+IM(k.ft) 8809.909 10017.89 9788.789

The equation to compute the stresses from these live loads at the top of the section is:
$f_{L L + I M} = \frac{M_{L L + I M}}{S_{t c}}$

And the values are:

Type 3 Type 3S2 Type 3-3

f_LL+IM(ksi) 0.144 0.164 0.160

The values for rating factors are:

Type 3 Type 3S2 Type 3-3

RF 12.06 10.61 10.86

Weight (Tons) 25 36 40

Safe Load Capacity (Tons) 301.5 381.96 434.4
Tension at bottom (Tension Stress RFs are for Service III Limit State)
${R F}_{T E N S}^{B O T} = \frac{f_{R}^{b o t} - γ_{D} f_{D}^{b o t}}{γ_{L} \times f_{L L + L}^{b o t}}$

f_R - flexural resistance

f_R = f_pb + allowable tensile stress

f_pb = compressive stress due to effective prestress: 2.562 ksi

Allowable compression stress $- 0.19 \times \sqrt{f_{c}} = - 0.19 \times \sqrt{5.5} = - 0.425 k s i$

Therefore, f_R = -0.446 ksi - 2.564 ksi = -2.987 ksi

γ_L=1.00; γ_D=1.00;
${R F}_{T E N S}^{B O T} = \frac{f_{R}^{b o t} - γ_{D} f_{D}^{b o t}}{γ_{L} \times f_{L L + L}^{b o t}} = \frac{- 2.987 - 1.00 \times (- 1.974)}{1.00 \times f_{L L + I}^{b o t}} = \frac{- 1.013}{f_{L L + I}^{b o t}}$

Now we need to compute ${R F}_{L L + I}^{B O T}$ for each legal load type. For this example S_bc is 1747 in³.

The Live Load moment for each type of load should be converted to kip.in as shown below:

Type 3 Type 3S2 Type 3-3

M_LL+IM(k.ft) 8809.909 10017.89 9788.789

The equation to compute the stresses from these live loads at the bottom of the section is:
${R F}_{L L + I}^{B O T} = \frac{M_{L L + I M}}{S_{b c}}$

And the values are:

Type 3 Type 3S2 Type 3-3

f_LL+IM(ksi) -0.504 -0.573 -0.560

The values for rating factors are:

Type 3 Type 3S2 Type 3-3

RF 2.01 1.77 1.81

Weight (Tons) 25 36 40

Safe Load Capacity (Tons) 50.25 63.72 72.4

	Type 3	Type 3S2	Type 3-3
RF	12.06	10.61	10.86
Weight (Tons)	25	36	40
Safe Load Capacity (Tons)	301.5	381.96	434.4

	Type 3	Type 3S2	Type 3-3
RF	2.01	1.77	1.81
Weight (Tons)	25	36	40
Safe Load Capacity (Tons)	50.25	63.72	72.4