Prestressing Steel Tension Capacity for Permit Load

The rating equation for prestressing steel tension is as follows:

{R F}_{I N V}^{P S S I T} = \frac{0.9 f_{y} - (F_{d} + F_{p})}{F_{I}}

The stress in strands shall be checked for tension. In this case, for permit load rating level as per Art. 6.5.4.2.2.2, the limiting steel stress is 0.9F_y.

f_py in turn is estimated to be as in the Table 6-10 from the LRFR Manual:

Type of Tendon	f_py
Low Relaxation Strand	0.9 f_pu
Stress Relieved Strand	0.85 f_pu

The prestressing steel type used in our sample is 1/2 (low relaxation steel) (f_pu = 270 ksi).

Therefore:

f_py = 0.9f_pu = 0.9 X 270 = 243ksi

And the limiting stresses for prestressing steel as per Art. 6.5.4.2.2.2 is:

0.9 X fpy = 0.9 X 243 = 218.7ksi

The dead load stress in strand is the final prestress stress after all losses. This can be calculated as f_pj-f_s. Note that these values are report in Precast/Prestressed Girder, but are based on the location of centroid of all prestressing steel. The stress in the bottom row is usually slightly higher, however, in lieu of better estimates, this value is used.

Based on initial stress of 202.5 ksi (0.75*f_ps), and total loss of 41.72 psi, the final strand stress is 160.78 ksi, which used for the dead load term D (F_d + F_p) from the formula of the Rating Factor.

The live load increment of stress is calculated by interpolating the girder top and bottom live load stresses, and finding the concrete stress at location of bottom strand. Then, using modular ratio to find the steel stress:

f_{p e r m i t}^{b o t t o m s t r a n d} = {\frac{E_{s}}{E_{c}} \times f_{P E R M I T}^{B O T} + [\frac{f_{P E R M I T}^{T O P} - f_{P E R M I T}^{B O T}}{H}] \times e_{b o t}}

Where:

f_bot- bottom fiber concrete stresses due to total live load;

f_top- top fiber concrete stresses due to total live load;

H - total section height (54 in);

e_bot- the eccentricity of the bottom row of strands which is assumed in Precast/Prestressed Girder to be located at 2 inches from the bottom flange of the beam;

E_s - modulus of elasticity of the prestressing tendon: 28500 ksi;

E_c - modulus of elasticity of 28-day strength concrete: 4030 ksi;

We should compute the live load stresses at top and at bottom. We have the Live Load Moment for Permit Truck Load = 1506.95 k.ft, previously computed, and the section modulus at top (Stc = 61012.22 in³) and at bottom (S_tc = 1747 in³).

Therefore, the formula to compute the stresses from these live loads at the bottom of the section is:

f_{P E R M I T}^{T O P} = \frac{M_{L L + I M}^{P E R M I T}}{S_{t c}} = \frac{1506.95 \times 12}{61012.22} = 0.296 k s i

f_{P E R M I T}^{B O T} = \frac{M_{L L + I M}^{P E R M I T}}{S_{t c}} = - \frac{1506.95 \times 12}{17471} = - 1.035 k s i

f_{P E R M I T}^{b o t t o m s t r a n d} = \frac{28500}{4030} \times {- 1.035 + (\frac{0.296 + 1.035}{54})} \times 2 = - 6.97 k s i

Therefore, the Rating Factor for Permit Load for prestressing steel tension is:

{R F}_{P E R M I T}^{P S S t T} = \frac{0.9 f_{p y} - (F_{d} + F_{p})}{- f_{L L + I}^{b o t t o m s t r a n d}} = \frac{218.7 - 160.78}{6.97} = 8.33