Stress Limits for Concrete [LRFD Art. 5.9.4.2]

1. Compression

   Due to permanent load,(i.e., girder self-weight, diaphragm weight, wearing surface, and barrier load) for load combination Service I

   = 0.45f`_c = 0.45 × 5.5 = 2.475 ksi

   Due to permanent and transient loads, i.e., all dead loads and live loads, for load combination Service I

   = 0.60 f`_c = 0.60 × 5.5 = 3.300 ksi

   Due to live load plus one-half of permanent loads, for load combination Service I

   = 0.40 f`_c = 0.40 × 5.5 = 2.200 ksi

2. Tension

   For components with bonded prestressing tendons, for load combination Service III

   $-0.19\sqrt{{f`}_c}=-0.19\sqrt{5.5}=-0.446ksi$

Check of Stresses at Midspan

To check compressive stresses at the top of the beam, the following three cases are checked.

1. Under permanent load, load combination Service I (Final 2):

   $f_t=\frac{P_{pe}}{A}-\frac{P_{pe}\times e_c}{S_t}+\frac{(M_g+M_D+M_{wz}+M_b)}{S_t}=\frac{736.456}{843}-\frac{736.456\times 18.48}{9571}+\frac{(1097.0+40.5+93.8+158.6)\times 12}{9571}=0.874-1.422+1.743=1.195$

   Compression stress limit for concrete = + 2.475 ksi OK

2. Under permanent and transient loads, load combination Service I (Final 1):
   $f_t=1.195+\frac{M_{LL+I}\times 12}{9571}=1.195+\frac{792.6\times 12}{9571}=1.195+0.993=2.189$

   Compression stress limit for concrete = + 3.300 ksi OK

3. Under live load plus one-half of permanent loads, load combination Service I (Final 3):
   $f_t=0.5\times (\frac{P_{pe}}{A}-\frac{P_{pe}\times e_c}{S_t})+0.5\times \frac{(M_g+M_D+M_{wz}+M_b)\times 12}{S_t}+\frac{M_{LL+I}\times 12}{S_t}=0.5\times (\frac{736.456}{843}-\frac{736.456\times 18.48}{9571})+0.5\times \frac{(1097.0+40.5+93.8+158.6)\times 12}{9571}+\frac{792.6\times 12}{9571}=0.874-1.422+1.743=1.591$

   Compression stress limit for concrete = + 2.20 ksi OK

Check of Bottom Tension Stress, Load Combination Service III (Final 1)

Tension stress limit for concrete = - 0.446 ksi OK