fr = modulus of rupture of concrete specified
in LRFD Article 188.8.131.52.
fcpe = compressive stress in concrete due to effective
prestress forces only (after allowance for all prestress losses) at extreme
of section where tensile stress is caused by externally applied loads
Mdnc = total unfactored dead load moment acting on the
monolithic or noncomposite section (kip-ft.)
Sc = section modulus for the extreme fiber of the
composite section where tensile stress is caused by externally applied loads
Snc = section
modulus for the extreme fiber of the monolithic or noncomposite section where
tensile stress is caused by externally applied loads (in.3)
The following factors account for variability in the flexural cracking strength of concrete, variability of prestress and the ratio of nominal yield stress of reinforcement to ultimate.
g1 = 1.56, which can
be reduced to 1.2 for precast segmental structures.
g2 = 1.1
g3 = the ratio of yield stress to ultimate stress of the
reinforcement. For prestressed concrete structures, use 1.0.
Appropriate values for Mdnc and Snc
shall be used for any intermediate composite sections. Where the beams are
designed for the monolithic or noncomposite section to resist all loads,
substitute Snc for Sc in the above equation
for the calculation of Mcr-mod .
- For nonprestressed members, 1.33 times the factored moment required by the applicable strength load combinations specified in LRFD Table 3.4.1-1.
This memorandum incorporates the recommendations for
Report 149, LRFD Minimum Flexural Reinforcement
Requirements. It revises 1.2Mcr to be some
coefficients multiplied by Mcr . These coefficients are a function
of component type’s affect on modulus of rupture, the effective prestress, and
the ratio of yield to ultimate stress in the prestressing steel.
If you have any questions regarding these issues, please contact Bijan Khaleghi at 705-7181.
cc: Mohammad Sheikhizadeh, Bridge Construction - 47354
F. Posner, Bridge and Structures – 47340
Note: Click here for a PDF of this design memo.