Flexural Strength

Flexural strength (resistance) is computed using the code-specified formulas. Both the Standard
Specifications and the LRFD Specifications yield very similar results in this regard.
Development of Reinforcement
Strand
Eriksson Girder fully considers transfer and development of strand during analysis. Effects of end debonding
and midspan debonding are also accounted for. For a thorough and detailed discussion of strand
development, see “Strand Transfer and Development” under “Prestress Effects” above.

Rebar
Reinforcing bars can be specified in the girder or in the deck to increase the flexural capacity of
the system. However, since girder rebar can extend beyond the ends of the girder and since deck
rebar can extend across multiple spans, all rebar specified in Eriksson Girder is assumed to be fully
developed. Detailing to ensure that rebar is developed is left up to the user.

Non-Composite and Composite Sections
Composite sections are idealized as either rectangular beams or T-beams, depending upon whether the
neutral axis remains in the top flange of the beam or drops below the top flange and into the web
of the member. The top flange of a T-beam is assumed to be rectangular in shape.

Composite sections are also idealized as rectangular sections or T-beams. The concrete strength
used in the analysis is the lesser of the strength of the deck concrete and the beam concrete. If
T-

Eriksson Girder 4 User Manual 145
beam behavior occurs (i.e., the neutral axis drops below the deck), the width of the web of the
beam is used as the width of the stem of the tee.
For the special case of a composite section where the width of the flange of the precast section is
exactly equal to the width of the width of the composite deck, the thickness of the flange is
considered in the calculation of the depth of the compression block. If the flange is not the same
width as the composite deck, it is ignored.
Strain Compatibility
The depth to the neutral axis is solved for by an iterative strain-compatibility procedure that considers
the force in each individual bar or strand. This assures that multiple reinforcement layers are properly
accounted for in the final flexural resistance moment. Additionally, the concrete stress-strain curve is
used to calculate the force in the compression block. This procedure sidesteps the question as to which
β1 value to use, that of the girder or that of the deck (or a weighted average of the two). Note
that for this algorithm to function properly if you are using channel beams or decked bulb tees,
you should remove any shear keys at the outside face of the decks.
Maximum Steel
The Standard Specifications specifies that prestressed concrete members shall be designed so that the
reinforcement index is limited to 0.36β1 (Art. 9.18.1). However, it can be shown that this is
equivalent to limiting the ratio of the depth of the neutral axis to the depth of the prestress
force (c/de) to 0.42. That is,
0.42
d
c
e
≤
(LRFD Eq. 5.7.3.3.1-1)
for which:

A f d + A f d d = ps ps p s y s

(LRFD Eq. 5.7.3.3.1-2)

Apsfps

• As fy

This is the approach that the LRFD Specifications used prior to 2005 and the approach Eriksson Girder
currently uses to check maximum reinforcement limits per the Standard Specs. For the current
version of the LRFD Specs, the maximum reinforcement limit (Art. 5.7.3.3.1) has been eliminated. A
unified approach in which phi is now variable has been introduced (Art. 5.5.4.2.1), which
effectively covers this check. For prestressed members, the variation in phi is computed according
to the following:

0.75 ≤ ϕ = 0.583 + ⎜⎛ dt
⎝

− ⎟⎞ ≤ 1.0
⎠

(LRFD Eq. 5.5.4.2.1-1)

Minimum Steel
Both specifications require that enough reinforcement be present in the beam to develop a moment of
1.2 times the total moment required to crack the beam. For convenience, the ratio of Mr/Mcr is
shown
in the output (which must equal or exceed 1.2).