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(Comment It may be prudent to reduce Vn by the torsional | Mu |
shear when web crushing governs the capacity. Provisions for + 0.5 N u + 0.5 | Vu - Vp | cot - Aps f po
dv
considering the combined flexural shear and torsional shear are Calculate x =
2 (Es As + E p Aps )
required by Article 12.3.1 of the Segmental Guide Specification
and LRFD Equation 5.8.6.5-3 for segmental bridges.) (Equation 5.8.3.4.2-1) using the equivalent factored shear
force, Vu, determined in Step 4.
Increase web width if Equation 5.8.3.3-2 is not satisfied.
(Comment This simply adds the tensions due to flexural
Step 4 Calculate Shear Stress shear and to torsion for the exterior web where the flexural
shear and torsional shear are additive and appears to be con-
Check if torsion must be considered: servative. Collins and Mitchell (1980) pages 399400, use an
equivalent longitudinal tension for combined flexural shear
Tu > 0.25Tcr (Equation 5.8.2.1-3)
and torsion equal to the square root of the sum of the squares of
2
Acp f pc the individually calculated tensions for flexural shear and for
Tcr = 0.125 fc 1+ (Equation 5.
.8.2.1-4)
pc 0.125 fc torsion.)
If whole-width design is used, forces acting on the total sec-
For Tu > 0.25Tcr, calculate the equivalent factored shear tion are applied. In this case, the shear force is conservatively
force, Vu, acting on the web where the flexural shear and the taken as the equivalent factored shear force, Vu, determined
torsional shear are additive as follows: in Step 4 multiplied by the total number of webs.
Vu = Vu (flexure) + Tuds/(2Ao) (Equation 5.8.2.1-7) (Comment Whole-width design is not specifically addressed
and would benefit from clarification in this area.)
(Comment Vu is determined for a single girder and Tu is act-
ing on the total cross section.) This accounts for the increased longitudinal tensile force
General Comment The fifth paragraph of Commentary due to torsion and will be used to determine and from
C5.8.2.1 regarding the equivalent factored shear force would Table 5.8.3.4.2-1.
benefit from additional clarification. There is a mention of a Using the calculated values of v u /fc and x, find and
stress limit for the principal tension at the neutral axis of the sec- from Table 5.8.3.4.2-1.
tion but the specific code section was not referenced. Article 5.8.5
provides limits on the principal tensile stress in the webs of seg-
Step 6 Determine Required Spacing
mental concrete bridges at the Service III limit state and during
of Stirrups
construction. As the principal stresses are checked using service
load, Vu is not applicable. It appears that the intent of the equiv- The amount of transverse reinforcement required for shear
alent factored shear force is to consider the increased shear force is found from
and resulting shear stress due to torsion in calculating x, , ,
and Vc. It appears that equivalent factored shear force should not Vu Vn
be considered in determining the required shear capacity, Vn, or
the required tensile capacity specified in Article 5.8.3.5. (Comment Clarify that the factored flexural shear, not the
equivalent factored shear force, is used for Vu, as the transverse
Using the equivalent factored shear force, Vu, acting on the
reinforcement for torsion is determined separately.)
exterior web where the flexural shear and the torsional shear
are additive, calculate the shear stress as follows: Vn = Vc + Vs + Vp (Equation 5.8.3.3-1)
vu = (Vu - Vp)/(bvdv) (Equation 5.8.2.9-1)
Where
(Comment Note that vu includes the effects of flexural shear
and torsional shear.) Vc = 0.0316 fc bvdv (Equation 5.8.3.3-3)
Vs = (Avfydvcot )/s (Equation C5.8.3.3-1)
and x and Find
Step 5 Calculate vu / fc Av/s = Vs/(fydvcot )
and
The amount of transverse reinforcement required for tor-
Calculate v u /fc using vu calculated in Step 4. This accounts sion is found from
for the increased shear stress due to torsion and will be used
to determine and from Table 5.8.3.4.2-1. Tu Tn