Proportioning limits

AASHTO (2004) Article 6.11.2 defines the following proportioning limits unique to box girders:

• A 1 to 4 limit on the inclination of the web plates is recommended relative to an axis normal to the bottom flange. Larger web inclination is allowed, but the effects of changes in the St. Venant and/or flexural web shears on lateral bending of the top flanges will be larger during construction (see the discussion in Section 2.3). Also, highly inclined webs are generally less efficient for transmitting shear. However, the width of the bottom flange may be reduced by using a larger web inclination.

• The webs shall be attached to the mid-width of the top flanges. Attachment of the webs other than at the top flange mid-widths would cause additional flange lateral bending that would require special investigation.

• Extension of the box flanges at least one inch beyond the outside of each web is recommended to facilitate welding of the webs to the flange.

Otherwise, the web and top flange proportioning requirements for box girders are the same as those for I-girders (discussed previously in Section 5.3.2), with the exception that Eq. (5.3.2-6) is not applicable. Article 6.11.2 specifies that the inclined distances along the web are to be used in checking the web proportioning limits as well as all other pertinent design requirements.

Although it is discussed in Article 6.11.3.2 on Constructibility, AASHTO (2004) provides one additional limit that deserves mention with the above proportioning limits. This article suggests

bf > L/85 (5.4.5-1)

for the top flanges of tub girders, in cases where a full-length lateral bracing system is not provided within a tub section, with L taken as the larger of the distances between panels of lateral bracing, or between a panel of lateral bracing and the end of the piece. This limit is similar in intent to Eq. (5.3.2-7) discussed previously for I-section flexural members.

5.4.6 Compact Composite Sections in Positive Flexure

The Article 6.11.6.2.2 requirements for composite sections in positive flexure to be

considered as compact are the same as in Article 6.10.6.2.3 for I-sections (see Section 5.3.3 of this Chapter), except that the bridge must also satisfy the requirements of Article 6.11.2.3 for use of the simplified live load distribution factor (see Section 5.4.2(A)) and the box flange must be fully effective based on the provisions of Article 6.11.1.1 (also discussed in Section 5.4.2(A)).

The corresponding Article 6.11.7.1 resistance calculations and ductility requirements are the same as for compact composite I-sections in positive flexure (see Section 5.3.3) except that, for continous spans, the nominal flexural resistance is always subject to the limitation of Eq. (3-2, AASHTO 6.10.7.1.2-3). Either Eq. (3-2) or Eq. (5.3.3-3, AASHTO 6.10.7.1.2-2) will usually govern, thus limiting the nominal flexural resistance to a value less than the full plastic moment of the cross-section but larger than the cross-section yield moment.

5.4.7 Noncompact Composite Sections in Positive Flexure

AASHTO Article 6.11.6.2.2 specifies that all box sections in positive bending that do not meet the restrictive requirements discussed above must be designed as noncompact composite sections. As such, the flexural resistance is always less than or equal to the cross-section yield moment. Similar to the procedures for noncompact composite I-sections in positive flexure, discussed previously in Section 5.3.4, the resistances are expressed in terms of the elastically computed flange stresses.

For tub sections, the Article 6.11.7.2 calculation of the resistance based on the top flange stress is the same as that for noncompact composite I-sections in positive flexure (see Section 5.3.4). However, for closed-box sections, the nominal resistance of the top (compression) flange is taken as Fnc = RbRhFyc Δ (5.4.7-1, AASHTO 6.11.7.2.2-2) where 2 yc v F f 3 1 _⎟⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = Δ (5.4.7-2, AASHTO 6.11.7.2.2-3)

fv = the St. Venant torsional shear stress in the flange due to the factored loads at the section

under consideration, calculated as

fc o v t A 2 T f = (5.4.7-3, AASHTO 6.11.7.2.2-4)

Rb = the web load-shedding strength reduction factor specified in Article 6.10.1.10.2, and

Rh = the hybrid web strength reduction factor specified in Article 6.10.1.10.1, with the bottom

Also, in Eq. (5.4.7-3),

T = the torque due to the factored loads and

Ao = the enclosed area within the box section.

Equation (2) reduces the effective yield resistance of the top flange accounting for the influence of the St. Venant torsional shear stress via the von Mises yield criterion. The participation of the concrete deck in transferring the shear stresses is neglected by using just the thickness of the steel top flange for tfc in Eq. (3). Also, the flange shear stress due to flexure is considered

negligible and is not included in Eq. (2). The term Δ appears in many places in the different box flange resistance equations presented in this Section. In all cases, this term gives a reduction in the effective yield strength under longitudinal tension or compression due to the St. Venant torsional shear stress.

Similar to the above, the nominal resistance of the bottom tension flange is taken as

Fnt = RhFyt Δ (5.4.7-4, AASHTO 6.11.7.2.2-5)

Article 6.11.1.1 requires that box flanges also must generally satisfy

3 F 75 . 0 f_v ≤ φ_v yf (5.4.7-5, AASHTO 6.11.1.1-1)

This magnitude of torsional shear stress is rarely, if ever, encountered in practical box girder designs. However, this limit ensures that Δ (Eq. (2)) will never be smaller than 0.66.

The Article 6.11 provisions imply that box flange shear stresses associated with flexure do not need to be considered in any cases. However, for situations with tf only slightly larger than tw,

consideration of these shear stresses is prudent. The elastic shear flow f = VQ/I in a box flange at the web-flange junctures is essentially the same as the corresponding elastic shear flow in the webs at these locations.

As a refinement on Eq. (3), for composite box flanges, the St. Venant torsional shear in the steel plate may be determined by multiplying the shear on the top of the composite box section by the ratio of the transformed concrete deck to the total thickness of the top flange plus the transformed deck. The St. Venant torsional shear in the concrete deck may be determined similarly. Adequate transverse reinforcing should be provided in the concrete deck to resist the shear forces due to St. Venant torsion.

The requirements for checking the slab stresses in shored construction are the same as those for I-section members