Task Number: 7.2 Transverse Design

In the absence of a more refined three-dimensional computer analysis, the "strip" method is typically used to perform a conservative two-dimensional transverse analysis of concrete box girders. This predominately hand-calculation method employs the use of Pucher or Homberg influence surfaces to determine the maximum live-load effects experienced by each component of the box section. The engineer uses these live-load actions, appropriately combined with other loads effects, to efficiently size the box section and to detail both transverse post-tensioning and mild reinforcing.

The strip method of analysis considers a full-depth transverse cross-section of the box girder that is usually one unit (1 m or 1 ft depending on system of units) in length. Working lines that run through the mid-thickness of the top and bottom flanges and through the webs, neglecting any haunches, are used to establish design lengths for these components. Stiffness and carry-over factors that include the effect of the haunches can be determined for each component through calculation or use of pre-generated tables similar to those found in the PCA Handbook of Frame Constants.

Possible live load combinations are placed appropriately within lanes on the top flange of the box girder. The Pucher or Homberg surfaces are used to reduce the 3-dimensional force effects from multiple wheel loads to fixed-end bending moments acting on the frame strip. Fixed-end moments due to all appropriate load effects are generated for each member. Moment distribution is used to apportion the bending effects of both the permanent loads and each of the live load cases throughout the frame strip.

Maximum and minimum design moments are then determined by combining all appropriate force effects at each critical section. For the top flange, the critical design sections are at the face of the web both inside and outside the box section, at the haunch ends and at the middle of the top flange that spans between webs.

Post-tensioning is detailed along the length of the top flange as needed to meet the loading demands. Due to the secondary effects of the post-tensioning on the top flange spanning between webs this is usually an iterative procedure. Checks are made at all critical sections before and after post-tensioning losses to insure that service load stress levels are within the limits specified.

Overload or ultimate strength checks are also made at each critical section using combinations of factored loads. In addition to the minimum reinforcement requirements of the design provisions, mild steel is detailed to satisfy the force effects in the webs and bottom flange of the box section, and any allowable tension stress in the top flange.

Deflection limits are checked on the cantilever portions of the top flange.

Submitted by:

Joey Hartmann
Structural Research Engineer
Turner-Fairbank Highway Research Center
Mclean, Virginia