Critical Section for Shear

The critical section for shear is located relative to, or at, the face of support. The face of support location is defined by the boundary conditions and connection geometry at an abutment or pier. Detailed information for face of support location is available in Face of Support.

This section provides a discussion of the requirements and assumptions for the algorithm to determine the critical section for shear location.

Article 5.7.3.2 (pre-2017: 5.8.3.2) states that the critical section for shear may be taken as d_v from the face of support.

‍NOTE: Prior to LRFD 3rd Edition, 2004, the critical section was taken as the larger of d_v or 0.5d_vcot(q) from the face of support.

The LRFD Specification does not provide any guidance as to where d_v and q are to be taken. Common practice is to take them at the location of the critical section. This makes the determination of the critical section for shear an iterative process since d_v and q vary based on location and limit state.

Locating Critical Section for Shear, LRFD 3rd Edition, 2004, and later

The algorithm used to locate the critical section is as follows:

1. Guess the location of the critical section X.
2. Find d_v at X from the face of the support. Call this value X1.

If X1 is equal to X, the critical section for shear is at X.

Locating Critical Section for Shear, prior to LRFD 3rd Edition, 2004

Prior to LRFD 3rd Edition, 2004, the critical section for shear is located as:

1. Guess the location of the critical section X.
2. Find d_v at X from the face of the support. Call this value X1.
3. Find q at X from the face of the support.
4. Using q from Step 3 and d_v from Step 2, compute 0.5d_vcot(q). Call this value X2.

If X is not equal to the maximum of X1 and X2, go to Step 1 and repeat. Otherwise, X is the location of the critical section for shear.

Repeat for each limit state used for shear design.

A graphical solution would look as follows:

Although accurate and true to the Specifications, this method is impractical because of the large computational cost of calculating force envelopes at each guessed location in order to determine q(X) (a complete live load analysis would have to be run for every point). However, examination of many d_v and q graphs reveals that their shape is well-behaved. Hence, it is practical to approximate the d_v and q near the support. A piecewise linear interpolation is used. The control points used to create the curves will be at the 0.00, 0.05, and 0.10 points along the girder. It is believed that the critical section for shear should always fall within this range.