Sometimes, yes. Infrequently, material is discovered after delivery to be beyond mill tolerances. When material received from the rolling mill does not conform to the requirements of ASTM A6/A6M (or more restrictive tolerances that are specified in the contract documents and purchasing documents), the fabricator can use controlled heating, mechanical straightening, or a combination of both methods, consistent with manufacturer recommendations, to adjust cross-section, flatness, straightness, camber and/or sweep.

The appropriate tolerances for a welded cross-section are specified in AWS D1.1/D1.1M clause 7.22. Depth variation is addressed in clause 7.22.9. 

“For welded beams and girders, the maximum allowable variation from specified depth measured at the web centerline shall be

For depths up to 36 in [1 m] incl. ± 1/8 in [3 mm]
For depths over 36 in [1 m] to 72 in [2 m] incl. ± 3/16 in [5 mm]
For depths over 72 in [2 m] + 5/16 in [8 mm] or – 3/16 in [5 mm]"

AISC recommends that the permissible deviations for girder depth given by AWS D1.1/D1.1M be applied to depth at bolted splices as well. Any differences within the prescribed tolerances at such joints should be taken up, if necessary, by shimming.

The appropriate tolerances for a welded plate girders are specified in AWS D1.1/D1.1M clause 7.22. Variation in Web Flatness is addressed in clause 7.22.6.

For members in statically loaded structures, web flatness does not affect the structural integrity of a girder because it primarily resists shear. Accordingly, neither the AISC Specification nor the AISC Code of Standard Practice includes a limitation on the out-of-flatness of girder webs.

Shrinkage of web-to-flange welds and/or welds that attach stiffeners to the web can create operational difficulties in girder webs, particularly those less than 5∕16 in. thick. Therefore, webs under 5∕16 in. thick should be avoided. If a girder web less than 5∕16 in. thick is specified, the dimensional tolerance for deviation from flatness, with or without stiffeners, in statically loaded structures should be determined as the larger of ½ in., from ASTM A6/A6M, or the value determined in AWS D1.1/D1.1M clause 7.22.6.2. In cyclically loaded structures, the value in AWS D1.1/D1.1M clause 7.22.6.3 should be observed. 

If architectural considerations require a more restrictive flatness tolerance, it should be specified in the contract documents. In all cases, the web thickness specified should be adequate to minimize such distortion.