Web stiffeners is not an efficient way of increasing moment capacity in either direction.

They're not only inefficient, they do nothing at all for moment strength.

 

The usual way to increase the flexural capacity of a section is to either "box in" the section by adding side plates to form a rectangular/square section, or by adding a lap plate to the top or bottom (or both) of the section.  Stiffener plates are to primarily stiffen the flange to prevent localized flange buckling.

How much do you need to increase it ? Simply weld a cover plate on the HP exposed flange. Proper welding of the steel plate to the HP flange is also critical.

If you stitch weld the waler to the sheeting you do not have to worry about lateral torsional buckling. Depending on the span, that can give you significant additional strength.

You state at the strut location, sounds to me like negitive moment. A cover plate would be the best solution because the high moment at the strut locations does not extend far from the support.

As others have said, flange cover plates are the answer for increasing the moment capacity.  But I would also consider decreasing the spacing of the bracing to avoid having to stiffen the walers, especially if the walers are part of a temporary system which can be reused.

Stiffeners are generally provided to increase the web buckling capacity when there is large point load applied to a member, such as a column reaction applied to a supported beam.  They will not provide any extra flexural capacity.
 

Post tensioned cables off stiffener plates on the tension flange side can double or triple the flexural capacity.  Use eccentricity to PNA to match moment diagram.

When using HP as beams always remember that their dimension are optimized for use as piling: flange thickness = web thickness on purpose to withstand being driven and so that no part corrodes away too quickly after they are in place.

When compared to a typical W shape with it's thick flanges and thin web, the HP geometry is "wrong" for use as a beam: the flanges are thin but wide.

As beams, HP may have lower allowable stresses since they tend to be non-compact shapes.

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Sliderule,

I see, and specifiy, HP sections used as walers for sheet pile shoring all the time. Though they are not designed for this, they generally are the most econmical as pile driving contractors often have stacks of different HP sections sitting in thier yard.

DWHA

Stitch welding walers to the sheetpiles is usually not possible. Even when driving frames are used, sheet piles do not go in straight. You are likely to have gaps of an inch or more where welds are requied. If the piles are driven wild, chances go from slim to none.

However, walers are generally supported at intervals by I or T stubs welded to the pile. Welding the walers to the stubs can provide adequate bracing.

gwynn - Very good reasons. As a bridge contractor in the 1970's, I did exactly the same thing. We would use the HP as temporary falsework beams, too. Since these beams would be reused (sometimes slightly damaged when wrecking concrete forms), have holes cut in them for handling, be short lengths spliced together, etc., I limited working stress (for A36 steel) to 20 ksi. Never had a problem at that level, but would not have wanted to go any higher (for used material).

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and they are nearly always Class 2 or Class 3 sections due to b/t and h/w limitations

Sliderule - I agree on limiting the stress. We generally assume extra weight as well (not so critical for walers), after seeing just how many stiffeners can end up in a reused beam.