Firstly, is it a steel structure or concrete structure? the connection could be very different for those different structures.

the waler design is majorly a bending moment check. you take the soldiers as 2 supports, and the earth pressure distributed evenly on the waler, then it's like a simply supported beam. if you know how to solve the bending moment and shear force under this loading and supporting condition, then check the capacity of the waler member to see if it can take this bending moment and shear. The bending capacity of a member is then a matter of material mechnics problem which requires you to check the max. stress in this material. comparing with the design strength of the material, then you say it's safe or not.

Key words: 1. Simply supported beam;
2. Bending moment and Shear force in the beam;
3. Section modulus of the waler
4. Design strenth of the waler material.

This is what is known as a braced cofferdam:
* Lateral soil pressure should be determined per Terzaghi, not Rankine or Coulomb.
* You may be using lagging with soldier piles, or you may be using sheet piling with walers. These are bending members.
* A 60' long excavation will almost certainly require internal struts, bracing one side to the other. These are unbraced compression members.
* Heaving and piping must also be checked.

You should be able to find an example design in a soil mechanics textbook.

DaveAtkins

I believe the rule of thumb that "Terzaghi must be used instead of Rankine," etc., is appropriate for non-cohesive soils, not necessarily for cohesive, if that makes any difference.

Just something to ponder: we have found using HSS for waler frames seems to be the best approach. Aside from being easier to handle, they can be shop welded in whole or partial assemblies. We tend to put them together in the field using simple welded "hinge" connections at moment inflection points.

They seem to be stronger per pound than wide-flange shapes.

1st solve your soldier beam (or sheet piling) to get the reaction to the wale. Then design the wale as you would any beam with either point loads for soldier beams or uniformly distributed loads for sheet pile. Depending on the strut layout some folks would reduce the calculated moment in the wale to account for some soil arching, but I tend to ignore this in the wales. I always include a nominal eccentricity in the axial load of the struts to account for the misalignment that will exist.

I wouldn't use HSS for the wales as W or H shapes are more efficient in bending, but pipes or square HHS are ideal for the struts but I rarely see contractors use them. They tend to have various W or H shapes in their yard that they prefer to use.

A tip I learned long ago as a bridge contractor: For wales, H shapes are much preferred to equivalent W shapes. An H shape's superior Y-axis strength helps it resist plastic bending when the wales are pulled upward for removal. This improves the likelihood that they will be suitable for reuse in the future.

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Quote (SRE)

This improves the likelihood that they will be suitable for reuse in the future

Have you ever had to determine this? What would be some criteria to use?

EIT
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Quote (RFreund)

Have you ever had to determine this? What would be some criteria to use?

Oh, yes, many times. We would have left over piling cut offs of HP 12 X 53 and HP 10 X 42. Would butt weld these cutoffs into usable lengths. This was in the 1970's, so I made all calcs using "old" ASD, of course. Only rarely used the HP 10 X 42 because of their lighter capacity. An A36, HP 12 X 53 is an noncompact shape with allowable bending of 22 KSI for a new member. I had access to a Contractor's previous falsework and cofferdam plans. From these determined that downrating the maximum allowable bending stress for a typical used member from 22 KSI to 19.6 KSI, never caused a problem.

Naturally, that raises the question of what is a "typical used member". Surprisingly, it can "look" pretty bad, with "dings" in the flanges (that are more or less straightened with a sledge hammer), fair sized handling holes in the web, small holes in the flanges, fair amount of rusting, and the butt welded joints - sometimes 3 or 4 in a nominal 30' long beam. The beam does have to be reasonably straight. Never set an objective criteria, but if you could not see the "bend" unless you looked along the length of the beam that was straight enough. Even then, the visible "bend" had to be small. The assumed 19.6 KSI was maximum, normally I would work about 15 or 16 KSI - reducing deflection was always a concern.

I always enjoyed doing the calculations for use of these members "backwards". The question was NOT "What size members do I need?". It was "How do I make the members that I have work?"

We did this type of thing so often I drew up my own "Maximum Allowable Load Graph" for both HP 12 & HP 10. Have attached a (1978) copy for the HP 12 X 53. When you look at it, you'll see that I ran the lengths out unusually long. We did have some times to use very lengthy beams. The longest was a 65 feet, laterally unsupported HP 10 X 42. Taking a walk on that one was a real trip! Like being on a trampoline - but bouncing vertically and horizontally with each step.

Hope this gives you some insight into a (former) Contractor's wacky world of engineering.

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