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A Cold Molded Shell for USS Constellation

Andrew Davis
Keith Gallion
Tri-Coastal Marine, Inc.
Berkeley, CA 94710


The hull and gun deck planking of the USS Constellation is currently being replaced with a cold molded planking shell. This paper summarizes the design of that shell. In addition, the paper discusses the inappropriateness of using classical beam theory to analyze traditional wooden ship structures.

Table of Contents

Table of Contents
Causes of hogging failure
Inadequacy of beam theory for wooden ships
The cold molded shell

Analysis Summary
Beam analysis
Unstiffened finite element shell analysis
Stiffened finite element shell analysis
Composite Properties of Shell

Stress Contours
Maximum Deflections

Interpreting the results
Measuring residual strength of decayed wood.
Application to other vessels
Failures of other repair methods


Condition of the USS Constellation

Prior to docking in December 1996, the USS Constellation was in a bad state. It had been completely de-rigged, was closed to visitors and was essentially an unattractive and dangerous hulk floating in Baltimore's Inner Harbor. All of the structure above the gun deck was either completely rotten, historically bogus or both. The hull had lost so much of its original strength that it was unable to resist the relatively modest still water bending loads, and the hull had developed effectively 36" of hog at the keel. In spite of the general decay of the vessel, most of the structure below the gun deck, believed to be original historic fabric, was largely intact.

Causes of hogging failure

There are at least three false ideas about wooden ship structure that, somewhat amazingly, are still current:

Wooden ships need to flex.
There are discrete strength members like the keel forming a "backbone".
Traditional wooden ships can be analyzed with beam theory.

The principle mode of failure1 for the hulls of large wooden ships is “hog”. In wooden ships, this is a long term, inelastic deformation (akin to settling in a house) where the vessel arches up amidships and droops at the ends due to imbalance in the distribution of hydrostatic and weight forces. It is also associated with lateral hull deformations like oil canning of the bilges. Without a doubt it is long term and inelastic and not a linear response to still water bending forces.

The mechanism of the hull failure is rot. As the wooden ship structure rots it softens -- as it softens it succumbs to the forces which cause it to hog. The hogging causes seams to open in the topsides, allowing more fresh water to enter, exacerbating the rot, etc.

Inadequacy of beam theory for wooden ships

In the past, engineers have attempted to analyze the structures of wooden ships as homogeneous box girders. This is a common misapplication of beam theory. In traditional wooden ship building, the planking is not joined along the sides and inadequately at the ends. The ship itself, especially as it ages and rots, more closely resembles a bundle of reeds, loosely bound at the ends, with the planks free to slide past each other. If traditionally built wooden ships were box girders, then one would expect to see many tensile failures amidships in the upper deck of a severely hogged vessel; however, this is not the case. Failures in longitudinal structure are infrequent and tend to be scattered almost uniformly throughout the vessel. A simple calculation of the still water bending moment and the sectional properties of the USS Constellation (as if it were a beam) demonstrate this:

Click here to see Figure 1 - The 1854 Stucture.
Hogging moment 2322 ft-Ltons
Sectional Moment of Inertia 4.39E+08
Depth 400 in
Height of "neutral axis" 223 in
Keel stress 22 psi
Deck stress 18 psi
Linear beam deflection 0.04 in
Observed hog 36 in

Clearly a new wooden ship is more beam like, old ones much less so as the table above shows. The calculated stress at the keel, 22 psi, is proportional to a true hog deflection of a fraction of an inch. That stress is also far below that which would cause any true creep in the wood itself.

Consequently, the ideas of strength deck, neutral axis and extreme fiber are irrelevant to an analysis of old wooden ships. With regards to longitudinal strength, there is no proportionality between distance from the neutral axis and direct stress as there is in a true beam. Indeed, microscopic investigations (ref. 3) reveals a generally low level of stress in "hogged" structural members. However, there often is evidence of plastic behavior, creep, around the fastenings. It seems that large overall hog deflections are largely the result of small movements in structure and small rotations and creep around the fastenings - hog does not imply large direct stresses.

Continuing with the bundle of reeds metaphor implies that the ship, due to a weakness in shear, is comparatively poor at resisting longitudinal loads. Although wooden ships are generally stiffer in lateral loading (since the transverse frames are comparatively massive and beam like), as a vessel ages and softens, even these relatively stiff beams can suffer large deformation. USS Constellation was a good example of an old, soft wooden ship with large lateral deflections as well as hog -- behaving more like a wet wicker basket than a bundle of reeds. Pushing up on the bottom of the basket caused the bottom to hog, the sides to bulge out and the bilges to drop as well.

The cold molded shell

We looked at various methods for rebuilding hull strength and preserving the historic fabric of the USS Constellation. From the beginning, the idea of replacing the hull and gun deck planking with a cold molded shell seemed the most promising. This shell would carry all the principal loads, allowing the historic fabric to be preserved, repaired or replaced without regard to how it would affect the strength of the ship.

Analysis Summary

Structural analysis is based on the concept of allowable stress for the materials in question. Allowable stresses are some fraction of the actual, empirically derived, failure stresses. For our analyses, the design stresses were the maximum allowable stresses as specified for the MCM class minesweepers which are a similar size vessel. In addition, we assumed initially that the ship structure had no residual strength and that the hull was completely unstiffened. This turned out to be an exceedingly conservative assumption since the existing hull structure, although slowly yielding, was still resisting all the forces on the ship.

Table 1 Douglas Fir allowable stresses

Stress (psi)
Douglas Fir, Coast Type, Dry Extreme Fiber, Bending Tension Parallel to Grain Compression Parallel to Grain Compression Perpendicular to Grain Shear Parallel to Grain / Horizontal Shear
Allowable Stress (MCM 1 Ship Specifications, February 8, 1982, Section 100) 2,000 1,140 1,466 385 150
Allowable Stress, Douglas Fir Select Structural (Standard no. 17, Grading Rules for West Coast Lumber, Table 11) 1,500 1,000 1,150 625 85
Failure Stress (Wood Handbook, 1987) 12,400 (11,000) 7,230 800 1,130

Beam analysis

Beam analysis is the classical method of looking at global strength in a steel ship. Since the vessel will continue to be a moored attraction, we only looked at the still water loads, which derive from an in balance in the distribution of the hydrostatic and weight forces. Using an estimated lightship weight distribution and several different ballast conditions, we examined several different loading conditions. This table summarized the worst case.

Table 2 Beam analysis results

Units Tension Parallel to Grain Compression Parallel to Grain Maximum Horizontal Shear
1" thick shell, maximum psi 793 1,314 438
Location of maximum -- gun deck shell at bottom shell at neutral axis
Maximum allowable stress, Douglas Fir psi 1,140 1,466 1502
Required shell thickness for longitudinal bending and shear in 0.70 0.90 2.92

This implies that less than an inch of longitudinally oriented wood would be required in the hull and deck planking to resist direct bending stresses, but that three inches of longitudinally oriented fiber is needed to resist the shearing forces. Again, the effect of the transverse framing and other structure was ignored.

Unstiffened finite element shell analysis

The finite element model

Classical beam analysis can not address lateral deflections of the hull. Clearly, the vessel had large deflections in its current condition and we felt that a global f.e. model would give us some insight. We used a three-dimensional, elastic shell half-model to evaluate the stress level of the cold molded shell due to the combination of global and local loads. Again, this was a highly conservative since the ability of the existing structure to limit the deflections of the molded shell was completely ignored.

Table 3 Model parameters

hull thickness 6 "
deck thickness 3 "
modulus of elasticity 1.0 E6 psi
density 34 lb/ft3

Loading and restraints

We did not separately model the mass of the wood structure above the gun deck / hull intersection. Instead, we distributed this mass over the shell in this simple model. Clearly, the hull and deck structure above the gun deck intersection exerts a weight force on the shell. Some of that weight is applied in the plane of the shell, some through the frames, and some through the centerline pillars into the keel. The distribution of that force is problematic and we did not attempt to determine it. The limiting cases are:

All the weight above the gun deck applied along the centerline.
All the weight applied along the sheer.

The method used is closer to a uniform distribution, which we intuitively feel it is closer to the actual loading than the two limiting cases.

Stress results

Neglecting some highly localized effects, maximum stresses in the model were within acceptable limits as summarized in Table 5. The longitudinal and vertical stress in the f.e. model is compared to the allowable tensile stress parallel to the grain for Douglas Fir.

Table 4 Summary of f.e.analysis (unstiffened)

Deflection Normal to Shell Vertical Deflection Long. Stress Vertical Stress Horizontal Shear
(in) (in) (psi) (psi) (psi)
FEM model 0.5 2.0 800 1,000 149
Doug. Fir max. allowed  n/a n/a 1,140 1,140 150

Stiffened finite element shell analysis

To get a more accurate picture of the stress distribution in support of detail design, we enhanced the model to include the orthotropic analysis of the gun deck and side shell, the effect of the residual strength of the internal structure, and improved load distribution.

Residual Strength and Stiffness of Existing Structure

For the purpose of this analysis, our primary interest was the effect of the internal structure on the proposed repair. If the stresses in the shell and the critical connections are acceptable, the existing structure will experience less stress than previously with traditional planking. Since the exact condition of the existing structure was unknown at the time of this analysis, we looked at two extreme cases to estimate the range of possible stresses. Load Case A has a highly effective stiff structure. Load Case B has a soft, ineffective structure.


We used three-dimensional orthotropic shell half-model to evaluate the stress level of the wood shell due to the combination of global and local loads using high order shell elements with midside nodes. As with the previous model, the shell included the side shell up to the gun deck and the gun deck planking. In addition, the new gun deck beams were modeled.

We assumed a portion of the internal structure had some undetermined residual strength and would play a role in stress distribution in the cold-molded shell. The structure modeled included the keel, deck beams for the orlop and berth decks, and stanchions. We varied the load carrying capacity of this structure by changing the elasticity of the material associated with these components. The strength of all the structure above the gun deck as well as the orlop and berth decks was neglected.

However, the weight of all the additional internal structure, including the orlop deck, the berth deck, the spar deck and beams, and the side shell and frames above the gun deck was modeled to get an accurate load transfer to the structure below. To do this we used highly elastic material that was unable to carry significant load.

In all, nearly 2/3 of the lightship weight (minus ballast and rigging loads which was modeled as nodal forces) was represented by this model, using over 13,000 degrees of freedom. Structure not modeled included the keelson, gun deck clamp, gun deck spirketting, all ceiling planks, hanging knees, berthing and orlop deck planking, and others In addition, none of the renewed structure, including the topside planking and ceiling, and spar deck was modeled. In reality, those structures carry some load. The following figures show the arrangement of the f.e. model:

Click here to see Figure 2 Beam elements

Click here to see Figure 3 Shell and beam elements

Composite Properties of Shell

Laminae schedule

We used composite shell elements to model the cold molded planking in the new model. The laminae schedules used in the analyses are summarized below.

Table 5 Laminae schedule used for analysis

Side Shell Laminae Schedule
2” T&G Douglas Fir, 0 o
1" Douglas Fir, 45 o
1" Douglas Fir, -45 o
1" Douglas Fir, 0 o

Gun Deck Laminae Schedule
1" Douglas Fir, 0 o
1" Douglas Fir, 90 o
1.5" Douglas Fir, 0 o

The laminae schedule and the total shell thickness are governed primarily by production issues, the need to match the existing hull thickness, and the requirement to simulate the original planking lines on the final layer.


As discussed previously, two analyses were run to simulate two extreme states of the internal structure. For both extremes, all stresses were within the more conservative allowable limits for the material. Contour plots of this stress are shown on the following page.

Stress Contours

Click here to see Figure 4 Horizontal Shear Stress TX -- Case A

Click here to see Figure 5 Horizontal Shear Stress TX -- Case B

Maximum Deflections

Click here to see Figure 6 Shell Deflection -- Case A

Click here to see Figure 7 Shell Deflections -- Case B

Composite shell results

As expected, the shell is higher stressed when the internal structure is nearly ineffective in Load Case B.

Table 6. Composite shell stresses

Description Variable Units Load Case A Load Case B Allowable for Douglas Fir Select Structural Governing Load Case
Maximum Deflection USUM in 0.87 2.17 -- B
Longitudinal Tensile Stress3 SX+ psi 492 611 1,000 B
Longitudinal Compressive Stress3 SX- psi -463 -992 1,150 B
Tangential Tensile Stress3 SY+ psi 18 104 -- B
Tangential Compressive Stress3  SY+ psi -30 -311 625 B
Shear Stress3 SXY psi 75 100 1504 B
SYZ psi 50 75 150 B
SXZ psi 50 75 150 B
Interlaminar Shear ILMAX psi 14 58 -- B

Additional findings

Because so much of the existing structure was modeled, it was possible to look at stresses in areas of interest. Stresses in existing structure, stresses along attachments to existing structure (e.g. along the keel and stem), and the local effects due to spar and rigging loads. In all of these cases, we found the calculated stresses to be well below the design stresses.

A particular concern was stresses in the original structure. Overall, the stress in the existing structure is very low for both load cases. Since the cold molded shell will be stiffer than the traditional planking, the net result of adding the shell will mostly be to reduce the stress in the internal structure and thus reduce the possibility of failure of original structural members.

Using the composite shell elements, we were also able to look at the interlaminar stresses which were found to be below the design stresses for the materials. A final interesting table is a comparison of direct stresses and deflections found by the different analysis methods.

Table 7 Summary of maximum stresses

Model sigmax  taumax mumax 
Shell alone5 800 psi  149 psi -
Shell + ineffective structure 611 psi 100 psi 2.17"
Shell + effective structure 492 psi 75 psi .87"
All longitudinal structure (beam) 22 psi - .04"


Interpreting the results

Clearly, the results for the stresses in the cold molded shell are very conservative since the longitudinal strength of most of the longitudinal structure was ignored. In general, the detailed finite element results demonstrated what we already knew -- the stiffer the framing, the smaller the lateral deflections and the more the shell behaves like a beam. The shell stresses are higher with the nearly ineffective internal structure, but still acceptably low. For the internal structure itself, the stress levels go up in proportion to its stiffness.

The shell stress levels are generally so low, that it would be possible to save materials by making the shell thinner. However, as stated previously, the shell thickness has to match the current planking thickness, so very little saving is possible. However, the finite element model has helped us optimize the repair to some extent. Now that the Constellation has been opened up, it's clear that the framing is generally in better than expected condition. Therefore, fewer frame futtocks need to be replaced in order to have acceptable transverse strength. In addition, it's clear that the stresses in the core layers of the laminate are generally very low which may allow the substitution of lower modulus materials or the reorientation of the direction of the cores to facilitate the repair. Using three-dimensional orthotropic shell elements allowed us to predict the quantity of shell fasteners needed and their distribution.

Measuring residual strength of decayed wood.

We were not able to accurately model the residual strength of the USS Constellation. It's a difficult task. There have been some attempts to measure the linear/elastic deflection of the bottom panel of a floating vessel by adding or removing weight. We got unsatisfactory results with this method.

As a wooden ship ages, there are three primary effects that degrade the residual strength and stiffness of the structure. These are: degradation of wood properties due to environmental effects (rot, etc.), metal sickness and local bearing failure around fasteners, and true material creep. In addition, in the case of severe rot, whole timbers become effectively disconnected from the structure as a whole. This degradation can be evaluated, to some extent, by local mechanical tests. Because the properties of the wood varies greatly throughout the ship depending on the extent of rot and the age of the wood, a large number of samples must be taken to get a clear picture of the weak points in the vessel. It may be possible to incorporate this data into an accurate analytical model of the structure.

Application to other vessels

This method seems practical for other large wooden vessels where the hull girder has lost much of its original strength and a traditional replacement repair is inadequate. The best candidates are vessels with deep hulls and continuous strength decks such as the USS Constellation; however, it could also be applied to wider, shallower vessels such as the C.A. Thayer or the Wapama at this museum. Regarding the C.A. Thayer, the late Karl Kortum spoke convincingly about the wonderful patina of the ceiling planking and the need to preserve it. With this repair method, it could be preserved.

Failures of other repair methods

Replacement repair

The traditional method of repairing a vessel that has lost much of its original hull strength is to replace rotten material with new. In the USS Constellation most of the vessel was rotten to some degree. The required replacement repairs would have been so extensive, that nearly all the fabric of the ship would have to have been replaced, given the interconnected nature of traditional structure.

Since a hogged wooden ship is not a beam, pieces of longitudinal structure have particular individual importance. Ships hog because of an accretion of small movements. Even a vessel which has no rotten wood can hog. Look at the USS Constitution. Periodically, attempts have been made to restore its hull strength by installing additional structure to the vessel. This, along with refastening and recaulking, may mitigate the hogging somewhat, but does not address the fundamental problem of hull strength.

Adding high modulus structure at "extreme fibers"

It has been suggested in the past that severely hogged wooden ships can be repaired by adding new stiff materials at the deck or keel. If one accepts the wicker basket metaphor for the severely hogged ship, then this method is like attaching a stiff new rim to the old basket - it does nothing to halt the deformation of the rest of the structure.

If a steel box beam large enough to take the entire still water bending moment were attached to the keel of a hogged ship, then all the bending forces would have to be transmitted through the interfaceÉthe fastening problem would be great.

Hogging cables and other external devices

Many people have suggested the use of external devices like cables or buoyancy chambers to supply an external force to counteract the hogging forces. Theoretically, this is possible, but the application is almost always ludicrous. Recently, some well meaning souls attempted to prevent the USS Constellation from hogging by attaching hogging cables to the bow and stern and tensioning them over a support amidships. An elementary calculation would have shown them that the even if the cables were tensioned to the required amount, they would have broken the fittings, cut through the bow and stern, and pushed the support through the deck.


1 We looked for a better word. Failure implies some kind of breaking or fracture. Wooden ships don’t break in half, and some may continue in service for years in a hogged condition. In others, such as Wapama, the hog may induce leaking that is so severe that the ship can’t be kept afloat.
2 This analysis is assuming that all the shell material is oriented at 0o and simply edge glued or edge fastened some way.
3 Maximum value in the shell laminae.
4 Maximum allowable for MCM class vessels.
5 6 inch shell


Tri-Coastal Marine, "Hull Repair Plan for the Sloop of War USS Constellation", June 26, 1997.
Davis, Andy, "Hog - Understanding the Longitudinal Deformation of Wooden Ships," WoodenBoat, August 1993.
Witherell, P.W., et al., "Using Today's Technology to Help Preserve the USS Constitution", Naval Engineer's Journal, Vol. 104, No. 3, pp. 124-134, May, 1992.
Wood Handbook: Wood as an Engineering Material, Forest Service, U.S. Dept. of Agriculture, Agricultural Handbook 72, 1987.

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