Analysis of an 1864 Long-Span Truss Roof
Donald Friedman, P.E., F. ASCE
Old Structures Engineering, PC
90 Broad Street
New York, NY 10004
Philadelphia’s Wagner Institute has a long-span roof completed in 1864, consisting of
wood-and-iron arched trusses supporting wood purlins. The plaster ceiling below the
roof is extensively cracked, and gaps in truss joints are present in some locations. The
truss structure that supports the roof can be analyzed in several diﬀerent ways, and
this ambiguity makes interpretation of the signs of damage diﬃcult. This paper in-
cludes a review of the possible mechanisms that could have been used at the time of
construction incorporating the visible materials, including various forms of truss and
tied arch. This review provided the key to analysis and interpretation of the damage.
In any era, cutting-edge technology may be more diﬃcult to understand than ordinary
work. New technology of the past may have been a dead end that bears little relation to
modern forms. This paper will use the long-span roof at the Wagner Free Institute in
Philadelphia to illustrate the diﬃculty in analyzing structural technology that was ad-
vanced for its time and now obsolete.
Wagner’s 1864 main building houses a natural-history museum. The three-story high
exhibition hall at the second ﬂoor of the building is covered by a single-span roof that is
a “balloon shed,” or arched-truss roof. The roof form is a shallow segmental barrel vault
supported by exposed trusses. These roofs were often used in the nineteenth century
for railroad stations and armories; early examples in the United States include the 1866
Cleveland Union Depot, and the 1871 Grand Central Station and 1879 Seventh Regi-
ment Armory in New York. Unlike these buildings, the Wagner roof arches begin four
stories in the air, not at grade, and rest on relatively thin walls. This roof was built
while structural analysis was still in its infancy. The ﬁrst practical American treatise on
analysis, Squire Whipple’s A Work on Bridge Building, was published in 1847, and
structural engineering was still rare in building design when Wagner was built 17 years
later. (Whipple 1847; Condit 1960, 113-115, 208-210)
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Minor but pervasive damage – cracks in the plaster ceiling below the purlins between
the arched trusses, cracks in the fourth-ﬂoor wall plaster, and open splice joints in the
truss lower chords – were investigated as part of a structural analysis of the roof. Vari-
ous possible mechanisms for carrying load were examined, including the trusses work-
ing as tied arches, the truss top chord working as tied arches with the lower chords and
web braces acting only as local stiﬀening, the ceiling plaster and/or roof deck acting as
tied vaults, and the trusses acting as beam-trusses, not dependent on arching action.
The analysis showed that the method by which the trusses function depending on the
amount of load: under dead load only, the top chord is a suﬃcient arch to carry the load,
while under full snow load the bottom chord is also required.
The original designers worked with a new structural form, but neglected issues that af-
fect load distribution such as wood creep, elongation of the tie rods, wall rotation, and
looseness in the connections. These issues had to be accounted for to perform an analy-
sis accurate to current standards. In short, the technology of the 1860s provided a last-
ing roof, but one that does not work in the way that the builders intended.
Figure 1: Overall view of the main museum space, showing the 2nd ﬂoor, the 3rd and 4th ﬂoor galleries,
and the arched trusses. (n.a. 2000)
General Description of Structure
The main building of the Wagner Institute has a mixed structural system, including
brick exterior bearing walls, interior cast-iron columns, and wood-joist ﬂoors. The build-
ing has four nominal ﬂoors: oﬃce and theater space at the ground ﬂoor, the main mu-
seum ﬂoor above, and two partial gallery ﬂoors at the top. The barrel- vaulted roof
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spans the full width of the building (18.3 m out to out) and consists of a waterprooﬁng
membrane over a wood deck, wood purlins (spanning perpendicular to the vault curve),
and a plaster ceiling on wood lath. The obvious structural support for the roof is a set of
eight arched trusses which are located below the roof so that the truss top chords are
just barely embedded in the plaster. (See Figures 1, 2, and 3.)
Figure 2: Roof Section, Visible Structure
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Figure 3: Roof Section, Major Structure
The trusses fairly represent ordinary building technology of the mid-1800s. The top and
bottom chords each consist of a single wood member with one scarf-type splice. (See
Figure 4.) At the splices, each half of the chord is tapered in width and connected to the
other half by three horizontal bolts. The wood cross-bracing within each truss panel is
not positively connected to the chords but simply bears on prismatic wood blocks. The
wrought-iron “verticals” that run perpendicular to the chords and deﬁne the truss pan-
els are simply bolted through the bearing blocks and chords. (See Figure 5.) In other
words, the verticals are capable of resisting tension but no compression, and the braces
are capable of resisting compression but no tension. Finally, the wrought-iron tie rod at
each truss passes through wood bearing blocks at each end to plate washers. The bot-
tom chord is fastened into the end bearing block with a birds-mouth cut. (See Figure 6.)
The wood deck and ceiling lath are through-nailed to purlins. The purlins rest on top of
the trusses, so most of the purlin- to-truss connections are simple bearing with toe-nails;
four connections per truss are reinforced with vertical bolts through the purlins and
truss top chord.
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Figure 4: Figure 4: Close up of typical scarf splice in truss bottom chord. The two horizontal bolts tie the
splice; two pairs of vertical rods and their bolted ends are visible.
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Figure 5: Typical lower-chord connection.
Figure 6: Truss end connection, with lower chord bird's-mouthed to bearing block.
Several patterns of damage were visible at the roof, but no gross deformation or deteri-
oration of structural material. The most obvious damage was the presence of numerous
cracks across the plaster ceiling, typically parallel or perpendicular to the vault and
spaced at approximately 0.9 to 1.5 m on center. There was little separation or out-of-
plane movement at the cracks in the ceiling; the only cracks observed with signiﬁcant
movement were similar vertical cracks in the side-wall plaster.
The side walls were out of plumb, with their tops tilted away from the interior. The tilt
varied from zero to roughly 100 mm. There is no corresponding damage to the stucco
on the exterior face of the walls; in most cases there was no diﬀerence between the inte-
rior plaster damage at the most-tilted and least-tilted areas.
Two forms of truss movement were observed: lateral sway and open joints. The ﬁrst is
sideways movement of the bottom chords accompanied by out-of-plane tilting of the
cross-braces and verticals. The upper chords are restrained against lateral sway by
their embedment in the plaster ceiling and the bolted purlins, while the remainder of
the truss is free to move laterally. The lower-chord movements were in the form of a
single or a double “S” curve along the chord length, up to roughly 75 mm sideways.
Open joints were observed at the lower-chord splices, with up to 10 mm separations. No
similar separation was observed in the upper-chord splices. Finally, as many as one-
third of the cross-brace to bearing-block joints showed separation up to 6 mm.
Much of the information gained by probing was negatively useful, in that expected dam-
age was not found. For example, even though the decorative wood cornice was in poor
condition, with numerous repairs and rotted areas, truss ends exposed through probing
were in good condition, apparently protected by the continuous main roof directly
above. No splitting or crushing was seen at the truss end probes or the center top chord
probe. Old weathering damage (deteriorated mortar) and repairs to the brick, including
rebuilding and repointing, were observed at some locations. Given that the interior ﬁn-
ish was observed to be wet-applied plaster over wood and expanded-metal lath, the re-
pairs were probably made between the 1880s and 1930s.
Because the roof was built before accurate truss and arch analysis methods were well
known and because the vertical and bracing connections only allow force transfer in one
direction, the trusses were likely were not designed in the current sense. Modern struc-
tural analysis of the roof encompassed both the expected structural mechanism (the
trusses working as tied arches) and alternates. While the analysis showed that the alter-
nates could not work, they help explain some of the damage noted.
The dead load of the roof, including the wood structure, plaster ceiling, and waterproof-
ing, totals 1.2 kPa. Using the standard ASCE 7, Minimum Design Loads for Buildings
and Other Structures (n.a. 2005), the maximum snow load is 1.1 kPa and the maximum
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wind pressure 0.48 kPa downward or 0.72 kPa upwards. Since the maximum down-
ward wind pressure will not act simultaneously with the maximum snow load (the
sloped roof and lack of parapets allow snow to drift entirely oﬀ of the building during
high winds) and the wind uplift is less than the dead weight of the roof, the governing
load combination is the sum of the dead and snow loads. The analyses below were per-
formed for both this combination and for dead load only.
Mechanism 1: Tied Arch A (Figure 7)
The roof was analyzed with the purlins as simple-span truss-to-truss beams and the
trusses as arches consisting of the top chords only.
The tie rods were modeled as ending in plate washers that cover the rear of the end
bearing blocks; later investigation conﬁrmed the plate washers’ existence. (See Figure
8) In this scenario, the truss verticals, cross-bracing, and lower chord serve only as local
stiﬀeners to prevent small areas of unbalanced load from creating signiﬁcant bending in
the top chord arch. Under dead load only, this analysis provided acceptable results in
terms of stress. The tie rods would lengthen approximately 10 mm under dead load and
19 mm under full load. Under full dead and snow load, the top chord would be over-
stressed in compression. Under a 16C temperature change, the truss center moves ver-
tically roughly 6 mm. Under wind load from the side or unbalanced snow load caused
by a combination of wind and snow, the arches could deﬂect asymmetrically as much as
40 mm. All of these movements would contribute to the ceiling cracks observed.
Because the loaded tie rods elongate and the masonry walls are too weak to resist the
arch thrust, the walls would move outward as the roof was completed and the dead load
increased from zero to its maximum. The truss ends, embedded in the masonry walls,
are wood tie-rod bearing blocks. As the trusses were originally loaded, the tie rods
would stretch, allowing the horizontal reaction caused by the arch form to push apart
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Figure 7: Tied Arch A Structural Model
the bearing blocks. This reaction, transferred from the bearing blocks to the surround-
ing masonry, and applied more than 2 m above the upper gallery ﬂoor, would cause out-
ward rotation of the walls. Any tie-rod slack or looseness in the end connections would
cause similar outward rotation. When signiﬁcant snowfall increased the truss loads, the
tie rods would temporarily lengthen, likely causing additional permanent outward tilt.
Forced outward rotation of the masonry would crack the mortar joints on the interior
face and possibly crush them on the outside face and therefore would tend to be one-
way motion. This type of ratchet mechanism, where walls move in only one direction af-
ter they have ﬁrst moved, is common in old and unreinforced masonry. The amount of
tilt observed was far less than would be required to create instability in the walls and is
therefore not dangerous as long as the masonry condition is maintained.
Mechanism 2: Tied Arch B (Figure 9)
The roof was analyzed in a similar manner to Tied Arch A, but using both the top and
bottom chords as compression members. The only diﬀerent result is that the stresses
were within acceptable limits for the combined dead and snow load.
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Figure 8: Truss End Detail
Mechanism 3: Untied Arch (Figure 10)
This analysis is similar to Tied Arch 1, but neglecting the action of the tie rods to ap-
proximate conditions if the rods were installed with their end connections too loose to
take up the outward arch thrust. The stresses in the truss itself are the same as in
Mechanisms 1 and 2, but the bending stresses in the masonry wall from restraining the
thrust are unacceptably high. Using the maximum allowable masonry bending tension,
the roof can support less than 2 percent of the combined dead and snow load.
Mechanism 4: Vault A (Figure 11)
The wood plank that makes up the roof surface was analyzed as a vault. Skylights inter-
rupt half of the between-truss vault panels, so this is a combined mechanism, where
vault action takes place in the uninterrupted panels and the interrupted panels are car-
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Figure 9: Tied Arch B Structural Model
Figure 10: Untied Arch Structural Model
ried by the trusses as tied arches. This type of load sharing is common when deﬂection
from load in a primary structural member (in this case, the trusses) allows load to fall
onto secondary members (the vaults). The stress in the wood was high, but not neces-
sarily unacceptably so. However, the vaults create end thrust similar to the untied arch
and therefore create unacceptably high bending stress in the walls.
Mechanism 5: Vault B (Figure 12)
The combination of the wood plank and plaster ceiling was analyzed as a vault, similar
to Vault A. The stress in the wood and plaster was acceptable, however the thrust prob-
lem is identical. It should also be noted that this mechanism contradicts empirical ob-
servation: if the plaster were in compression in half of the panels, there would be little
or no cracking in those panels, which is not true.
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Figure 11: Vault A Structural Model
Figure 12: Vault B Structural Model
Mechanism 6: Trussed Beam (Figure 13)
The truss was analyzed working as a double-diagonal truss (ignoring the arch shape).
The overall depth of 0.71m is shallow for the span of 18.3m, leading to calculated com-
pressive and tensile stresses in the wood of roughly 34 MPa. This is so far from the al-
lowable stresses in wood that this mechanism cannot be considered realistic.
The roof likely functions in the manner that it appears to, with tied-arch trusses carry-
ing the purlins above. Given the lack of insulation and the open space allowing heat
from three ﬂoors of radiators to collect at the roof, snow load has likely never reached
the code maximum; maximum snow is rare even if the roof is a cold surface. In addi-
tion, the absence of parapets means that there are no valleys to collect snow. For most
of the building’s life, the roof has carried dead load plus small live loads from less-than-
maximum wind and snow. It is likely that the ordinary and maximum load-carrying
mechanisms are not identical: under ordinary load, the top chord is suﬃcient as an
arch; as load increases during snowfall, the trusses deﬂect downward and shorten.
When the lower chords shorten suﬃciently to close the gaps at the splices, the lower
chord will begin to carry load as an arch as well, eﬀectively doubling the arch strength
The gaps at the lower-chord splices may represent nothing more threatening than wood
shrinkage. Eighteen meters of timber can be expected to shorten 20 mm or more along
the grain from drying in service. As the trusses shrank after their installation, the en-
tire arch curve would have lowered, but not all pieces of lumber shrink equally. The
diﬀerence between the gaps may represent diﬀerent original rates of shrinkage be-
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Figure 13: Trussed Beam Structural Model
tween the various top and bottom chord pieces. Since the top chord is necessarily
loaded in compression at all times, it cannot contain shrinkage gaps.
The upward motion of the roof from expansion on hot days, the downward movement
from contraction on cold days and when snow or high winds load the roof, and the dis-
tortion caused by asymmetrical loads are suﬃcient to crack the plaster. Cracks in the
wall plaster can be caused by similar thermal movement. The visible cracks by them-
selves were not dangerous but may be a sign that the portions of plaster keyed through
the lath are cracked. The investigation showed no physical evidence or analytical result
suggesting structural overstress. The damaged plaster was a life- safety hazard but one
caused by natural movement of a long-span roof.
Condit, C. (1960). American Building Art: The Nineteenth Century, Oxford University
Press, New York.
n.a. (2005) Minimum Design Loads for Buildings and Other Structures, ASCE/SEI 7-
05, ASCE, Reston, VA.
n.a. (2000) Library of Congress, Prints & Photographs Division, HABS PA, 51- PHILA,
Whipple, S. (1847). A Work on Bridge Building: Consisting of Two Essays, One Ele-
mentary and General, the Other Giving Original Plans and Practical Details for Iron
and Wooden Bridges., H. H. Curtis, Utica, NY.
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