Simulated seismic testing of two pitched roofs constructed using timber trusses extracted from vintage unreinforced masonry buildings

Two roof structures representing vintage unreinforced masonry (URM) building components were subjected to longitudinal pseudo‐static cyclic loading. The overall roof dimensions were 8.94 m (span) by 3.1 m (length), with each roof incorporating a pair of as‐built timber trusses that were retrieved from two demolished URM buildings. Both roofs were tested first with nailed connections representing original construction and then again with connections that included proprietary metal brackets and straps representing a remediation of the original construction. The loading was applied perpendicular to the trusses, hence parallel to the diaphragm purlins. Damage patterns and deformation profiles were used to interpret the mechanics governing the roof behaviour utilizing existing modelling techniques for timber floors. It was found that the roof behaviour was shear‐dominated, akin to the in‐plane response of timber floors. For the direction of applied loading, both roof stiffness and roof strength were governed by the strength of the connections between the trusses and the diaphragm purlin members and the purlin spacing. Consistent with these findings, a method was suggested to estimate the stiffness and strength of similar roof structures that may have different aspect ratios using the results from the tests. A comparison between the various test results showed that implementing upgrades that were focused on the connections significantly improved the roof stiffness and roof strength.


INTRODUCTION
Earthquake damage to vintage unreinforced masonry (URM) buildings has frequently included the out-of-plane collapse of chimneys, parapets, gable end walls, and top-storey walls. 1,2It is well-established that the actions applied to these building components during an earthquake are influenced by the dynamic properties of the building's primary lateral-load-resisting-system (LLRS), which entails a combination of in-plane loaded masonry walls and the floor/roof diaphragms. 3,4These effects generally include amplification of the ground motion, with a decrease in magnification if the building response becomes inelastic.In a review of empirical evidence, it was concluded 5 that the typical flexible timber diaphragms of URM buildings resulted in the input motion being amplified by a factor close to 2, on average, for many building/earthquake scenarios with PGA values as high as 0.35 g.Similarly, diaphragm stiffness can significantly influence both the magnitude and the distribution of the building base shear that is resisted by the in-plane loaded walls. 6n addition to these effects of horizontal diaphragms, the diaphragm stiffness can also influence the earthquake damage patterns in URM buildings. 7Therefore, the response of horizontal flexible timber diaphragms has attracted considerable research.However, it is high-lighted that with few exceptions (e.g., refs.8-10), most studies have focused on timber floors rather than timber roof diaphragms.The availability of research data including analytical formulations for floors provides the opportunity to study the response of building roofs when recognizing some similarities in the construction forms.Nonetheless, many URM buildings have sloped roofs and include structural elements such as trusses, which are absent in the case of timber floors.Finally, roofs typically have an outer covering such as galvanized corrugated iron (CGI), which is absent for the case of timber floors.Consequently, this study was developed with an overall aim of producing experimental data on the structural earthquake behaviour of pitched roofs including as-built trusses and CGI coverings.
8] Empirical formulations to calculate floor deformation, stiffness, and natural period are based on a fundamental assumption that the floor deformations are primarily a result of nail slip between the floorboards and the joists.This assumption facilitates the use of shear beam theory to derive the respective equations.To formulate the floor in-plane response, the common approach [11][12][13][14] has been to calculate the initial stiffness, K d , following an idealization of the experimental force-displacement curve.The floor stiffness, K d , has next been used to estimate a dimension-independent diaphragm shear stiffness, G d , by assuming pure shear (angular) deformation across the diaphragm.A similar approach was taken in New Zealand Society for Earthquake Engineering guidelines, 18 but with a secant stiffness replacing the initial stiffness used in previous formulations.The utilized secant stiffness corresponds to the ultimate displacement, which has been suggested to be taken as 50% of the thickness of the out-of-plane loaded URM walls.The justification for this proposal is that the out-of-plane wall stability is significantly compromised beyond this displacement.Although the formulations governing the response of floors are not expected to be directly applicable to roofs due to the significant configuration differences highlighted above, it will be demonstrated herein that the inplane response of roofs is also governed by the behaviour of nailed connections.Therefore, the same overall modelling methodology as used for flexible timber floor diaphragms can also be used to derive an empirical formulation for roof stiffness.
In the following, a discussion of typical vintage URM building roofs is provided based on details from textbooks on historical construction.This discussion is followed by the description of four as-built trusses that were retrieved from demolition yards of vintage URM buildings and used to construct two roofs in the laboratory.An account of the roof construction and testing is provided, along with accompanying observations and experimental results.Finally, the general methodology explained above in relation to the in-plane response of timber floors is adopted to characterize the roof stiffness and strength properties.

URM building roof construction forms
Many existing vintage URM buildings have pitched or hipped sloped roof shapes, with recent characterization studies (e.g., refs.19-21) reporting that approximately 50% of all pre-1945 URM buildings in the State of Queensland, Australia, had a pitched roof.A review of historical academic textbooks on roof construction [22][23][24][25] suggests that various structural forms may be encountered in these roofs.A full description of truss and roof types is beyond the scope of this study and the details can be found in textbooks, but in summary it can be concluded that small-dimension buildings with a roof span of less than approximately 3.3 m (11 feet) typically have no prefabricated roof trusses, and instead the roof is commonly constructed using a combination of rafters and struts.In contrast, the roof of URM buildings that have larger spans can include standardized timber trusses, such as the two examples shown in Figure 1.The trusses shown in Figure 1 are a King-Post truss (KP; Figure 1A) and a King-Rod truss (KR; Figure 1B), with the names 'King', 'Post' and 'Rod' referring to the central vertical member of each truss.These trusses are suitable for diaphragm spans of up to 10 m, with URM buildings having larger spans being roofed with other types of trusses such as a Queen-Post truss which has no central member and is suitable for spans of up to 15 m.A KP truss (Figure 1A) is made up of six timber members, including two principal rafters (PR), a main horizontal member at the bottom called a 'tie beam', two struts and one vertical 'post' at the center of the truss.A KR truss (see Figure 1B) is a close variation of a KP truss, in which a rod replaces the central timber post.During building construction, a typical truss spacing of approximately 3 m (10 feet) was assumed, with various secondary members being used to create the final roof as shown in Figure 1(A).It can be seen from Figure 1(A) that two purlins were connected to the principal rafter of the truss and provided support for the common rafters (CRs).While only a few (2-3) purlins are used at relatively large (e.g., ∼2 m) spacing, the CRs are closely-spaced with a typical C/C distance being 800 mm (not shown in Figure 1A).The CRs were supported by both the purlins and the ridge beam and provided a support for timber boarding, which was used as a support for the exterior roof covering.Alternatively battens (B; timber joists with relatively small cross-section dimensions of 25-50 mm) were used in place of timber boards as a support for external covering.Finally, a ceiling may be present in some roofs (e.g., visible in Figure 1A, B) although it may be missing in some buildings.To construct the ceiling, timber joists were spaced at approximately 300 mm and connected to the truss tie beam either from below (Figure 1A) or above (Figure 1B).However, the role of the ceiling in increasing the roof stiffness may not be significant and any improvement should be considered with caution.Due to the general flexibility of the trussed roof structures, the primary roof response affecting the out-of-plane stability of the connected gable ends is the relative in-plane deformation of the roof diaphragm (excluding the ceiling; see also ref. 8).For analytical modelling of buildings including a pitched roof with ceiling, especially for the purpose of seismic assessment of the connected masonry gable ends, it is advisable to model the roof and ceiling diaphragms separately as these can have different and/or out-of-phase behaviour.
The construction form shown in Figure 1(A), in which the trusses, purlins, and CRs are present is here referred to as 'elaborate'.An alternative, simpler, roof construction using timber trusses has also been documented in the related literature (ref.23; Figure 1B).In this simpler construction (here referred to as 'simple'), the purlins are laid at a closer spacing than usual (e.g., at about 800 c/c).The closely-spaced purlins provide sufficient support for battens, or alternatively roof boards, or even for directly attaching the CGI covering without the need for CRs.

AS-BUILT TIMBER TRUSSES
Recent demolition of two URM buildings in the State of New South Wales (NSW), Australia, provided an opportunity to retrieve two KR and two KP trusses, with each set belonging to a different building.The KR and KP trusses belonged to, respectively, a hospital building and a commercial warehouse.The hospital building (Former Orange Base Hospital; Figure 2A) was erected in 1933 and included several wings, each featuring a hipped roof with terracotta roof covering.The existing architectural and structural drawings for this hospital building were found to have minimal details, although a part of the roof cross-section was visible, as reproduced in Figure 2(B, C).During the demolition in 2017, many Queen-Post and KR trusses (see Figure 2D) were extracted by the involved contractor and stored in a warehouse (see Figure 2D).The details in Figure 2(B, C) suggest that these trusses were seated on a concrete beam at the top of the URM walls and supported a ceiling.Similarly, two KP trusses that had been extracted from another building by a demolition contractor and stored outdoor in the conditions shown in Figure 2(E) were found in another demolition yard in NSW.It is highlighted that both Figure 2(D, E) show typical trusses from the respective buildings and the actual available trusses that were used are shown in other photos in this report.In particular, the used KP trusses had a recess in half length of the tie beam, potentially created to add more room space.This recess is visible in some of the figures of this report.These trusses were extracted from a commercial warehouse in the Alexandria suburb of Sydney, although no other information was available from the F I G U R E 2 Assumed two-way spanning wall prototypes for a two-storey building.
F I G U R E 3 Surface texture and cross-section of the wood species.
contractor.Two trusses from each building were transferred from NSW to the structural testing facilities of Queensland University of Technology and then used in the construction of representative roofs.
The construction form of the stored trusses matched that discussed earlier and included a tie beam at the bottom, two PRs at the sides, two struts, and a central vertical member.In addition to these members, two tension rods that assisted in sustaining the tie beam at two intermediate locations were provided.Most member connections were tenon and mortise (see Figure 3A for one tenon example) and/or metal straps (one is visible in the PR connection to the tie beam in Figure 4A).However, some internal truss connections were made up of only two nails, which had undergone severe corrosion.
The timber species of both trusses was visually identified as Douglas Fir (Oregon).This wood species was predominant in the Australian construction industry up until the 1980s, when its supply became limited due to environmental reasons.Similarly, visual observations of the surface texture and cross-section (see Figure 3) suggested that apart from the surface deterioration and discoloration, the timber was overall in a good condition.It was found that the tension rods were not positively engaged, with the end bolts standing greater than 20 mm away from the member face.The likely reasons for the slack tension rods were attributed to shrinkage and creep of the timber.These bolts were fastened before testing to ensure that the tension rods were engaged in resisting forces.The timber density was determined by weighing a part of the truss and is listed in Table 1 along with various geometrical properties.

ROOF CONSTRUCTION
Two representative roofs (see Figure 4) were constructed using the as-built trusses and new secondary members, and each roof was tested twice.The first tests were conducted with conditions that were deemed to have been similar to the original construction details shown in Figure 1, including nailed connections between all new members and the trusses.However, the second tests on each roof included a strengthening scheme that focused on the upgrade of connections and/or sheathing.
Based on visible evidence on the retrieved trusses of prior nailing, it was determined that the KR trusses from the hospital building belonged to a roof that was referred to in the Introduction as 'elaborate' construction (Figure 4A).Conversely, the KP trusses were derived from 'simple' roof construction similar to that shown in Figure 4(B), with the roof type excluding the use of common rafters and battens.Accordingly, the trusses were used to build roofs with respective construction forms and with CGI covering but without a ceiling, irrespective of the original construction.
The trusses were spaced 3100 mm apart on a strong floor and supported at their ends with boundary conditions that are explained in the next sections.Although the KR and KP truss lengths were slightly different (see Table 1), the end supports were positioned so that identical plan dimensions of 8940 mm span by 3100 mm depth were obtained for both roof types as detailed in Table 2 (see also Figures 5 and 6).The major geometrical difference between the two roofs was their heights (see Table 2), which was a result of the different truss pitch angles as detailed in Table 1.
Each roof was subject to two tests, with the first test including ordinary nail/screw connections and the second test including upgraded connections and/or sheathing.The test designations in Table 2 represent these four tests, with RX and RXU indicating tests without and with connection upgrade, respectively.
Due to the nonavailability of Oregon construction timber, widely available machine-graded pine (MGP) of Grade 12 (MGP12 with characteristic bending and tensile strengths of 28 and 12 MPa) was used as purlins, common rafters, and battens.This timber species has a Young's Modulus of 12,700 MPa that is comparable to that of Douglas Fir species

Roof upgrade
From the observations during the first test on each roof (Tests R1 and R2) it was determined that most damage occurred at the purlin connections to the principal rafter of the trusses (P-PR connections).Therefore, proprietary timber connection products from Pryda, Australia, and New Zealand were used to improve a selected number of connections in preparation for Tests R1U and R2U.In addition, Test R2U included a timber underlay to improve the diaphragm action.The connection upgrade was made using two Pryda Unitie© 170 × 32 at each P-PR connections, with the locations marked by X in Figure 5(A, C) (also see Figure 7(B-E) for connection details).In addition, R1-specific connections CR-P and batten-CR were strengthened using, respectively, one Unitie© (Figure 7B) and one Multigrip© (Figure 7C).Approximately 50% of batten-CR connections (i.e., every other joint) were strengthened due to the relatively large number of these joints.An exception to the upgrades described above was that steel straps had to be used at the top-most (Figure 7D) and the bottom-most P-CR connections in R1U due to the lack of suitable access for Unities.As per the manufacturer's recommendations, a minimum of 4 × 35 × 3.15 timber nails (see Figure 7A) was used, with rare exceptions, on each connecting timber member.The sheathing diaphragm of R2 was stiffened using a 21 mm thick, F11 structural grade, tongue-and-grooved, plywood underlay with details shown in Figure 7(E).The plywood was connected to purlins using 8 -10 × 50 mm Phillip screws at every 200 mm.

Boundary conditions
Each roof was connected to the strong floor at only four points, which were comprised of basically both ends of the tie beams (see Figures 4A, 5, and 8).The tie beams are commonly either seated on a wall plate or mortised and receive specific tenons from the wall plate. 22No evidence of designated mortised areas could be found on the tie beams of the trusses that were used in this study, indicating that the trusses were simply seated on the walls of the original buildings.Trusses in these conditions are susceptible to out-of-plane rocking which can initiate under relatively small amounts of diaphragm in-plane forces.However, it was impractical to replicate this boundary condition in the tests because if simply seated on wall plates, the trusses would be susceptible to uplift given the aspect ratio of the roof and even potentially sliding.In real buildings the uplift force is relatively small due to the roofs being typically much longer than that constructed in this study.Nonetheless, limited truss out-of-plane rocking can still occur because the relative flexibility of the timber posts.To ensure data are provided on the realistic contribution of trusses to the roof in-plane stiffness, it was decided to assume different truss base fixity in the tests.Roof R1 was tested with pinned ends that allowed the truss to rotate out-of-plane about the base (see Figure 8A, B).In Roof R2, the tie beam ends were 'propped' to prevent shear sliding but allow restrained rocking (see Figure 8C).It is acknowledged that this configuration makes direct comparison between the roof responses difficult; however, as explained later it was found that the trusses had inherent weaknesses that caused pre-mature out-of-plane mechanisms forming at the PR-Tie beam connection irrespective of the base fixity.Assuming a typical building plan aspect ratio of two, a real-world roof can include approximately seven trusses if spaced at 3100 mm.Therefore, the roof sheathing is continuous at several truss intersections, which is a condition that was impractical to reproduce in the tests conducted herein.As discussed later, the effect of the roof length can instead be analytically included in predictive methods by ignoring truss out-of-plane stiffness based on the observations made in this study.

TESTING AND OBSERVATIONS
The roofs were subject to reverse cyclic displacements (push-pull) that were delivered through a pinned connection at the apex of the trusses referred to as 'T1' (see Figures 4B, 5, and 7D).Although roof inertial forces including that from attached gables have a distributed nature, the application of distributed force was difficult to achieve.For practicality, it was considered that a point load is applied, and a study of load effects is completed analytically in future stages of the research.
In addition, for the considered typology (also described in Khattak et al. 20 ), the inertial forces from attached masonry gable ends considerably outweigh the light roof self-inertia.Therefore, roof can be subject to forces primarily delivered to one of the trusses that are nearest to the gable end.In unretrofitted conditions, these forces are to be transferred through the roof via the ridge beam and the nearby purlins.Therefore, no tie rods or distributing beams were used to transfer the forces across the roof length during these tests.The response of the other truss (T2) was constrained to T1 by a ridge beam and two purlins that were located within 300 mm on either side of the apex (see Figure 5), in addition to the general diaphragm action.As explained later, responses of T1 and T2 were found to be similar, with the largest differences recorded at the extreme 'pull' displacements.In these cycles the various roof connections responsible for load transfer were subject to tensile forces, and as a result T2 could not recover all the applied displacements.
Displacements were incrementally increased, with the increments progressively increasing throughout the testing.Increments of 1, 2, and 5 mm were used, respectively, for displacement ranges of 0-10, 10-30, and 30-150 mm.The speed of testing was initially 0.5 mm/s and increased up to 2.5 mm/s for longer ranges of displacements, and each displacement cycle was completed twice.
Roof R1 was tested up to 65 mm, which was sufficient to measure low displacement range response.The incurred damage was limited to nail slip, and the roof at the end of testing had a residual displacement of 30 mm at zero applied load.At this state, the nails at damaged connections were hammered back to their original positions, where possible, and connection upgrades were undertaken for re-testing as R1U.
Roof R2 was tested to 150 mm and underwent major damage before it was repaired, upgraded, and retested.The repair included replacement of CGIs, the top hat, and the six lower-most purlins in addition to the upgrade as described in the previous sections.
The observable damage to both roofs at the small to intermediate range of displacements was primarily nail slip at P-PR connections but also to a lesser degree at CR-P connections (present in R1 only).It is highlighted that the purlins were oriented parallel to the loading direction, and therefore their connections to PRs are critical for roof shear resistance.Batten-CR connections that were present in R1 were visually assessed as being undamaged, likely due to the nail slip mechanisms that formed underneath the battens and between the purlins and truss PRs.At extreme displacements, localized damage also occurred to the truss members and/or internal connections.Testing of the upgraded roofs resulted in damage that was focused in the same areas and included both nail slip and metal connector bending/tearing as further discussed in the following sections.

Roof R1
At the conclusion of testing R1, nail slip had occurred in many P-PR and CR-P connections, but the diaphragm sheathing above the common rafters (i.e., CGI and battens and their connections) appeared to be intact.This damage distribution is due to the loads being applied directly to the trusses and transferred to battens and CGIs only through the connection between purlins and truss PRs.Both P-PR and CR-P connection damage was more severe in the joints located closer to the tie beam end supports, with the reason being attributed to the larger shear forces.Figure 9(A) shows the extreme level of P-PR damage, which was recorded at the pinned supports (either ends of the T2 tie beam) and Figure 9(B) shows similar damage to a CR-P connection near the pinned end support.This nail slip was likely due to the extreme curvature at the end of CRs that were subject to bending as a result of the perpendicular loads.This condition is analogous to bending of joists in timber floors subject to forces oriented perpendicular to joists.At the end of R1 testing, 0.9% inelastic drift (30 mm displacement) was recorded at zero applied load.
During testing of R1U that included displacements of up to 150 mm it was observed that the increasing roof displacements were accommodated by a combination of overall flexibility of timber members, buckling of the top hat (Figure 10A), and nail slip at the strengthened joints (Figure 10B).However, the ultimate mechanism was formed by a complete failure of the metal connector at the lower-most purlins and cracking of one end of the tie beam close to those connections (see Figure 10C, D).

Roof R2
Test R2 resulted in major damage to P-PR connections, especially for the lower purlins.Approximately half of the purlins that were located closer to the tie beam end supports had completely separated from the truss PRs (Figure 11A) at the end of testing and had to be replaced before Test R2U was begun.In addition, the top hat underwent buckling and distortion due to the roof displacements.Testing of the strengthened R2U resulted in tearing or bending of the proprietary Unities and nail slip that was distributed among all P-PR connections.The roof peak strength was reached due to a mechanism forming at the supports that included cracking of the tie beam and rotation of the PRs about their connections to the tie beams (Figure 11C).It is highlighted that the main connection shown in Figure 11(C) between the PR of the truss and the tie beam was a bolt, which was unable to prevent PR out-of-plane rotation.Therefore, it is likely that the truss did not contribute significantly to the roof in-plane stiffness.In summary from the above discussions, damage was observed to P-PR and CR-P connections that was consistent with, respectively, direct shear at joints or extreme flexural curvature at the joints.Both these connections were most severely damaged when located near the end supports, with the reason being attributed to, respectively, larger shear forces and larger CR curvature in these areas.This pattern was repeated for both non-strengthened and strengthened roof cases.Localized damage to the truss tie beam occurred under extreme displacements.In addition to the visible damage, it was found that the top hat that was situated at the location of maximum bending had buckled.

Roof R1
The force-displacement curves of R1 and R1U corresponding to the apex of T1 are shown in Figure 12(A, B), respectively.The force-displacement curves corresponding to the apex of T2 were effectively the same as these plots and not shown Force-displacement curves corresponding to truss T1 of R1 and R1U.

F G U R E 1 3
Force-displacement response of R2 and R2U.
for clarity (unlike that for R2, which is discussed later).The data in Figure 12(A) shows a pinched hysteresis response with stiffness degradation but with increasing resistance until the test stopped at 67 mm displacement.The deformations that were imposed during loading push cycles were mostly recovered during unloading cycles, but at the end of each pull unloading there was a residual displacement including 30 mm in the last cycle.The behavioural data in Figure 12(B) shows that progressive inelastic deformations occurred during both push and pull cycles and that at the extreme cycles, residual displacements were in the order of 65 and 35 mm, respectively, for pull and push cycles.A plateau started to form at an applied force of 13.5 kN which corresponded to approximately 3% lateral drift.

Roof R2
The hysteresis behaviour of both T1 and T2 trusses of R2 are overlapped (as solid and dash-dot lines) in Figure 13(A).The main difference between these two responses is in the last few cycles, where the progressive roof damage resulted in T2 displacements being smaller than those of T1 by up to 20 mm.The roof strength in the push direction was 14.5 kN and reached at a displacement of 120 mm.The roof gradually lost about 30% of its strength in the next few cycles due to the separation of purlins from rafters (see Figure 11A).Additional strength was gained with increasing displacement due to the re-distribution of the forces to the other members.At a maximum displacement of 175 mm (pull cycle) the testing was discontinued to prevent damage to the test setup.It can be inferred from the plots in Figure 13(A) that the progressive roof damage resulted in residual displacements of up to 60 mm.The behavioural data Trusses T1 and T2 in test R2U is shown in Figure 13(B).Similar to the case of R2, the displacements recorded at were smaller than those for T1, especially in the long displacement range.The maximum recorded strength was 29.7 kN, and as discussed earlier this applied force resulted in severe damage to the lower-most purlin connections.The strength was more than 100% greater than that of R2.A detailed discussion of the improvement in the roof stiffness and strength due to upgrades is presented using idealized behavioural models in the next sections.

Backbone curve idealization
Backbone curves of T1 are shown in Figure 14 overlapped by respective idealized bilinear models.These models were constructed assuming that the post-peak stiffness is equal to the average gradient of the experimental data from 50 to 100 mm (or the maximum experimental datapoint of 67 mm for Test R1).This assumption was made for consistency with the related literature 11,27,28 and also due to the experimental stiffness remaining near constant in this region.The yield force was calculated using the equal energy principle and assuming an ultimate displacement of 100 mm for both experimental and idealised models.Key response parameters were calculated from these curves as listed in Table 3.The values in Table 3 and the comparisons in Figure 14 suggest that the upgrades in each roof improved the behaviour, with the initial stiffness, K 1 , increasing by 50% in each case.Similarly, the post-peak stiffness, K 2 , was increased by about 150% for both roofs due to the upgrades.As the improvements due to both the simple upgrade (R1) and the more extensive upgrade (R2) were similar, may conclude that the enhancement due to plywood overlay was less pronounced than that reported for plywood overlays on horizontal floors. 27,28The reason for this difference is predominantly attributed to the discontinuity that existed at the ridge beam in the tested roofs.
The comparisons also show that yield force, F y , was increased by 36% and 40%, respectively, for R1 and R2 because of the upgrades, while the bilinear ultimate strength (at 100 mm) was increased by 79% and 86%, respectively.These results indicate that significant improvements in the long range of displacement can be expected by undertaking simple connection upgrades, while more significant strengthening is required to achieve meaningful improvement of roof behaviour in the small range of displacements.Finally, it can be concluded from Table 3 that yield drift were the same (1.4%) for both R1 and R2, but the value slightly decreased to 1.3% in the upgraded test cases (R1U and R2U).
The stiffness and strength data from these idealized models are used in the next section to propose diaphragm stiffness values for use with roofs having other aspect ratios.

ROOF STIFFNESS AND STRENGTH
The roof displacements at six main locations (see Figure 5B, D) were used to construct the deformed profiles shown in Figure 15.As the measurement points were located on the face of the trusses, the shown profiles represent truss deformations.It can be seen from these diagrams that both horizontal and vertical profiles have parabolic shapes.This deformation pattern is consistent with shear-dominant behaviour that is associated with a greater intensity of damage at locations closer to the supports (truss ends).
A schematic of roof deformation pattern is shown in Figure 16 that is based on a similar concept to that assumed for floor diaphragms (e.g., in refs.11-14, 29) except that the purlins in Figure 16 have replaced the floorboards in a timber floor study.Due to symmetry, only half the area is shown for a roof with a total valley (inclined) dimension of L and subject to a total in-plane force F. The applied force generates a maximum deformation of D at the apex.
It is highlighted that several sources of deformation can theoretically contribute to Δ but many of them have been neglected in the following empirical formulation.This simplification is based on the damage observations that suggest most deformations occurred at P-PR connections.Nonetheless, deformation can theoretically take place in all load path elements.For simple construction, the second-most important source of deformation is the shear behaviour of CGI, whose effect in the formulation presented in the current study is aggregated with P-PR nail slip.For elaborate construction, the second-most important factor contributing to deformations appeared to be P-CR connection damage.Conversely, damage to CR-batten connections and CGI connections was not visually detected.
With simplifications inherent in Figure 16, and using the notations therein, an equivalent shear stiffness G d can be obtained using static equilibrium such that, Equation ( 1) can be rearranged to obtain the roof stiffness, which is equal to K d = F/Δ, This equation is applicable for a point load at the centre of the roof and is the same as that cited by ref. can also be traced back to FEMA 273. 30It is noted that refined formulations have also been proposed in refs.13, 14 and in ref. 16 that are based on a parabolic applied force pattern.
As K d can be calculated experimentally, that is, using the bilinear data in Table 3, the equivalent G d can be estimated by rearranging Equation (2) as, Similarly, the diaphragm yield strength per unit width (B in Figure 16), v y , can be obtained from Equation (1) as: and after simplification, The roof dimensions from Table 2 and the bilinear properties from Table 3 were used to calculate diaphragm strength and stiffness parameters G d,1 , G d,100, and v y , as summarized in Table 4.In addition, Table 4 includes default values (where available) of these parameters for timber diaphragms with straight sheathing as suggested by NZSEE 18 and ASCE. 29rom Table 4 it can be found that the strength per unit length, v y , for non-strengthened roofs (R1 and R2) were, respectively, 0.8 and 1.6 kN/m, and that these values improved by 38% when the roofs were strengthened.
The 100% higher strength of R2 compared to R1 is attributed to the larger density of P-PR connections in R2.A total of four purlins existed on each valley of R1, while in R2 this number was six in addition to the ridge beam.As a result, more shear-resisting purlin connections existed in the vicinity of the wall plate of R2 than that in R1.Based on this observation, it can be concluded that purlin spacing is a key parameter affecting strength and stiffness of pitched roofs in the direction perpendicular to the trusses.For the elaborate construction form, this spacing is rather large (in the order of 1800 mm as implied from Figure 5), whilst for cases where common rafters are absent and the roof covering is directly laid on frequent purlins, the spacing is typically relatively small (in the order of 800 mm).The average recorded strength per length was 1.2 kN/m in non-upgraded conditions, which is significantly smaller than the default values suggested in NZSEE 18 and ASCE 29 for floors with straight sheeting.The relatively large differences are attributed to several factors, including the smaller aggregated number of nails in all P-PR connections (in total four for each purlin) compared to a significantly larger number of nails in a typical floor.The structural form of the roofs dictated that a total of 16 and 28 PR-P connections existed, respectively, in R1 and R2.In comparison, a typical floor with a span of 10,000 mm can include 50 floorboards, each being secured using two nails at every joist intersection.Other factors contributing to the smaller recorded strength include the lack of a ceiling in the current tests, as opposed to the assumptions made in proposing NZSEE 18 values.Similar reason as explained above contributes to the smaller G d values shown in Table 4 for roofs compared to ASCE 29 and NZSEE 18 recommendations.
In summary from this study, it is recommended that the stiffness and strength values obtained from Table 4 be used when assessing existing pitched roofs with similar construction details.The yield strength per meter (v y ) of a pitched trussed roof with 'elaborate' and 'simple' construction and original nailed connections can be taken as, respectively, 0.8 and 1.6 kN/m.These strength values can be increased by 38% by utilising connection improvements.Similarly, initial and postpeak stiffnesses G d,1 and G d,2 from Table 4 can be used to create idealised bilinear roof models for the purpose of response calculation.Alternatively, secant stiffness G d,1 and G d,100 can be used to assess similar roofs following methodologies described in, respectively, refs 29 and 18.

CONCLUSIONS
Two pairs of as-built timber trusses were used to construct two different pitched roofs representing that of vintage URM buildings.Each roof was subjected to two reverse cyclic static tests, one with normal nailed connections and one including upgraded connections and other improvements representing a remediation of existing roofs.Each roof had a distinct construction form that was referred to as either simple or elaborate.However, both roofs had CGI covering and excluded ceilings.The tests showed that roof deformations were primarily accommodated by damage to connections between the PR of trusses and the purlins, especially closer to the truss ends (near wall plate).Therefore, a small purlin spacing is a key parameter that is associated with increased strength and stiffness of pitched roofs in the direction perpendicular to the trusses.Force-displacement curves showed successive inelastic deformations that took place as a result of connection damage, with each cycle including residual displacements.The bi-linearized stiffness and strength properties were estimated and discussed in the context of available data from research elsewhere.It was concluded that a construction form that was referred to as 'simple' in this research was associated with a greater strength and stiffness due to the smaller spacing of purlins, hence a more effective distribution of shear-resisting PR-P connections near the end of the truss span.
The test results suggest that the roofs had smaller strength, v y , and stiffness, G d , when compared to typical timber floors.These differences are mainly attributed to the difference in the number of shear-resisting nailed connections that are present in the horizontal shear load path.Empirical formulae were suggested for calculating stiffness and strength based on the concepts borrowed from timber floor modelling.
The testing and data interpretation suggest that for the purpose of calculation of stiffness and strength parameters of roofs with similar configurations, an initial shear stiffness G d,1 in the range between 128 and 288 kN/m can be used for the roof diaphragm excluding the ceiling depending on the roof construction.Other stiffness parameters such as post-peak stiffness and stiffness at 100 mm were also recommended, which may be useful in different assessment procedures.

F I G U R E 4
URM building roofs.TA B L E 1 Details of retrieved trusses.

( 10 ,
300-13,400 MPa), although the strength of MGP12 is smaller than that of Douglas Fir.Based on prior nail usage observed on the trusses, two 75 × 3.75 mm bullet-head nails (see Figure7A) were used to connect the purlins (2 × 45 × 90 for Roof R1 and 190 × 45 for Roof R2) at each PR connection.A similar nail pattern was used for CR-P connections, which only existed in R1.A ridge beam of dimensions 180 × 35 mm was connected to the trusses using either standard joist hangers (R1) or tenoned into a designated mortise area in R2.Sheets of zinc-coated, 762 mm wide, corrugated galvanized iron (CGI) with 0.42 mm base metal thickness were used to cover each valley of the roofs, and 0.55 mm thick bent iron was used to join the two valleys at the ridge.The CGIs were connected using roof screws (12 -11 × 65 mm Hex type) except in R2 where standard 60 × 3.75 mm roof nails (see Figure7A) were used.An overview of various nail and screw details used in the roof construction is shown in Figure7(A).

F I G U R E 6
Diagrams of roof R2.

F I G U R E 7 F I G U R E 8
Different connection materials used in roofs.Boundary conditions.

F I G U R E 9
Roof damage during test R1.
11 for floor diaphragms and underpins recommendations in ASCE 29 for floor diaphragm assessment.The original of the equation F I G U R E 1 6 Roof deformation mechanism in plan.
Details of roof tests.
TA B L E 2 F I G U R E 5 Diagrams of roof R1.
1 4 Backbone curves and bilinear properties.Summary of experimental data and idealized response.
a Extrapolated value.
Shear strength and stiffness.