The behaviour of mixed timber-masonry structures

The behaviour of mixed timber-masonry structures

The main aim of this Master Dissertation, by the author Dhairya Patel is to gain a better understanding of the behaviour of mixed timber-masonry structures through the case study of The West Mill, a mixed timber-masonry structure in Eastern Ontario, Canada using numerical simulation.

 

 

STATE OF THE ART

 

Conducting a numerical seismic analysis of historic constructions is becoming increasingly important in the field of civil engineering as it helps predict the types of failure that the structure can be subjected to in case of a seismic event and is crucial for developing strengthening measures.

Using numerical methods, it is possible to determine if the structure will experience local failure or global failure.

 

 

Seismicity in Ontario, Canada

The seismicity of the site where the West Mill is located is essential to understanding the hazard associated with a seismic event. The West Mill is in the city of Smiths Falls, Ontario which is geographically located in Eastern Canada.

 

Eastern Ontario experiences around 450 earthquakes every year, with most of them being of low magnitude. Natural Resources Canada (NRCan), the governmental department in charge of studying seismicity in Canada, suggests that approximately 3 earthquakes in this region will exceed a magnitude of 5.0 every 10 years.

 

 

Seismic Analysis Techniques

• Response-spectrum Modal Analysis

Modal analysis is a widely used analysis method for the assessment of the seismic vulnerability of a structure. It is a linear analysis method which uses a linear-elastic response spectrum to provide the dynamic response of a structure.

• Pushover Analysis

The pushover analysis is a non-linear static analysis performed by applying an appropriate lateral load to the structure until it reaches collapse, or a specific limit consideration is attained. 

• Non-linear Time History Analysis

A non-linear time history analysis applies a variable acceleration to a structural model with non-linear properties to replicate the ground acceleration that would be caused during a seismic event. The variable acceleration can come from a previously recorded earthquake or can be artificially generated from the seismicity of the region.

 

 

Analysis of Timber Structures

The modelling and analysis of timber-framed structures depend on the wide characteristics of the elements themselves. The elements’ sizes and connection types are important aspects to be considered when modelling timber elements.

 

 

Modelling of Joints

The modelling of joints is the most important aspect when modelling timber-framed structures. The joints are used to model the non-linear behaviour of the timber structure. To model the joints, the lumped plasticity approach is used with a few assumptions:

• First, the timber beam and column elements are assumed to be linear elastic.
• The connections between the elements are modelled using plastic hinges or non-linear springs.

Micro-Modelling

Micro-modelling strategies are useful when the anisotropic behaviour of the timber elements needs to be modelled. In these instances, complex material models need to be used to depict the response of the timber. For the modelling of the interaction between the different members, a friction model needs to be used. 

 

Overall, micro-modelling of timber elements themselves is complex, costly and requires a lot of computational power. Due to these restraints, it is only suitable for the modelling of structural details where localized failures need to be simulated.

 

Another micro-modelling strategy that can be used to model timber structure is modelling the nonlinearity concentrated at the joints, which represents the weakest link of the structure and is where failure usually occurs. This method simplifies the model by using linear-elastic timber elements and lumping the non-linearity in the joints.

 

This approach is appropriate for the West Mill as there are many different types of joints in the building, each with its own stiffness values.

 

 

Macro Modelling

This method is similar to the simplified micro-modelling strategy but instead of modelling the behaviour of every joint, they are congregated into one.
Macro Modelling simplifies the non-linearity of the timber elements for the numerical modelling. It is used to express the global behaviour of the structure rather than describing the detailed behaviour of all components.

The West Mill has many different joint types and geometries with varying stiffnesses so to consider all the different types of non-linearity as one would be inaccurate for this particular case study.

 

 

Analysis of Masonry Walls

 

 

Limit Analysis

Using the limit analysis approach, it is possible to determine the ultimate capacity of a predetermined mechanism for an unreinforced masonry structure with minimal computational power.

 

Micro-Modelling

Micro-modelling strategies are used when the masonry unit and mortar are modelled separately. There are two types of micro-modelling strategies: a detailed model and a simplified model.

Macro-Modelling

Macro-modelling strategies are used when the masonry units and the mortar are modelled as one material with isotropic or anisotropic properties.

Macro-modelling strategies are useful when the masonry wall is solid and suitably large so that the stresses are uniform throughout. It is a more practical approach than micro-modelling due to the lower computational power and time required. This makes the macro-modelling appropriate for the modelling of the West Mill.

 

 

 

 

Analysis of Timber-Masonry Structures

Of the few research works on the topic of mixed timber-masonry structures similar to the West Mill, Ciocci, Sharma & Lourenço (2018) have addressed the possibilities of modelling such structures. They numerically modelled the Ica Cathedral in Peru using linear elastic beam elements for the timber and shell elements for the masonry (Figure 2.25).

Due to the complexity of the structure, the masonry and timber elements were modelled separately and then combined to create the complete structure. The timber and masonry elements were connected by joining the nodes of the beam and shell elements.

The modelling of hybrid timber-masonry structures is not a simple process and can be done in various ways depending:

• on the complexity of the structure,
• the goal of the analysis,
• the extent of the information available.

For conducting the seismic analysis of whole buildings, it is recommended that macro-modelling for the masonry and micro-modelling of the timber joints are used to simplify the complexities of the structures.

 

 

THE WEST MILL

 

The West Mill, which is a part of the larger Wood’s Mill complex, is located in Smiths Falls, Ontario, Canada. The mill is designated by the Government of Canada as a Recognized Federal Heritage Building.

 

 

Historic Overview

The West Mill was originally built in 1852–1855 as a grain mill. It is a part of the larger Wood’s Mill Complex which includes another grain mill, the East Mill, and a grain elevator.

Grain mills started as small timber structures, but as demand grew over the century, so did the size of the structures. As the industry grew, the mills started to be multi-storied structures made of masonry and heavy timber elements, such as the West Mill.

 

Over time, the milling complex has lost most of its functionality with the removal of most of the milling machinery from the mills. Despite this, there is an abundance of evidence as to the previous use and importance of the complex and the buildings within it.

 

 

Design of the Mill

The West Mill is a two story, gable-roofed structure with a basement and an attic:

• The walls of the mill are constructed using coursed and uncoursed limestone blocks.
• When the West Mill was first completed in 1855, the basement was fully below ground along the east façade, and fully exposed along the river facing west and north façades.
• The east façade, which was the principal façade, was five bays long and had the main entrance in the central bay.
• The north and south façades consisted of two windows at each level.
• The west façade consisted of three main windows on the second level and one on the first.
• The mill’s rectangular plan, large stone masonry walls and gabled roof resembles the contemporary architecture of the residential buildings at the time.

Over time, the appearance of the West Mill has changed due to alterations made to it:

• In 1887, the roof was changed from a gabled roof to a mansard roof as seen today, in order to accommodate larger machinery as more space was needed in the attic.
• New limestone masonry was carefully added at the gaps left between the old and new roof.

 

 

MODELLING OF THE WEST MILL

 

Geometry

• The West Mill is comprised of four exterior masonry walls, and a heavy timber-framed interior.
• The building is 18.5 m long, 11.8 m wide and 13.5 m tall at its extents.
• The four masonry walls have a consistent thickness of 610 mm throughout the building.
• The heavy timber frame has varying dimensions for the beams and columns throughout the building. The dimensions were obtained by a thorough laser scan of the building conducted by Carleton University.

 

Definition of the Model

The finite element software DIANA FEA was used to construct the model of the West Mill. The numerical model includes all the timber elements of the structure as well as the four exterior masonry walls. The structure was directly modelled in the DIANA software.
The timber elements were modelled using ClassIII 3D beam elements, and the masonry walls were modelled using curved shell elements.

 

After generating the FE mesh, which was set to a desired size of 0.2 m, it resulted in a model with 69,972 nodes, 9719 CL18B Class-II 3D beam elements, and 16,530 curved shell elements.

 

 

Material Properties

• Timber

The material properties used for timber are assumed based on the results obtained from material testing conducted at the Laurentian Forestry Centre in the City of Quebec, Canada.

• Masonry

The material properties used for the masonry are based on typical limestone and aerial limestone mortar values for historic buildings as stated in ‘Acquiring reference parameters of masonry for the structural performance analysis of historical buildings’ by Kržan et al. (2015).

 

For the non-linear properties of masonry, a total strain-based crack model was used with a rotating crack orientation.

Rayleigh damping was also applied to West Mill, in both the masonry and timber elements. A damping ratio of 5% was used as that is the typical value for civil engineering applications. To calculate the Rayleigh damping parameters, an eigenvalue analysis was run to determine the first two main modes of the structure, and their frequencies.

 

Connections

 

In regard to the boundary conditions for the numerical model of the West Mill, the masonry walls are fixed, while the columns on the basement level are pinned.
For the connections between the timber-timber and timber-masonry joints, two different models were made:

• one with all hinged connections
• other with spring connections between the timber-timber joints.

The timber-timber joints in the roof were kept as rigid connections because the type of connection is unknown and implementing hinges or springs caused a mechanism to occur.

 

The spring model simulates a more realistic way of representing the structure and its behaviour as it allows for the connections to have different stiffnesses. The spring model also accounts for translational stiffnesses whereas the hinged model assumes that the translations between the elements are fixed. The stiffnesses of the various connections were calculated using the components method.

 

In the spring model, the connections between the timber-timber joints are modelled using linear-elastic springs (depicted by purple/orange connectors) and the timber-masonry joints are modelled using hinges (depicted by blue/red connectors). In the hinged model, all connections are modelled using hinge (Figure 4.5).

 

STRUCTURAL AND SEISMIC ANALYSIS

 

A linear elastic analysis, an eigenvalue analysis, and multiple pushover analyses are used to study the structural and seismic behaviour of the structure

 

 

Linear Elastic Analysis

The linear elastic analysis is the primary analysis conducted to ensure that the model of the structure is behaving appropriately under its own self-weight.

 

Eigenvalue Analysis

An eigenvalue analysis was also performed in order to provide a preliminary understanding of the seismic response of the West Mill. It determines the natural frequencies and modes of the structure. The frequencies of the first two modes of the eigenvalue analysis were also used to determine the Rayleigh damping parameters.

 

The percentage of mass of the structure that contributes to the seismic behaviour is calculated for all the modes of the structure. Modes that have a percentage of effective mass higher than 5% were considered to be high modes, and as such were deemed the important modes of the structure

 

Pushover Analysis

A pushover analysis was performed in order to understand the behaviour of the structure under a lateral load until it reaches collapse or until a specific limit consideration is attained. The pushover analysis is considered to be a good predictor of the envelope of the seismic response for the structure.

 

-X Direction

-Y Direction

 

– Elastoplastic Springs

To be able to model the behaviour of the connections more precisely, elastoplastic springs can be used. In the case of elastoplastic springs, ultimate forces and moments for translational and rotational springs, respectively, need to be calculated for each connection type and inputted into the model.

 

PARAMETRIC ANALYSIS

 

A parametric analysis was conducted on the numerical model with springs considering different spring stiffnesses and different masonry material properties. The spring stiffnesses were increased and decreased by 50%, and the material properties of masonry (Young’s modulus, compression, and tension) were also increased and decreased by 50%.

 

 

Increase/Decrease Spring Stiffness

To analyze the effect of the spring stiffnesses on the structure, two models were created where the stiffnesses were increased and decreased by 50%. The masonry material properties remained the same as the original model.

Spring stiffnesses effect on the seismic behaviour of the structure can be seen in Figure 6.1.

 

Increase/Decrease Masonry Material Properties

To analyze the effect of the masonry material properties on the structure, two more models were created where the Young’s modulus, compression and tension of the masonry were increased and decreased by 50%. The spring stiffnesses remained that same as the original model.

Masonry material properties influence on the seismic behaviour of the structure can be seen in figure 6.3

 

CONCLUSION

 

To assess the seismic performance of the mixed timber-masonry structure of the West Mill in Smiths Falls, Canada, the finite element modelling software DIANA was used to numerically simulate the structural and seismic behaviour of the West Mill.

Two different models of the West Mill were created:

• The first model consisted of hinged connections between the timber-timber joints and timber-masonry joints.
• The second model consisted of spring connections with finite stiffnesses between the timber-timber joints and hinged connections between the timber-masonry joints.

Throughout the structure, four different types of connections were identified: contact, nailed, bolted, and mortice and tenon.

 

 

Results:

• Through the linear elastic analysis, it was clear that the model with spring connections showed a more flexible behaviour. This was attributed to the translational stiffness applied to structure that allowed translational movement between the joints.
• Additionally, from the eigenvalue analysis, which was run to obtain the frequencies for the calculation of the Rayleigh damping parameters, it was evident that the structure exhibits box behaviour.
• Multiple pushover analyses were carried out in all directions due to the asymmetry present in the structure.
  • Overall, through the numerous pushover analyses, it was found that the model with spring connections was possibly more accurate in representing the behaviour of the structure as it provided a more realistic description of the joints with different rotational and translational stiffnesses that could be applied.
• • The highly stiff behaviour of the hinged model did not allow the structure to progress past the linear range when conducting a pushover analysis in the Y direction. Applying the spring and then conducting the same analysis allowed the structure to reach the non-linear range in the analysis and conceivably showed a better representation of the behaviour of the structure under seismic loading.
• Two models with elastoplastic springs were also run to observe the influence of these springs on the behaviour of the structure.
  • The first model changed the rotational springs of the mortice and tenon from linear elastic to elastoplastic. It was found that, although minor, this did have an effect of the stiffness of the structure in the non-linear range.
  • The second model which changed the rotational springs of the bolted connection from linear elastic to elastoplastic showed that it also affected the stiffness of the structure in the non-linear range. It was evident that the change to the bolted connections had a higher influence on the structure than the changes to the mortice and tenon connections.
• A parametric analysis was also conducted on the structure to determine if the timber-timber connection stiffnesses and masonry material properties had a large influence on the behaviour of the structure. Overall, it was found that the spring stiffnesses had very minor effects on the overall structure.
• In the linear range of the pushover curves, no differences could be identified between the different models. Slight differences became noticeable in the non-linear range of the curves but not enough to make a significant difference in the overall stiffness and behaviour of the structure.
• The masonry material properties had a significant influence on the overall structure. A reduction in the material properties reduced the load factor that the structure enters the non-linear range by 29% and 32% in the positive and negative X direction, respectively. An increase in the material properties increased the load factor that the structure enters the non-linear range by 19% and 10% in the positive and negative X direction, respectively. The differences in the reduction and increase in the different directions can be attributed to the asymmetry of the structure.

 

 

Future Work

 

The following analyses were identified as next steps in developing the study of the West Mill:

• Further research into elastoplastic springs and the possible laws/equations that may be used in establishing them into the model;
• Modelling the structure with updated elastoplastic springs for all connections to obtain more precise results in terms of the behaviour of the connections;
• Updated parametric analysis to see the influence of the elastoplastic springs on the entire structure;
• A non-linear time history analysis to determine the dynamic behaviour of the structure and comparison with the pushover curves to determine if the structure falls within its envelope;
• Research into various retrofitting solutions as needed.