Conference PaperPDF Available

Analytical Modelling of Heavy Timber Assemblies with Realistic Boundary Conditions Subjected to Blast Loading

Authors:

Abstract and Figures

Several existing studies, investigating the performance of heavy timber assemblies with realistic boundary conditions, have concluded that using simplified modelling tools such as single-degree-of-freedom (SDOF) modelling may not be sufficient to adequately describe their behaviour and predict the level of damage observed during blast events. A two-degree-of-freedom (TDOF) model, dubbed BlasTDOF, that captures the effects of boundary conditions in the overall system response and includes considerations for high strain-rate effects and semi-rigid boundary conditions is presented and discussed in this paper. Sensitivity analyses were conducted for various cases using single- and two-degrees-of-freedom modelling in order to make recommendations on the needs and appropriateness of using more advanced modelling. It was determined that the use of SDOF modelling is adequate when the connection resistance and stiffness exceed those of the timber element by ratios of one and ten, respectively. For the cases where these conditions could not be met, the use of TDOF modelling was determined to be required in order to accurately model the timber assembly.
Content may be subject to copyright.
MAT063-1
CSCE Annual Conference
Growing with youth Croître avec les jeunes
Laval (Greater Montreal)
June 12 - 15, 2019
ANALYTICAL MODELLING OF HEAVY TIMBER ASSEMBLIES WITH
REALISTIC BOUNDARY CONDITIONS SUBJECTED TO BLAST LOADING
Viau, Christian1,2 and Doudak, Ghasan1
1 University of Ottawa, Canada
2 cviau037@uottawa.ca
Abstract: Several existing studies, investigating the performance of heavy timber assemblies with realistic
boundary conditions, have concluded that using simplified modelling tools such as single-degree-of-
freedom (SDOF) modelling may not be sufficient to adequately describe their behaviour and predict the
level of damage observed during blast events. A two-degree-of-freedom (TDOF) model, dubbed BlasTDOF,
that captures the effects of boundary conditions in the overall system response and includes considerations
for high strain-rate effects and semi-rigid boundary conditions is presented and discussed in this paper.
Sensitivity analyses were conducted for various cases using single- and two-degrees-of-freedom modelling
in order to make recommendations on the needs and appropriateness of using more advanced modelling.
It was determined that the use of SDOF modelling is adequate when the connection resistance and stiffness
exceed those of the timber element by ratios of one and ten, respectively. For the cases where these
conditions could not be met, the use of TDOF modelling was determined to be required in order to
accurately model the timber assembly.
1 INTRODUCTION
Threats of blast explosions on buildings and infrastructure are typically addressed through blast design
provisions (e.g. Unified Facilities Criteria Program 2008, ASCE 2011, CSA 2012). These standards provide
designers with guidance to perform blast analysis and design, and include items such as high strain-rate
effects, response limits, pressure-impulse diagrams, etc. The majority of these provisions deal with the
response of the load-bearing elements (e.g. columns, walls) under idealized boundary conditions and
requires that connections be overdesigned relative to the loaded structural elements. This approach may
not adequately reflect the performance of structural systems with relatively flexible end conditions. This is
generally the case for structural steel and timber assemblies, where the joints are generally assumed to be
pinned or (for properly detailed steel connections) fully fix. Having some deformation in the connections of
timber assemblies may even be desired since the wood structural elements are likely to experience brittle
failure (mainly in flexure and/or shear) when subjected to a blast load. The connections could help in
absorbing some of the imparted energy on the structure, however, it is imperative that the connections
themselves do not fail prior to achieving full capacity in the main structural element. This balancing act
between providing energy dissipation in the connections while still maintaining the deformation capacity
such that premature failure in the system is not experienced requires careful investigation of the behaviour
of the connections in isolation as well as systems containing such connections.
MAT063-2
It is common for designers to use single-degree-of-freedom (SDOF) analysis, based on idealized boundary
conditions, which does not explicitly consider the behaviour of the connections. As stated in CSA (2012),
more refined methods should be used if the dynamic response of the structural system cannot be
represented by SDOF methods. While this statement provides some guidance for designers, it does not
explicitly specify when it is appropriate or even necessary to resort to more robust modelling techniques.
The majority of studies investigating the applicability of simplified modelling methodologies (such as SDOF)
in blast research have dealt primarily with idealized boundary conditions (Jacques et al. 2012, Lacroix and
Doudak 2015, Viau and Doudak 2016a, Poulin et al. 2017, Lacroix and Doudak 2018). Studies investigating
structural elements with realistic boundary conditions subjected to blast loads have generally concluded
that limiting the modelling to SDOF will often lead to inaccurate predictions (Viau and Doudak 2016b, El-
Hashimy et al. 2017, Côté and Doudak 2019). Without resorting to a more resource-intensive finite element
analysis (FEA), other methods have been used effectively to model these assemblies, including energy
methods (Lavarnway and Pollino 2015), SDOF analysis with modified resistance curve (Whitney 1996,
Gagnet et al. 2017), and two-degree-of-freedom (TDOF) modelling (Park and Krauthammer 2009, Jacques
and Saatcioglu 2018).
Numerical solutions available through the use of FEA are generally not justified when considering the
computational efforts involved in the development and validation of these models. This is particularly the
case when dealing with non-homogenous materials (e.g. cross-laminated timber) and nonlinear
connections. A good balance between simplicity and accuracy can be obtained with TDOF modelling, which
consists of lumping the behaviour of each subcomponent (i.e. connections and load-bearing elements) into
equivalent subsystems. This inherently allows for two failure modes, as well as the effects of realistic
boundary conditions (i.e. translational and rotational flexibility), to be captured by the model. This paper
summarizes the findings of an investigation on the applicability of SDOF and TDOF modelling for timber
assemblies with realistic boundary connections subjected to blast loads. This investigation was conducted
through sensitivity analyses of various parameters such as capacities and stiffness of both the connections
and the load-bearing timber element.
2 TWO-DEGREE-OF-FREEDOM (TDOF) ANALYSIS
The following section describes the development and process of the proposed TDOF model. While the
model is developed for cross-laminated timber (CLT) and glued-laminated timber (glulam) assemblies with
various end connections, the methodologies can be extended beyond this application provided that proper
material and connection characteristics are obtained.
2.1 Model Definition
The wood assembly can be represented as a continuous frame element connected at its ends with
translational and rotational springs. In order to discretize the continuous wood beam element, the deflected
shape function must be determined in order to obtain the appropriate load-mass factor (kLM). The factor is
obtained by equating the kinetic energy and strain energy of the real structural system, based on the
assumed static deflected shape, to that of the equivalent system. The end springs account for the
translational and rotational stiffness of the connections by associating their behaviour to a load-
displacement relationship. As the end translational connections are acting in parallel, they can be lumped
together into a single equivalent translational spring. The equivalent mass of the wood member and
connections are represented as mwood and mconn., respectively, while their respective stiffnesses are
represented by kwood and kconn. In the full-scale test, the force enacted onto the system consists of a pressure
collected by a load-transfer-device (LTD) and applied to the specimens via two concentrated point loads
(see Figure 1). The stiffness of the assembly can be modelled as two springs in series, each represented
with a SDOF, as shown in Figure 1c.
MAT063-3
(a) Actual CLT Test Assembly
(b) Actual Glulam Test Assembly
(c) Idealized TDOF System
Figure 1: Two-Degree-of-Freedom Idealization
For the undamped TDOF system shown in Figure 1c, the following two equations of motions must be solved
simultaneously:
[1]
[2]
where  is the load-mass transformation factor, used to transform the continuous wood member into an
equivalent SDOF, m and R are the component masses and resistances, respectively,  is the applied
concentrated blast force, and  are the component accelerations.
The system described through Equations 1 and 2 can be solved numerically using the constant average
acceleration method (Newmark 1959). The absence of the stiffness terms can be observed in Equations 1
and 2, as they have been replaced with the respective resistance terms. The nonlinear response expected
though yielding in the connections as well as the post-peak response of the CLT panels make it desirable
to introduce the resistance term since this makes for a more stable numerical solution. Numerical
instabilities may be encountered in cases where the stiffness term approaches zero or becomes negative.
MAT063-4
2.2 Model Inputs
The linear-elastic portion of the resistance curve can be defined by the maximum resistance () which
occurs at the elastic limit (). For a beam with two equal point loads at third spans, these parameters can
be obtained from Equations 3 and 4:
[3]
 
[4]

where  is the maximum dynamic moment, which can be obtained experimentally or from published
static data, modified for high strain-rate effects (CSA 2012), and is the clear-span of the flexural wood
member.
The initial stiffness of the wood member for two concentrated point loads () can be modified to consider
the rotational stiffness of the connections at the beam ends. This is done through the derivation of an
analytical solution of an Euler-Bernoulli beam with semi-rigid springs at its ends. The solution considers a
nondimensional constant () defined as the ratio of the rotational stiffness () to that of the beam stiffness,
() (Equation 5). The solution for the modified stiffness is presented in Equation 6.
[5]
 

[6]
  
 
  
By setting   , the solution in Equation 6 corresponds to the case of simply-supported beam, and by
setting   , the solution corresponds to a beam with fully-fixed ends. The input values of the rotational
stiffness can also be obtained via experimental testing of the joints in question. It should be noted that in the
case of timber joints, the effects of rotational stiffness are generally low and tend not to affect the response
significantly.
Research done on glulam beams subjected to blast loads has shown that the dynamic behaviour can be
modelled using a linear-elastic resistance curve since little-to-no post-peak behaviour was observed (Lacroix
and Doudak 2018). For CLT, the cross-laminations allow for some post-peak resistance, which can be
described as ratios of the maximum resistance. Research on CLT under blast loads shows that the post-
peak behaviour tends to be consistent, in that failure of the outer tension laminates causes a drop-in load to
an intermediate region based on the remaining transverse and longitudinal layer (Poulin et al. 2017).
The mass of the wood assembly is assumed to be that of the wood member as well as the weight of the load
transfer device (Figures 1a and 1b). While the mass of the connections is negligible, a non-zero mass must
be entered in the TDOF model, otherwise the dynamic analysis will not converge to a solution.
For the purpose of TDOF modelling, the translational (i.e. out-of-plane) stiffness of the end connections can
be idealized as a separate axial spring with associated load-displacement relationship. Considerations of
high strain-rate effects in timber connections are not well developed yet, however, ongoing research is
underway at the University of Ottawa to address this issue (McGrath et al. 2019, Viau and Doudak 2019).
MAT063-5
2.3 BlasTDOF Algorithm
In order to conduct TDOF analysis for a wide range of structural components, a numerical algorithm
(BlasTDOF) was developed. BlasTDOF is capable of analyzing two-component systems subjected to blast
loads, and permits the user to input custom resistance curves and masses, as well as the pressure-time
histories. BlasTDOF is comprised of three modules; an input module, a dynamic analysis module, and an
export module. A flowchart of the program’s algorithm is presented in Figure 2.
Figure 2: BlasTDOF Algorithm
MAT063-6
3 SENSITIVITY ANALYSES
The main objective of the sensitivity analyses was to establish cases where the use of TDOF modelling
would be required and where SDOF modelling could be justified and not lead to significant erroneous
results. Two parameters, namely the ratio of the connection stiffness and maximum resistance to the
corresponding values for the wood member, were evaluated. For all analyses, a bi-linear resistance curve,
with a ductility limit of 2.0, was used to represent the behaviour of the connections. This was consistent
with observed behaviour from experimental studies. The reference resistance curves of the CLT and glulam
members are shown in Figures 3a and 3b, respectively. These are based on proposed models from recent
studies on CLT panels (Poulin et al. 2017) and glulam members (Lacroix and Doudak 2018) subjected to
blast loads. A mass of 385 kg for the CLT panel and load-transfer-device was used for the CLT groups,
while a mass of 321 kg was used for the glulam groups. Forcing functions described by idealized triangular
pressure-time histories were used and are presented in Figures 3c and 3d for the CLT and glulam cases,
respectively. The forcing functions represent a reflected pressure and impulse (i.e. area under the pressure-
time curve) combination which will allow the CLT and glulam member to reach their respective ultimate
failure displacement. The sensitivity analyses are summarized in Table 1.
(a) CLT Resistance Curve
(b) Glulam Resistance Curve
(c) Pressure-Time History for CLT Groups
(d) Pressure-Time History for Glulam Groups
Figure 3: Reference Resistance Curves and Pressure-Time Histories for Sensitivity Analyses
0
20
40
60
80
100
120
140
160
180
020 40 60 80
RCLT (kN)
Displacement (mm)
0
20
40
60
80
100
120
140
160
0 5 10 15 20 25 30
Rglulam (kN)
Displacement (mm)
0
10
20
30
40
50
60
010 20 30
Reflected Pressure (kPa)
Time (ms)
0
10
20
30
40
50
60
010 20 30
Reflected Pressure (kPa)
Time (ms)
MAT063-7
Table 1: Sensitivity Analyses
Groups
Variable
Variable Ratios
Constants
CLT-K
Kconn / KCLT
0.1, 0.5, 1.5, 10, 50
Case 1: Rconn / RCLT = 0.5
Case 2: Rconn / RCLT = 1.5
CLT-R
Rconn / RCLT
0.5, 0.8, 1, 1.05, 1.125, 1.25
Case 1: Kconn / KCLT = 0.5
Case 2: Kconn / KCLT = 1.5
Case 3: Kconn / KCLT = 10
LAM-K
Kconn / Kglulam
0.1, 0.5, 1.5, 10, 50
Case 1: Rconn / Rglulam = 0.5
Case 2: Rconn / Rglulam = 1.5
LAM-R
Rconn / Rglulam
0.5, 0.8, 1, 1.05, 1.125, 1.25
Case 1: Kconn / Kglulam = 0.5
Case 2: Kconn / Kglulam = 1.5
Case 3: Kconn / Kglulam = 10
Groups CLT-K and LAM-K consisted of varying the stiffness ratios for two cases of maximum connection
resistance, one being smaller and one larger than the maximum resistance of the wood member. This is
meant to represent two different design philosophies, where the connection is overdesigned to reach the
ultimate capacity of the structural member, or where the connection is intentionally under-designed in order
to dissipate energy in the ductile connections rather than the brittle wood member. Figures 4a and 4b show
that for the case where the connection is stronger than the wood member, SDOF analysis can accurately
predict the response only if the stiffness of the connection is at least ten times that of the wood member.
Using SDOF analysis to analyze a case containing connections with lower stiffness may lead to significant
error in results, and in those cases, the use of TDOF may be required. For the case of overdesigned wood
member, the results clearly show that using SDOF analysis can no longer adequately predict the correct
displacement or failure mode, regardless of the stiffness ratio. Additionally, it can be observed that
convergence is faster for the CLT panel, which may be attributed to its significant post-peak region.
Groups CLT-R and LAM-R consisted of varying the maximum resistance ratio for three values of connection
stiffness. As shown in Figures 4c and 4d, for both groups, a plateau seems to form when the ratio of
connection to wood member resistance becomes greater than one. This can be explained by the fact that
beyond a ratio of one, the behaviour of the wood member will tend to govern the overall displacement, and
additional connection resistance will no longer play a role. It is also observed that the more flexible the
connections are, the higher the TDOF/SDOF ratio is for the plateau values. As seen in the previous analysis,
once the resistance of the connection becomes less than that of the wood member, the SDOF predictions
will diverge from the actual displacement and failure mode. It is interesting to note that when CLT is used,
the use of SDOF analysis seems adequate for all stiffness ratios as long as the connection capacity is
greater than the panel capacity. A better fit is obtained when the stiffness of the connection is relatively
higher than the panel stiffness, however in general all cases produce a reasonable agreement between the
two analysis methods. Interestingly, the outcome looks significantly different for glulam, where only the case
with very high relative connection stiffness ratio (i.e. > 10) yields adequate use of the SDOF modelling
methodology. As expected, the scenario where the connection stiffness is ten times that of the wood
member and with a resistance that is half that of the CLT panel yields the least accurate prediction when
using SDOF modelling. This is attributed to the fact that the connection will fail at a significantly lower
displacement than that of a more flexible connection, and the wood member will play a significantly lesser
role in the response of the system as a whole.
MAT063-8
(a) CLT-K
(b) LAM-K
(c) CLT-R
0.0
0.5
1.0
1.5
2.0
2.5
0 5 10 15 20 25 30 35 40 45 50
TDOF/SDOF
Kconn/KCLT
Rconn / RCLT = 0.5
Rconn / RCLT = 1.5
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 5 10 15 20 25 30 35 40 45 50
TDOF/SDOF
Kconn/Kglulam
Rconn / Rglulam = 0.5
Rconn / Rglulam = 1.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
TDOF/SDOF
Rconn/RCLT
KConn / KCLT = 0.5
KConn / KCLT = 1.5
KConn / KCLT = 10
MAT063-9
(d) LAM-R
Figure 4: Results of Sensitivity Analyses for Predictions of Maximum Deflection
4 CONCLUSIONS AND RECOMMENDATIONS
This paper discusses the applicability of SDOF and TDOF modelling for timber assemblies with realistic
boundary connections subjected to blast loads. A TDOF analysis program, BlasTDOF, was presented, and
the developed numerical algorithm was described. The sensitivity of varying stiffness and capacity of
connections relative to the timber structural elements was investigated. The results from the sensitivity
analyses show that:
- In the case where the connection is stronger than the wood member, SDOF analysis can accurately
predict the response only if the stiffness of the connection is at least 10 times that of the wood
member. For the case of overdesigned wood members, the results clearly show that using SDOF
analysis can no longer adequately predict the correct displacement or failure mode, regardless of
the stiffness ratio.
- In general, a consistent ratio of SDOF to TDOF results is obtained when the ratio of connection to
wood member resistance becomes greater than one. Once the resistance of the connection
becomes less than that of the CLT panel, the SDOF predictions will diverge from the actual
displacement and failure mode.
- When CLT is considered, the use of SDOF analysis seems adequate for all stiffness ratios as long
as the connection capacity is greater than the panel capacity. For glulam, only the case of
overdesigned connections with a very high relative stiffness ratio yields adequate use of the SDOF
modelling technique.
References
ASCE. 2011. Blast Protection of Buildings. ASCE/SEI 59-11. Reston, VA: American Society of Civil
Engineers.
Côté, D., and Doudak, G. 2019. Experimental investigation of cross-laminated timber panels with realistic
boundary conditions subjected to simulated blast loads. Engineering Structures, 187: 444-456.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
TDOF/SDOF
Rconn/Rglulam
KConn / Kglulam = 0.5
KConn / Kglulam = 1.5
KConn / Kglulam = 10
MAT063-10
CSA. 2012. Design and assessment of buildings subjected to blast loads. CSA S850. Mississauga, ON:
CSA Group.
El-Hashimy, T., Campidelli, M., Tait, M., and El-Dakhakhni, W. 2017. Modeling of Reinforced Masonry
Walls with Boundary Elements Under Blast Loading. 13th Canadian Masonry Symposium, Halifax, NS,
4-7 June 2017.
Gagnet, E. M., Hoemann, J. M., and Davidson, J. S. 2017. Blast resistance of membrane retrofit
unreinforced masonry walls with flexible connections. International Journal of Protective Structures,
8(4): 539-559.
Jacques, E., Lloyd, A., and Saatcioglu, M. 2012. Predicting reinforced concrete response to blast loads.
Canadian Journal of Civil Engineering, 40(5): 427-444.
Jacques, E., and Saatcioglu, M. 2018. Computer Software for the Design of Blast Resistant Window
Retention Anchors. CSCE 2018 Annual Conference, Canadian Society for Civil Engineering,
Fredericton, NB, June 13 - 16.
Lacroix, D. N., and Doudak, G. 2015. Investigation of Dynamic Increase Factors in Light-Frame Wood
Stud Walls Subjected to Out-of-Plane Blast Loading. Journal of Structural Engineering, 141(6):
04014159.
Lacroix, D. N., and Doudak, G. 2018. Determining the Dynamic Increase Factor for Glued-Laminated
Timber Beams. Journal of Structural Engineering, 144(9): 04018160.
Lavarnway, D., and Pollino, M. 2015. Mitigation of Air-Blast Pressure Impulses on Building Envelopes
through Blast Resistant Ductile Connectors. Journal of Engineering and Architecture, 3(2): 9-24.
McGrath, A., Viau, C., and Doudak, G. 2019. Investigating the Response of Bolted Wood Connections to
the Effects of Blast Loading. CSCE 2019 Annual Conference, Canadian Society for Civil Engineering,
Laval, QC, June 12 - 15.
Newmark, N. M. 1959. A Method of Computation for Structural Dynamics. Journal of the Engineering
Mechanics Division, 85(EM 3): 67-94.
Park, J. Y., and Krauthammer, T. 2009. Inelastic two-degree-of-freedom model for roof frame under
airblast loading. Structural Engineering and Mechanics, 32(2): 321-335.
Poulin, M., Viau, C., Lacroix, D. N., and Doudak, G. 2017. Experimental and Analytical Investigation of
Cross-Laminated Timber Panels Subjected to Out-of-Plane Blast Loads. Journal of Structural
Engineering, 144(2): 04017197.
Unified Facilities Criteria Program. 2008. Structures to resist the effects of accidental explosions (UFC 03-
340-02). Washington, D.C.: United States of America Department of Defense.
Viau, C., and Doudak, G. 2016a. Investigating the Behavior of Light-Frame Wood Stud Walls Subjected
to Severe Blast Loading. Journal of Structural Engineering, 142(12): 04016138.
Viau, C., and Doudak, G. 2016b. Investigating the behaviour of typical and designed wall-to-floor
connections in light-frame wood stud wall structures subjected to blast loading. Canadian Journal of
Civil Engineering, 43(6): 562-572.
Viau, C., and Doudak, G. 2019. Effect of High Strain-Rates on Heavy Timber Connections. CSCE 2019
Annual Conference, Canadian Society for Civil Engineering, Laval, QC, June 12 - 15.
Whitney, M. G. 1996. Blast Damage Mitigation Using Reinforced Concrete Panels and Energy Absorbing
Connectors. San Antonio, Texas: Wilfred Baker Engineering, Inc.
... CLT panels FT 5.2-9.3 Sanborn et al. (Sanborn et al., 2018) 2018 CLT panels --Viau et al. (Viau and Doudak, 2019a, 2019c 2019a, 2019b, 2019c ...
... Cross-laminated timber is perhaps one of the most studied type of EWPs under blast effects (see Table 1). This can be attributed to the fact that CLT panels have less variable mechanical properties than dimensional timber, leading to much more accurate design processes, which makes it an excellent candidate for blast protection purposes (Côté and Doudak, 2019;Viau and Doudak, 2019a, 2019c. The failure mode of CLT members is reported to exhibit strain rate sensitivity. ...
... Linear-elastic relationships were found to adequately capture the dynamic response of glulam beams. As for CLT, step-wise relationships with drops in resistance, representing the loss of the bottom laminates, have been proposed by several authors, delivering accurate predictions on the behaviour of CLT members under blast loading (Côté et al., 2018;Côté and Doudak, 2019;Viau et al., 2018;Viau and Doudak, 2019a, 2019c. SDOF modelling has also been employed to predict the behaviour of light-frame wood stud walls. ...
Article
The response of structures subject to impulsive loads remains a field of intense research. Whilst traditional construction materials, such as steel and concrete/masonry, have been the focus of most studies, further research on the performance of alternative materials for blast-resistant applications has been driven by their growing use in sustainable construction. Over the last years, engineers have been re-evaluating the use of timber as a prime construction material for a range of building types, from small office to high-rise residential buildings. As a result, there is now a growing need to study the blast resistance of timber structures, as they may become potential targets of terrorist attacks or being placed in the blast-radius of other critical buildings. A review of existing research on the blast resistance of timber structures is presented and key factors on the blast analysis and design of such structures are discussed. Most of the research has been conducted on light-frame wood stud walls, glued- and cross-laminated timber, and addresses material properties under high strain rates, typical failure modes, behaviour of structural connections and retrofitting solutions. Failure modes are reported to be highly dependent on the element layout and manufacturing aspects, and dynamic increase factors for the modulus of elasticity and maximum strength in the ranges of [1.05, 1.43] and [1.14, 1.60], respectively, have been proposed for different timber elements. Mechanical connectors play a significant role in dissipating energy through plastic deformation, as the brittle nature of timber elements compromises the development of their full capacity. Regardless the element type, SDOF models can accurately predict the dynamic response as long as idealised boundary conditions can be considered. Overall, although a good amount of research is available, more extensive research is needed to guide the design and engineering practice and contribute to the development of design codes and testing standards for timber structures under blast loading.
... 21,22]. However, such simplified approach has been shown to be unsuitable for modelling assemblies with realistic end conditions, mainly due to their inability to capture the behaviour of the connections, as well as the limitation associated with capturing multiple failure modes [8,[10][11][12]23]. The use of two-degree-of-freedom (TDOF) analysis has been shown to accurately model the behaviour of an assembly without significant additional computational effort. ...
... This methodology has been successfully used to model beams supported on girders [24], blast-resistant window systems [25], CLT panels with bearing connections [11], and glulam beams with bolted connections [12]. To verify whether TDOF is appropriate for modelling timber assemblies with EACs, the specimens reported in this paper were modelled and analyzed using BlasTDOF, a TDOF blast analysis software that has been validated for typical CLT and glulam connections [11,12,16,23,26]. Figure 8a, the assembly consists of a timber element supported at both ends by EACs, which in turn are connected to the rest of the structure. Enacted onto the timber element is a forcing function representing the blast pressure, which can be described as a uniformly distributed time-varying force. ...
Conference Paper
Full-text available
This paper presents the results of a study investigating the use of energy-absorbing connections designed as part of mass-timber assemblies to help resist a potential blast loading. Cross-laminated timber and glued laminated timber assemblies, including connections developed specifically to optimize the energy-absorbing capabilities of the system, were subjected to simulated blast loads through the use of a shock tube. The study also investigated the validity of current blast design provisions for timber connections. The results show that energy-absorbing boundary connections have the potential to significantly increase the energy dissipation in the timber assembly. A two-degree-of-freedom (TDOF) blast analysis software was developed and validated using the test results. Such analysis was deemed necessary when realistic end connections are used.
... The behaviour of the connection was found to significantly affect the overall behaviour of the assemblies. Without resorting to computational-heavy finite-element analysis (FEA), twodegree-of-freedom (TDOF) modelling has been found to predict the behaviour of such assemblies with reasonable accuracy, when compared to SDOF [17,25,26]. As such, the full-scale test specimens were modelled using TDOF analysis, and the predictions were compared with the experimental full-scale results. ...
... BlasTDOF, a TDOF blast analysis software [27], was used in the current study to perform the two-degree-of-freedom analyses. Previous studies performed on heavy timber assemblies have shown that this modelling tool was capable of accurately predicting the behaviour of timber assemblies subjected to blast loads [17,25,26,28]. The glulam assembly, consisting of the glulam beam and bolted connections, can be represented as a continuous frame element connected at its ends with translational springs. ...
Conference Paper
Full-text available
The paper presents an investigation of the behaviour of glulam assemblies with bolted connections when subjected to simulated blast loading. Static characterization of the bolted joints as well as dynamic testing of the glulam members in isolation was undertaken prior to the dynamic testing of the assemblies. The investigation consisted of varying the edge distance in order to determine the influence of connection geometry on the dynamic failure mode, as well as investigating the use of self-tapping screws as a reinforcement method against brittle failure modes. The study showed that allowing yielding in the connections provides significant energy dissipation to the timber assembly. Splitting failure was eliminated by reinforcing the member with self-tapping screws. A two-degree of freedom analysis software was developed and validated using the experimental data. The model was also compared with a SDOF analysis and the need for more refined analysis for structures with non-idealized or flexible end connections was highlighted. The implications of the findings on the design of bolted connections against brittle splitting failure is also presented.
Article
Full-text available
An experimental program investigating the behavior of glued laminated timber (glulam) assemblies with various bolted connections subjected to simulated blast loading was undertaken. A total of 14 full-scale tests on 137×267-mm glulam members with idealized and realistic boundary conditions were carried out using a shock tube apparatus capable of simulating the effects of far-field blast explosions. Full-scale glulam specimens with bolted connections designed to yield in bolt bending performed better than those that were overdesigned. Proper detailing of the bolt group geometry was found to be sufficient to achieve the desired failure sequence. Reinforcement with self-tapping screws changed the failure mode from that of splitting to a combination of bolt yielding and wood crushing and provided additional ductility in the assembly. A two-degree-of-freedom blast analysis was found to adequately capture the system response with reasonable accuracy. An investigation of the current Canadian blast design provisions showed that the design approach does not allow for energy dissipation in the assembly. An approach is proposed that requires more stringent provisions for the design of brittle failure modes in connections and ensures that ultimate failure will occur in load-bearing timber elements.
Conference Paper
Full-text available
Boundary elements (BEs) have been shown to enhance the in-plane performance of reinforced masonry (RM) walls, in terms of both section capacity and ductility. For this reason, in 2014 these elements were introduced in the Canadian standard S304-14 as a seismic force resisting system. When their out-of-plane performance is considered, BEs can significantly increase the load-bearing capacity of RM shear walls when subjected to blast overpressure from live explosives. However, the mechanism by which the wall capacity is affected is still unclear. To shed some light on this problem, a BE-wall was tested statically by the authors to examine the interaction between BEs and the web as well as the change in wall's stiffness beyond its elastic range. In this investigation, two approaches are proposed to model the post-elastic stiffness of the test specimen and their predictive capabilities are discussed on the basis of data from static testing. Furthermore, a single-degree-of-freedom model is used to simulate the maximum out-of-plane displacement experienced by the same wall when subjected to blast overpressure. The numerical results are compared to data from field testing of nominally identical BE-walls, to verify the adequacy of the adopted model. The current study contributes to the growing understanding of BEs' influence on the deformation of the wall central panel.
Article
Full-text available
Presented in this paper are the results of an experimental program investigating the out-of-plane behavior of CLT panels under static and blast loading. A total of 18 CLT panels, with panel thicknesses of 105 and 175 mm corresponding to a 3-ply and 5-ply panel, respectively, were investigated with the aim to determine the dynamic increase factor (DIF). An average dynamic increase factor of 1.28 on the resistance and no apparent increase in stiffness from static to dynamic loading were observed. Two resistance material predictive models that account for high strain-rate effects and the experimentally observed post-peak residual behavior were developed. A single-degree-of-freedom model was validated using full-scale simulated blast load tests, and the predictions were found to match well with the experimental displacement-time histories.
Article
Full-text available
An understanding of the behavior of wood stud walls in a region corresponding to hazardous-blowout damage levels is currently lacking. The focus of the current study is on investigating the flexural response of full-scale wood stud walls subjected to pressure-impulse combinations that would yield severe damage levels. Static material properties were determined and used as input in an analytical model that considers the nonlinear behavior of stud-to-sheathing joints, as well as high strain-rate effects. Experimental results showed that premature sheathing failure could occur prior to full flexural stud response, and that sheathing panel debris could be generated. The use of thicker sheathing and screws shifted the failures to the studs, while decreasing the amount of debris. Welded wire mesh was successfully used as a reinforcement of the sheathing or as a catcher system while maintaining the residual axial capacity of the studs. A single-degree-of-freedom material-predictive model was successfully validated using the experimental test results.
Article
Full-text available
The performance of light-frame wood stud walls under simulated blast loading has so far been limited to investigating the behaviour of structural elements with idealized boundary conditions. The current study investigates, experimentally and analytically, whether walls with prescriptive connection detailing for low and high seismic and wind regions are capable of resisting blast loadings such that the walls’ ultimate capacity can be reached. The study also investigates the behaviour of different connections with various design capacity levels in order to develop failure in the stud wall system rather than in the connection. A total of ten full-scale walls with different boundary conditions were tested dynamically. The results showed that typical prescriptive connection detailing did not perform adequately. Designed connections performed well, but the findings show that basing the connection design solely on capacity may be inadequate. Single degree-of-freedom modelling may only be utilized if damage in the connections is limited.
Article
Full-text available
The results of an experimental program investigating the dynamic increase factors of light-frame wood stud walls under blast loading are presented in this paper. A total of 20 walls with two different sheathing types and thicknesses were tested to failure under static and dynamic loading. The study found that the observed failure mode for both static and dynamic loading was flexure; however, a difference in the type of flexural failure was observed. Average increase factors of 1.40 and 1.18 on the resistance and stiffness, respectively, were found. A detailed literature review combined with the test results from the current project yielded a strong correlation between the increase in strain rate and the relative increase in strength and an equation relating the dynamic increase factor (DIF) on the resistance to strain rate was proposed for strain rates in the ranges of 1.67- 1.65 × 10 3 ∈ ∈ s - 1.
Article
Recent research efforts have established key dynamic characteristics of cross-laminated timber (CLT) panels and developed parameters that are suitable for analysis and design. Despite such effort, no information is available on the critical role connections play in the behaviour of CLT when subjected to blast loads. The current study investigates a total of thirteen full-scale CLT wall panels with varying connection detailing by simulating the blast loading through a shock tube apparatus. The study found that typical connections with end grain screws into wall elements as well as angled double-threaded screws performed poorly and failed prematurely in tension perpendicular to grain. Reinforcing the connection with screws applied on the panel face did not mitigate the brittle failure. It was found that connection types where the wood is bearing on steel angles or directly on other wood members performed well even when under-designed according to the blast design standard. Whereas thin steel angles provided significant energy dissipation in bending of the angle resulting in reduced panel deflection and damage, thicker steel angles provided the energy dissipation through yielding in the screws as well rotational restraint of the panel ends. Using balloon type assemblies provided significant rotational restraint at the panel ends. The study also found that simplified models developed for idealized simply-supported conditions were not adequate to describe the behaviour of the system.
Article
This paper presents the results from an experimental program that investigated the flexural behavior of glulam beams subjected to dynamic loading. A total of thirty-eight beams consisting of three different cross-sections were tested destructively under both static and dynamic loads. The analysis resulted in a dynamic increase factor (DIF) of 1.14 for strain-rates ranging between 0.14 and 0.51 s-1, however, the increase was only observed when the outer tension laminate did not include continuous finger-joints (single laminate width) or closely aligned finger-joints (multiple laminates width) in the high moment region causing a straight fracture across the width. No increase due to high strain-rate effects was found when a continuous failure across the width due to finger-joints (FJs) were present in the outer tension laminate, and thus if continuous laminates, uninterrupted by FJs cannot be guaranteed, a dynamic increase factor of unity is suggested for design. Since the beams exhibited little to no ductility, it is recommended that a linear-elastic resistance curve be used to generate the dynamic resistance curve. An equivalent single-degree-of-freedom (SDOF) model accounting for high strain-rate effects using the derived DIF, where appropriate, captured the displacement at failure, time to failure, and displaced shape with reasonable accuracy.
Article
Unreinforced masonry infill walls are one of the most economical and widely used exterior wall systems. However, they can produce secondary fragments due to their brittle failure modes when subjected to an impulsive blast load. One retrofit to reinforce existing masonry walls is to install a membrane that prevents fragments from entering the building’s interior. Previous research focused on defining the resistance provided by the wall membrane system, but did not include flexibility of the attachments and their influence on the retrofitted wall system. This article addresses that issue through (1) a review of existing membrane retrofit resistance definitions, (2) a derivation of the resistance definition that includes connection flexibility, (3) validation of the derived resistance definition through nonlinear finite element analyses, and (4) comparison of the resistance in a single-degree-of-freedom framework against full-scale blast testing.
Article
Mitigation of Air-Blast Pressure Impulses on Building Envelopes through Blast Resistant Ductile Connectors Daniel Lavarnway, Michael Pollino Abstract The rise of intentional or unintentional explosions on both defense critical and conventional buildings requires development of enhanced solutions for the blast protection of structures. This study investigates use of a simple, effective building envelope connector that provides an energy absorbing mechanism for mitigating the effects of a blast event onto a building. The application of the blast resistant ductile connector was assessed by applying principles of conservation of energy and momentum on a generalized single degree of freedom dynamics model (simplified approach) followed by transient nonlinear finite element model to verify the results. The simplified approach allows for rapid design for a range of blast scenarios and potentially varying envelope systems. Conceptual BRDC designs were then evaluated through nonlinear finite element analysis and experimental testing. This study found that the proposed blast resistant ductile connectors were able to safely dissipate the energy for a reasonably wide range of blast scenarios and prevent damage to a minimally reinforced envelope panel. Full Text: PDF DOI: 10.15640/jea.v3n2a2
Article
When a roof frame is subjected to the airblast loading, the conventional way to analyze the damage of the frame or design the frame is to use single degree of freedom (SDOF) model. Although a roof frame consists of beams and girders, a typical SDOF analysis can be conducted only separately for each component. Thus, the rigid body motion of beams by deflections of supporting girders can not be easily considered. Neglecting the beam-girder interaction in the SDOF analysis may cause serious inaccuracies in the response values in both Pressure-Impulse curve (P-I) and Charge Weight-Standoff Diagrams (CWSD). In this paper, an inelastic two degrees of freedom (TDOF) model is developed, based on force equilibrium equations, to consider beam-girder interaction, and to assess if the modified SDOF analysis can be a reasonable design approach.