Plank (tongue and groove) wood decking is a product that is commonly used in post and beam timber construction to transfer gravity loads on roofs and floors. In 2010, The National Building Code of Canada changed the application area of the specified concentrated roof live loads from 750 mm x 750 mm to 200 mm x 200 mm. The change was made to better reflect the area which a construction worker with equipment occupies. Preliminary analysis showed that the change in the application area of concentrated loads may have a significant impact on the design of decking systems. Little research or development has been done on plank decking since the 1950’s and 1960’s. An experimental program was undertaken at the University of Ottawa’s structural laboratory to better understand the behaviour of plank decking under uniformly distributed and concentrated loads. Non-destructive and destructive tests were conducted on plank decking systems to investigate their stiffness and failure mode characteristics under uniformly distributed as well as concentrated loads. The experimental test program was complimented with a detailed finite element model in order to predict the behaviour of a plank decking system, especially the force transfer between decks through the tongue and groove joint. The study showed that the published deflection coefficients for uniformly distributed loads can accurately predict the three types of decking layup patterns specified in the Canadian Design Standard (CSA O86, 2009). For unbalanced uniformly distributed loads on two-span continuous layup, it was found that the deflection coefficient of 0.42 was non-conservative. It was also found that under concentrated loads, the stiffness of the decking system increased significantly as more boards were added. A deflection coefficient of 0.40 is appropriate to calculate the deflection for the three types of decking layup patterns specified in the Canadian Design Standard (CSA O86, 2009) under concentrated load on an area of 200 mm by 200 mm. Significant load sharing was observed for plank decking under concentrated loads. An increase in capacity of about 1.5 to 2.5 times the capacity of the loaded boards was found. Furthermore, it was found that placing sheathing on top of a decking system had a significant effect in the case of concentrated load with an increase of over 50% in stiffness and over 100% in ultimate capacity.

Plank (tongue and groove) wood decking is a product that is commonly used in post and beam timber construction to transfer gravity loads on roofs and floors. In 2010, The National Building Code of Canada changed the application area of the specified concentrated roof live loads from 750 mm x 750 mm to 200 mm x 200 mm. The change was made to better reflect the area which a construction worker with equipment occupies. Preliminary analysis showed that the change in the application area of concentrated loads may have a significant impact on the design of decking systems. Little research or development has been done on plank decking since the 1950’s and 1960’s. An experimental program was undertaken at the University of Ottawa’s structural laboratory to better understand the behaviour of plank decking under uniformly distributed and concentrated loads. Non-destructive and destructive tests were conducted on plank decking systems to investigate their stiffness and failure mode characteristics under uniformly distributed as well as concentrated loads. The experimental test program was complimented with a detailed finite element model in order to predict the behaviour of a plank decking system, especially the force transfer between decks through the tongue and groove joint. The study showed that the published deflection coefficients for uniformly distributed loads can accurately predict the three types of decking layup patterns specified in the Canadian Design Standard (CSA O86, 2009). For unbalanced uniformly distributed loads on two-span continuous layup, it was found that the deflection coefficient of 0.42 was non-conservative. It was also found that under concentrated loads, the stiffness of the decking system increased significantly as more boards were added. A deflection coefficient of 0.40 is appropriate to calculate the deflection for the three types of decking layup patterns specified in the Canadian Design Standard (CSA O86, 2009) under concentrated load on an area of 200 mm by 200 mm. Significant load sharing was observed for plank decking under concentrated loads. An increase in capacity of about 1.5 to 2.5 times the capacity of the loaded boards was found. Furthermore, it was found that placing sheathing on top of a decking system had a significant effect in the case of concentrated load with an increase of over 50% in stiffness and over 100% in ultimate capacity.

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Previous studies have mainly focused on the behaviour of timber under uniformly distributed compression perpendicular to the grain (CPG) loads. However, there are many practical applications in which timber is loaded by non-uniformly distributed CPG loads. Different design and test codes like the Eurocode 5 (EC5), DIN 1052:2004, ASTM D143- 94 and EN-408:2010 only account for load configurations where timber is subjected to uniformly distributed loads. For specific uniformly distributed load (UDL) configurations the bearing capacity of timber (solid softwood timber or Glulam) in compression is adapted by using a load configuration factor (kc,90) according to EC5, the European code for design of timber structures. EC5 has no guidelines for cross-laminated timber (CLT) under UDL with the exception of the Austrian National Regulations for EC5. In this work, an experimental and numerical study on the bearing capacity and displacement behaviour of CLT subjected to non-uniformly distributed loading (NuDL) is conducted on eight different load configurations. A steel-CLT connection in which the CLT is partially loaded is used in this study. Finite element modelling, performed using the commercial software Abaqus CAE is used as the numerical simulation of the experimental study and is validated by experimental results. Load configuration factors (kc,90) from experimental results are compared with values from the Swedish CLT handbook (KL-Trähandbok). The outcome of the study shows that load configuration factor for NuDL cases is higher than for UDL cases. Hence, for same load configurations a lower CPG strength is required in NuDL than in UDL. Moreover, numerical results feature overall good congruence with the elastic phase of the experiments and have the potential to augment experiments in further understanding other complex steel-CLT connections

This thesis consists of five articles mainly devoted to problems in dynamical systems and ergodic theory. We consider non-uniformly hyperbolic two dimensional systems and limit distributions of point measures which are absolutely continuous with respect to the Lebesgue measure. Let $f_{a_0}(x)=a_0-x^2$ be a quadratic map where the parameter $a_0\in(1,2)$ is chosen such that the critical point $0$ is pre-periodic (but not periodic). In Papers A and B we study skew-products $(\th,x)\mapsto F(\th,x)=(g(\th),f_{a_0}(x)+\al s(\th))$, $(\th,x)\in S^1\times\real$. The functions $g:S^1\to S^1$ and $s:S^1\to[-1,1]$ are the base dynamics and the coupling functions, respectively, and $\al$ is a small, positive constant. Such quadratic skew-products are also called Viana maps. In Papers A and B we show for several choices of the base dynamics and the coupling function that the map $F$ has two positive Lyapunov exponents and for some cases we further show that $F$ admits also an absolutely continuous invariant probability measure. In Paper C we consider certain Bernoulli convolutions. By showing that a specific transversality property is satisfied, we deduce absolute continuity of the to these Bernoulli convolutions associated distributions. In Papers D and E we consider sequences of real numbers in the unit interval and study how they are distributed. The sequences in Paper D are given by the forward iterations of a point $x\in[0,1]$ under a piecewise expanding map $T_a:[0,1]\to[0,1]$ depending on a parameter $a$ contained in an interval $I$. Under the assumption that each $T_a$ admits a unique absolutely continuous invariant probability measure $\mu_a$ and that some technical conditions are satisfied, we show that the distribution of the forward orbit $T_a^j(x)$, $j\ge1$, is described by the distribution $\mu_a$ for Lebesgue almost every parameter $a\in I$. In Paper E we apply the ideas in Paper D to certain sequences which are equidistributed in the unit interval and give a geometrical proof of an old result by Koksma.

We consider the problem of designing revenue-optimal mechanisms for selling two heterogeneous items to a single buyer. Designing a revenue-optimal mechanism for selling a single item is simple: Set a threshold price based on the distribution, and sell the item only when the buyer’s valuation exceeds the threshold. However, designing a revenue-optimal mechanism to sell two heterogeneous items is a harder problem. Even the simplest setting with two items and one buyer remains unsolved as yet. The partial characterizations available in the literature have succeeded in solving the problem largely for distributions that are bordered by the coordinate axes. We consider distributions that do not contain (0; 0) in their support sets. Specifically, we consider the buyer’s valuations to be distributed uniformly over arbitrary rectangles in the positive quadrant. We anticipate that the special cases we solve could be a guideline to un-derstand the methods to solve the general problem. We explore two different methods – the duality method and the virtual valuation method – and apply them to solve the problem for distributions that are not bordered by the coordinate axes. The thesis consists of two parts. In the first part, we consider the problem when the buyer has no demand constraints. We assume the buyer’s valuations to be uniformly distributed over an arbitrary rectangle [c1; c1 + b1] [c2; c2 + b2] in the positive quadrant. We first study the duality approach that solves the problem for the (c1; c2) = (0; 0) case. We then nontrivially extend this approach to provide an explicit solution for arbitrary nonnegative values of (c1; c2; b1; b2). We prove that the optimal mechanism is to sell the two items according to one of eight simple menus. The menus indicate that the items must be sold individually for certain values of (c1; c2), the items must be bundled for certain other values, and the auction is an interplay of individual sale and a bundled sale for the remaining values of (c1; c2). We conjecture that our method can be extended to a wider class of distributions. We provide some preliminary results to support the conjecture. In the second part, we consider the problem when the buyer has a unit-demand constraint. We assume the buyer’s valuations (z1; z2) to be uniformly distributed over an arbitrary rectangle [c; c + b1] [c; c + b2] in the positive quadrant, having its south-west corner on the line z1 = z2. We first show that the structure of the dual measure shows significant variations for different values of (c; b1; b2) which makes it hard to discover the correct dual measure, and hence to compute the solution. We then nontrivially extend the virtual valuation method to provide a complete, explicit solution for the problem considered. In particular, we prove that the optimal mechanism is structured into five simple menus. We then conjecture, with promising preliminary results, that the optimal mechanism when the valuations are uniformly distributed in an arbitrary rectangle [c1; c1 + b1] [c2; c2 + b2] is also structured according to similar menus.