Die evangelische St. Pankratius-Kirche in Lucka wird aktuell genutzt und dient wöchentlich zehn bis 20 Menschen als Ort der Messe. Die Kirche befindet sich zu Teilen in einem sanierungsbedürftigen Zustand, vor allem im Dachstuhl sind Schäden an der historischen Bausubstanz nicht zu übersehen. Zum Erhalt dieses Baudenkmals ist neben der Sanierung und konstruktiven Ertüchtigung auch ein Konzept zur erweiterten Nutzung geplant. In Anbetracht sinkender Mitgliederzahlen der Kirche ist eine Erweiterung des kulturellen Angebotes in diesem Gotteshaus notwendig, um die aktive Nutzung auch in den nächsten Jahrzehnten sicherzustellen. Diese Thesis soll als Vorarbeit und Grundlage für die Umsetzung von Sanierungsmaßnahmen dienen. Darin soll zum Einen die Tragkonstruktion des Daches vermessen und aus statischer Sicht betrachtet werden. Zum Anderen erfolgt eine Bauzustandsanalyse, welche Schadensuntersuchungen und Sanierungsempfehlungen beinhaltet.:1. Einleitung 1.1. Motivation 1.2. Aufbau der Arbeit 2. Vorstellung des Objektes 2.1. Geschichtliche Einordnung 2.2. Beschreibung der Kirche 3. Vermessung und Aufnahme des Dachstuhls 3.1. Messtechnik und Messablauf 3.2. Bestandsaufnahme 3.2.1. Bauteile 3.2.2. Tragwerk 3.2.3. Verbindungen 3.2.4. Bauteilquerschnitte 3.2.5. Visuelle Sortierung und Festigkeit 3.2.6. Verformungen 3.3. Überführung in ein 3D-Modell 4. Holz als Baustoff 4.1. Allgemein 4.2. Bemessung von Holz 4.3. Versagensmechanismen im Holzbau 4.4. Materialkennwerte von Holz 5. Lastannahme nach DIN EN 1991-1 5.1. Eigenlasten 5.2. Nutzlasten 5.3. Schneelasten 5.4. Windlasten 5.5. Zusammenfassung Lastfälle 6. Bildung des statischen Modells 6.1. Kraftfluss 6.2. Modellierung der Verbindungen 6.3. Tragverhalten 6.4. Statische Systeme 7. Statische Nachweise des Ist-Zustandes 7.1. Szenario 1 - System intakt 7.2. Szenario 2 - Ausfall Sparrenfußpunkt 8. Erfassen der Schadensbilder 8.1. Untersuchungen 8.1.1. Visuelle Untersuchungen 8.1.2. Feuchtemessung 8.1.3. Nachweis Sulfat und Bor 8.1.4. Nachweis chlorierter Kohlenwasserstoffe 8.1.5. Bestimmung der Käfernagsel 8.2. Bestimmung der Holzarten 8.3. Fotodokumentation 9. Schadensursachen 9.1. Biologische Einflüsse 9.1.1. Pilzbefall 9.1.2. Insektenbefall 3 9.2. Mechanische Einflüsse 9.3. Bauphysikalische Einflüsse 10.Bauliche Maßnahmen 10.1. Konstruktiver Holzschutz 10.2. Chemischer Holzschutz 10.3. Instandsetzung und Ertüchtigung 11.Denkmalschutz 12.Wirtschaftlichkeitsanalyse 13.Sanierungskonzept 14.Statische Nachweise der Ertüchtigungen 15.Zusammenfassung / The protestant St. Pankratius church in Lucka is currently in use and serves ten to 20 people as a place of mass every week. Parts of the church require redevelopment, especially the roof truss showing damage to the historic structure. To preserve this architectural monument, in addition to the renovation and structural reinforcement, a concept for expanded use is foreseen. Given the church’s declining membership, expanding the cultural offerings in this house of worship is necessary to ensure its active use in the coming decades. This thesis aims to serve as preliminary work and a basis for implementing renovation measures. It consists of two parts: First, the roof’s supporting structure will be measured and examined from a structural point of view. Second, the condition of the building will be analysed, including an investigation of damages and recommendations for renovations.:1. Einleitung 1.1. Motivation 1.2. Aufbau der Arbeit 2. Vorstellung des Objektes 2.1. Geschichtliche Einordnung 2.2. Beschreibung der Kirche 3. Vermessung und Aufnahme des Dachstuhls 3.1. Messtechnik und Messablauf 3.2. Bestandsaufnahme 3.2.1. Bauteile 3.2.2. Tragwerk 3.2.3. Verbindungen 3.2.4. Bauteilquerschnitte 3.2.5. Visuelle Sortierung und Festigkeit 3.2.6. Verformungen 3.3. Überführung in ein 3D-Modell 4. Holz als Baustoff 4.1. Allgemein 4.2. Bemessung von Holz 4.3. Versagensmechanismen im Holzbau 4.4. Materialkennwerte von Holz 5. Lastannahme nach DIN EN 1991-1 5.1. Eigenlasten 5.2. Nutzlasten 5.3. Schneelasten 5.4. Windlasten 5.5. Zusammenfassung Lastfälle 6. Bildung des statischen Modells 6.1. Kraftfluss 6.2. Modellierung der Verbindungen 6.3. Tragverhalten 6.4. Statische Systeme 7. Statische Nachweise des Ist-Zustandes 7.1. Szenario 1 - System intakt 7.2. Szenario 2 - Ausfall Sparrenfußpunkt 8. Erfassen der Schadensbilder 8.1. Untersuchungen 8.1.1. Visuelle Untersuchungen 8.1.2. Feuchtemessung 8.1.3. Nachweis Sulfat und Bor 8.1.4. Nachweis chlorierter Kohlenwasserstoffe 8.1.5. Bestimmung der Käfernagsel 8.2. Bestimmung der Holzarten 8.3. Fotodokumentation 9. Schadensursachen 9.1. Biologische Einflüsse 9.1.1. Pilzbefall 9.1.2. Insektenbefall 3 9.2. Mechanische Einflüsse 9.3. Bauphysikalische Einflüsse 10.Bauliche Maßnahmen 10.1. Konstruktiver Holzschutz 10.2. Chemischer Holzschutz 10.3. Instandsetzung und Ertüchtigung 11.Denkmalschutz 12.Wirtschaftlichkeitsanalyse 13.Sanierungskonzept 14.Statische Nachweise der Ertüchtigungen 15.Zusammenfassung

Probabilistic methods have been widely used in structural engineering to model uncertainties in loads and structural properties. The subjects of structural reliability analysis, random vibrations, and structural system identification have been extensively developed and provide the basic framework for developing rational design and maintenance procedures for engineering structures. One of the crucial requirements for successful application of probabilistic methods in these contexts is that one must have access to adequate amount of empirical data to form acceptable probabilistic models for the uncertain variables. When this requirement is not met, it becomes necessary to explore alternative methods for uncertainty modeling. Such efforts have indeed been made in structural engineering, albeit to a much lesser extent as compared to efforts expended in developing probabilistic methods. The alternative frameworks for uncertainty modeling include methods based on the use of interval analysis, convex function representations, theory of fuzzy variables, polymorphic models for uncertainties, and hybrid models which combine two or more of alternative modeling frameworks within the context of a given problem. The work reported in this thesis lies in the broad area of research of modeling uncertainties using non-probabilistic and combined non-probabilistic and probabilistic methods. The thesis document is organized into 5 chapters and 6 annexures. A brief overview of alternative frameworks for uncertainty modeling and their mathematical basis are provided in chapter 1. This includes discussion on modeling of uncertainties using intervals and issues related to uncertainty propagation using interval algebra; details of convex function models and relevance of optimization tools in characterizing uncertainty propagation; discussion on fuzzy variables and their relation to intervals and convex functions; and, issues arising out of treating uncertainties using combined probabilistic and non-probabilistic methods. The notion of aleatoric and epistemic uncertainties is also introduced and a brief mention of polymorphic models for uncertainty, which aim to accommodate alternative forms of uncertainty within a single mathematical model, is made. A review of literature pertaining to applications of non-probabilistic and combined probabilistic and non-probabilistic methods for uncertainty modeling in structural engineering applications is presented in chapter 2. The topics covered include: (a) solutions of simultaneous algebraic equations, eigenvalue problems, ordinary differential equations, and the extension of finite element models to include non-probabilistic uncertainties, (b) issues related to methods for arriving at uncertainty models based on empirical data, and (c) applications to problems of structural safety and structural optimization. The review identifies scope for further research into the following aspects: (a) development of methods for arriving at optimal convex function models for uncertain variables based on limited data and embedding the models thus developed into problems of structural safety assessment, and (b) treatment of inverse problems arising in structural safety based design and optimization which takes into account possible use of combined probabilistic and non-probabilistic modeling frameworks. Chapter 3 considers situations when adequate empirical data on uncertain variables is lacking thereby necessitating the use of non-probabilistic approaches to quantify uncertainties. The study discusses such situations in the context of structural safety assessment. The problem of developing convex function and fuzzy set models for uncertain variables based on limited data and subsequent application in structural safety assessment is considered. Strategies to develop convex set models for limited data based on super-ellipsoids with minimum volume and Nataf’s transformation based method are proposed. These models are shown to be fairly general (for instance, approximations to interval based models emerge as special cases). Furthermore, the proposed convex functions are mapped to a unit multi-dimensional sphere. This enables the evaluation of a unified measure of safety, defined as the shortest distance from the origin to the limit surface in the transformed standard space, akin to the notion used in defining the Hasofer- Lind reliability index. Also discussed are issues related to safety assessment when mixed uncertainty modeling approach is used. Illustrative examples include safety assessment of an inelastic frame with uncertain properties. The study reported in chapter 4 considers a few inverse problems of structural safety analysis aimed at the determination of system parameters to ensure a target level of safety and (or) to minimize a cost function for problems involving combined probabilistic and non-probabilistic uncertainty modeling. Development of load and resistance factor design format, in problems with combined uncertainty models, is also presented. We employ super-ellipsoid based convex function/fuzzy variable models for representing non-probabilistic uncertainties. The target safety levels are taken to be specified in terms of indices defined in standard space of uncertain variables involving standard normal random variables and (or) unit hyper-spheres. A class of problems amenable for exact solutions is identified and a general procedure for dealing with more general problems involving nonlinear performance functions is developed. Illustrations include studies on inelastic frame with uncertain properties. A summary of contributions made in the thesis, along with a few suggestions for future research, are presented in chapter 5. Annexure A-F contain the details of derivation of alternative forms of safety measures, Newton Raphson’s based methods for optimization used in solutions to inverse problems, and details of combining Matlab based programs for uncertainty modeling with Abaqus based models for structural analysis.