<p>This master thesis deals with steel girders subjected to patch loading caused by concentrated moments. There exist no good methods to calculate by hand the ultimate resistance for this load case. In “tunnplåtshandboken”, (Handbook for sheet metal, which is published by SSAB), one calculation method is presented. It’s however fairly difficult to use, because of many calculation steps and many graphs. This study concentrates on how to calculate the resistance for this load case in a better way. The load case arises for example when a small steel plate (attachment) is welded to the flange above the web of a girder and the attachment is pulled in a direction parallel to the beam. It’s possible view the load as two components, a moment and a horizontal load. The moment will push the attachment into the girder and finally yielding in combination with web buckling will govern the ultimate resistance. In this report, only the moment part of the load is studied.</p><p>This study was made in three steps. First an FE-model was built. This model was verified against physical tests on patch loading from a force acting perpendicular to the beam axis. This approach was taken because no tests were found for the load case with a local moment. As step number two the FE-model was numerically adjusted to work for tests with patch loading caused by a local moment. A number of experiments were made, for which two parameters were varied, the thickness of the web and the length of the attachment. The loaded attachment was made very stiff, because it should not be deformed in order to simulate a sharp concentrated moment. In the last step a hand calculation model was developed for the investigated load case.</p><p>The FE-model that was created for comparison to the physical experiments gave resistances 10 % below the resistances, from the physical tests. This was mainly due to the sensitivity of the girder to initial imperfections and that the most severe buckling mode was used in the modeling of the imperfections.</p><p>The handcalculation model was developed to imitate the one for patch loading in EN 1993-1- 5 (EC3), because it may then work as an addition to EC3. The model was developed in three steps: yield resistance, critical elastic buckling load and the resistance function. The model for yield resistance is analytical and has a form equivalent to the one in EC3. The expressions for the critical elastic buckling load were taken as simple as possible, since they are the main area of this study. The method essentially uses the same equations as EC3 except from two small changes. The results are on the safe side but the safety margin increases when the length of the loaded attachment decreases and the slenderness of the web panel increase. Consequently formulas for calculating the critical load may be improved. The chosen reduction function was slightly increased compared to the function in EC3 but the results will still have a good safety margin. The complete model gives results where the safety margin increases as the length of the loaded attachment decreases. The calculation model was designed to be easy to use. In comparison to the FE-analysis, all the tested beams except a few with low slenderness gave results on the safe side.</p> / <p>Detta examensarbete behandlar stålbalkar utsatta för lokal intryckning orsakade av en lokal momentbelastning. För lastfallet finns ännu inga bra handräkningsmetoder, i plåthandboken som ges ut av SSAB finns en beräkningsmetod presenterad. Den är väldigt krånglig med många beräkningssteg och diagram. Denna studie är inriktad på att utreda hur man kan räkna på belastningsfallet på ett enklare och bättre sätt. Lastfallet uppkommer t.ex. då en lastögla svetsas till flänsen rakt över livet på en balk. Om lastöglan dras parallellt med balkens riktning så kan belastningen ses som två komponenter, ett moment och en horisontalkraft. Momentet kommer att trycka in lastöglan i balken och till slut blir det ett brott p.g.a. en blandning av att materialet flyter och att livet bucklar. I den här rapporten behandlas bara momentdelen av lasten.</p><p>Studien är gjord i tre steg. Först byggdes en FE-modell i Abaqus. Denna modell verifierades mot fysiska försök på lokal intryckning från en vertikal kraft, eftersom inga försök hittades på intryckning av ett lokalt moment. Som steg nummer två anpassades FE-modellen till försök med lokal intryckning från ett moment. Ett antal experiment gjordes med variation av två parametrar, livplåtens tjocklek och lastöglans längd. Lastöglan var väldigt styv eftersom den bara skulle skapa momentbelastningen. Sista steget var att utifrån resultaten ta fram en beräkningsmodell för lastfallet.</p><p>FE-modellen som skapades för testerna visade sig ge bärförmågor ca 10% under bärförmågan från de fysiska försöken. Detta berodde mycket på att balken var känslig för hur initialimperfektionerna såg ut och att första bucklingsmodens form användes vid modelleringen av de geometriska imperfektionerna.</p><p>Beräkningsmodellen utvecklades så att den skulle efterlikna den som gäller för lokal intryckning från vertikal last i EN 1993-1-5. Detta för att modellen skulle kunna användas som ett tillägg till EK3. Modellen utvecklades i tre delar, flytbärförmågan, kritiska bucklingslasten och reduktionsfaktorn för buckling. Modellen för flytbärförmågan togs fram analytiskt och fick en form som efterliknar den i EK3. Beräkningsmetoden för den kritiska bucklingslasten använder sig i princip av formlerna i EK3 förutom två små ändringar. Reduktionsfunktionen som valdes är en liten ökning av funktionen i EK3 men resultaten ligger ändå med bra marginal på säkra sidan. Den kompletta beräkningsmodellen ger resultat där säkerhetsmarginalen ökar vid minskande längd på lastöglan. Den har utformats så att den är lätt att använda och vid jämförelse med FE-försök gav beräkningsmodellen resultat på säkra sidan för alla balkar förutom några få av balkarna med låg slankhet. </p>

This master thesis deals with steel girders subjected to patch loading caused by concentrated moments. There exist no good methods to calculate by hand the ultimate resistance for this load case. In “tunnplåtshandboken”, (Handbook for sheet metal, which is published by SSAB), one calculation method is presented. It’s however fairly difficult to use, because of many calculation steps and many graphs. This study concentrates on how to calculate the resistance for this load case in a better way. The load case arises for example when a small steel plate (attachment) is welded to the flange above the web of a girder and the attachment is pulled in a direction parallel to the beam. It’s possible view the load as two components, a moment and a horizontal load. The moment will push the attachment into the girder and finally yielding in combination with web buckling will govern the ultimate resistance. In this report, only the moment part of the load is studied. This study was made in three steps. First an FE-model was built. This model was verified against physical tests on patch loading from a force acting perpendicular to the beam axis. This approach was taken because no tests were found for the load case with a local moment. As step number two the FE-model was numerically adjusted to work for tests with patch loading caused by a local moment. A number of experiments were made, for which two parameters were varied, the thickness of the web and the length of the attachment. The loaded attachment was made very stiff, because it should not be deformed in order to simulate a sharp concentrated moment. In the last step a hand calculation model was developed for the investigated load case. The FE-model that was created for comparison to the physical experiments gave resistances 10 % below the resistances, from the physical tests. This was mainly due to the sensitivity of the girder to initial imperfections and that the most severe buckling mode was used in the modeling of the imperfections. The handcalculation model was developed to imitate the one for patch loading in EN 1993-1- 5 (EC3), because it may then work as an addition to EC3. The model was developed in three steps: yield resistance, critical elastic buckling load and the resistance function. The model for yield resistance is analytical and has a form equivalent to the one in EC3. The expressions for the critical elastic buckling load were taken as simple as possible, since they are the main area of this study. The method essentially uses the same equations as EC3 except from two small changes. The results are on the safe side but the safety margin increases when the length of the loaded attachment decreases and the slenderness of the web panel increase. Consequently formulas for calculating the critical load may be improved. The chosen reduction function was slightly increased compared to the function in EC3 but the results will still have a good safety margin. The complete model gives results where the safety margin increases as the length of the loaded attachment decreases. The calculation model was designed to be easy to use. In comparison to the FE-analysis, all the tested beams except a few with low slenderness gave results on the safe side. / Detta examensarbete behandlar stålbalkar utsatta för lokal intryckning orsakade av en lokal momentbelastning. För lastfallet finns ännu inga bra handräkningsmetoder, i plåthandboken som ges ut av SSAB finns en beräkningsmetod presenterad. Den är väldigt krånglig med många beräkningssteg och diagram. Denna studie är inriktad på att utreda hur man kan räkna på belastningsfallet på ett enklare och bättre sätt. Lastfallet uppkommer t.ex. då en lastögla svetsas till flänsen rakt över livet på en balk. Om lastöglan dras parallellt med balkens riktning så kan belastningen ses som två komponenter, ett moment och en horisontalkraft. Momentet kommer att trycka in lastöglan i balken och till slut blir det ett brott p.g.a. en blandning av att materialet flyter och att livet bucklar. I den här rapporten behandlas bara momentdelen av lasten. Studien är gjord i tre steg. Först byggdes en FE-modell i Abaqus. Denna modell verifierades mot fysiska försök på lokal intryckning från en vertikal kraft, eftersom inga försök hittades på intryckning av ett lokalt moment. Som steg nummer två anpassades FE-modellen till försök med lokal intryckning från ett moment. Ett antal experiment gjordes med variation av två parametrar, livplåtens tjocklek och lastöglans längd. Lastöglan var väldigt styv eftersom den bara skulle skapa momentbelastningen. Sista steget var att utifrån resultaten ta fram en beräkningsmodell för lastfallet. FE-modellen som skapades för testerna visade sig ge bärförmågor ca 10% under bärförmågan från de fysiska försöken. Detta berodde mycket på att balken var känslig för hur initialimperfektionerna såg ut och att första bucklingsmodens form användes vid modelleringen av de geometriska imperfektionerna. Beräkningsmodellen utvecklades så att den skulle efterlikna den som gäller för lokal intryckning från vertikal last i EN 1993-1-5. Detta för att modellen skulle kunna användas som ett tillägg till EK3. Modellen utvecklades i tre delar, flytbärförmågan, kritiska bucklingslasten och reduktionsfaktorn för buckling. Modellen för flytbärförmågan togs fram analytiskt och fick en form som efterliknar den i EK3. Beräkningsmetoden för den kritiska bucklingslasten använder sig i princip av formlerna i EK3 förutom två små ändringar. Reduktionsfunktionen som valdes är en liten ökning av funktionen i EK3 men resultaten ligger ändå med bra marginal på säkra sidan. Den kompletta beräkningsmodellen ger resultat där säkerhetsmarginalen ökar vid minskande längd på lastöglan. Den har utformats så att den är lätt att använda och vid jämförelse med FE-försök gav beräkningsmodellen resultat på säkra sidan för alla balkar förutom några få av balkarna med låg slankhet.

When a concentrated load is introduced perpendicular to the flanges of a steel beam, this condition is referred to as Patch loading (Gozzi, 2007). This occurrence is common in many steel structures, for example at supports or during launching of bridges. Because of the usual slenderness of I-beams and other plated structures, these are sometimes reinforced with stiffeners in order to avoid buckling. Modifications, such as adding stiffeners to a beam, are done to make greater plastic deformations possible before buckling can occur; thereby increasing the resistance against failure. Transverse stiffeners are added in areas where the beam is exposed to concentrated loads (Lagerqvist, 1994). The descriptions of calculating patch loading in the Eurocode are presented for cases of double stiffeners, with the load applied in between two stiffeners with same distance to each of them, or when there is one single stiffener that is acting in line with the load. In the Eurocode there are also descriptions on how to calculate on the resistance against patch loading when there are no stiffeners added. However, the Eurocode lacks descriptions for cases when the stiffeners are misaligned. The purpose of this paper is the evaluation of the impact from transverse stiffeners to the resistance of welded I-beams, when the stiffeners are misaligned and where the length of the beam varies. Because of the complexity of such of problems it is almost impossible to find theoretical solutions (Lagerqvist &amp; Johansson, 1996). Therefore, in this study as well as in almost all studies that aim to predict the ultimate resistances of steel beams subjected to patch loading, the results are gained empirically. The tests herein were done by FE-modeling and the results from the physical experiments done in Lagerkvist’s doctoral thesis were used for validation of the model, as conducting experiments ourselves was not economically possible. 6 The study was made in two steps. In the first step FE-models were produced under the same circumstances as the results obtained by Lagerqvist (1994). Those analyses were not part of the aim of the study; the intention for making the initial analyses was to strengthen the reliability of the results. From there, the final analyses were made with the aim in investigating the influence of stiffeners on the resistance, when these are misaligned. In this step, observations were also made with regards to the impact of the bending moment of the beam on its resistance. The initial analyses, which were made for validation of the modeling, had a satisfying correspondence to the physical experiments; hence the final analyses are assumed valid of acceptance. From observations of the results in the final analyses it is noticed that adding stiffeners is a highly preferred way of increasing the resistance for slender beams. For full utilization it is however important to have the stiffeners optimally placed, because a small deviation from this position gives an unwanted decrease in resistance.

Fiber reinforced polymer (FRP) composites are considered very promising for infrastructure applications such as repair, rehabilitation and replacement of deteriorated bridge decks. However, there is lack of proper understanding of the structural behavior of FRP decks. For example, due to the localization of load under a truck tire, the conventionally used uniform patch loading is not suitable for performance evaluation of FRP composite deck systems with cellular geometry and relatively low modulus (compared to concrete decks). In this current study, a simulated tire patch loading profile has been proposed for testing and analysis of FRP deck. The tire patch produced significantly different failure mode (local transverse failure under the tire patch) compared to the punching-shear mode obtained using the conventional rectangular steel plate. The local response of a cellular FRP composite deck has been analyzed using finite element simulation and results are compared with full scale laboratory experiment of bridge deck and structure. Parametric studies show that design criteria based on global deck displacement is inadequate for cellular FRP deck and local deformation behavior must be considered. The adhesive bonding method is implemented for joining of bridge deck panels and response of structural joint analyzed experimentally. Strength, failure mode and fatigue life prediction methodologies for a cellular FRP bridge deck are presented in this dissertation. / Ph. D.