Causative agent of the crayfish plague: Aphanomyces astaci Schikora, 1906

Riječni rakovi važan su element slatkovodnih ekosustava. U posljednjih 200 godina došlo je do drastičnog smanjenja brojnosti autohtonih vrsta riječnih rakova na području Europe. Kao jedan od ključnih uzroka tog smanjenja navodi se izbijanje epidemija račje kuge uzrokovane patogenom Aphanomyces astaci. Infektivne čestice ove bolesti sekundarne su zoospore koje se stvaraju na krajevima hifa ovog obligatnog parazita. Osim riječnih rakova, kao vektori širenja ovog patogena opisane su i druge vrste rakova. Postoji pet opisanih sojeva A. astaci, od kojih su za dva opisani podtipovi. Smatra se da sojevi potječu iz dva vala unosa alohtonih sjevernoameričkih vrsta riječnih rakova na područje Europe. Opaženo je više oblika horizontalnog prijenosa A. astaci, poput prijenosa ribama, pticama i antropogenim djelovanjem (ribolovna oprema, brodovi i trgovina kućnim ljubimcima). Na Balkanu su pronađene latentno zaražene populacije, za koje se smatra da su zaražene u prva dva vala širenja ovog patogena. Razlike podtipova unutar sojeva A. astaci, kao i njihov utjecaj na ekosustave u kojima se nalaze, još su nedovoljno istraženi. Također su potrebna dodatna istraživanja metoda suzbijanja zaraze ovim patogenom kako bi se umanjio utjecaj A. astaci na europske autohtone vrste riječnih rakova.Crayfish represent an important element of freshwater ecosystems. However, there has been a drastic decrease in the number of autochthonous species of crayfish in Europe over the past 200 years. Epidemic outbreaks of crayfish plague caused by the pathogen Aphanomyces astaci have been reported as one of the main causes of this decrease in abundance. The infective units of the disease are secondary zoospores produced at hypha ends of this obligatory parasite. Apart from crayfish, other crustacean species have also been identified as pathogen’s hosts and carriers. There are five described genotype groups, two of which have multiple subtypes. It is considered that the all of the strains originate from two waves of introduction of North American crayfish species into Europe. Multiple types of horizontal transmission of A. astaci have been observed, such as by fish, birds and anthropogenic activities (fishing equipment, ships and pet trade). Latent infections have been discovered in the Balkan region, which are considered to have been caused by the strains introduced by the first two phases /waves. Subtype differences within the different strains of A. astaci and their effect on ecosystems in which they are present are still inadequately studied. Furthermore, additional research of infection control methods of this pathogen is required to reduce the impact of A. astaci on European freshwater crayfish and ecosystems in general

Challenges of torrential flood risk management in Serbia

Torrential floods are the natural hydrological hazards manifesting as a consequence of extreme rainfall episodes which have a quick response from the watersheds of small areas, steep slopes and intensive soil erosion. Taking in consideration the nature of torrential flood (sudden and destructive occurrence) and the fact they are the most frequent natural hazards in Serbia, torrential flood risk management is a real challenge. Instead of partial solutions for flood protection, integrated torrential flood risk management is more meaningful and effective. The key steps should be an improvement of the legal framework on national level and an expansion of technical and biological torrent control works in river basins. Consequences for society can be significantly reduced if there is an efficient forecast and timely warning, rescue and evacuation and if affected population is educated about flood risks and measures which can be undertaken in case of emergency situation. In this paper, all aspects of torrential flood risk management are analyzed

Methodische Unterrichtsgestaltung aus der Sicht der Grundschullehrer

The variety of didactic methods and approaches to teaching, which can stimulate and unlock learning potential, is recognised as influence of pluralist teaching. Pluralism in teaching is determined by various methods which can improve the quality of learning and make teaching more active, interesting, of high-quality and complete. The authors of this paper wanted to examine which teaching strategies are employed by primary and secondary school teachers. Furthermore, they alsoinvestigated to what extent teaching really is pluralistic, i.e. whether teachers use multiple sources of knowledge and teaching aids in their classrooms. The results show that problem and programmed teaching, topic-based and integrative teaching, project, computer-assisted teaching and field work are least frequently used in everyday lessons. Motivation, creativity and educational influences are significantly in decline, not only in secondary but also in higher classes of primary school. According to teachers\u27 assessments, multiple-source and pluralistic teaching approaches are only sometimes used. Research and development of learning and teaching methods are considered to be an important component of a modern school, which aims to direct learning towards students and their needs. In conclusion the authors point out the need for greater freedom of choice and decision making for teachers.Raznolikost didaktičkih i metodičkih oblika nastave, koji mogu potaknuti i osloboditi potencijale učenja, prepoznaju se kao metodički pluralistički utjecaji. Metodička pluralnost s obzirom na vrste i stilove učenja određena je različitim metodama koje potiču kvalitetu učenja i nastavu čine aktivnom, zanimljivom, kvalitetnom i cjelovitom. U ovom se poglavlju izlažu rezultati istraživanja kojemu je cilj bio ispitati kojima se nastavnim strategijama, metodama i postupcima (od ponuđenih 48, mapiranih u 6 kategorija), ispitani učitelji i nastavnici (N=150) najviše, a kojima najmanje koriste, odnosno rasvijetliti višeizvornost i pluralnost nastave unutar osnovne i srednje škole. U statističkoj obradi rezultata uporabljene su standardne metode deskriptivne statistike, a za testiranje statističke značajnosti razlika među uzorcima učitelja razredne i predmetne nastave te nastavnika srednje škole primijenjen je Kruskal-Wallisov test, neparametrijski ekvivalent analizi varijance za nezavisne uzorke. Rezultati su pokazali da problemsko i programirano poučavanje, tematsko i integrativno učenje, projektna, računalna i izvanučionička nastava zauzimaju najniže rangove primjene. Motiviranost, kreativnost i odgojni utjecaji u srednjoj školi, ali i višim razredima osnovne škole značajno opadaju, a glazbeni izričaji gotovo su zanemareni. Višeizvornost i pluralnost nastave, prema procjenama učitelja i nastavnika, samo je ponekad zastupljena. Ispitivanje i razvoj metoda učenja i poučavanja pokazuje se kao važna odrednica suvremene škole koja teži nastavu usmjeriti prema učeniku i njegovim potrebama. Teorijski i praktični nalazi ovog istraživanja upućuju na potrebu višeizvornosti i pluralnosti suvremene nastave na svim razinama, veću mogućnost izbora i odlučivanja, iznošenja vlastitoga iskustva, samostalnoga razmišljanja i djelovanja uporabom optimalnih strategija odgoja i obrazovanja, kreativnoga rješavanja problema, što ne prestaje nakon nastavnoga sata ili školskoga dana, već predstavlja cjeloživotni proces.Die Vielfältigkeiten der didaktischen und methodischen Unterrichtsformen, die das Lernpotenzial fördern und entfesseln können, werden als methodische und pluralistische Einflüsse erkannt. Die methodische Pluralität ist bezüglich der Lernstile und Lernarten durch eine Vielzahl von Methoden bestimmt, die die Lernqualität fördern und den Unterricht aktiver, interessanter, hochwertiger und vollständiger machen. In dieser Studie werden die Ergebnisse der Untersuchung präsentiert, mit der erforscht werden sollte, welche Unterrichtsstrategien, Methoden und Verfahren (von 48 angebotenen, in sechs Kategorien eingeteilt) die befragten Lehrer (N = 150) am meisten und welche am wenigsten einsetzen, bzw. es sollte die Vielfältigkeit der Quellen und die Pluralität des Unterrichts in Grund- und Mittelschulen verdeutlicht werden. Bei der statistischen Analyse der Ergebnisse wurden Standardverfahren der deskriptiven Statistik verwendet, und für die Prüfung der statistischen Signifikanz der Unterschiede zwischen Grundschul- und Mittelschullehrern wurde der Kruskal-Wallis-Test angewendet, ein parameterfreier Äquivalent der Varianzanalyse für unabhängige Stichproben. Die Ergebnisse zeigten, dass problemorientierter und programmierter Unterricht, thematisches und integratives Lernen, Projektunterricht, computerisierter und außerschulischer Unterricht am seltensten angewendet werden. Motivation, Kreativität und pädagogische Einflüsse in der Mittelschule, aber auch in den höheren Grundschulklassen, sind deutlich zurückgegangen, und der musikalische Ausdruck wird fast ignoriert. Die Vielfältigkeit der Quellen und die Pluralität des Unterrichts ist nach Schätzungen von Grundschullehrern nur manchmal vertreten. Die Prüfung und Entwicklung von Lehr- und Lernmethoden zeigt sich als eine wichtige Determinante der modernen Schule, die sich nach einem schülerorientierten Unterricht und den Bedürfnissen der Schüler richtet. Die theoretischen und praktischen Ergebnisse dieser Studie weisen auf die Notwendigkeit der Vielfältigkeit der Quellen und der Pluralität des Unterrichts auf allen Ebenen hin, eine größere Auswahl- und Entscheidungsmöglichkeit, Präsentation der eigenen Erfahrungen, selbstständiges Denken und Handeln mit Hilfe der optimalen Bildungsstrategien, kreative Problemlösung, was nicht nach einer Lektion oder einem Schultag aufhört, sondern einen lebenslangen Prozess repräsentiert

On the possibility of using biological toxicity tests to monitor the work of wastewater treatment plants

The aim of this study was to ascertain the possibility of using biological toxicity tests to monitor influent and effluent wastewaters of wastewater treatment plants. The information obtained through these tests is used to prevent toxic pollutants from entering wastewater treatment plants and discharge of toxic pollutants into the recipient. Samples of wastewaters from the wastewater treatment plants of Kragujevac and Gornji Milanovac, as well as from the Lepenica and Despotovica Rivers immediately before and after the influx of wastewaters from the plants, were collected between October 2004 and June 2005. Used as the test organism in these tests was the zebrafish Brachydanio rerio Hamilton - Buchanon (Cyprinidae). The acute toxicity test of 96/h duration showed that the tested samples had a slight acutely toxic effect on B. rerio, except for the sample of influent wastewater into the Cvetojevac wastewater treatment plant, which had moderately acute toxicity, indicating that such water should be prevented from entering the system in order to eliminate its detrimental effect on the purification process

GM uljana repica tolerantna na herbicide-uticaj na životnu sredinu i poljoprivredu

The introduction of genetically modified herbicide tolerant rapeseed has raised questions concerning the possible transfer of transgenes into wild relatives or neighbouring fields with similar crops. Pollen of rapeseed can be spread in the area and if a non-GM crop is fertilised by GM pollen, some percentage of the collected seed product will contain GM. Current regulation in the EU limits the allowed content. For conventional crops the critical level of GM contamination is in practice below 0.9%, which is the threshold value for labelling of GM in food and feed by the EU, although the limit for seeds is 0.1% in Serbia. In organic farming, the regulations do not allow the use of genetic engineering in the grain production system.Uvođenje genetski modifikovane uljane repice koja je otporna na herbicide nameće pitanja u vezi sa potencijalnim prenošenjem transgena sa genetski modifikovane uljane repice na njene divlje srodnike ili susedna polja sa sličnim kulturama. Polen uljane repice širi se u prostoru, te ukoliko je genetski nemodifikovan usev oplođen genetski modifikovanim polenom, određeni broj biljaka biće genetski modifikovan. Važeća zakonska regulativa u Evropskoj uniji ograničava dozvoljen sadržaj genetske modifikacije u usevima. Za konvencionalne useve najviši dozvoljen nivo kontaminacije u praksi je 0,9%, što je istovremeno i granična vrednost za obeležavanje GM hrane i hrane za životinje u Evropskoj uniji. U Srbiji kritična granica za semena iznosi 0,1%. U organskoj proizvodnji zakonska uredba ne dozvoljava upotrebu genetičkog inžinjeringa u sistemu proizvodnje semena

Effect of metatopolin on micropropagation and rooting apple type Gala

Zbog nuspojava benzilaminopurina (BAP-a) kao što su nekroza vrha izdanka, inhibicija zakorjenjivanja te teškoće pri aklimatizaciji u literaturi se kao alternativa BAP-u navodi hidroksilirani analog BAP-a – metaTopolin (mT). Kroz ovaj rad istraživao se utjecaj metaTopolina i BAP-a na mikropropagaciju jabuke sorte Gala pri čemu se procjenjivala duljina i razvijenost izdanaka te količina klorofila; duljina, širina i površina lista te broj puči po površini lista. Izdanci su zakorjenjeni na MS mediju s dodatkom 2 mg/l IAA i procijenjena je uspješnost zakorjenjivanja s obzirom na prethodni medij (prethodno korišten citokinin). Izdanci razvijeni na podlozi sa citokininom mT imali su veću lisnu površinu, duljinu i širinu listova. Sadržaj klorofila u listu i broj puči po površini lista se nisu statistički razlikovali za biljke sa oba tretmana dok je zakorjenjivanje bilo uspješnije kod biljaka sa tretmana BAP-om.Due to the side effects of benzylaminopurine (BAP), such as shoot top necrosis, inhibition of rooting, and difficulty in acclimatization, a hydroxylated analogue of BAP - metaTopolin (mT) has been cited as an alternative to BAP. Through this work, the influence of metaTopolin and BAP on micropropagation of Gala apples was investigated, estimating the length and development of shoots and the amount of chlorophyll; the length, width and area of the leaf and stomatal density. The shoots were rooted on MS medium supplemented with 2 mg / l IAA and the rooting performance was evaluated with respect to the previous medium (cytokinin previously used). The shoots developed on cytokinin mT substrate had larger leaf area, leaf length and width. Chlorophyll content in the leaf and stomatal density were not statistically different for plants with both treatments, whereas rooting was more successful with plants with BAP treatment

ANALIZA PODATAKA FINANCIJSKIH IZVJEŠTAJA LISTANIH PODUZEĆA IZ DJELATNOSTI GRAĐEVINARSTVA : završni rad

Temeljni financijski izvještaji su: bilanca, račun dobiti i gubitka, izvještaj o ostaloj sveobuhvatnoj dobiti, izvještaj o novčanom toku, izvještaj o promjenama kapitala i bilješke. Ovi izvještaji pružaju informacije o financijskom položaju, uspješnosti, novčanim tokovima i promjenama kapitala poduzeća. Pomoću analize financijskih izvještaja koja podrazumijeva korištenje različitih instrumenata i postupaka, podaci iz financijskih izvještaja pretvaraju se u informacije relevantne za donošenje poslovnih odluka širokog kruga korisnika. U ovom radu, provedena je analiza financijskih izvještaja na šest listanih poduzeća iz djelatnosti građevinarstva u Hrvatskoj te je donesen zaključak da poduzeća ne ostvaruju ni sigurno ni profitabilno poslovanje.Basic financial statements are: balance sheet, income statement, statement of comprehensive income, cash flow statement, statement of changes in equity and notes. These statements provide information about the financial position, performance, cash flows and changes in equity companies. With the analysis of financial statements, which implies the use of different instruments and methods, data from the financial statements are transformed into information relevant for decision making wide range of users. In this graduate work, is provide an analysis of the financial statements on the six-listed companies in the construction industry in Croatia and conclusion is that these businesses do not present safe or profitabile operation

Possibilities of using a database in the strategy of conserving the biodiversity of inland water macroinvertebrates at a national level

Za efikasno upravljanje različitim oblastima, pa i aktivnostima vezanim za zaštitu biološke raznovrsnosti, veoma je važan kvalitet, kvantitet i organizacija podataka. Iz tog razloga su formirane brojne baze podataka koje omogućavaju skladištenje, proveru i analizu podataka. Dosadašnja istraživanja ukazuju da su baze podataka važne za konzervaciju biodiverziteta. Ciljevi ovog istraživanja bili su: formiranje baze podataka na osnovu koje se stiče uvid o biodiverzitetu akvatičnih ekosistema Srbije, sa posebnim osvrtom na akvatične makrobeskičmenjake; izrada spiska svih vrsta makrobeskičmenjaka konstatovanih u kopnenim vodama Srbije; određivanje centara diverziteta makrobeskičmenjaka po rečnim slivovima i, konačno, data je koncepcija strategije i prioritet konzervacije akvatičnih makrobeskičmenjaka na nacionalnom nivou. Kako bi se primenila razrađena strategija konzervacije akvatičnih makrobeskičmenjaka na nacionalnom nivou, formirana je baza podataka pod nazivom Biodiverzitet Akvatičnih Ekosistema Srbije, ex situ zaštita, BAES ex situ. Baza podataka BAES sadrži podatke o nalazima makrobeskičmenjaka u vodenim ekosistemima na području Srbije, počevši od prvog bibliografskog nalaza iz 1873. godine do danas. Na osnovu podataka iz baze formiran je i koncipiran spisak vrsta makrobeskičmenjaka zabeleženih u vodenim ekosistemima Srbije u periodu obuhvaćenom istraživanjem (do 2012. godine). Spisak trenutno čine 995 vrsta, koje su svrstane u 23 životinjske grupe. Najveći diverzitet je zabeležen u grupama Diptera i Trichoptera, zatim slede Plecoptera, Ephemeroptera Oligochaeta i Odonata. Anlizom baze podataka određeni su centri diverziteta za pojedine grupe makrobeskičmenjaka. Brdsko-planinska područja Srbije, na kojima se najvećim delom nalaze slivovi Južne i Zapadne Morave su centri diverziteta za grupe Insecta, i to pre svega za grupe Diptera, Trichoptera, Plecoptera i Ephemeroptera, dok su ravničarske reke Dunav i Sava centri diverziteta: Gastropoda, Bivalvia, Oligochaeta, Hirudinea, Amphipoda i Odonata. Predlog strategije se ogleda u nadovezivanju na IUCN kategorije, ali filtriranjem podataka iz baze vrši se selekcija i izdvajaju se vrste koje su označene kao lokalno značajne jedinice konzervacije (LZJK). Na osnovu globalnih i regionalnih IUCN kriterijuma izvršena je procena stepena ugroženosti za taksone sa statusom LZJK. Kao rezultat dobija se lokalna Crvena lista ugroženih vrsta akvatičnih makrobeskičmenjaka. Kako bi se odredio rizik od izumiranja i prioritet konzervacije na lokalnom nivou izvršeno je testiranje modifikovanog modela ESHIPPO. Model ESHIPPO je primenjen na sledećim grupama organizama: Plecoptera, Ephemeroptera i dekapodni rakovi iz fam. Astacidae. Primenom strategije pokazalo se da 14 vrsta iz grupe Plecoptera i 10 vrsta iz grupe Ephemeroptera imaju umeren nivo rizika od izumiranja i II stepen prioriteta konzervacije na nacionalnom nivou. Prioritet u konzervaciji i I stepen zaštite ima vrsta plemenitog rečnog raka Astacus astacus u odnosu na vrstu Austropotamobius torrentium. Strategija je pokazala da vrste sa istim stepenom ugroženosti mogu imati različit nivo rizika od izumiranja, a samim tim i prioritet konzervacije na lokalnom nivou. Krajnji rezultat našeg istraživanja su finalni izveštaji baze za ugrožene vrste akvatičnih makrobeskičmenjaka u kojima se predlažu mere konzercavije koje se propisuju na osnovu IUCN kriterijuma, kao i na osnovu procene stepena lokalnog rizika od izumiranja. Strategija ne samo da ima naučni, već i ekonomski značaj, jer se posebnom analizom elemenata modela „ES“ i „HIPPO“ izdvajaju faktori koji najviše utiču na ugroženost date vrste i na taj način se preduzimaju najracionalnije mere konzervacije na nacionalnom nivou.For effective management of diverse areas and activities related to biodiversity conservation, the quality as well as quantity and organization of data are very important. For this reason a number of databases that allow storing, testing and analysis were formed. Previous researches suggest that databases are important for biodiversity conservation. The objectives of this study were: the establishment of a database based on which an insight into the biodiversity of aquatic ecosystems of Serbia is acquired, with special emphasis on aquatic macroinvertebrates; the creation of a list of all identified species of macroinvertebrates in the inland waters of Serbia; the determination of the centers of diversity of macroinvertebrates on river basins, and finally, presenting a strategy concept and a conservation priority in regard to aquatic macroinvertebrates at the national level. In order to implement the developed conservation strategy for aquatic macroinvertebrates at the national level, a database was created under the title Biodiversity of Aquatic Ecosystems of Serbia, ex situ conservation, BAES ex situ. The BAES database contains information on the findings of macroinvertebrates in aquatic ecosystems in Serbia, starting from the first bibliographic findings in 1873 until today. Based on the data from the database a list of macroinvertebrates was designed and constructed, with all the species recorded in the aquatic ecosystems of Serbia during the survey period (up to 2012). The list currently consists of 995 species, which are divided into 23 groups of animals. The highest diversity was recorded in groups of Diptera and Trichoptera, followed by Plecoptera, Ephemeroptera, Oligochaeta and Odonata. By analysing the database specific centers of diversity for each group of macroinvertebrates were determined. The mountainous areas of Serbia, where the basins of South and West Morava are mostly situated, are centers of diversity for the group of Insects, primarily for groups of Diptera, Trichoptera, Plecoptera and Ephemeroptera, whereas the plains of the Danube and Sava are centers of diversity: Gastropoda, Bivalvia, Oligochaeta, Hirudinea, Amphipoda and Odonata. The proposed strategy can be seen in reference to the IUCN categories, but by filtering the data from the database, the selection is made and the species, which are designated as significant to local units of conservation (lokalno značajne jedinice konzervacije - LZJK), are allocated. Based on the global and regional IUCN criteria levels of threat to the taxa with LZJK status were assessed. The result is a local Red List of endangered species of aquatic macroinvertebrates. In order to determine the risk of extinction and the priority of conservation on a local level the testing of a modified ESHIPPO model was carried out. The ESHIPPO model was applied to the following groups of organisms: Plecoptera, Ephemeroptera, and decapod crustaceans from the family of Astacidae. By applying the strategy it became clear that 14 species of the Plecoptera group and 10 species of the Ephemeroptera group have a moderate level of extinction risk and a degree II conservation priority at the national level. A species of the noble crayfish Astacus astacus has the conservation priority and protection level I in regard to the type Austropotamobius torrentium. The strategy has shown that species with the same degree of vulnerability may have a different level of extinction risk, and therefore a conservation priority at the local level. The end result of our research are the final reports of the base for endangered species of aquatic macroinvertebrates in which conservation measures are proposed that are prescribed based on the IUCN criteria, and based on the assessment of the degree of risk of local extinction. The strategy is not only of scientific, but also of economic importance. By seperately analysing elements of the models "ES" and "HIPPO", the factors were identified that most influence the vulnerability of the given species and thus take the most rational conservation measures at the national level

ANALIZA PODATAKA FINANCIJSKIH IZVJEŠTAJA LISTANIH PODUZEĆA IZ DJELATNOSTI GRAĐEVINARSTVA : završni rad

Temeljni financijski izvještaji su: bilanca, račun dobiti i gubitka, izvještaj o ostaloj sveobuhvatnoj dobiti, izvještaj o novčanom toku, izvještaj o promjenama kapitala i bilješke. Ovi izvještaji pružaju informacije o financijskom položaju, uspješnosti, novčanim tokovima i promjenama kapitala poduzeća. Pomoću analize financijskih izvještaja koja podrazumijeva korištenje različitih instrumenata i postupaka, podaci iz financijskih izvještaja pretvaraju se u informacije relevantne za donošenje poslovnih odluka širokog kruga korisnika. U ovom radu, provedena je analiza financijskih izvještaja na šest listanih poduzeća iz djelatnosti građevinarstva u Hrvatskoj te je donesen zaključak da poduzeća ne ostvaruju ni sigurno ni profitabilno poslovanje.Basic financial statements are: balance sheet, income statement, statement of comprehensive income, cash flow statement, statement of changes in equity and notes. These statements provide information about the financial position, performance, cash flows and changes in equity companies. With the analysis of financial statements, which implies the use of different instruments and methods, data from the financial statements are transformed into information relevant for decision making wide range of users. In this graduate work, is provide an analysis of the financial statements on the six-listed companies in the construction industry in Croatia and conclusion is that these businesses do not present safe or profitabile operation

Stress constraints applied to the optimization of a thin-walled Z-beam

Razmatran je jedan pristup optimizaciji tankozidih otvorenih poprečnih preseka oblika Z - profila, izloženih savijanju i ograničenoj torziji. Za data opterećenja, materijal i geometrijske karakteristike, problem se svodi na određivanje minimalne mase, odnosno minimalne površine poprečnog preseka konstruktivnih tankozidih poprečnih preseka izabranog oblika. Površina poprečnog preseka je izabrana za funkciju cilja. Uvedena su naponska ograničenja. Primenjuje se Metoda Lagranžovog množitelja. Rezultati analitički dobijenih jednačina za matematički model, numerička rešenja, kao i ušteda u masi, izračunati su za tri slučaja opterećenja. Neki rezultati su provereni primenom programa COSMOS.One approach to the optimization of a thin-walled open section Z-beam subjected to the bending and to the constrained torsion is considered. For given loads, material and geometrical characteristics, the problem is reduced to the determination of minimum mass i.e. minimum crosssectional area of structural thin-walled beam of the chosen shape. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. The Lagrange multiplier method is applied. Solutions of analitically obtained expressions for the mathematical model, numerical solutions, as well as the saved mass, are calculated for three loading cases