UNIVERSITY OF PRETORIA Department of Mechanical and Aeronautical Engineering MACHINE DESIGN MOW323

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1 Copyright reserved UNIVERSITY OF PRETORIA Department of Mechanical and Aeronautical Engineering MACHINE DESIGN MOW323 November 2003 External Examiner: Dr E Terblanche Time: 2h30 Internal Examiners: P.R. de Wet Marks: 120 Instructions: 1. Read the paper carefully before answering any questions 2. Section A is closed book and will be taken in after 1/2 hour 3. Section B are open book (Only SABS0162, Structural Steel Handbook and Shigley SECTION A Question 1 Figure 1 show a finite element model of a bracket using first order tetrahedrons. a) Comment on the choice of elements and make a suggestion. b) Discuss the element size and how you would decide whether it is fine enough. Figure 1 Question 2 (2) What do you understand under the terms, aspect ratio, and skewness, and what is the effect on the accuracy of the FEA model. (Use sketches if necessary) Question 3 Comment on the following statements: a) When your FEA software reports no error, the solution will be correct. b) If only the natural frequencies are required a coarser mesh can be used. c) Solids give the best results because they model the geometry accurately (6) Question 4 Discuss the relative importance of the geometry, loads and boundary conditions on the accuracy of a finite element model. Question 5 Explain the difference between serviceability and ultimate limit states and how this differs from the normal stress analysis.

2 SECTION B Question 6 (30) In Figure 2 a structure is shown to which a hoist is attached. The horizontal beam is a 152x152x23 H section 3320mm long. It is connected to the vertical legs using a welded end plate bolted to the vertical sections. The original design was for a 1 tonne capacity, but the client now wants to lift 2 tonnes. Determine whether the horizontal beam will comply with SABS The following design values are prescribed: Load factor for ultimate load: 1.5 Load factor for limit load. 1.2 Recommended maximum displacement: Span/600 All Material : 300W State all assumptions clearly Question 7 The pedestal for a chairlift (similar to a ski lift) is shown in Figure 3. The total rope force on the structure is 60kN. For safety reasons, the load factor for ultimate load is 2.2, and for limit loads, 1.8. The structure is fabricated from welded plate (material 300W) a) The pedestal has been checked for bending resistance. There is concern over the possibility of shear buckling in the side panels. Calculate the shear strength of these panels according to SABS (20) b) The pedestal is fastened using 4 x M30 bolts (grade 8.8). For adjustment these bolts can slide in slots. The connection therefor relies on friction to carry the shear load. Calculate if the bolted connection is sufficient to carry the combined shear and tension. (Ignore prying) (20) c) The base plate is made of 25mm steel. Prying is a major concern. Determine if the plate can handle the prying load and make a suggestion if it is necessary to use gussets. (30)

3 UNIVERSITEIT VAN PRETORIA Departement Meganiese en Lugvaartkundige Ingenieurswese MASJIENONTWERP MOW323 Kopiereg voorbehou November 2003 Eksterne Eksaminator: Dr E Terblanche Tyd: 2h30 Interne Eksaminators: P.R. de Wet Punte: 120 Instruksies: 1. Lees die vraestel sorgvuldig voor u enige vrae antwoord 2. Afdeling A is toeboek en sal na 1/2 uur ingeneem word. 3. Afdeling B oopboek (Slegs SABS0162, Struktuur staal handboek en Shigley) Afdeling A (Toeboek) Vraag 1 In figuur 1 word n eindige element van n vashegting getoon. Eerste orde tetrahedrons is gebruik vir die model. a) Lewer kommentaar oor die keuse van elemente en maak n voorstel b) Bespreek die grootte van die elemente en hoe u sou besluit dat die rooster fyn genoeg is. Figuur 1 Vraag 2 (2) Wat verstaan u onder die terme slankheidsverhounding en skeefheid (skewness) en watter implikase het dit op die akkuraatheid van n EEA model. (Gebruik sketse indien nodig) Vraag 2 (6) Lewer kommentaar oor die volgende stellings: a) Wanneer die eindige element model geen foute gee nie, is die model korrek. b) As slegs die natuurlike frekwensies benodig word kan n growwer rooster gebruik word. c) Soliede elemente gee die beste resultate aangesien hulle die geometrie die beste modelleer. Vraag 3 Bespreek die relatiewe belangrikheid van die geometrie, belastings en randwaardes op die akkuraatheid van n eindige element model. Vraag 4 Verduidelik die verskil tussen limiet- en grens-toestand analise en hoe dit verskil van die normale spanningsanalise.

4 Afdeling B (Oop boek) Vraag 6 (30) Figuur 2 toon n oorhoofse struktuur waaraan n hysblok hang. Die horisontale balk is n 152x152x23 H seksie, 3320mm lank. Die balk is aan weerskante vasgeheg met n endplaat wat aan die balk gesweis is en aan die vertikale seksie vasgebout is. Die oorspronklike struktuur was ontwerp vir n 1 ton kapasiteit, maar die klient wil die vermoë opstoot na 2 ton. Bepaal of die horisontale balk steeds sal voldoen aan SABS Die volgend ontwerp waardes word voorgeskryf: Lasfaktor vir uiterste toestand: 1.5 Lasfaktor vir diens toestande. 1.2 Aanbevole maksimum verplasing: Span/600 Alle Materiaal : 300W Noem alle aannames duidelik Vraag 7 Die staander vir n stoelhyser (soortgelyk aan ski-hysers) word in Figuur 3 aangetoon. Die totale tou krag op die struktuur is 60kN. Vir veiligheidsredes word n uiterste lasfaktor van 2.2 op uiterste grenstoestante, en 1.8 op dienstoestande, voorgeskryf Die struktuur word vervaardig uit gesweisde plaat (materiaal 300W) a) Die staander is nagegaan vir buigweerstand. Daar is egter n bekommernis dat die sykante dalk skuif knikking kan ondergaan. Bereken die skuif weerstand van die kant panele volgens SABS (20) b) Die staander word vasgebout met 4 x M30 boute (graad 8.8). Die boute kan verstel word in gleuwe. Die verbinding maak dus staat op wrywing om die krag oor te dra. Bereken of die boute voldoende is om die gekombineerde skuif en trekkrag te kan dra. (Ignoreer prying ) (20) c) Die basisplaat is van 25mm staal plaat. Die lokale buig ( prying ) is n groot bekommernis. Bereken of die plaat dit sal kan hanteer en maak n voorstel of verstywers nodig sal wees. (30)

5 3320 FIGURE 2 / FIGUUR A A SECTION AA (NOT TO SCALE) FIGURE 3 / FIGUUR 3