Final 06 with Solution

Final 06 with Solution - McGILL UNIVERSITY . FACULTY OF...

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Unformatted text preview: McGILL UNIVERSITY . FACULTY OF ENGINEERING Department of Civil Engineering and Applied Mechanics CIVE 317 Structural Engineering I FINAL EXAMINATION Co-Examiners: Prof. .G. McClure Date: 18 December 2006 Prof. S. Shrivastava Time: 9h00 — 12h00 NOTES: , This is an open book examination. The faculty-approved calculator is the only type permitted. The questionnaire contains 5 pages. ‘ Attempt all six parts. The examination will be marked out of 100. 9:593”? Part 1 (20 marks total) a) 15 marks 7 Use the principle of virtual work with visual integration to compute the vertical displacement of joint D for the structure in Fig. 1 due to the load shown. The pole structure-(member AC) is a steel tube with I = 2 x 107 m4. Member DC is a steel cable with a cross-sectional area of 32 m2. MemberDB is a rigid strut that can resist axial forces only. Take Ema = 200 GPa. ' b) 5 marks If a turnbuckle is used to remove 100 mm of cable length in DC, how does it affect the displacements at D? Does it affect the stress state in the pole? Justify your answer. 3m 9m W ' Figure 1 Part2 (20 marks) Consider the plane flame of Fig. 2. Calculate the flexibility matrix corresponding to the three degrees of freedom at joint No. 1. You may use the analysis method of your choice _ to determine the flexibility coefficients. Neglect the axial and shear-deformations in the flame. ' ' 1'5'01-kN -~ m @ ' 10m E V: 200 GPa - I: 4100. (106) m4 A. = 4,000 Figure 2 . "s": Part 3 (15 marks) Sketch the quantitative influence lines of the beam shown in Fig. 3 for: /a)’ The vertical reaction at support A; b) The vertical reaction at the fixed end B; c) The fixed-end moment ME. Repeat for the beam where the hinge at C is removed (obtain qualitative lines only this time) so that AB is continuous. In each case indicate the loading pattern (partial or full uniform load) that creates the most critical effects. - Comment on the effect of the internal hinge on the support reactions. Figure 3 Part 4 (20 marks total) Consider again the plane frame shown ianig. 2. Use the conventions shown for labelling joints, members and degrees of freedom. State clearly the set of units used. 4 marks Obtain the local stiffiress matrices for the two members. I Mmarks Transform the local stiffness matrices obtained in a) in the global coordinate system. c) 4 marks Assemble the partition S of the global stiffiress matrix corresponding to the free degrees of freedom. (1) 1 mark - Establish the load vector {Q} and write the system of equations {Q} = S {d}. e) 4 marks Our teaching assistant has run a computer analysis of this problem and found the displacements {d}T = 10'4 [0.5924m, 1.0259m, —24.829rad]. Calculate the support reactions and the end forces on the members using the element matrices found in a) and b). ' f) 3 marks Sketch the internal force diagrams (axial forces N, shear forces V and bending moments Mf) in the structure. ' Part 5 (5 marks) List five design criteria for your large screen support design project. Indicate whether they are “structura ” or “non structura ”. ‘ Part 6 (20 marks total) Figure 6 shows typical elevations and a plan View of the steel structure of an industrial building located in Laval. Details are not repeated here but you will have recognized the problem of Assignment 1 Part 4. Without performing calculation , describe how the loads are resisted by the structure, from the direct surface of application (roof or walls) to the foundation, for the following loads: a) 8 marks _ The roof gravity loads b) 4 marks The roof wind suction loads. ' c) 6 marks The wall wind loads. (1) 2 marks The earthquake effects. 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Final 06 with Solution - McGILL UNIVERSITY . FACULTY OF...

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