Final 07 - CIVE 317 Structural Engineering I Page 1 McGILL...

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Unformatted text preview: CIVE 317 Structural Engineering I Page 1 McGILL UNIVERSITY FACULTY OF ENGINEERING Department of Civil Engineering and Applied Mechanics CIVE 317 Structural Engineering I FINAL EXAMINATION Examiner: Prof. G. McClure Date: 12 December 2007 Associate examiner: Prof. Y. Shao Time: 9h00 — 12h00 NOTES: This is an open book examination. The faculty-approved calculator is the only type permitted. The questionnaire contains 12 pages. Attempt all SIX parts. The examination will be marked out of 100. P‘PPNT‘ 'Part 1 (20 marks total) Frame ABCD shown in Fig. P1 is pinned at D and supported by cable BE at point B. For the frame, I = 150x106 mm4 and A = 2000 mmz. - For the cable, A= 500 mm-Z. Take E = 70 GPa for each member. Neglect the axial and shear deformations in the frame. ' Use the method of virtual work with graphical integration to determine a) the horizontal deflection at A; b) the vertical deflection at C. Figure P1 CIVE 317 Structural Engineering I Page 2 Part2 (20 marks) Use the flexibility method to determine the fixed-end moments of a prismatic beam of length L and bending rigidity EI subjected to a uniform load w (See Figure P2). Neglect the axial and shear deformations in the beam. You are free to use the method of your choice to evaluate displacements. Figure P2 - w .,| (\IA ' BE:._1 FLD'IA H J ENIBA I L I CIVE 317 Structural Engineering I V ' Page 3 Part 3 (15 marks total) Figure P3a shows a simple beam with overhangs where the dimensions are given in m. Sketch the quantitative influence lines (1 mark each) for: a) The vertical reaction at support A; b) The shear force at the right of support A; c) The bending moment at A; d) The shear force at the mid span; 6) The bending moment at the mid span. Figure P3a l, , 2 Movement of the load 10 m 105" 8m 1 22m Consider that the beam is subjected to a permanent load of 8.0 kN/m and a live load consisting of a distributed uniform load of 20.0 kN/m and a series of three point loads with the fixed position shown in Fig. P3b. Assume that all these loads have already been factored for an ultimate limit states evaluation. V Figure P3b 70 kN 70 kN 15 kN 1 ‘4m 4111‘ ‘rlflr’uiit'l‘ i "m rout Wilfrid when] when] 0 (5 marks) Determine and clearly show on a sketch the combined loading pattern that creates the maximum positive bending moment at the mid span of the beam and calculate the value of this maximum moment. g) (5 marks) Sketch the shear force and bending moment diagrams of the beam for the critical loading pattern determined in part f. CIVE 317 Structural Engineering I I Page 4 Part 4 (25 marks total) Figure P4a represents a typical cross. section showing the steel frame of a grandstand at a football stadium. Our teaching assistant, Ali Ghafari, has created a SAP 2000 computer model of a typical plane truss which is the main element of the roof structure. The joint labels are shown in Fig. P4b while the element labels are shown in Fig P4c. The truss is assumed to be resting on a pinned support at joint 1 and is suspended at joint 7 by member 26 which is pin-supported at joint 15. A table listing the nodal point coordinates and member connectivity and length is appended. The truss members are made of rectangular tubes with cross-sectional areas as indicated in the following: Member 26 (Joint 7 to Joint 15): 83 cm2 Top boom Joint 1 to Joint 7: 68.0 cm2 Top boom Joint 7 to Joint 13: 28.9 cm2 Bottom boom Joint 2 to Joint 14: 55.5 cm2 ' All the remaining web members: 18.4 cm2 For steel, use E= 200 000 MPa and Fy = 275 MPa. ' The truss is adequately stabilized in the transverse direction and all the individual members have sufficient buckling capacity. Figures P4d to P4f represent three static loading cases analysed: the resulting member forces are listed in the following pages. Note the units are N and m. o The first load case “GRAVITY” represents the effects of downward point loads of 30 kN and 60 kN applied to the top chord of the trust. These point loads are transferred by purlins acting in the transverse direction. 1 The second load case “UPLIFT” represents the effects of upward point loads of 13 kN and 26 kN also applied to the top chord of the trust. . 0 Finally, the “POINTLOAD” case represents the effects of a downward point load ' of 100 kN applied at the free end of the truss at joint 13. All the loads considered are unfactored. a) 1 mark Determine the degree of indeterminacy of this truss. b) 4 marks State the detailed steps of the procedure to follow to calculate the vertical displacement of the free end of the truss under gravity loads. c) 20 marks Apply the procedure stated in b and calculate the displacement at the free end of the truss under gravity loads. Make use of the analysis results provided as necessary. CIVE 317 Structural Engineering I Page 5 Figure P4 a {p N 4—5-— l , 11:, [3'5 i - . i _ *_ Ii ‘ 9 5i ' _ N '2! . I 2009;“ {HO/[0“; Frames 6L6 7'5 M CWVQS E _ 60/6 pas/MM‘SWM) (3 bag-Q o T r w - . g , U3 ' ee 01/01/3661! data/«(I “ E% of (cuter beam 1 9% I‘; A I L_ J_ . L __é;ga.._gw._Z-_5m__ 3.0% T T “i T TYPICAL SECTION Showim STEEL FRAME Oil/E 3/7 Payé "X Element labels: . 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L ®NA® meANnomwwm meANwaw© L NmNONCNNN L waowbwwm -wNNL meL mm -wNNL N.me mm PmmmL o BrammL o -©.wL mL 0 -mbL mL 0 00000000 LwL mombwww -AwmemNowV mmeL L .mL m mmeL L .3 m wommmL LAN oommm L .534 5 OOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOO_ S OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO_ , 2-3 OOOOO-OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO' OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO‘ OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO' CIVE 317 Structural Engineering I Page 12 Part5 (15 marks) Evaluate the stiffiiess coefficients that enter the global stiffiiess matrix of the plane truss structure of Part 4 for the two translational degrees of freedom at Joint 7, u7 and v7 in directions X and Y, respectively. Clearly indicate the units. Part 6_ (5 marks) _ List five design criteria for your Atwater Market Canopy project and indicate whether they are “structural” or “non structural”. Give only a brief description in point form. 12 ...
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This note was uploaded on 12/01/2009 for the course CIVE 317 taught by Professor Mcclure during the Fall '08 term at McGill.

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Final 07 - CIVE 317 Structural Engineering I Page 1 McGILL...

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