Download Stiffness Matrix Method - Advanced Theory of Structures - Past Exam and more Exams Data Structures and Algorithms in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2009/
Module Title: Advanced Theory of Structures
Module Code: CIVL
School: Building and Civil Engineering
Programme Title: B Eng (Hons) in Structural Engineering
Programme Code: CSTRU_8_Y
External Examiner(s): Dr. MG Richardson Mr. J O’Mahony
Internal Examiner(s): Mr JJ Murphy
Instructions: Answer all four questions. All questions carry equal marks.
Duration: 2 hours
Sitting: Summer 2010
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
Q1. The beams AE, DE, EB and EC shown in Fig. Q1 are rigidly connected at E and the structure, which lies on a horizontal plane, is loaded vertically and rigidly supported at A, B, C and D. (a) Use the stiffness matrix method to determine the joint displacements. (12 Marks) (b) Determine the bending moments at A, B, C, D and E. Hence draw the bending moment diagrams for the beams, noting all significant values. (13 Marks)
EI = 40000 kNm^2 ; GJ = 32000 kNm^2 (= 0.8EI)
Q2. (a) Fig Q2(a) shows a structure housing ore crushing machinery. Each floor has a mass of 10000 kg. The ore crusher is permanently fixed to the lower floor, BE adding its mass of 10000 kg to that floor. The crusher operates at 1.75 hz (11 rads/ sec) but sets up large resonant vibrations in the structure. In an effort to reduce the vibrations, it is proposed to attach a large mass of 10000 kg to the structure. Calculate whether it is better to attach the extra mass to the upper (CD) or lower (BE) floor. The beams may be assumed to be infinitely stiff. For columns AB and EF: EI = 4500 kNm^2 For columns BC and DE: EI = 2250 kNm^2
(D.L.F. = ((1-β^2 ) 2 + (2ξβ) 2 ) -0.5^ β = ω l /ω ω = k^ M )
(13 Marks) (b) Use qualitative analysis to sketch the bending moment diagrams and deflected shapes for the beams and frames shown in Fig Q2(b). Indicate also the direction in which the reactions are acting. Use Answer Sheet provided. Draw the bending moment diagrams on the tension faces of the members. (12 Marks)
