Download Muller-Breslau Principle - 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: 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. A steel beam BD is attached to a pinned support at B and a roller support at D. It is also supported by a vertical steel tie at C. The tie is attached to a semi-circular steel arch at F. The arch is of 10 m diameter and is pinned to supports at A and E. The beam is subjected to a uniform vertical load of 30 kN/m. Determine the force in the tie and the horizontal reactions at the supports of the arch. Hence determine the vertical reactions at A, B, D and E, the bending moment at F on the arch and the maximum bending moment in the beam BD. Beam, Arch: I = 100 x 10-6^ m^4 Ties: A = 500 x 10 -6^ m^2 E = 205 kN/mm^2 The beam and arch may each be assumed to have infinite axial stiffness while the tie has zero flexural stiffness. (25 Marks)
Q2. (a) Use the Muller-Breslau principle to derive an expression for the influence line for the bending moment at A (the support) in the continuous two-span beam shown in Fig. Q2. (12 Marks)
(b) Hence calculate the maximum bending moment at A due to two point loads of magnitude 40 kN at a spacing of 2 m traversing the beam between A and B. (6 Marks)
(c) Determine the maximum bending moment at A due to a uniformly distributed load of magnitude 20 kN/m and length 4 m traversing the beam between A and B. (7 Marks)
