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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2010/
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 D Coleman Mr JJ Murphy
Instructions: Answer all four questions Use seperate answer books for each section
Duration: 2 hours
Sitting: Summer 2011
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.
SECTION A
Q1. The frame shown in Fig. Q1 has rigid joints at B, C and D and is attached to a fixed support at A and a roller support at E. The roller support at E is tied to the support at A by means of a tie member AE. Determine the force in the tie and the vertical reaction at E when the frame is loaded as shown. Hence determine the bending moments at A, B, C and D and sketch the bending moment diagram for the frame. Frame ABCDE: EI = 100,000 kNm^2 Tie AE: EA = 50,000 kN The frame may 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 vertical reaction at A in the continuous two-span beam shown in Fig. Q2. (10 marks) (b) Hence calculate the maximum upward reaction at A due to two point loads of magnitude 50 kN at a spacing of 2 m traversing the beam. (4 marks) (c) Determine the maximum downward reaction at A due to a point load of magnitude 60 kN traversing the beam. (5 marks) (d) Determine the vertical reaction at A due to a uniformly distributed load of magnitude 12 kN/m extending over the entire length of the beam. (6 marks)
