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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2011/
Module Title: Solid Mechanics & Structures 1
Module Code: CIVL
School: Building and Civil Engineering
Programme Title: BEng (Hons) in Structural Engineering
Programme Code: CSTRU_8_Y
External Examiner(s): Dr M. Richardson, Mr J. O’Mahony Internal Examiner(s): Mr J.J. Murphy
Instructions: Answer all four questions
Duration: 2 hours
Sitting: Winter 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.
Q1. A uniform beam is loaded and supported as shown in Fig. Q1. (a) Write the equation for the bending moment using Macaulay’s notation and hence determine the vertical deflection at C. (16 marks) (b) Draw the shear force and bending moment diagrams for the beam, noting the principal values (including all local maximum and minimum values). (9 marks) E = 210 kN/mm^2 I = 1800 cm^4
Q2. A frame, which is attached to pinned supports at A and B, incorporates a hinge at C and is loaded as shown in Fig. Q2. Determine the reactions at A and B and hence draw the axial force, shear force and bending moment diagrams for the frame, noting all significant values. (25 marks)
Q3. (a) A compound shaft comprises a solid bronze section of diameter 120 mm securely connected to a hollow steel tube of external diameter 100 mm and internal diameter 50 mm as shown in Fig. Q3(a). A torque of 20 kNm is applied at B. (i) Determine the rotation at B. (ii) Determine the maximum shear stresses in the steel and bronze. (iii) Determine the maximum torque that can be applied at B if the maximum permissible shear stresses in the steel and bronze are 80 N/mm^2 and 30 N/mm^2 respectively. (17 marks) GSteel = 80 kN/mm^2 GBronze = 35 kN/mm^2 (b) A solid steel shaft of diameter 200 mm is subjected to a torque, T, so that yielding occurs to a depth of 40 mm. Determine the magnitude of T. If the shaft is subsequently unloaded, sketch the residual stress distribution along a radius of the shaft. (8 marks) Shear stress at yield = 165 N/mm^2
