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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2009
Module Title: Solid Mechanics & Structures 1
Module Code: CIVL
School: Building and Civil Engineering
Programme Title: Bachelor of Engineering (Honours) in Structural Engineering – Stage 2
Programme Code: CSTRU_8_Y
External Examiner(s): Prof. P O’Donoghue, Mr. P. Anthony Internal Examiner(s): Mr JJ. Murphy
Instructions: Answer all four questions
Duration: 2 Hours
Sitting: Autumn 2009
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. (b) Draw the shear force and bending moment diagrams for the beam, noting the principal values (including all local maximum and minimum values). E = 205 kN/mm^2 I = 4000 cm^4
Q2. A frame, which is attached to pinned supports at A and B, incorporates a hinge at D 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. Sketch also the deflected shape of the frame.
Q3. (a) A hollow steel bar of internal diameter 60 mm and external diameter 100 mm is securely connected to a solid bronze bar of diameter 100 mm as shown in Fig. Q3. The composite unit is fixed securely at its ends (A and B) and is subjected to a torque of 14 kNm at C. Determine the maximum stresses in the steel and bronze and the rotation at C. (b) A solid steel shaft of diameter 200 mm is subjected to a torque, T, so that yielding occurs to a depth of 50 mm. Determine the magnitude of T. If the shaft is susequently unloaded, determine the residual stress distribution in the shaft. GSteel = 80 kN/mm^2 GBronze = 45 kN/mm^2 τ = 165 N/mm^2
Q4. Fig. Q4(a) shows a beam consisting of a rectangular aluminium alloy section securely bonded to a steel T section. The composite beam is 1.6 m long, is simply supported at its ends and carries a uniformly dstributed load of 3 kN/m over half its length and 5 kN/m over the remaining half as shown in Fig. Q4(b). (a) Determine the maximum bending stresses in the steel and aluminium. (b) Determine the maximum shear stress in the steel. (c) Determine the maximum shear stress at the interface between the steel and the aluminium. ESt = 205 kN/mm^2 EAlum = 71.75 kN/mm^2
