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An examination paper for the structural analysis module of the beng in civil engineering program at the cork institute of technology. The paper includes three questions covering topics such as shear force and bending moment diagrams, stress determination, and deflection calculation for beams and shafts. The document also provides instructions for the examination, including duration and sitting information.
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Semester 1 Examinations 2011/
Module Code: CIVL
School: Building and Civil Engineering
Programme Title: BEng in Civil Engineering
Programme Code: CCIVL_7_Y
External Examiner(s): Ms M Kyne Mr. J Murphy Internal Examiner(s): Mr JJ Murphy Mr A MacIlwraith
Instructions: Answer all three 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) A steel beam is loaded and supported as shown in Fig. Q1(a). The cross-section of the beam is shown in Fig. Q1(b). (i) Draw the shear force and bending moment diagrams for the beam, noting all significant values. (3 marks) (ii) Determine the bending stress at point O on the cross-section (immediately to the right of the support at B). (3 marks) (iii) Determine the flexural shear stress at O. (3 marks) (iv) Determine the principal stresses at O. (3 marks) (v) Determine the maximum shear stress at O. (2 marks) (vi) Determine the normal and shear stresses on plane XX at 40° to the vertical at O as shown in Fig. Q1(c). (3 marks) (vii) Determine the reading on a strain gauge attached to the beam at an angle of 70° to the horizontal at O as shown in Fig. Q1(d). (3 marks) E = 210 kN/mm^2 ν = 0. (b) Fig. Q1(e) shows the stresses acting at a point in a structure. Direct stresses of magnitudes σx = 240 N/mm^2 and σy = - 2 0 N/mm^2 and a shear stress τ are applied. Determine the magnitude of τ required to cause yield at the point if the yield criterion is the maximum shear strain energy and the yield stress in a simple tension test is 275 N/mm^2. (5 marks) Aide memoire: Shear strain energy: (1/12G) x [(σ 1 - σ 2 )^2 + (σ 1 - σ 3 )^2 + (σ 2 - σ 3 )^2 ] x Volume
Q2. A uniform beam is loaded and supported as shown in Fig. Q2. (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 = 1500 cm^4