Download Examination Paper: Advanced Theory of Structures (CORK Institute of Technology, 2011) and more Exams Data Structures and Algorithms in PDF only on Docsity! Page 1 of 8 CORK INSTITUTE OF TECHNOLOGY INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ Semester 2 Examinations 2010/11 Module Title: Advanced Theory of Structures Module Code: CIVL8002 School: Building and Civil Engineering Programme Title: B Eng (Hons) in Structural Engineering Programme Code: CSTRU_8_Y4 External Examiner(s): Dr. MG Richardson Mr. J O’Mahony Internal Examiner(s): Mr JJ Murphy Instructions: Answer all four questions 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. Page 2 of 8 Q1. The uniform frame shown in Fig. Q1 has rigid joints at B and C and fixed foundation connections at A and D and is loaded as shown. (a) Use the stiffness matrix method to determine the joint displacements at B and C. (b) Determine the bending moments at A, B, C and D and hence draw the bending moment diagram for the frame, noting all significant values. Axial and shear deformations may be neglected. EI = 10 4 kNm 2 (25 marks) Q2. (a) Fig. Q2(a) shows the buckled shape of a pin-ended strut of constant EI value between supports, which are a distance l apart. The load P is applied through a rigid member of length 0.4l connected to the end of the strut. Show that the critical load may be found from the equation tan(kl) + 2kl/3 = 0, where k 2 = P/EI. (8 marks) (b) The uniform frame shown in Fig. Q2(b) is attached to pinned supports at B and C and roller supports at A and D. It is subjected to equal vertical loads P at E and F as shown. Formulate equations in terms of stability functions, which express the conditions of instability of the frame in its own plane and hence determine the critical value of P. (8 marks) (c) Fig. Q3(c) shows a strut, which is fixed at one end and free at the other end. It is subjected to an axial force P at the free end. The section of the strut between 0 and 0.5l has flexural stiffness 2EI, while the remainder has flexural stiffness EI. If an approximation of the buckled shape of the strut is given by the equation 4 4 2 2 0 6 5 l x l xy y where x is measured from the fixed end and y0 is the deflection at the free end, use the Rayleigh energy method to obtain an upper bound approximation of the critical buckling load. (9 marks) Table of Stability Functions s c sc s(1+c) s(1-c*c) m m1 0.19 0.685 3.744 0.552 2.066 5.810 2.603 1.192 3.577 0.20 0.702 3.730 0.555 2.070 5.800 2.581 1.205 4.253 0.21 0.720 3.716 0.558 2.074 5.790 2.558 1.218 5.266 0.22 0.737 3.702 0.561 2.078 5.779 2.536 1.231 6.956 0.23 0.753 3.688 0.564 2.081 5.769 2.513 1.245 10.334 wm
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