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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2009/
Module Title: Advanced 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 JJ Murphy
Instructions: Answer all four questions All questions carry equal marks
Duration: 2 hours
Sitting: Autumn 2010
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. The pin-jointed steel framework shown in Fig. Q1 is attached to pinned supports at A and B and a roller support at D. The framework is loaded as shown. The cross-sectional area of each member is 600 mm^2. Use the stiffness matrix method to determine the horizontal and vertical deflections at C and the horizontal deflection at D. Hence determine the resulting forces in each of the members, the horizontal and vertical reactions at A and B and the vertical reaction at D. (25 marks) E = 205 kN/mm^2
Q2. (a) Fig. Q2(a) shows a frame, which is fixed to a support at A and pinned to a support at B. The beam CD has a mass of 12000 kg and may be assumed to be infinitely stiff. The flexural rigidity of each column is the same at 8 MNm^2 and the mass of the columns may be neglected. Calculate the fundamental natural mode frequency of the frame and hence determine the maximum horizontal deflection of point C when the beam CD is subjected to a sinusoidally varying horizontal load of frequency 2 hz and amplitude 12 kN, if the damping coefficient = 0.06. (13 marks)
(D.L.F. = ((1-^2 )^2 + (2)^2 )-0.5^ = l / = kM )
(b) Use qualitative analysis to sketch the bending moment diagrams and deflected shapes for the frames shown in Fig Q2(b). Indicate also the direction in which the reactions are acting. (12 marks) Use Answer Sheet provided. Draw the bending moment diagrams on the tension faces of the members.
Q4. A thin elastic rectangular plate of length 2 l and width l and uniform flexural rigidity D is simply supported along its edges. It is subjected to a load p = - p o Cos(x/2 l ) Cos(y/ l ), where x and y are rectangular coordinates measured from the origin at the centre of the plate as shown in Fig. Q4. Derive an expression for the deflection of the plate and hence determine: (i) the maximum value of the bending moment Mx in the plate, (ii) the maximum value of the bending moment My in the plate, (iii) the maximum value of the twisting moment Mxy in the plate, (iv) the concentrated vertical reactions at the corner of the plate, (v) the maximum value of the shear force Qy along the edge y = l /2. = 0. (25 marks) (^442 24244) 4
x x y y
^4 w = q/D
Mx = D
2
2 2
2 y
w x
w^ My = D
2
2 2
2 dx
w y
w^ Mxy = D(1-)
x y
(^2) w
Qx = D
2
3 3
3 x y
w x w Qy = D
x y
w y
w 2
3 3
3
Vy = Qy + M x^ xy Vx = Qx + M y^ xy
