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Structural Engineering Exam Questions - Autumn 2005, Exams of Data Structures and Algorithms

Punjab Engineering CollegeData Structures and Algorithms

Five structural engineering exam questions from the autumn 2005 semester at cork institute of technology. The questions cover topics such as determining joint displacements, bending moments, deflections, and natural mode frequencies using methods like the stiffness matrix method and simple beam theory. The questions also involve calculating maximum deflections and bending stresses, and sketching bending moment diagrams and deflected shapes.

Typology: Exams

2012/2013

Uploaded on 04/01/2013

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Cork Institute of Technology
Bachelor of Engineering (Honours) in Structural Engineering - Award
(Bachelor of Engineering in Structural Engineering – Award)
(NFQ – Level 8)
Autumn 2005
Advanced Theory of Structures
(Time: 3 Hours)
Instructions
Answer any FIVE questions.
All questions carry equal marks.
Examiners: Mr. J. J. Murphy
Mr. T. Corcoran
Prof. P. O’Donoghue
Q1. The uniform frame shown in Fig Q1 has rigid joints at B and C and fixed foundation
connections at A and D.
(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 = 10000 kNm2
Q2. The pin-jointed steel framework shown in Fig. Q2 is pinned to supports at B, C, D and E.
The cross-sectional area of each member is 800 mm2. A vertical force of 60 kN is applied
at A.
(a) Use the stiffness matrix method to determine the horizontal and vertical deflections at A.
(b) Determine the resulting forces in each of the members.
(c) Determine the horizontal and vertical reactions at B, C, D and E.
E = 205 kN/mm2
pf3
pf4
pf5
pf8

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Cork Institute of Technology

Bachelor of Engineering (Honours) in Structural Engineering - Award

(Bachelor of Engineering in Structural Engineering – Award)

(NFQ – Level 8)

Autumn 2005

Advanced Theory of Structures

(Time: 3 Hours)

Instructions Answer any FIVE questions. All questions carry equal marks.

Examiners: Mr. J. J. Murphy Mr. T. Corcoran Prof. P. O’Donoghue

Q1. The uniform frame shown in Fig Q1 has rigid joints at B and C and fixed foundation connections at A and D. (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 = 10000 kNm^2

Q2. The pin-jointed steel framework shown in Fig. Q2 is pinned to supports at B, C, D and E. The cross-sectional area of each member is 800 mm^2. A vertical force of 60 kN is applied at A. (a) Use the stiffness matrix method to determine the horizontal and vertical deflections at A. (b) Determine the resulting forces in each of the members. (c) Determine the horizontal and vertical reactions at B, C, D and E. E = 205 kN/mm^2

Q3. A cantilever beam of rectangular cross-section has a length l , thickness t and depth d and carries a vertical downward load P at its free end as shown in Fig. Q3. Show that the stress function, as calculated by simple beam theory, can be represented by the stress function: Ø = Axy + Bxy^3 +Cy 3 and determine the coefficients A, B and C.

Q4. (a) A load of P = 800 kN is supported on a structure comprising two 533 mm deep steel beams spanning longitudinally across the centre of 533 mm deep steel beams, which are located at intervals of 1.2 m and span 5.0m, as shown in Fig. Q4(a). Assuming that the structure can be analysed as an infinite beam on an elastic foundation, determine the maximum deflections and bending stresses in both the longitudinal and cross beams. E = 205 kN/mm^2 I = 55000 cm^4 (for single beam) (Note: P is applied midway between adjacent cross beams as shown.) (13 marks) (b) Use qualitative analysis to sketch the bending moment diagrams and the deflected shapes for the structures shown in Fig. Q4(b). Indicate also the direction in which the reactions act. Use Answer sheet provided (7 marks)

Q5. Fig. Q5 shows a two storey portal frame fixed to supports at A, B, C and D and pinned to supports at E and F. The beams GH and IJ may be assumed to be infinitely stiff and to have masses 10000 kg and 15000 kg respectively. The columns are of uniform stiffness with E = 205 kN/mm^2 and I = 4000 cm^4. The mass of the columns may be neglected. Calculate the natural mode frequencies of the frame and sketch the corresponding mode shapes.