Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Advanced Theory of Structures Exam - Bachelor of Engineering in Structural Engineering, Exams of Data Structures and Algorithms

Punjab Engineering CollegeData Structures and Algorithms

A set of questions from an exam for the advanced theory of structures course, part of the bachelor of engineering (honours) in structural engineering program at the cork institute of technology. The exam covers various topics such as stiffness matrix method, stress analysis, cantilever beams, uniform frames, and concrete shell roofs.

Typology: Exams

2012/2013

Uploaded on 04/01/2013

asin
asin 🇮🇳

4.5

(4)

44 documents

1 / 8

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Cork Institute of Technology
Bachelor of Engineering (Honours) in Structural Engineering- Award
(NFQ Level 8)
Summer 2006
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 E and F. It is fixed to supports at
A, B and D and pinned to the support at C.
(a) Use the stiffness matrix method to determine the joint displacements at C, E and F.
(b) Determine the bending moments at A, B, D, E and F and hence draw the bending moment
diagram for the frame, noting all significant values.
Axial and shear deformations may be neglected.
EI = 1000 kNm2
Q2. The pin-jointed steel framework shown in Fig. Q2 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 750 mm2. Use the stiffness matrix method to determine the vertical
deflections at C and D and the horizontal deflection at C. Hence determine the resulting
forces in each of the members and the horizontal and vertical reactions at A and B.
E = 205 kN/mm2
pf3
pf4
pf5
pf8

Partial preview of the text

Download Advanced Theory of Structures Exam - Bachelor of Engineering in Structural Engineering and more Exams Data Structures and Algorithms in PDF only on Docsity!

Cork Institute of Technology

Bachelor of Engineering (Honours) in Structural Engineering- Award

(NFQ Level 8)

Summer 2006

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 E and F. It is fixed to supports at A, B and D and pinned to the support at C. (a) Use the stiffness matrix method to determine the joint displacements at C, E and F. (b) Determine the bending moments at A, B, D, E and F and hence draw the bending moment diagram for the frame, noting all significant values. Axial and shear deformations may be neglected. EI = 1000 kNm^2

Q2. The pin-jointed steel framework shown in Fig. Q2 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 750 mm^2. Use the stiffness matrix method to determine the vertical deflections at C and D and the horizontal deflection at C. Hence determine the resulting forces in each of the members and the horizontal and vertical reactions at A and B. E = 205 kN/mm^2

Q3. A cantilever beam of unit thickness carries a uniform load as shown in Fig. Q3. The Airy stress function:

2 2 32 3 3 2 3 3 5 23 3 2

4 d xy wlxy wl d y d x y w d y w d

w d x y wl d

w (^) x w + − + − 

φ=− − +^ +

is proposed as a solution to the stress analysis problem. Show that φ satisfies the internal compatibility conditions and obtain the distribution of stresses within the beam. Determine also the extent to which the static boundary conditions are satisfied. If d = 0.8 m, l = 0.6 m and w = 120 kN/m, determine the maximum value of σx in the beam and compare this with the value obtained from simple bending theory.

Q4. (a) A uniform cantilever of length 2.5 m supports a mass M = 2500 kg at its free end and is also subjected to a sinusoidally varying load of magnitude F = 8 kN and frequency 40 radians per second as shown in Fig. Q4(a). Determine the maximum upward and downward displacements of the free end of the cantilever, if EI = 30 MNm^2 and the value of the damping coefficient ξ = 0.06. (10 marks) (b) Fig. Q4(b) shows a three-storey portal frame fixed to supports at A and B. The beams may be assumed to be infinitely stiff and to have masses as shown. The columns are of uniform stiffness with EI = 20000 kNm^2. The mass of the columns may be neglected. Formulate the stiffness matrix for the frame and calculate the value of one of the natural frequencies of the frame if it is known that it lies between 25 rads/ sec. and 25.5 rads/sec. (10 marks)

Q5. (a) A load of P = 400 kN is supported at the end of a structure comprising two 457 mm deep steel beams spanning longitudinally across the centre of 457 mm transverse deep steel beams, which are located at intervals of 0.8 m and span 4.0 m, as shown in Fig. Q5(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. (10 marks) E = 205 kN/mm^2 I = 40000 cm^4 (for single beam) (b) Use qualitative analysis to sketch the bending moment diagrams and the deflected shapes for the beams/ frames shown in Fig. Q5(b). (10 marks) Use Answer sheet provided. Draw the bending moment diagrams on the tension face.