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EXAM COVER SHEET

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paper from the exam venue

EXAM DETAILS

2hr 15min

Total number of pages (incl. this cover sheet) 6

ALLOWABLE MATERIALS AND INSTRUCTIONS TO CANDIDATES

1. Write your full name and student number on each exam booklet together with the number of exam books used.

2. Students must not write, mark in any way any exam materials, read any other text other than the exam paper or

do any calculations during reading time.

3. All mobile phones must be switched off and placed under your desk. You are in breach of exam conditions if it is

on your person (i.e. pocket).

4. This is a CLOSED BOOK Exam.

5. Commence each question on a new page. Carry out the instructions on the front cover of the exam script book

and the front of this exam paper.

6. Non text storing calculators are allowed.

7. The examination paper contains 4 questions.

8. Attempt all questions and all parts of the chosen questions.

9. Marks given for each question are shown with the question in brackets.

10. No personal notes or textbooks may be used.

11. Attempt all parts of every question. Partial credit may be awarded for incomplete answers.

12. No marks will be given for any question where there is a fundamental error in your answer.

13. Clearly state the sign convention you are using if it is different from the one used in the lectures.

14. Show all units. Marks will be deducted for not using the valid units, and/or for not showing units at all.

15. Refer to formulae. If any data is missing, it may be assumed, but this should be clearly stated.

Course Code: CIVE1143

Course Description: Analysis of Complex Structures

Date of exam: Start time of exam: 19:00 Duration of exam:

2

DATA SHEET (Select Appropriate Formulas)

Table:

Deflections of Beams

EI

Pl

23

3

δmax =

Slope-Deflection Equations:

( i j ij ) ij F

ij

L

For pin supported end span ( N ij )

N M

EI

M = 3 θ -ψ +

L

ij M

EI

M = 2 2θ + θ – 3ψ + ( j i ij ) F ji

ij

ji M

EI

M = 2 2θ +θ – 3ψ +

NF

ij

L

δmax

3

Fixed-end moments:

The stiffness matrix of a beam element:

–

– – –

– –

=

L L L L

L L L L

L L L L

L L L L

EI

i

6 2 6 4

12 6 12 6

6 4 6 2

12 6 12 6

2 2

3 2 3 2

2 2

3 2 3 2

k

The structure stiffness equation:

F = KD

12

wL2

12

wL2

–

8

PL

8

PL

–

4

Question 1 [20 Marks]

A continuous beam ABC is shown in Figure 1. Support at C is a pin. Supports A and B

are rollers. A downward linear distributed load starting from 10kN/m at B and ending

20kN/m at A. A concentrated moment of 10 kN·m is applied anticlockwise at B as

shown in Figure 1. EI is constant for all spans.

(a) Determine the direction of reaction forces, plot the deflected shape, point out the

tension side and points of contraflexure and draw bending moment diagram

using qualitative analysis [8 marks];

(b) Determine all the reactions at supports by using force method and plot shear

force and bending moment diagrams. [12 marks].

Figure 1

Question 2 [30 Marks]

A continuous beam ABCD shown in Figure 2 is fixed at A. Supports B, C and D are pin

supports. A downward distributed load 20 kN/m is applied on the whole beam. A

100kN force acts downward in span AB as shown in Fig. 2 and there is 15mm

downward settlement at point B C and D. EI is constant for AB and CD, and 2EI is for

BC. Take E = 20 GPa, I = 120×106 mm-4.

(a) Determine the internal moments at A, B and C by using the slope-deflection

method [20 marks].

(b) Determine all the reactions at supports. [5 marks]

(c) Draw the shear force diagram and bending moment diagram and specify the

corresponding values at point A, B and C. [5 marks]

Figure 2

A C

B

20kN/m

10m 10kN·m 10m

10kN/m

20kN/m

EI 2EI EI

5

Question 3 [20 marks]

The symmetry frame ABCDEF is shown in Figure 3. Supports A and D are fixed and

Point B and C are rigid joints (fixed connections). A triangular distributed load acts on

span EBCF as shown in Figure 3. EI is constant for all spans.

(a) Determine the internal moments at each joint of the frame by using the slopedeflection method. [10 marks]

(b) Draw the bending moment diagrams and qualitative deflected curve, point out

the tension side and points of contraflexure if necessary. [10 marks]

Figure 3

Question 4 [30 Marks]

Analyse the beam shown in Figure 4 using the stiffness method. Node ① and④ are

fixed and node ② and ③ are rollers. A uniform distributed load of 2 kN/m is acting on

member 1 . And a load of 10 kN is acting at the middle of member 2 . EI is for

members 1 and 3, 2EI is for member 2.

a) Identify the force vector of the structure; [6 marks]

b) Identify the displacement vector of the structure; [2 marks]

c) Determine the stiffness matrices of the members; [6 marks]

d) Assemble the global stiffness matrix of the structure; [ 4 marks]

e) Establish the force-displacement relationship and calculate the unknown

displacements; [6 marks]

f) Calculate the reaction forces at supports. [ 6 marks]

Figure 4

8m

B C

A

4m

D

10m

48kN/m

E

F

4m

4

3

2kN/m

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