Analysis of Complex Structures

FIND A SOLUTION AT Academic Writers Bay

1
Seat No
________________________________
Student Name
________________________________
Student ID
________________________________
Signature
________________________________
EXAM COVER SHEET
NOTE: DO NOT REMOVE this exam
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

READ ALSO...   RICHMOND REHABILITATION
Order from Academic Writers Bay
Best Custom Essay Writing Services

QUALITY: 100% ORIGINAL PAPERNO PLAGIARISM – CUSTOM PAPER