CN223
Mechanics Of Structures
Page
1
of
5
s
School of the Environment
Semester 1 Examinations 2005

2006
CN223
MECHANICS OF STRUCTURES
Instructions to candidates:
Time allowed:
TWO
hours
Answer only
THREE
questions
Question FOUR is COMPULSORY
Q1 (33marks)
Q2 (33 marks)
Q3 (33 marks)
Q4 (34 marks,
compulsory
)
A formulae catalogue is provided
Wednesday 1 February 2006 9:30
–
11:30 hours
CN223
Mechanics Of Structures
Page
2
of
5
Question
1
Figure 1 shows a beam
with variable loading
as indicated.
(a)
find the reactions of the beam using equilibrium equations
(3 mar
ks)
(b)
write the equations of the bending moment diagram for the regions
m
1
0
x
and
m
4
1
x
(8 marks)
(c)
find the equation
s
of the deflection curve
for the regions
m
1
0
x
and
m
4
1
x
. Assume tha
t
the
cross
section stiffness
as
2
4
10
1
m
kN
x
EI
.
(22 marks)
Figure 1
. Simply supported beam under vertical load
CN223
Mechanics Of Structures
Page
3
of
5
Question
2
The cantilever
beam of Figure 2 has
constant
section stiffness
EI
= 415 kN m
2
and
is subjected t
o a combination of uniformly distributed loads and a point load as
indicated.
(a)
Write the equation of the bending moment diagram for the region
5
.
1
0
x
m
(6 marks)
(b)
Write the equation of the bending moment diagram for the
region
m
3
m
5
.
1
x
(7 marks)
(c)
Apply
Mohr theorems
to find the vertical
deflection at midspan
(
i.e
. at
x
= 1.5 m)
(20 marks)
Figure 2
. Cantilever beam under vertical loading
CN223
Mechanics Of Structures
Page
4
of
5
Q
uestion
3
Figure 3 shows a statically indetermina
te beam loade
d with variable loading
as
indicated. Assume that the section stiffness is constant along the beam
and has a
value
2
m
kN
600
EI
. Note that
support 2 is flexible
as represented by the
spring with stiffness
k
.
(a)
A
pply the flexibility method to find the central support reaction (
i.e
. the
reaction at node 2)
(26
marks)
(b)
Knowing the central reaction, use equilibrium equations to find the support
reactions at nodes 1 and 3.
(2 marks)
(c)
If
suppo
r
t 2 w
ere rigid (such as
support 1); w
ould you expect
a higher or a
lower reaction at
support 2?. Give reasons for your answer
.
(5 marks)
Figure 3
. Statically indeterminate beam under vertical loading
CN223
Mechanics Of Structures
Page
5
of
5
Question
4
(Compulsory)
The frame shown in Figure 4 is par
t of a roof system subjected to uniformly
distributed load
q
equal to
3.5 kN/
m
(vertical force per unit member length).
T
he
refore, the
total vertical load is
kN
85
.
18
1
5
.
2
2
5
.
3
2
2
x
.
The cross section
stiffness
of
both
members
is
2
5
m
kN
10
9
x
EI
.
(a)
Write the slope

deflection equations for the two members accounting for the
boundary conditions.
(8
marks)
(b)
Find the rotation of nodes 1
, 2
and 3
(20 marks)
(c)
Find the end moments o
f member 1
(2
marks)
(d)
Find the support reactions
(4 marks)
Figure 4
. Statically indeterminate framework
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