# Question 2

Urban and Civil

Nov 15, 2013 (4 years and 5 months ago)

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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

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

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

CN223
Mechanics Of Structures

Page
4

of
5

Q
uestion

3

Figure 3 shows a statically indetermina
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

.

(5 marks)

Figure 3

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
q

equal to
3.5 kN/
m

(vertical force per unit member length).
T
he
refore, the

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