# Question 2

Urban and Civil

Nov 15, 2013 (4 years and 7 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

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