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Copyright 2019 University of Southampton Page 1 of 13
UNIVERSITY OF SOUTHAMPTON CENV2031W1
______________________________________________________
SEMESTER 1 EXAMINATIONS 2018-19
TITLE: Structural Analysis
DURATION: 120 MINS
______________________________________________________
This paper contains Four Questions
Please use separate answer books for Sections A, B and C.
Answer ALL questions on this paper.
Section A carries 25% of the total marks for the exam paper and you
should aim to spend about 30 minutes on it.
Section B carries 25% of the total marks for the exam paper and you
should aim to spend about 30 minutes on it.
Section C carries 50% of the total marks for the exam paper and you
should aim to spend about 60 minutes on it.
An outline marking scheme is shown in brackets to the right of each
question.
An Engineering Data Book by Calvert and Farrar is provided
Note that a formula sheet is provided at the end of this paper
Only University approved calculators may be used.
A foreign language direct ‘Word to Word’ translation dictionary (paper
version ONLY) is permitted, provided it contains no notes, additions
or annotations.
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SECTION A (Answer ALL Questions)
A.1
(i) The statically indeterminate truss of Figure A.1.1 is loaded by
a single horizontal force as shown. Write an expression of
deformation compatibility linking the extension or compression of
members AD, BD and AC.
Notes: All members are made of the same material and have the
same cross sectional area.
Joints B and D will displace in both directions.
Due to the symmetries present, the displacements of joints B and
D are linked: it is useful to determine how.
Joint C will displace horizontally twice as much as joints B and D.
[10 marks]
(ii) For the three-pin arch shown in Figure A.1.2, calculate the
reaction forces at the supports A and E.
[15 marks]
[Total 25 marks]
Figure A.1.1: A statically indeterminate truss.
A
B
C
D
L
L
F
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Figure A.1.2: A three-pin arch.
A
B
C
D
E
10kN
5kN/m
10m 10m
10m 10m
15m
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SECTION B (Answer ALL Questions)
(i) The I-beam with the cross-section shown in Figure B.1 is
subjected to a vertical shear force equal to 600 kN.
(a) Calculate the shear stress at Section B-B in the web where
the web meets the flange.
[5 marks]
(b) Calculate the shear stress at the neutral axis of the
section.
[5 marks]
(c) Sketch the variation of shear stress along the depth of the
web.
[2 marks]
(ii) Figure B.2 shows a hollow brick chimney with height equal to 20
m. The cross-section of the chimney is shown in Figure B.2.
The chimney is subjected to a horizontal uniform wind load
equal to 4 kN/m as shown in Fig. B.2. The self-weight of the
brickwork is assumed equal to 20 kN/m3
.
(a) Calculate the area of the cross-section and the second
moment of area of the cross-section with respect to axis z z.
[2 marks]
(b) Calculate the maximum compressive stress in the
brickwork.

[5 marks]
(c) What is the maximum height to which the chimney may be
extended, with the same cross-section, without tensile
stress occurring in the brickwork
[6 marks]
[Total 25 marks]
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Figure B.1: Cross-section of I-beam
Figure B.2: Hollow brick chimney
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SECTION C (Answer ALL Questions)
C.1
(i) Without performing a detailed structural analysis, sketch the
expected deflection profile of the beam shown in Figure C.1.1.
[2 marks]
(ii) Consider the “Cantilever “T” structure” shown in Figure C.1.2.
Using first principles (i.e. using Free-Body Diagrams) draw the
influence lines for:
(a) vertical reaction at support A [3 marks]
(b) moment at support A [4 marks]
(Hint: the unit load moves from B to C)
(iii) The plastic moment capacity of the span BC of the beam
shown in Figure C.1.3 is kMp (k is a scalar and k>1). The
plastic moment capacity of all other beam spans is Mp.
(a) By considering upper bound plastic analysis involving the
collapse of span AB, determine the collapse load.
[3 marks]
(b) By considering upper bound plastic analysis involving the
collapse of span BC, determine the collapse load.
[2 marks]
(c) Calculate the value of k that will ensure spans AB and
BC fail simultaneously. [1 mark]
(iv) Using slope-deflection method of structural analysis
determine the beam end rotations of the continuous beam
shown in Figure C.1.4. [10 marks]
[Total 25 marks]
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Figure C.1.1: Two-span beam
Figure C.1.2: Cantilever “T” structure
Figure C.1.3: Three-span continuous beam
Figure C.1.4: Two-span continuous beam
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C.2
(i) Consider structural analysis of a three-span continuous beam.
(a) state two advantages of the use of moment distribution
method compared to use of the slope-deflection method.
[2 marks]
(b) state one advantage of the use of slope-deflection
method compared to the use of moment distribution
method. [1 mark]
(ii) Figure C.2.2 shows a loaded two-span continuous beam
where span AC is thicker than span CE (note: both spans are
made from the same material). Using the lower bound theory
of plastic analysis determine the safe design plastic moment
capacities for the two beam spans. [8 marks]
(iii) Using moment-distribution method of structural analysis
determine the beam end moments of the three-span
continuous beam shown in Figure C.2.3. [8 marks]

(iv) A tubular column has an effective length of 2.5 m. This
column should be designed to carry a safe axial compressive
load of 300 kN. Assuming that the ratio of the external
diameter to the thickness of the column is 16, using Rankine
formula write down an equation that can be used to determine
a practical diameter and thickness for the tubular column ( s=
330 N/mm2
; and k = 1/7500). Use a design safety factor of 3.
(Hint 1: It is not required to solve your equation and determine
the thickness and the diameter of the tubular column. Hint 2:
For a circle of radius r, the cross section area, =
2
, and
second moment of area, I =

4

4
)
[6 marks]

[Total 25 marks]
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Figure C.2.2: Two-span continuous beam
Figure C.2.3: Three-span continuous beam
END OF PAPER (Formula sheet overleaf)
Copyright 2019 University of Southampton Page 10 of 13
Useful Formulae
Section B
Quadratic formula: =
±√
2 4
2
Simple bending (Engineers’ bending theory):

=

=

= ( )
=

Second moment of area:
Rectangle : =

3
12
Circle : =

4
64

′ = + 2
Torsion of a circular section:
T
J
=
t
r
=
Gq
L
2
2
dx
d v
M EI
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Shear
z
b I
SA y
0
‘

Copyright 2019 University of Southampton Page 12 of 13
12.8 Asymmetric bending (cont.)
Angle of inclination of neutral axis is given by:

y z zy y
z y zy z
I M I M
M I M I

tan
Iyz=IYZ +abA
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Section C
Member stiffness matrix of a pin-jointed truss member inclined by
an angle (anti- clockwise) to the horizontal is given by:

where c = cos and s = sin and A and L are the cross sectional
area and the length of the member and E is the Young’s modulus.
Slope-deflections equations (with standard notations)
A B
AB
F
AB M
L
E M 2 3
2 I

B A
BA
F
BA M
L
E M 2 3
2 I
Von-Mises yield criterion

1/ 2 2 2 2
2
1
I III III II II I y
Rankine Buckling formula

2
1

r
k
L
A
P
e
s
E
k
s
2

Where P is the failure load and other terms have the respective
usual meanings.
Southwell equation

1
( )
( )
0
P
P
x
x
cr

2 2
2 2
2 2
2 2
s sc sc s
cs c cs c
s sc s cs
cs cs c c
L
K
AE
END OF FORMULA SHEET