联系我们： 手动添加方式: 微信>添加朋友>企业微信联系人>13262280223 或者 QQ: 1483266981

Copyright 2021 v01 University of Southampton Page 1 of 9
UNIVERSITY OF SOUTHAMPTON CENV2031W1
SEMESTER 1 ASSESSMENT PAPER 2020/21
TITLE Structural Analysis
DURATION – 24 hours
______________________________________________________
This paper contains Three questions
Answer ALL questions.
Each Question carries 1/3 of the total marks for the exam paper
An outline marking scheme is shown in brackets to the right
of each question.
A Sheet of some useful formulae is provided with this examination paper.
You may also use any formulae used in the course materials of module CENV2031
Only University approved calculators may be used.
Copyright 2021 v01 University of Southampton Page 2 of 9
Answer ALL Questions
Q.1
(i) The I-beam with the cross-section shown in Figure Q.1 is
subjected to a vertical shear force of 800 kN.
(a) Calculate the shear stress at Section B-B in the web where
the web meets the flange.
[9 marks]
(b) Calculate the shear stress at the neutral axis of the
section. [9 marks]

(c) The maximum allowable direct tensile stress (i.e. due to
bending) of this beam section is 150 N/mm2
. Determine
the maximum permissible bending moment for this I-beam
section. [5 marks]
(ii) A concrete column with a square cross section of 200 mm x
200 mm subjects to a constant axial force of 1200 kN. What is
the maximum bending moment M that the column can take
without developing tensile stresses anywhere in the column
cross section. [10 marks]
[Total 33 marks]
Figure Q.1: Cross-section of I-beam
CENV2031
TURN OVER
Copyright 2021 v01 University of Southampton Page 3 of 9
Q.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.
[4 marks]
(b) state one advantage of the use of slope-deflection
method compared to the use of moment distribution
method. [2 mark]
(ii) The plastic moment capacity of the span BC of the beam
shown in Figure Q.2.2 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.
[5 marks]
(b) By considering upper bound plastic analysis involving the
collapse of span BC, determine the collapse load.
[4 marks]
(c) Calculate the value of k that will ensure spans AB and
BC fail simultaneously. [3 marks]
(iii) Using slope-deflection method of structural analysis
determine the beam end rotations of the continuous beam
shown in Figure Q.2.3. [15 marks]
[Total 33 marks]
Copyright 2021 v01 University of Southampton Page 4 of 9
Figure Q.2.2: Three-span continuous beam
Figure Q.2.3: Two-span continuous beam
CENV2031
TURN OVER
Copyright 2021 v01 University of Southampton Page 5 of 9
Q.3
(i) State the lower bound theory of plasticity. [5 marks]
(ii) Discuss the main differences between the concept of lower
bound theory of plasticity and upper bound theory of plastic
analysis. [5 marks]
(iii) Figure Q.2.3 shows a simple model of a uniform beam.
Determine and show the influence lines, indicating salient
values, for:
(a) Support reaction at D [5 marks]
(b) Bending moment at C [5 marks]
(iv) (a) To apply the moment distribution method to solve the
moments at Joints A, B, C and D of the frame shown in
Figure C.2.4, determine the fixed-end moments at each
joint. [4 marks]
(b) Determine the moment distribution factors at joints B and
C. [2 marks]
(c) Determine the moments at A, B, C and D after balancing
the initial out-of-balance fixed end moments. [7 marks]

[Total 33 marks]
Copyright 2021 v01 University of Southampton Page 6 of 9
Figure Q.2.3: Simple model of a horizontal beam
Figure Q.2.4: A symmetrical frame loaded by a vertical load
CENV2031
TURN OVER
Copyright 2021 v01 University of Southampton Page 7 of 9
END OF PAPER (Formula sheet overleaf)
Useful Formulae
Second moment of area:
Rectangle : =

3
12
Circle : =

4
64

′ = + 2
Torsion of a circular section:
Shear stress
z
b I
SA y
0
‘
=
T
J
=
t
r
=
Gq
L
Copyright 2021 v01 University of Southampton Page 8 of 9
CENV2031
TURN OVER
Copyright 2021 v01 University of Southampton Page 9 of 9
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)

( 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

END OF THE PAPER
( A B
) AB
F
AB M
L
E M + + = 2 3
2 I

=
2 2
2 2
2 2
2 2
sc s sc s
cs c cs c
s sc s cs
cs c cs c
L
K
AE