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UNIVERSITY OF SOUTHAMPTON CENV2031W1
SEMESTER 1 FINAL ASSESSMENTS 2021/22
STRUCTURAL ANALYSIS
DURATION: 2 Hours
______________________________________________________
This paper contains 4 questions
Answer ALL questions.
Each question carries 25 marks out of a total of 100 marks for the exam paper.
Note that marks will only be awarded when appropriate working is given.
An outline marking scheme is shown in brackets to the right of each question.
Some useful equations and the Structures Data Sheet are provided at the end
of this paper.
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Q1. The steel cross
= 500 kN applied at A
-section in
and a shear force load
Figure Q1 is subjected to a
=
tensile
27 kN. The
force
yield stress is 235 MPa.
i. Determine the second moment of area of the cross-section
about the z axis.
[6 marks]
ii. Calculate the shear stress xy at B.
[10 marks]
iii. Calculate the longitudinal stress σx at B due to combined
bending and axial load.
[5 marks]
iv. Find the safety factor at B using the Von Mises criterion.
[4 marks]
[Total 25 marks]
Figure Q1. Steel cross-section.
G
A
[Point of action
of tensile force P]
B
25 mm
175 mm
15 mm
250 mm
12.5 mm
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Q2. Consider the truss shown in Figure Q2.
i. Examine whether the truss is statically determinate or
indeterminate. If the latter condition applies, determine the
degree of indeterminacy.
[5 marks]
ii. Set up the equilibrium equations at joint D. Note that there is
a roller support at D.
[4 marks]
iii. Set up the compatibility equations at joint D.
[6 marks]
iv. Determine the axial force in each truss member and the
reaction force at D.
[10 marks]
[Total 25 marks]
Figure Q2. Truss.
TURN OVER
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Q3. Use the flexibility method to analyse the frame shown in Figure Q3.
i. Choose the releases.
[6 marks]
ii. Calculate the release displacements due to the external
load.
[2 marks]
iii. Calculate the flexibility coefficients.
[7 marks]
iv. Solve the flexibility equation.
[10 marks]
[Total 25 marks]
Figure Q3. Frame structure.
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Q4. The rectangular portal frame in Figure Q4 is loaded by a 100 kN
horizontal force. Axial rigidity may be assumed. The second
moment of area is 30×104 cm4 and the Young’s modulus is 200
kN/mm2
. Use the direct stiffness method to analyse the structure.
i. Identify the freedoms.
[5 marks]
ii. Determine the stiffness coefficients by releasing each of the
freedoms in turn.
[15 marks]
iii. Set up the structure stiffness equation.
[5 marks]
[Total 25 marks]
Note. When a unit displacement/rotation is imposed in the
direction of one freedom, the remaining freedoms are fixed.
Figure Q4. Rectangular portal frame
TURN OVER
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Useful equations
Second moment of area about the z and y axes:
= ∑[ , +
( G i
)
2
]
= ∑[ , +
( G zi
)
2
]
Shear stress :
=

′

The equivalent stress (Von Mises criterion):
= √
2 + 3
2
Truss member elongation:
=

Degree of indeterminacy (only for beams and frames):
= 3 + 3
Flexibility equation:
=
Stiffness equation:
=
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Structures Data Sheet
Flexibility coefficients due to a unit moment
1,1 =
3

2,1 =
6

Rotations due to external loads
1= 2=
16

2
1= 2=
24

2
Stiffness coefficients due to unit displacements and rotations
1,1 =
3

1,1 = 2,1 =
3

2
1,1 =
4

2,1 =
2

1,1 = 2,1 =
6

2
1,1 = 2,1 =
6

2
1,1 = 2,1 =
12

3
1,1 =
3

2
1,1 = 2,1 =
3

3
Volume integrals

2
( + )
2

2

3
(2 + )
6

2

6
( + 2 )
6
( + )
2
(2 + )
6
(
6
2 + )
+
(
6
+ 2 )
( +4 + )
6
( + 2 )
6
(
6
+ 2 )
+
(
6
2 + )
END OF PAPER
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