CVEN2301 Past Final 2015

THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING
SEMESTER 1 2015 EXAMINATIONS

CVEN2301: MECHANICS OF SOLIDS
1. TIME ALLOWED – 3 hours
2. READING TIME – 10 minutes
3. TOTAL NUMBER OF QUESTIONS – 4
4. TOTAL MARKS AVAILABLE – 100
5. MARKS AVAILABLE FOR EACH QUESTION ARE SHOWN IN THE EXAMINATION PAPER
6. ALL ANSWERS MUST BE WRITTEN IN INK
7. THIS PAPER MAY BE RETAINED BY CANDIDATE
8. CANDIDATES MAY BRING ANY AIDS TO THE EXAMINATION INCLUDING ELECTRONIC CALCULATORS AND
HAND-HELD COMPUTERS (CALCULATORS WITH ALPHANUMERIC CAPABILITY). THIS IS AN OPEN BOOK
EXAMINATION.
9. IPADS, LAPTOPS, NOTEBOOKS OR COMPUTERS (EXCEPT CALCULATORS WITH ALPHANUMERIC CAPABILITY)

ARE NOT PERMITTED.
Question 1 (Total 25 Marks)
For the cross-section shown in Figure 1 (all units are mm) determine the following:
• Position of the centroid with respect to the x’ and y’ axes.

• The rotation about the horizontal axis x at the centroid to the principal axes.
• The principal second moments of area I1 and I2 about the centroid C.
• Draw the Mohr’s circle for the second moment of area and indicate I1 and I2, and Ixx and Iyy.
y’ y
20
10 4
100
10 C
x
2 20
10
10 1
O x’
100
Not to Scale
Figure 1
A Super Tee Girder Type T4 made of material A is constructed in a precast yard. The overall depth of
the Super Tee Girder is 1500 mm. The elastic modulus of material A is EA=50000 MPa and the
section properties for the girder on its own are given in Figure 2a). A 200 mm thick by 2000 mm long
concrete road deck is cast onto the top of the girder to produce a composite bridge (see Figure 2b).
The concrete road deck is made of material B with an elastic modulus of EB=25000 MPa. The
constructed composite bridge is 35 m in length, is simply supported and carries a distributed uniform
load of 30 kN/m. Under this load the stresses can be assumed to be elastic.
What is the maximum bending moment in the composite bridge?

What are the maximum tensile and compressive stresses?
Draw the distribution of stress through the depth of the composite section.
Figure 2 a)
Figure 2b)
The two span beam ABCD shown in Fig. 3 has a hinge support at A and roller supports at B and C.
The support at C is settled by ∆ = 0.10 m. The span AC carries a uniformly distributed load of
2
20 kN/m. The flexural rigidity of EI = 20,000 kNm is constant throughout the beam.
(i) What are the boundary conditions?

(ii) Determine the bending moment equation for the beam using step functions in terms of the
reactions at A and B.
(iii) Determine the equation for the deflection of the beam in terms of the reaction at A.
(iv) Find the reactions (unit kN) at A, B and C.
(v) Determine the bending moment (unit kNm) at point D.
20 kN/m
A B D C
∆ = 0.10 m
4m 2m 2m
Figure 3
A composite shaft ABC shown in Fig. 4a is made from a cylindrical hollow aluminium shaft with a
cylindrical solid steel shaft. There is perfect strain compatibility between the two shafts and both are
fixed at end A and free to twist at end C. The aluminium shaft has an outside diameter of 100 mm and
an inside diameter of 70 mm while the solid steel shaft has a diameter of 70 mm. The length AB is
0.40 m, and the length BC is 0.60 m. Torques of 10 kNm and 20 kNm are applied at points B and C,
respectively. A uniform axial compression force of 300 kN is also applied to the shaft at the free end
C, in which the axial strains between the two shafts are compatible.
For the steel shaft, the shear modulus is 80 GPa and the Young’s modulus is 200 GPa. For the
aluminium shaft, the shear modulus is 25 GPa and Young’s modulus is 70 GPa.
(i) Draw the distribution of torque through the shaft from A to C.

(ii) Calculate the maximum shear stress τmax in the shaft.
(iii) At the free end C, calculate the angle of twist ϕ (in degrees).
(iv) Draw the Mohr’s circle for the state of stresses developed at an outer surface of the
aluminium shaft at C (see Fig. 4b). Determine the corresponding principal stresses and the
maximum shear stress.
Steel
B 20 kNm
Aluminium
0.4 m C
10 kNm 30 kN
0.6 m
(a)
σx
τxy
(b)
Figure 4

CVEN2301 Past Final 2015

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THE UNIVERSITY OF NEW SOUTH WALES

SCHOOL OF CIVIL AND ENVIRONMENTAL ENGINEERING

SEMESTER 1 2015 EXAMINATIONS

1. TIME ALLOWED – 3 hours

2. READING TIME – 10 minutes

3. TOTAL NUMBER OF QUESTIONS – 4

4. TOTAL MARKS AVAILABLE – 100

6. ALL ANSWERS MUST BE WRITTEN IN INK

7. THIS PAPER MAY BE RETAINED BY CANDIDATE

9. IPADS, LAPTOPS, NOTEBOOKS OR COMPUTERS (EXCEPT CALCULATORS WITH ALPHANUMERIC CAPABILITY)

• Position of the centroid with respect to the x’ and y’ axes.

What is the maximum bending moment in the composite bridge?

(i) What are the boundary conditions?

(i) Draw the distribution of torque through the shaft from A to C.

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