University of Southern Denmark
The engineering programmes in Sønderborg
ME-MOM1 Mechanics of Materials 1
MID-TERM EXAMINATION
Wednesday 26 March 2025
Problem 1 starts on the next page
Page 1 of 4
ME-MOM1
Mid-term Examination – March 2024
Problem 1 (10 Points)
Consider the problem sketched in Figure 1. The figure depicts a spider camera system, where
the camera setup is connected to four wires. By changing the length of the wires using four
winches, the position of the camera can be adjusted. For simplicity we look at a symmetric situation where all wires are equal length. In the figure we can only see two wires as the other two are
perpendicular to the paper.
Let the wires be made of steel with E=180GPa and have a circular cross section with diameter
10mm. The wires and the camera setup are connected in such a way that no torsion or other moment transmission can take place. We also consider the wires to be massless, for simplicity.
A) In the sketched situation, determine the reaction forces on each of the four supports holding the wires. The supports are indicated by circles, representing winches.
B) Determine the maximum tensile stress in each of the steel wires
C) Determine the elongation of each of the four wires due to the tensile loading
D) Assuming an allowable tensile stress of 50MPa, determine the minimum distance h of the
camera system to the plane of the winches, assuming the symmetry is kept.
Figure 1: Simplified spider camera setup
Page 2 of 4
ME-MOM1
Mid-term Examination – March 2024
Problem 2 (10 Points)
Consider the simplified transmission system shown in Figure 2. The system consists of two shafts
made of steel with G = 80GPa. One shaft is the output shaft of a motor delivering 10kW mechanical power at a rotational speed of 1000rpm at its output shaft – the one connected to the 15 teeth
gear in Figure 2. This is connected through a gear to another shaft that is connected to two
wheels (for example of a car). The gear ratio of the motor shaft to wheel shaft is 1:4 – see Figure
2. The car is going a constant speed, so the torque from the wheels balances out the torque from
the motor. The motor output shaft is a solid shaft with diameter 30mm while the wheel shaft is a
hollow shaft with an outer diameter of 20mm and a thickness of 4mm.
A) Determine the torque that the motor is delivering to the system
B) Determine the maximum torsional stress in both shafts. If you did not solve part A you can
use an input torque of 100Nm for question 3B and 3C.
C) You are asked to replace the wheel shaft to be a hollow shaft with an outer diameter of
20mm – determine the thickness of the hollow shaft if the allowable shear stress is
30MPa. Give the result in full mm.
Figure 2: Sketch of the motor and gear system covered in Problem 2. The sketch is not to scale
and the gears mesh perfectly, even though the sketch indicates a gap.
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ME-MOM1
Mid-term Examination – March 2024
Problem 3 (10 Points)
Consider the setup shown in Figure 3. The setup shows a steel post reinforced with a brass core,
i.e. the inside material is brass while the outer is steel. Let 𝐸𝐸𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 180GPa and 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 =
105GPa.. AlphaBrass = 12e-6 per K and alphaSteel = 18e-6 per K.
A) Sketch the free body diagram and give the compatibility condition
B) Determine the average normal stress in the brass and steel portions of the post, respectively
C) Determine the average compressive stress in the brass and steel portions, respectively if
the post is stress free at T=20∘ C and is heated up to T=80∘ C. Use the thermal expansion
coefficients 𝛼𝛼𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 12 ⋅ 10−6 /K and 𝛼𝛼𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 18 ⋅ 10−6 /K. For this part of Problem 3
please neglect the 100kN external load.
Figure 3: Compressive load on reinforced post. The inner radius is 25mm while the outer is
50mm
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