Question,

Calculate the thermal stress σ acting on the manifold in the following example of settings.
However, your calculations should be based on the assumptions given below.

Overall length of the manifold L = 150 mm
Room temperature of a molding factory in Japan in December = 18°C
Plastic used = ABS plastic
Manifold steel material = S55C

Sample Answer

Firstly, we obtain the change in the dimensions Δl due to temperature rise as follows.

Where,
α (alpha): Linear thermal expansion coefficient of the manifold steel material (mm/°C)
In the case of S55C, we assume that α is equal to 12×10-6 (mm/°C)).
Δt: Temperature change from room temperature up to the set temperature of the manifold (°C)

Therefore, the thermal stress σ is given by:

Where,
ε (epsilon): strain (%), and
E: Young's modulus of the manifold steel material (MPa or kgf/mm2).
In the case of S55C, E = 21,000 kgf/mm2.
Δl (delta) = Amount of thermal expansion of length (mm)
L: Overall length of the manifold (mm)