The University of Western Ontario
Faculty of Engineering
ES 1021B – Properties of Engineering Materials
Assignment
Due (via OWL): Tuesday March 31, 2026, 11.59 pm
Instructions:

This is the only assignment in the course. Please submit your work on OWL as a single
PDF file.

All solutions must be typed. Handwritten submissions will not be graded by the
TAs.

Any selection charts copied from EduPack must be clear and legible, with text large
enough to read easily.

No extensions will be granted, so please ensure your assignment is submitted by the
deadline.

Submissions will be checked using Turnitin, and any similarities between submissions will
be detected.
Helpful Resources
Demo videos (available on OWL) will be helpful for completing this assignment.
Question 1 – Materials Selection
You have been tasked with choosing a material from which to construct a simply supported beam
of length (L), width (b), and thickness (h) as shown in the figure, below. Your objective is to
minimize the mass of the beam while ensuring that the total deflection remains less than the
maximum allowable deflection, 𝛿𝑚𝑎𝑥 . The width and length of the beam are fixed. You have
control over the final thickness. The deflection of a centrally loaded beam with a rectangular crosssection is given by the formula:
𝐹𝐿3
𝛿=
4Ε𝑏ℎ 3
where F is the load and E is the Young’s modulus of the material.
a) Derive the material index that satisfies the design objective, and express it in a form that
should be maximized.
𝑚

Objective: minimize mass → 𝑚 = 𝜌𝑏ℎ𝐿, so ℎ = 𝜌𝑏𝐿

Constraint: 𝛿 ≤ 𝛿𝑚𝑎𝑥 → solve for h from the deflection formula: ℎ = (4𝐸𝑏𝛿

Substitute h into the mass equation and group material properties:
𝐹𝐿3
1
𝑚 ∝ 𝜌 ⋅ ( )1/3
𝐸

To minimize mass, maximize the index:
1
𝐸3
𝑀= 𝜌
𝑚𝑎𝑧
)1/3
b) Using your derived material index, show the steps required to determine how to construct
the selection chart. Clearly state: what property should be plotted on the y-axis of the
desired bubble chart, what property should be plotted on the x-axis, and the slope of the
selection line.
1
𝐸3

Taking log of 𝜌 = 𝑀 𝑔𝑖𝑣𝑒𝑠 log 𝐸 = 3 log 𝜌 + 3 log 𝑀:

Y-axis: Young's Modulus 𝐸 (Pa)

X-axis: Density 𝜌 (kg/m³)

Slope of selection line: 3
c) Based on your results from part (b), use the Level 1 EduPack database to perform material
selection. Show your chart in your solution and use SI units. Identify approximately five
candidate materials, and rank them according to their performance for this design problem.
1. Rigid Polymer Foam (LD)
2. Rigid Polymer Foam (MD)
3. Wood, typical along grain
4. Bamboo
5. Flexible Polymer Foam (VLD)
d) Suppose an additional constraint is introduced requiring the material to be recyclable. In
that case, what would be the best material choice for this design? Note that your answer
does not have to come from your previously selected top five if those materials are not
recyclable.
When applying the recyclability constraint, the best option that also satisfies the original
criteria is Magnesium Alloys. None of the materials from the previously selected list meet
the recyclability requirement.
Question 2 – Materials Selection
A solid piece of material is to be fixed between two rigid supports in a structure that is exposed to
a fluctuating temperature environment.
The bar must not yield during these temperature
fluctuations. The bar fits perfectly between the rigid supports when installed at an ambient
temperature of 22°C.
a) Develop a material index that could be used to select a material with the largest operating
temperature range. Express it in a form that should be maximized.
𝜎

Constraint (no yielding): 𝐸𝛼𝛥𝑇 ≤ 𝜎𝑦 → 𝛥𝑇 ≤ 𝐸𝛼𝑦

To maximize operating temperature range 𝛥𝑇:
𝑀=
𝜎𝑦
𝐸𝛼
b) Using your derived material index, show the steps required to determine how to construct
the selection chart. Clearly state: what property should be plotted on the y-axis of the
desired bubble chart, what property should be plotted on the x-axis, and the slope of the
selection line.

𝜎
Rearranging 𝐸𝛼𝑦 = 𝑀 𝑔𝑖𝑣𝑒𝑠 log(𝜎𝑦 ) = 1log(𝐸𝛼 ) + log 𝑀:

Y-axis: Yield strength 𝜎𝑦 (Pa)

X-axis: 𝐸 ⋅ 𝛼 or equivalently, plot 𝜎𝑦 𝑣𝑠. 𝐸 on a log-log chart with lines of constant 𝐸𝛼𝑦

Slope of selection line: 1
𝜎
c) Based on your results from part (b), use the Level 1 EduPack database to perform material
selection. Show your chart in your solution and use SI units. Identify which family of
materials outperforms the others.
Elastomers outperform all other material families, as their bubbles sit highest above the
selection line
d) Using your knowledge of the structure and properties of this material class, explain why it
outperforms other classes of materials. Your explanation should be brief (not exceeding 3
lines).
Elastomers have a very low Young's modulus (E), which minimizes thermal stress (σ = EαΔT)
when expansion is constrained by rigid supports. This allows the material to withstand larger
temperature fluctuations before yielding.
Question 3 – Composite Material
An aligned fiber composite is manufactured with 45% carbon fiber (E f=480 GPa, ρf=1850 kg/m3)
in a polyester matrix (Em=2.4 GPa, ρm=1200 kg/m3).
a) Estimate the density of the composite material.
𝜌𝑐 = 𝑉𝑓 𝜌𝑓 + 𝑉𝑚 𝜌𝑚 = (0.45)(1850) + (0.55)(1200) = 832.5 + 66 = 𝟏𝟒𝟗𝟐. 𝟓
𝒌𝒈
𝒎𝟑
b) Estimate the Young’s modulus of the composite material when measured:
i.
Parallel to the fiber direction
𝐸|| = 𝑉𝑓 𝐸𝑓 + 𝑉𝑚 𝐸𝑚 = (0.45)(480) + (0.55)(2.4) = 216 + 1.32 = 𝟐𝟏𝟕. 𝟑 𝑮𝑷𝒂
ii.
Perpendicular to the fiber direction
𝐸⊥ =
𝐸𝑓 𝐸𝑚
(480)(2.4)
1152
=
=
= 𝟒. 𝟑𝟑𝑮𝑷𝒂
𝑉𝑓 𝐸𝑚 + 𝑉𝑚 𝐸𝑓 (0.45)(2.4) + (0.55)(480) 1.08 + 264
c) Assuming that the composite material behaves perfectly elastically up to the point of
fracture, and knowing that the fibers will fracture at a strain of 2.1%,
i.
Estimate the fracture strength of the composite.
𝜎 ∗𝑐 = 𝐸|| ⋅ 𝜀 ∗ = 217.3 × 109 × 0.021 ≈ 𝟒. 𝟓𝟔 𝑮𝑷𝒂
ii.
Estimate the elastic energy stored in the composite at the point of fracture.
1
1
𝑴𝑱
𝑈 = 𝜎𝜀 = (4.56 × 109 )(0.021) ≈ 𝟒𝟕. 𝟗 𝟑
2
2
𝒎