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CE304 HW#2 F2023

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CE 304
Fall 2023
Homework #2
1. For the metals in Table 3.1, (pg. 85) compute strength-to-density and stiffness-to-density ratios, σu/ρ and
E/ρ. Plot σu/ρ versus E/ρ and briefly comment on the trends. Use both the lower and upper ranges on σu
and connect the resulting two points with a line. How are these trends related to the uses of these metals?
Ou/p versus E/p
30 000 000,00
Stiffnes to D. Pa.m^3 / kg
25 000 000,00
Iron and Steel
Aluminium
20 000 000,00
Titanium
Copper
15 000 000,00
Magnesium
10 000 000,00
Nickel
Tungsten
5 000 000,00
Lead
Cobalt
-
50 000,00 100 000,00150 000,00200 000,00250 000,00300 000,00350 000,00
Strength to D. Pa.m^3 / kg
Iron and steel
Strength-to-Density Ratio: Iron and steel have a high strength-to-density ratio, which means they are
very strong for their weight. This property makes them ideal for applications where structural integrity
and load-bearing capacity are crucial
Stiffness-to-Density Ratio: Iron and steel also have a relatively high stiffness-to-density ratio. This
means they are stiff and can maintain their shape under heavy loads. This property is advantageous in
applications where minimal deformation is required
Aluminum
Strength-to-Density Ratio: Aluminum has a good strength-to-density ratio, although it's not as strong
as iron and steel. However, its lower density makes it particularly suitable for applications where weight
reduction is critical.
Stiffness-to-Density Ratio: Aluminum has a moderate stiffness-to-density ratio, which means it can
provide adequate stiffness while keeping the overall weight of a structure or component relatively low.
Titanium
Strength-to-Density Ratio: Titanium has an excellent strength-to-density ratio, which is one of the
highest among metals. This makes it highly desirable for applications where a combination of high
strength and low weight is essential.
Stiffness-to-Density Ratio: Titanium also has a good stiffness-to-density ratio, which means it can
maintain its shape under load
Copper
Strength-to-Density Ratio: Copper has a relatively low strength-to-density ratio compared to metals
like steel and titanium. It is not as strong for its weight. As a result, copper is often used in applications
where electrical and thermal conductivity are more important than high strength
Stiffness-to-Density Ratio: Copper also has a moderate stiffness-to-density ratio. This property is useful
in applications where some rigidity is required
Magnesium
Strength-to-Density Ratio: Magnesium has a reasonably good strength-to-density ratio, making it one
of the lightest structural metals available. It is used in applications where weight reduction is critical
Stiffness-to-Density Ratio: Magnesium has a relatively low stiffness-to-density ratio compared to other
structural metals like steel or aluminum. This means it is not as stiff and may deform more under load,
which can limit its use in some high-stress applications.
Nickel
Strength-to-Density Ratio: Nickel has a moderate strength-to-density ratio. It is often alloyed with
other metals to improve its properties.
Stiffness-to-Density Ratio: Nickel has a reasonable stiffness-to-density ratio, making it suitable for
applications where a combination of strength, corrosion resistance, and stiffness is required.
Tungsten
Strength-to-Density Ratio: Tungsten has an exceptional strength-to-density ratio, making it one of the
densest and strongest naturally occurring elements. It is primarily used in applications that require
extremely high-density materials.
Stiffness-to-Density Ratio: Tungsten also has a good stiffness-to-density ratio, which is essential in
applications where high-temperature stability and mechanical strength are crucial.
Lead
Strength-to-Density Ratio: Lead has a relatively low strength-to-density ratio, which means it is not a
particularly strong material for its weight. However, lead is known for its high density, which makes it
useful for radiation shielding applications
Stiffness-to-Density Ratio: Lead also has a low stiffness-to-density ratio, meaning it is not very stiff.
This property is not well-suited for structural applications but is valuable for damping vibrations and
noise
Cobalt
Strength-to-Density Ratio: Cobalt has a moderate strength-to-density ratio. It is often used as an
alloying element in materials like superalloys, which are used in high-temperature applications
Stiffness-to-Density Ratio: Cobalt has a reasonable stiffness-to-density ratio, which contributes to its
suitability for high-temperature and high-stress applications. It can maintain its shape and structural
integrity under demanding conditions.
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