A typical value for the modulus of elasticity (E) of aluminum is 10,000 ksi and for steel is 29,000 ksi. Which of the following is a TRUE statement?

Question

BlackTom AI · Accepted Answer

We are given typical modulus of elasticity values: aluminum ~ 10,000 ksi and steel ~ 29,000 ksi. The modulus of elasticity (E) is a measure of material stiffness; a higher E means stiffer material under service loads.
Option by option analysis:

Option 1: 'Aluminum has 2.9 times less strength than steel'
This statement talks about strength, not stiffness. E relates to stiffness, not yield or ultimate strength. Therefore this option misinterprets the property being compared and is incorrect.

Option 2: 'Aluminum is 2.9 times less stiff than steel'
This aligns with the given E values. If steel has E ≈ 29,000 ksi and aluminum ≈ 10,000 ksi, aluminum’s stiffness is lower by a factor of 29,000 / 10,000 ≈ 2.9. Saying aluminum is 2.9 times less stiff than steel correctly describes the relationship between their moduli of elasticity.

Option 3: 'Aluminum has 2.9 times less toughness than steel'
Toughness is a measure of energy absorption before fracture and is not directly determined by E. Different materials can have similar E but very different toughness, depending on ductility and toughness properties. This statement confuses stiffness with toughness and is therefore incorrect.

Option 4: 'Aluminum is 2.9 times more stiff than steel'
This is the opposite of what the given E values indicate. Since aluminum's E is much smaller than steel's, aluminum is not more stiff; it is less stiff. This makes the option incorrect.

In summary, the only option that correctly matches the concept that stiffness scales with the modulus of elasticity and the given numerical values is the one stating that aluminum is 2.9 times less stiff than steel, while the others either misstate the property (strength or toughness) or invert the relationship of stiffness.

A typical value for the modulus of elasticity (E) of aluminum is 10,000 ksi and for steel is 29,000 ksi. Which of the following is a TRUE statement? 单项选择题

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