Given the stress-strain diagram below, if the diagram has its origin at a value of (0.00025, 0) and crosses a point where the stress is 25 ksi and the strain is 0.001, what is the calculated modulus of elasticity?

Question

BlackTom AI · Accepted Answer

Start by identifying what the problem provides: a stress-strain diagram with its origin shifted to (0.00025, 0). This means the true relationship between stress and strain has an intercept such that stress equals zero at strain 0.00025 when using the plotted axes.

Option A: 100,000 ksi. If the modulus were 100,000 ksi, the slope would be much steeper. Using the given point (strain = 0.001, stress = 25 ksi), the implied slope would be 25 / (0.001 − 0.00025) = 25 / 0.00075 ≈ 33,333 ksi, which is far from 100,000 ksi. So this is incorrect.

Option B: −33,333 ksi. A negative modulus would imply material response that increases stress as strain decreases, which contradicts the positive, forward-increasing stress–strain behavior observed in the diagram. Therefore this cannot be correct.

Option C: unable to be determined. The problem provides a clear point on the line and the offset of the origin, which is sufficient to compute the slope (modulus of elasticity). Hence, it is determinable. This option is not correct.

Option D: 25,000 ksi. If E were 25,000 ksi, the slope would be significantly smaller. Plugging into the same relation gives an implied slope incompatible with the given point unless the offset was different. Since the data specifies the origin shift and the point (0.001, 25), this value does not match.

Option E: 33,333 ksi. This option aligns with the calculation: E = stress / (strain − offset) = 25 ksi / (0.001 − 0.00025) = 25 / 0.00075 ≈ 33,333 ksi. The positive, reasonable modulus matches the observed linear portion after accounting for the origin shift.

In summary, using the shifted origin relation stress = E × (strain − 0.00025) and the given point (0.001, 25), the calculated modulus is approximately 33,333 ksi, validating option E as correct while the other choices fail based on the implied slope and sign considerations.

Given the stress-strain diagram below, if the diagram has its origin at a value of (0.00025, 0) and crosses a point where the stress is 25 ksi and the strain is 0.001, what is the calculated modulus of elasticity? 单项选择题

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