Is the beam operating within elastic limits (yield strain for steel ≈ 0.0015)? True or False

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The question asks whether the beam is operating within elastic limits, given a yield strain for steel of approximately 0.0015.

Option 1: True. This would be correct if the actual strain in the steel of the beam is at or below the yield strain of ~0.0015, meaning the material has not yet yielded and remains in the elastic portion of the stress–strain curve. In this case, any deformation is reversible and the stress stays within the elastic limit. The statement is therefore conditionally true, contingent on the measured or calculated strain being ≤ 0.0015.

Option 2: False. This would be correct if the beam experiences strains exceeding the yield strain of ~0.0015, indicating yielding has occurred and plastic deformation is taking place. In such a scenario, the material has left the elastic region, and the response includes permanent deformation beyond the elastic limit. Therefore, the claim of operating within elastic limits would be incorrect when the strain exceeds the yield value.

Key concept linkage: The determination hinges on the comparison between the actual strain in the steel and the yield strain (≈0.0015). If the strain is less than or equal to the yield strain, the beam is within the elastic regime; if it surpasses it, plastic deformation begins. Without numerical strain or stress data for the beam, you cannot definitively label the state as elastic or plastic, so both options are logically possible depending on the actual values.

Additional considerations: In practice, you would check the maximum principal strain or the equivalent plastic strain in the steel. If you have geometric or load data, you could compute the bending strain at critical sections and compare to 0.0015 to decide. If a stress–strain curve or material model is given, you could determine whether the operating point lies on the linear elastic portion. If the problem provides a factor of safety or explicit stress values, convert those to strain via Hooke’s law (ε = σ/E) for steel to confirm elastic behavior. If the calculated ε ≤ 0.0015, the statement would be true; if ε > 0.0015, it would be false.

MENG-4089-06/MENG-5072-01/MENG-5072-01D Strain Measurements of a BEAM

Is the beam operating within elastic limits (yield strain for steel ≈ 0.0015)? True or False

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