What conditions does an Euler-Bernoulli beam in bending satisfy?

Question

An Euler-Bernoulli beam in bending is assumed to satisfy A) both plane stress as well as plane strain conditions B) plane strain condition but not plane stress condition C) plane stress condition but not plane strain condition D) neither plane strain condition nor plane stress condition

Accepted Answer

The correct answer to this question pertains to the fundamental assumptions of Euler-Bernoulli beam theory regarding stress and strain states. Generally, an Euler-Bernoulli beam, under the assumption of small deflections and linear elastic material, is often treated under a state of **plane stress** at the cross-section. This means that the stress components perpendicular to the plane of the cross-section (e.g., in the z-direction if the beam lies in the xy-plane and bending is about the z-axis) are assumed to be zero (σz = 0, τxz = 0, τyz = 0). Plane strain, on the other hand, implies that strain components in one direction are zero (e.g., εz = 0). For slender beams, the assumption of plane stress is more appropriate for typical bending scenarios. Therefore, the beam is generally assumed to satisfy **plane stress condition but not plane strain condition**.

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