Plane strain conditions are typically assumed to exist in which of the following structural members?
- AThin-walled pressure vessels.
- BLarge, thick structures like gravity dams or retaining walls.Correct
- CThin plates loaded in their own plane.
- DSlender beams under lateral loading.
Solution
Concept
Plane Strain Condition
Formula
N/A
Step-by-step solution
1. Recall that plane strain occurs when strain along one dimension (length) is zero or constrained. 2. Recognize that this assumption applies to thick, massive structures like gravity dams or retaining walls. 3. Select Option (b) as the correct choice.
Explanation
Plane strain conditions occur in long, thick, or massive structures—such as gravity dams, retaining walls, or tunnels—where deformation or movement along the length (the third dimension) is prevented or constrained. Because the strain along this long axis is negligible or zero, the structural behavior can be simplified and analyzed using a 2D cross-section.
Shortcut
To easily remember Plane Strain vs. Plane Stress: - Plane Strain (STrain = Restrained): Applies to Thick or Massive structures (such as dams, retaining walls, and tunnels) where strain along the long length is constrained to zero. - Plane Stress (STress = Thin): Applies to Thin structures (such as thin plates loaded in-plane) where stress normal to the surface is zero.
Common mistake
A common mistake is selecting option C by confusing plane strain with plane stress. Plane stress applies to thin structures like plates loaded in-plane, whereas plane strain applies to large, thick structures like dams where strain in the third dimension is constrained to zero.
Correct answer: B) Large, thick structures like gravity dams or retaining walls.