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I think shell can take transverse loading whereas membrane can take only in-plane loading. Is that correct?
In brief I can answer you like this:
Membranes have in-plane stiffness : like a shear wall
Plates are elements with out-plane stiffness like a concrete slab (though we model slabs as membranes in Structural Analysis programs like Etabs to solve the problem easire)
Shells are a combination of both like a retaining wall
membranes only transfer in-plane forces and perpendicular moments as results of in-plane tensions and compressions. it has SDOF in rotation and2 DOF in displacement.
Plates can only endure Moments and lateral out-plane shears. it has SDOF in displacement and2 DOF in rotation.
Shell = Plate + Membrane
it has6 Degree Of Freedom.
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