Part III. True or False?

(Answers at the end of this section)

1. A basic difference between the theory of elasticity and strength of materials (“applied elasticity”) is that strength of materials solutions are based upon an approximation of either the stress field or the displacement field, while the theory of elasticity uses neither approximation.

2. Even for a nonhomogeneous beam, in Bernoulli–Euler straight beam bending theory both the displacements and the strains vary linearly in both centroidal coordinate directions over a compact beam cross-section.

3. Even for a nonhomogeneous beam, in Bernoulli–Euler beam bending theory the stresses vary linearly in both centroidal coordinate directions over the compact beam cross-section.

4. The number of Prandtl stress function BCs equals the number of internal boundaries plus one BC for the external boundary.

5. The membrane analogy for uniform torsion is based upon the extension of the Bernoulli–Euler beam bending approximations to membrane bending theory.

6. The membrane analogy for uniform torsion is useful for visualizing the torsional shearing stress distribution for both compact singly connected and compact multiply connected, beam cross-sections.

7. The equations that are useful for the analysis of a uniformly twisted, multicell, closed bar cross-section, with a sufficiently stiffened cross-sectional shape, are those deflection equations that say that the twist per unit length of each individual cell is the same, and those equilibrium equations that say that the resisting torque for each cell is the same.

8. For uniform torsion, the maximum shearing stress may occur at a fillet, but always occurs at an outer boundary point of the open, that is, singly connected, cross-section.

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