B.2. Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: 0, X (M.I¸— M₂I¸)y+(M₂I₂ − M₂I¸ )² (1,1-12) where My and M₂ are bending moments applied to a cross-section, and where ly, Iz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (i) What assumptions have been made in the derivation of the above expression? (ii) Indicate by means of a sketch the directions in which positive values of the bending moments My and Mz act on a cut plane facing in the positive x direction.
B.2. Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: 0, X (M.I¸— M₂I¸)y+(M₂I₂ − M₂I¸ )² (1,1-12) where My and M₂ are bending moments applied to a cross-section, and where ly, Iz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (i) What assumptions have been made in the derivation of the above expression? (ii) Indicate by means of a sketch the directions in which positive values of the bending moments My and Mz act on a cut plane facing in the positive x direction.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:B.2.
Elementary beam theory predicts that the axial bending stress ox in a
prismatic beam is given by:
σ, X
(M.1, M,1,)y+ (M, I. - M.1,-) z
(1,1.-1²-)
where My and M₂ are bending moments applied to a cross-section, and
where ly, Iz and lyz are second moments of area in the usual notation
(Oxyz is a Cartesian coordinate system in which the x axis corresponds
to the centroidal axis of the beam).
(i) What assumptions have been made in the derivation of the
above expression?
(ii) Indicate by means of a sketch the directions in which positive
values of the bending moments My and M₂ act on a cut plane
facing in the positive x direction.
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