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.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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System of Forces

A force is an external influence or agent that changes the state of a system. According to Newton's second law, the force applied to a body is proportional to the change in momentum of a body. Hence, whenever a force is applied to a body, its momentum changes. If the body is at rest, under the action of force, its state of rest changes to motion. In other words, the magnitude of the momentum of the body changes from zero to a measurable value. Similarly, if the body possesses some initial velocity, it has some associated momentum, the effect of force can cause the body to halt or come to rest, that is, the momentum reduces to zero.

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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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