Analysis of Partial Beam Section Assignment Help

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Analysis of Partial Beam Section:

Until now, we have seen forces & moments acting over the whole cross-section of the beam. Now, let us assume a part of the beam section and attempt to establish a relation for the normal force working on the partial beam section & the moment of the normal force regarding the neutral axis.

Normal Force

Consider a beam section as illustrated in Figure.

Consider σmax be maximum bending stress at the topmost layer and ymax be the distance of the top most layer from the neutral axis.

Let us discover the normal force on a partial area A, illustrated shaded in Figure. In that shaded area, consider da be an elemental area & y be its distance from the neutral axis.

2385_Analysis of Partial Beam Section.png

                                        Beam Section                           Bending Stress Distribution

 Figure

The stress, σ on elemental area is proportional to the distance y.

σ = σmax  ×(y/ ymax)

Normal force on the elemental area = σ × da

= σmax (y/ ymax)

Total normal force on the shaded area = ∑ σmax (y/ ymax)

                                                             = (y /ymax) ∑ y da

Let be the distance of the centroid of the shaded area from the neutral axis.

1964_Analysis of Partial Beam Section1.png

∴ Normal force on a partial beam section =  631_Analysis of Partial Beam Section2.png

Moment of Normal Force
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