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Progettazione Assistita di Organi di Macchina, primavera 2022

Lecture Notes

Planar beam structure i.p. and o.o.p. loadings

The beam structure centroidal axis lies on a plane, which is also a symmetry plane for the cross-sections.

Symmetric and skew-symmetric loads with respect to such a plane are called in-plane and out-of-plane loads, respectively.

If the superposition of effects holds (e.g., if the structure behaves linearly) each load set only induces an associated subset of the possible components of internal action, see

Symmetric and skew-symm. parts of a general load

(ipe source)

A general load is applied to a symmetric structure in a); in b), c) the loads applied on each half structure is treated separately. In d), e) the action on the loaded portion is halved, and symmetrically propagated to the other portion; those symmetric actions are accumulated in the symmetric part of the load f). In g), h) the action on the loaded portion is halved, and skew-symmetrically propagated on the unloaded portion; those skew-symmetric actions are accumulated in the skew-symmetric part of the load i).

Rollbar-like frame

Quarter ladder frame chassis

struttura simil Halo

Other stuff


Principal orientations for beam flexure. This gif animation presents the axial stress component map as a function of the bending moment vector orientation, as evidenced by the rotating needle. It clearly appears that, for a generic (vs. e.g. circular) cross section, the neutral axis may significantly deviate from the moment vector orientation; those two directions become parallel only in correspondence of the principal directions for bending (located at [18.4°-18.5°]+N·90° for the cross section under scrutiny). The bending moment rotates of 0.1° each increment.

foglio Maxima per calcolo risultanti momento e curvature in un esempio di piastra inflessa (provino a flessione a quattro punti).


Instabilità, euler_beam_buckling_2022_noplv.wxmx, 400mm_supported_bar_v2022a.mfd …b.mfd …c.mfd


wikipaom2022/start.txt · Ultima modifica: 2022/06/01 15:48 da ebertocchi