Description

It is studied the degree schematization (approximation) effect over the strength calculus of a structural element from a metallic construction. There are analyzed the effect of different conditioning used in strength calculus of a beam for classifying in the importance order. It is especially followed the assignation of recommended calculus hypothesis used in designing the component beams of metallic structures. There are defined some appreciation criteria of the applied hypothesis effect in the calculus strength schemes of metallic structures.

A metallic structure, that has a main strength role in the construction assembly, is designed to sustain effective loadings. Mostly, the strains are ignored or a coarse checking is made, based on arbitrary restrictions. Also there are often simplifications made that places us – in strength calculus – far away from the real phenomenon.
It is proposed the strength analysis of a static defined beam for distinguishing the quantitative effect of various simplifying assumptions. It will be researched the neglecting effect of own mass and elasticity (deformability) of supports; it is followed the effect of support idealization and the real mechanical phenomenon of coupling with the rest of the structure remainder.

SIMPLE SUPPORTED BEAM
The calculus scheme is presented in fig. 1.a, the reactions and moments are:

The moment diagram for balanced lengths and loadings (with appropriate values) is presented in fig. 1.b.
If we impose an admissible stress σa and an admissible deflection fa, we will have two sizing (from the strength and rigidity condition). The strength condition will lead to a necessary modulus Wn and a diameter dn:

To impose the strain condition, it will be used the Mohr-Maxwell method for strain calculus, considering only the bending moment. Having the loading schemes with the unitary force from fig 1.c and 1.d, the moment equations on beam’s spaces are:

The necessary diameter dns, from the deflection condition will be:

Usually the strength condition leads to a higher section: dns> dn.

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