Strength theory is a subsection of the technical mechanics and is concerned with the effect of forces on distortable solids. Contrary to the statics here material-dependent parameters are like the modulus of elasticity or the elongation limit of importance. Main content of the strength theory is it to forecast whether a construction unit withstands the applied load. The general description of the behavior of the solids is called continuum mechanics.

There are different beginnings of the strength theory. All beginnings confront the ruggedness of the body to the arising loads. Main differences between the beginnings are the allocation of the parameters on the ranges load and ruggedness. In the following today the furthest common beginning is described.

Arising loads

The arising loads are computed after the laws of the mechanics. In some cases also the laws of the fluid mechanics, thermodynamics or the heat transport are used, in order to compute boundary conditions or loads.

Important it is here that the loads analytically on the simplifying assumption (e.g. omitting weight) it is usually determined. In recent time however ever more frequently numeric methods are used like the finite element method (FEM).

The tensions arising during a load case in the body depend on:

• Kind of demand: Zug1), Druck1), thrust, bend, torsion or a combination (compound demand)
• Direction of the outside loads
• Amount of the outside loads
• Place of the outside loads
• Geometry of the body
• Temporal behavior of the loads (e.g. swelling, changing)

1) Course and pressure are regarded in general as a type of load (standard voltage).

Ruggedness of the body

The ruggedness of a body is determined in many cases, by converting the material indices of a standardized sample to the characteristic values of the body.

One avails oneself the general elasticity theory and/or also the theory of plasticity i. For simply formed (e.g. rod-shaped bodies) from it formulas can be theoretically derived. For more complicated bodies one uses computer programs, among other things applications finite element method-further influences (except form, type of load and material indices) is predominant:

• the scale effect (under the different influence of material defects)
• the surface influence, causes e.g. by roughness or solidification of the surface
• Influence of other boundary conditions, e.g. temperature (so far not already considered in the computation model), dry friction or aggressive media.

These influences are considered partially by empirically won factors.

In some cases the ruggedness of the bodies is purely empirically developed, i.e. by experiments at homogeneous bodies or models. When using models the laws of the similitude theory must be considered.

Within some ranges e.g. mechanical engineering or building industry exists uniform computation methods, which are to a large extent standardized.

Results of the strength calculation

The results are dimensionless values (values without physical units), which are called collateral. They are computed as relationship from ruggedness to the arising load. The collateral must be larger than minimum values. The height of these minimum values essentially depends on the following influences:

• Accuracy of the selected computation model
• Probability of the simultaneous occurrence of maximum values of independent loads
• Probability distribution of the material resistance values
• Effect of the failure of construction units on the entire wing unit

In many cases security must be proven against several failure modes, e.g.:

• Security against break
• Security against function loss by inadmissible deformation
• Security against fatigue (break after frequent variation in load, e.g. with axles)
• Security against stability loss, e.g. approximately breaks or dents

Example

As the simplest example a staff is to be regarded, that is pulled from both sides with Kraft F. With the cross-section area A the tension results s. (s =F/A).

If the staff consists of the steel S235, then now the tension can be compared s with the yield strength of this steel (approx. 235 N/mm2). If the tension is smaller than the yield strength, the staff does not deform durably.

Computation method

In particular the computation methods of the technical mechanics and the structural design are used, in addition 20 belonged to in. Century inside above all graphic procedures, how

• the Mohr Spannungskreis for the determination of the components of the stress tensor,
• the rope hitting a corner procedure for the determination of the situation and size of the resulting with several forces,
• the Cremonaplan for the determination of the in specialized works.

In addition analytic procedures of the force size method came, how

• the Ritter Schnittverfahren for the computation of individual in specialized works or
• the use of the sentences from Castigliano to the computation of the bearing forces and cut reactions in statically indefinite wing units.

Today mainly computer-assisted methods became generally accepted, which make the analysis possible of systems at relatively small expenditure, also complicated. In addition belong above all

• the finite element method and
• the edge element method.

Literature

• R.C. Hibbeler: Technical mechanics 2 - strength theory. 5. , and extended Aufl. Pearson study, Munich revised 2005, ISBN 3-8273-7134-1

Articles in category "Strength theory"

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