# Static calculation

A static calculation (colloquially also statics ) is the calculation of the forces , stresses and deformations of a construction, for example in

## purpose

The aim is to determine whether the structure will fail with sufficient safety and not under the planned load ( breaking , buckling , etc.), or to investigate which loads the structure can withstand without failing. Partial safety factors are applied to the loads and material parameters in order to compensate, among other things, for simplifications of the respective calculation method as well as variations in load assumptions and material properties. Furthermore, it is the task of statics to ensure the usability of individual components (to limit deformations and vibrations to a tolerable extent).

## proof

• Proof of structural safety, which prove that structural safety ( strength , buckling ...) is guaranteed with a certain probability
• Proof of usability, which prove that the object remains usable (crack width limitation, deflection , vibrations ...)

## Civil engineering

Example of a static calculation

In civil engineering, the entire construction planning of a building is referred to as structural planning . The static calculation is part of it; essentially this is the arithmetical part. The static calculation also includes static overview plans (so-called static position plans) in which the individual positions of the calculation and the essential component dimensions, building materials, etc. can be found.

Most building projects require approval from the responsible building supervisory authority. This can be obtained as part of the building application process. The required evidence includes, among other things, a static calculation of the structure prepared by an expert. It serves to prove the stability , the usability and the durability .

According to the last amendments to the building regulations, however, the statics are only to be submitted for examination together with the building application for special structures. For all other construction projects, a later template is sufficient - in most cases, however, this must be before construction begins.

For structures of medium difficulty or above, the client must have the statics checked by a structural engineer (external monitoring of the calculation). For simple construction projects such as single- or two-family houses, no external examination is usually required (in this case the structural planner himself, e.g. by a second engineer in the office or by comparing it with similar calculations from the past, is sufficient).

The structural calculations are carried out by structural engineers ( structural engineers ) who must have sufficient knowledge and experience. In most federal states, lists are now kept of structural engineers who are authorized to submit building documents and to which this applies formally. In some cases, the structural engineers are also required to provide evidence of adequate insurance coverage.

Excessive precision in the static calculation is not required, as the utilization is given in percent. That means, only 3 significant digits are necessary in the result. At the same time, both material parameters and load assumptions as well as, in some cases, the calculation models are subject to inaccuracies. These inaccuracies were taken into account when calibrating the (partial) safety factors. The use of calculating machines and computers nowadays results in great theoretical accuracies. In principle, however, accuracies of 3 to 4 significant digits (not decimal places) are still sufficient. At times when the static calculations were still made with the slide rule, an accuracy of 3 digits was considered sufficient. More is hardly readable on the slide rule.

## mechanical engineering

In mechanical engineering, static calculations are made for cranes and foundations, among other things.

## shipbuilding

The classification societies issue rules for dimensioning components that support and partially replace the static calculation. If there is a deviation from this, a proof of strength must be provided with your own static calculation. Static calculations consist of the longitudinal strength - the ship is approximately viewed as a bending beam under the unevenly distributed influence of weight, cargo and buoyancy - and of the transverse strength, in which a cut out "disc" is under the influence of dead weight, cargo and hydrostatic pressure according to the beam theory is calculated. Similar to the structural engineer in civil engineering, classification societies provide the service to certify strength calculations in shipbuilding and shipbuilding-related industries.

## Simple statics

With the formula for the bending moment of a uniform load on the single-span girder , many more difficult static systems can also be calculated to a good approximation (on the safe side). It is therefore often used for rough calculations - especially without EDP. With pre-dimensioning, experienced structural engineers can often determine the necessary dimensions without calculation.

## literature

• Helmut Nikolay: Introduction to the structural analysis of buildings . Bundesanzeiger-Verlag, Cologne 2014, ISBN 978-3-8462-0406-1 .
• Gottfried CO Lohmeyer: structural analysis . Part 2: Strength of Materials. BG Teubner, Stuttgart 1991, ISBN 3-519-05026-9 .
• Otfried Homann: Reinforced concrete. Introduction to the calculation according to DIN 1045. (= Teubner study scripts ). 3. Edition. Stuttgart 1982.