Line load

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Symbol for constant line load ,
i. d. Usually, however, a line load is not constant ( equal ) over the route

A line load is a length-related load (e.g. in Newtons per meter). The term can be found in technical mechanics , especially statics , but also in technical dynamics .

The line load is generally a mathematical idealization

  • a volume force (e.g. dead weight ) that is allocated to the member axis as effectively as possible, or
  • a surface tension , which integrates over the area of ​​influence, becomes a load related to the length of the associated rod axis section.

A line load has the dimension force per length :

with the shear force .


A line load for a static system is calculated from the integral of the volume force densities over the cross section and the integral of the surface tensions over the surface:


  • the link load vector
    • of the component in -direction
    • of the component in -direction
    • of the component in -direction
  • the volume force density , e.g. B. Own weights
    • the density
    • the gravitational field
  • the cross-sectional area
  • the surface tension , e.g. B. Surface pressure due to a contact force with another continuum
  • the circumference of the cross-section.

General line loads

Line loads
various loads

A general line load is any function , for example a Fourier series . A line load as a Fourier series can replace individual loads or bending moments with any precision.

A triangular load is a line load that tends towards a value of at one end and increases with a constant (possibly negative) gradient to the other end.

A trapezoidal load is a line load, applies when: . They can be put together from a constant line load and a triangular load.

Constant line load

A uniform line load is a line load which has a constant value over the respective member axis area:

Load model 71

A uniform load sometimes represents an unrealistic load pattern, but still serves a realistic dimensioning . An example of this is the load model 71 in railways , in which the wheel loads , which represent concentrated loads to a good approximation , are modeled as uniform loads . With this load model, the load envelopes of all common loads with the associated wheel spacings are mapped on the safe side as a good approximation .


q ges = q 1 ⊕q 2 ⊕q 3 ⊕… ⊕q n
therein bedeutet means: "to be superimposed with".

In the theory of the first order or for linear problems it follows:

q ges = ∑q i

Bending theory

From the equilibrium conditions with reference to the undeformed position, i.e. in the first order theory, it follows:

    • [kN * m] ... bending moment (stress resultant)
    • m (x) [kN * m / m] ... external moment per unit of length (moment load per length)

See also

Individual evidence

  1. ↑ In other words , a system in which in a Galilean reference system there are no annoyance forces.
  2. a b Bernhard Pichler, Josef Eberhardsteiner: Structural Analysis VO - LVA no. 202.065 . Ed .: E202 Institute for Mechanics of Materials and Structures - Faculty of Civil Engineering, TU Vienna. SS 2016 edition. TU Verlag, Vienna 2016, ISBN 978-3-903024-17-5 , angle of rotation method (520 pages, online - first edition: 2012). online ( Memento of the original from March 13, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  @1@ 2Template: Webachiv / IABot /