Line load
A line load is a lengthrelated 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 .
definition
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:
With
 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 crosssectional area
 the surface tension , e.g. B. Surface pressure due to a contact force with another continuum
 the normal vector
 the circumference of the crosssection.
General line 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:
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 .
Superposition
 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
 ↑ In other words , a system in which in a Galilean reference system there are no annoyance forces.
 ↑ ^{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 9783903024175 , 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.