Force lines is a method used in

solid mechanics Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation (mechanics), deformation under the action of forces, temperature chang ...

for visualization of internal forces in a deformed body. A ''force line'' is a

curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...

representing graphically the internal force acting within a body across imaginary internal surfaces. The force lines show the maximal internal forces and their directions.

Force lines drawing

The procedure for determining the force lines consists of two stages: 1) Defining the internal surface. The surface is perpendicular to maximum principal stress in every point of the solid. 2) Integration of internal stresses on the surface. Stress is a measure of the average amount of force exerted per unit area. The stress distribution can be obtained from known theoretical or numerical (

Finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...

) analysis. The researcher who builds up the force lines can choose a magnitude of the internal force and the initial border where the drawing procedure starts. Image: HoleForceLines.gif, Figure 1. Force lines in a plate with a hole. Image: CrackForceLines.gif, Figure 2. Force lines in a plate with a central crack. Image: BendingForceLines.png, Figure 3. Force lines in a beam under pure bending. Figure 1 shows an example of force lines in a body with a hole under tension. The force lines are denser near the hole. The visualization helps to explain the

stress concentration In solid mechanics, a stress concentration (also called a stress raiser or a stress riser or notch sensitivity) is a location in an object where the stress (mechanics), stress is significantly greater than the surrounding region. Stress concentra ...

. Figure 2 shows the force lines in a body with a crack. The cracks are the most dangerous stress concentrator: the intensity of the force lines is high in the crack tip (see

Fracture mechanics Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics t ...

). Figure 3 shows the case of pure

bending In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external Structural load, load applied perpendicularly to a longitudinal axis of the element. The structural eleme ...

of a beam with rectangular cross section. There are no internal forces at the neutral axis of the beam. The tensile and compressive force lines are symmetrical and are denser at the beam’s edge.

Application

The force lines pictures are used for 1) Analysis of stress concentration (Figure1 and Figure 2): the number of the force lines increases in areas with stress concentration.Milton Ohring. Engineering Materials Science. Academic Press, 1995
2) Optimization of structures: reinforcing the structure in the areas with concentration of force lines and deleting the components where there are no force lines.

References

{{reflist Structural engineering Materials science Continuum mechanics Fracture mechanics Solid mechanics Curves

Force lines drawing

Application

See also

References