Force lines method is 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 under the action of forces, temperature changes, phase changes, and ot ...
for visualization of internal forces in a deformed body. A force line represents 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
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
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
The 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 ...
) 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) is a location in an object where the stress is significantly greater than the surrounding region. Stress concentrations occur when there are irregularitie ...
.
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 load applied perpendicularly to a longitudinal axis of the element.
The structural element is assumed to ...
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.
See also
*Fracture
Fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displa ...
*Engineering stress
In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain ...
*Stress concentration
In solid mechanics, a stress concentration (also called a stress raiser or a stress riser) is a location in an object where the stress is significantly greater than the surrounding region. Stress concentrations occur when there are irregularitie ...
*Stress intensity factor
In fracture mechanics, the stress intensity factor () is used to predict the stress state ("stress intensity") near the tip of a crack or notch caused by a remote load or residual stresses. It is a theoretical construct usually applied to a h ...
*Strength of materials
The field of strength of materials, also called mechanics of materials, typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the re ...
*Structural fracture mechanics
Structural fracture mechanics is the field of structural engineering concerned with the study of load-carrying structures that includes one or several failed or damaged components. It uses methods of analytical solid mechanics, structural engineer ...
References
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Structural engineering
Materials science
Continuum mechanics
Fracture mechanics
Solid mechanics