Forces in a truss and Static Kinetic Friction

Forces in a truss refer to the internal forces that develop within the structural members of a truss when it is subjected to external loads. These forces can be either tension or compression forces, and they are critical in determining the stability and strength of the truss structure. In a truss, the forces are distributed along the various members in such a way that the entire structure remains in a state of equilibrium under the applied loads.

The analysis of forces in a truss involves identifying the various member forces and their directions, and determining whether they are in tension or compression. This information is crucial in designing and constructing trusses that are capable of withstanding the required loads and ensuring the safety of the structure.

Engineering mechanics – statics Forces in a truss,

Method of sections for plane trusses

Plane trusses are structures that only comprise straight bars. The bars are connected to nodes. To determine the support reactions and the forces and moments that are transferred to the nodes, we first make idealising assumptions:

The bars are connected to each other at the nodes, centrally and flexibly.
The external forces only act on the nodes.

These requirements for an ideal truss ensure that all bars are only subjected to tension or pressure. The support forces and bar forces are calculated using various methods of sections.

Method of joints

Note:

S bar forces,
A+B support forces,
F forces,
index V vertical forces,
index H horizontal forces

Using the method of joints, all nodes are isolated in succession. The equilibrium conditions are established at each node. Applying the method of joints requires that no more than two unknown forces are acting on the node. The advantage of this method is that no bar force is overlooked in complex trusses.

Ritter’s method of sections

Note:

S bar forces,
A+B support forces,
C nodes,
F force,
L bar length,
S2 wanted bar force

Ritter’s method of sections is used when only single bar forces need to be determined in a truss. Applying Ritter’s method of sections requires that the supporting and external forces are known. The section runs through three bars, of which two bars are connected in a node.

In the case of the equilibrium of moments, it makes sense to choose the intersection of the two bar forces as the reference point. Consequently, only one unknown bar force remains in the equation. The advantage of this method is that it is possible to calculate individual bar forces without having to consider every node.

Cremona diagram (forces diagram)

The Cremona diagram is a graphical method for determining bar forces in a truss. Applying the Cremona diagram requires that the support forces and the external forces are known or that they have been determined beforehand using the method of joints.

Then a force diagram is systematically plotted for each node with a known force and two unknown forces. The direction of force is plotted in the entire force diagram of the truss. The unknown bar forces can be derived from the triangle of forces. The advantage of this method is that no bar force is overlooked in complex trusses and all force directions are correctly plotte d.

Static and kinetic friction

While in statics, we study idealised bodies excluding frictional forces, in the study of static and kinetic friction, we investigate real solid bodies. Friction occurs in all solid bodies that are in contact and that are moved against each other. The cause of the occurring forces is, among other things, the surface roughness, which causes the surfaces to interlock.

Typical values for the coefficient of friction

Types of friction

We differentiate between two types of friction: static friction, where there is no movement of the bodies relative to each other and dynamic friction, where the surfaces move relative to each other. The roughness of the surfaces is described by the coefficient of friction μS, for static and μK, for dynamic friction.

Static friction

Static friction is present if displacing forces are acting on both bodies, but the bodies have not started to move relative to each other yet. This is why we also talk about static friction that has to be overcome if we want to move a body. Static friction is a reaction force; in statically determinate systems, it can be determined from the equilibrium conditions.

Note:

FG weight,
FH force of static friction,
FN normal force,
F external force, v velocity

The proportionality constant is called the coefficient of static friction μS. It depends on the material and the surface characteristics of the respective body. Whenever the applied force exceeds the maximum static friction, a body begins to slide.

Dynamic friction

Dynamic friction occurs when a body moves along another and in contact with it, i.e. it actually rubs against it. Dynamic friction increases with the roughnesses of the bodies’ surfaces and the pressure applied between the bodies. The dynamic friction force is a physical force (active force) and proportional to the normal force FN.