PLAIN AND CIVIL: 7.0 EQUILIBRIUM OF FORCE SYSTEMS

Thursday, 7 March 2019

7.0 EQUILIBRIUM OF FORCE SYSTEMS

Newton had defined equilibrium as the state of a body either at rest or moving on a straight path with a constant velocity. In statics, we consider the first situation where the system is at rest.

FREE-BODY DIAGRAM

In order to solve equilibrium problems, we are required to simplify the image of the system under consideration. Simplifying the system would mean making the image clear of physical properties but using simple lines instead. With the new system of lines, forces should be applied to show the probable result. This new system is called Free-Body Diagram. From this diagram, one can clearly identify the unknowns from the given parameters.

EQUILIBRIUM EQUATIONS

The probable motion of objects upon application to forces are horizontal, vertical and rotation. With these motion, the equations of equilibrium are as follows:

$\sum F_{x}=0$ $\sum M_{x}=0$

$\sum F_{y}=0$ $\sum M_{y}=0$

$\sum F_{z}=0$ $\sum M_{z}=0$

The complete set f six equations are used for spatial forces where there are the i-, j-, and k- axes present while only three equations are used for coplanar forces - $\sum F_{x}=0$ , $\sum F_{y}=0$ , and $\sum M_{z}=0$ .

SUPPORT REACTIONS IN TWO DIMENSIONS

Structural supports react depending on their make. With the applied load, there are instances that supports could not yield or react.

credits to VECTOR MECHANICS FOR ENGINEERS

1. Rollers, rockers, or frictionless surface. These are types of supports which only have a reaction perpendicular to the surface. When a force, parallel to the surface is applied, these supports will only slide along with the load, so they cannot oppose or react to the load.

2. Hinge, frictionless pin, or rough surface. These supports react on both parallel and perpendicular forces but they cannot oppose moment. When rotation is applied on the member, the member will still rotate. This is similar with a door hinge (thus the name). Forces pushing or pulling the door parallel to the jamb or perpendicular to the jamb will be resisted by the hinge, but the door can open or close freely by swinging on the hinge.

3. Fixed support. These supports react with the three application of forces and moments. Push, pull and rotation are all resisted by the fixed support.

EXAMPLE 7.0.1: EQUILIBRIUM OF CONCURRENT COPLANAR FORCES
EXAMPLE 7.0.2: EQUILIBRIUM OF CONCURRENT COPLANAR FORCES
EXAMPLE 7.0.3. APPLICATION OF EQUILIBRIUM OF CONCURRENT COPLANAR FORCES
EXAMPLE 7.0.4: EQUILIBRIUM OF COPLANAR FORCES
EXAMPLE 7.0.5: EQUILIBRIUM OF COPLANAR FORCES
EXAMPLE 7.0.6: EQUILIBRIUM OF SPATIAL FORCES
EXAMPLE 7.0.7: EQUILIBRIUM OF SPATIAL FORCES
EXAMPLE 7.0.8: FINDING REACTIONS
EXAMPLE 7.0.9: FINDING REACTIONS
EXAMPLE 7.0.10: FINDING REACTIONS IN TRUSSES
EXAMPLE 7.0.11: FINDING REACTIONS IN TRUSSES
EXAMPLE 7.0.12: FINDING REACTIONS OF INCLINED SUPPORTS