REACTIONS DETERMINATION IN DETERMINATE STRUCTURE...PART TWO

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Reactions as what support offers to restrain structure to its position, when subjected to loadings.

As the degree of indeterminacy of determinate structure n= 0, this means the reactions or forces are balancing each other with no extra reaction (structure is in equilibrium).

Due to balancing reactions, the reactions can easily be determined by using three equilibrium equations for the plane structure, which are the following






The magnitude and direction of support reactions in determinate structure can easily determined by adhering the following procedures

·         Drawing free body diagram FBD

·         Check for determinacy

·         Applying equilibrium equations


Example 1

Determine support reactions of the structure below



Solution

The first step is to draw free body diagram, this diagram show the directions (proposed) and position of forces and reactions, so they can easily analyzed.

The support A provide two reactions Ax   and Ay as at point A we have fixed support, and at point B we have only one reaction as we have roller support.

The direction arrows should be indicated as the directional reference to your analysis.


Second step is to check determinacy, this step help to know if the structure is statically determinate so we can analyze it by three equilibrium equation or not, unstable structures will not be analyzed as they cannot support desired loadings.

From degree of indeterminacy, n = r – 3

                                                         r = 3

                                                    n = 0 (the structure is statically determinate)

Step 3 Since it is statically determinate, then reactions can be determined by three equilibrium equations


 


             







Example 2

Determine the support reaction of the structure below carrying both point load inclined at 600 and distributed load.


Solution

The first step is to draw free body diagram, this diagram show the direction (proposed) and position of forces and reactions, so they can easily analyzed.

The support A provide only one reaction RA as at point A we have roller support, and at point C we have two reactions Cx and Cy as we have pin support.

But reaction RA at support A will have two directional effects as Ax and Ay because the reaction is inclined.

The direction arrows should be indicated as the directional reference to your analysis.


Second step is to check determinacy, this step help to know if the structure is statically determinate so we can analyze it by three equilibrium equation or not, unstable structures will not be analyzed as they cannot support desired loadings.

From degree of indeterminacy, n = r – 3

                                                         r = 3

                                                    n = 0 (the structure is statically determinate)

Step 3 Since it is statically determinate, then reactions can be determined by three equilibrium equations.

We need to resolve the inclined force into horizontal and vertical components for easy calculation in equilibrium equation.

Hz = 10cos 600

      = 5KN

Vt  =   10sin 600

      = 8.66KN














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