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Beams are the best examples of a system of coplanar non-concurrent systems. We will restrict our study only to finding reactions of such determinate beams
Determinate and Indeterminate structures
1. Determinate Structures : Structures in which the equilibrium equations are sufficient to find the forces and stresses associated with the structure
r = 3n
2. Indeterminate Structures : Structures in which the equilibrium equations alone are not sufficient to find the forces and stresses associated with the structure
r > 3n
where r - no. of reactions and n - no. of equilibrium equations
Type Of Supports
1. Simple Support : If one end of a beam simply rests on a support, the support is known as simple support. The beam is free to slide and rotate at simple support and the reaction is perpendicular to the surface. Eg : Scale resting on two tables
2. Roller Support : The end which is supported on a frictionless roller to permit contraction and expansion due to temperature or lateral forces is known as roller support. The reaction in roller support is normal to the surface
3. Hinged/Pined Support : This support does not permit movement along any direction but is free to rotate. The reaction components are taken along horizontal and vertical directions. Eg – Hinges of doors and windows
4. Fixed Support : At fixed support, the beam is not free to slide or rotate along any direction. The reaction components include horizontal, vertical and moment.
Types of Loadings
1. Concentrated load or Point Load: If a load acts at a point, either horizontal, vertical or inclined, it is called a concentrated load or point load. If the load acts at a very small area, it is taken as a point load. It is expressed in N or Kn.
2. Uniformly Distributed Load :This type of load is spread over acertain length with the intensity of load being constant. It is expressed in N/m or kN/m. The resultant load R=wL acts at a midpoint of udl.
3. Uniformly Varying Load: This type of load is spread over a certain length with the intensity of load varying linearly. The resultant load R=wL/2 acts at a distance of 1/3 from point of action of w N/m.
4. Pure Moment : A pure moment force or couple can also act on beams. The unit of moment is kNm.
B. EQUILBRIM OF GENERAL COPLANAR SYSEMS
Apart from beams there are a number of coplanar systems whose reactions is of interest. Here is one question put forth for those who wish to solve it.
1. Calculate the force and moment reactions at the bolted base O of the overhead traffic-signal assembly. Each traffic signal has a mass of 36 kg, while the masses of members OC and AC are 50 kg and 55 kg, respectively. The mass center of member AC is at G.