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Determinate and indeterminate structure

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structure can be called determinate if the equilibrium equation provides enough and sufficient condition for equilibrium. if all forces for a structure can be determined using equilibrium equations only, this structure is determinate, but if the unknown forces are more and cant be determined using equilibrium equations then this structure is indeterminate.in general we can determine if a structure is statically determinate or indeterminate by drawing free body diagram for a structure or part of it and comparing a number of unknown forces and moment component with number of available equation of equilibrium. for coplanar structures, we have  three equilibrium equations, if n is the total number of parts and r is the number of unknown forces and moment component then:

r=3*n determinate

statically indeterminate structure cant be solved using equilibrium equations, solving of a statically indeterminate structure by relating loads and reactions with slope and displacement at different point of structure, this known as compatibility equations, Compatibility equations involve the geometric and physical properties of the structure. the figure below showing some examples of statically determinate and indeterminate structures. 

Figure 1 


For frames members are connected together by rigid joint, therefore we can determine if the structure is statically determinate or indeterminate by cutting of members into parts as shown in figure 2, forces at cut point should be counted one time only. 







Figure 2


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