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Determinate and indeterminate structure-(Video-Youtube)

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Determinacy, a 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. if r = 3 times n, the structure is determinate. and if r  bigger than 3 times n, the structure is indeterminate .

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 here showing some examples of statically determinate and indeterminate structures. The first beam has 3 unknown reactions, we have 2 vertical forces and one horizontal force as shown in this figure. So r=3, the beam consist of one part so n=1. So r= 3 times n and the beam is determinate. We can apply same principle for the remaining beams. For this beam we have 10 unknow reaction, moment, vertical and horizontal forces near the fixed support. And 2 horizontal and vertical forces for the internal hinge. Hinge can’t carry moment unlike the fixed support. Therefore r=10, the beam composed of 3 parts. So r is less than 3 times n and the beam is indeterminate. 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 this figure.  forces at cut point should be counted one time only. this figure showing a bridge. this bridge consist of one span, this will have three unknown forces at both support. So r=3 and n=1. N is the number of structure parts. So n is equal  3 times 1 and the structure is determinate. This figure showing a bridge with two continuous span. We have 3 supports. for this bridge we have four reactions as shown in this figure. In total we have 6 unknown reaction. N for this bridge = 1. Therefore r is more than 3 times n and the structure is indeterminate. if r is lesser than 3 times n. let assume that this birdge is setting on two roller support. so we have only vertical forces and no horizontal forces. so r=2 and it is lesser than 3 times n. but if the bridge is seated on two roller, is it going to be stable. the answer is no because the bridge will be sliding because the horizontal force is not resisted. so if r is lesser than 3 times n, the structure will not be stable.

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