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Determinate and indeterminate truss structure

Determinate and indeterminate truss, distinguishing whether truss is determinate or indeterminate requires knowing b, b is the number of truss member, truss members are straight and carrying axial forces only, also we should know j, j is the joint numbers, each group of truss members is connected to one joint and since the members carrying only axial forces the sum of moment at joint will be zero, members of truss are coplanar and concurrent, therefore the rotational or moment equilibrium is satisfied at the joint. two equation of equilibrium remains for each joint ΣFx=0 and ΣFy=0, their determinacy of truss can be determined using the equations below

b+r=2j  determinate
b+r>2j indeterminate

r is the total number of external reaction at supports, the first term of equation (b+r) represent the number of unknown including axial forces for each member and external reaction at supports, the second term of the equation representing the number of available equilibrium equation that can be used to determine unknown, determinate structure can be analyzed using equilibrium equations, indeterminate structure cant be solved using equilibrium equations, determining unknown reactions will require relating displacement and slope with loads and reactions and 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

Figure 2

Figure 3


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