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I am confused as to whether the method of joints is only restrained to pin-jointed trusses or it can be applied to other statics problem, for example the one shown in the picture, and why?.

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In case of pin jointed trusses, every member acts as a rod element i.e. they bear either compressive or tensile load(there is no bending moment acting between elements i.e. applied by one element on another).This is because pin joints donot transfer moments.So if other types of joints are used, you have to include the moments acting at the joints while drawing the free body diagrams for the joints.

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It can't be applied to that problem, because the beam from A to the load is one continuous part of the structure.

If it was a pin jointed truss, there would be two separate members, one from A to C and the other from C to the load, and no bending moment would be transferred from one of those members to the other.

If the structure was a pin jointed truss, it would not support the weight at all. The bar between C and the weight would just pivot downwards, rotating about point C.

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