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What exactly does a web member with zero force in a triangular truss do?
The web member (zero member) in the triangular truss plays a supporting role. Without zero reinforcement, the hypotenuse of triangular truss is prone to deflection and instability under load, and the existence of zero reinforcement can greatly reduce the deflection of upper and lower chords, thus ensuring the stiffness of the structure.

Under the condition that the stress mentioned by your teacher is not ideal, if the force can't only act on the center of the structure, then the external force will produce a moment for the whole structure, so many members including the zero bar will produce internal forces, and even many members without bending will bend. At this time, the zero bar will play a role in resisting external force deviation and ensuring the relative stability of the structure. It is equivalent to zero bar blocking external force inside the structure.

Of course, the zero pole is not omnipotent, it does not resist the side. Therefore, the actual structure is not a plane structure, but a spatial structure is more stable. Members bear external forces to ensure the stability of the structure in all directions.