Which members of the truss are zeroforce members Solutionass

Which members of the truss are zero-force members?

Solution

assuming all members to be weightless.

at the joint E, the only force possible in the vertical direction is due to DE. so the vertical component of force in DE should be zero, because the joint E is at equilibrium. If the vertical component is zero means there is no force in that member; it is a pin jointed member and force will be along the bar and it is an inclined bar. if there is a horizontal component, there will be a vertical component.

EF is a zero force member, because there is no force in x direction at E as discussed before.

at joint D sum of forces along x direction should be zero. Since the DE is a zero force member, CD should also be a zero force member

DF should also be a zero force member because at D both others are zero force members and there will be no member to offer reaction force.

CF will have some force since it will have to compensate the vertical 10KN. and all other members will havesome force from there onwards. the values of force will depend on the lengths of the members.

so the zero force members are CD, DE, DF, and FE