1.The number of independent equations to be satisfied for the static equilibrium of plane structuresa) 1b) 2c) 3d) 4

Break Down the Problem

1. Identify the Concept: To understand how many independent equations are needed for static equilibrium in plane structures.
2. Types of Equilibrium: In static equilibrium, the sum of all forces and moments must equal zero.

Relevant Concepts

1. Equations for Equilibrium: In two-dimensional structures, the conditions for static equilibrium require:
   • The sum of horizontal forces must be zero ($\Sigma F_x = 0$)
   • The sum of vertical forces must be zero ($\Sigma F_y = 0$)
   • The sum of moments about any point must be zero ($\Sigma M = 0$)

Analysis and Detail

1. Equations Required: For a planar structure, three independent equations arise from the above conditions:
   • One for horizontal forces
   • One for vertical forces
   • One for moments

Verify and Summarize

1. Conclusion: We determined that for a plane structure to be in static equilibrium, three independent equations must be satisfied.

Final Answer

The number of independent equations to be satisfied for the static equilibrium of plane structures is 3 (Option c).