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How many fundamental equation of statics?
2
3
1
4
3
In 2D planar statics, the equilibrium of a rigid body is defined by three fundamental equations. These equations ensure that both the net translational force and the net rotational moment acting on a body are zero.
In 2D planar statics, the equilibrium of a rigid body is defined by three fundamental equations. These equations ensure that both the net translational force and the net rotational moment acting on a body are zero.
тИСFxтАЛ=0 тАФ Sum of horizontal force components must be zero
тИСFyтАЛ=0 тАФ Sum of vertical force components must be zero
тИСMOтАЛ=0 тАФ Sum of moments about any point O must be zero
For a system to be in static equilibrium, the vector sum of all forces must be zero, which resolves into two component equations (тИСFxтАЛ=0, тИСFyтАЛ=0), and the algebraic sum of moments about any point must be zero (тИСM=0). These three equations allow for the solution of up to three unknown reaction forces or moments in a determinate planar structure.
The three equations are sufficient to determine support reactions for statically determinate planar structures.
If the number of unknown reactions exceeds three, the structure is statically indeterminate.
In 3D space, the fundamental equations of statics increase to six (three force equations and three moment equations).
Provides a systematic method to analyze support reactions.
Formulates the basis for structural stability analysis.
Not directly sufficient for indeterminate structures without deformation compatibility conditions.
Assumes rigid body behavior which may be an approximation for flexible structures.
Calculation of reactions in beams and trusses.
Design of foundation and structural connections.
The 3 equations are specific to 2D coplanar force systems.
Option B (3) is correct because it covers the two force summations and one moment summation required for planar balance.
B is correct тАФ There are 3 fundamental equations of statics for a planar system, consisting of two force equilibrium equations and one moment equilibrium equation.
Always verify if the structure is determinate by comparing the number of unknowns to the number of available equilibrium equations (3 in 2D; 6 in 3D).
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