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CivilStructural Mechanics-II
PrevNext

How many fundamental equation of statics?

A

2

B

3

C

1

D

4

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleCivilStructural Mechanics-II
Option B

3

Quick Summary:

InтВВD 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.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

InтВВD 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.

ЁЯФв Key Formulas

тИСFx=0\sum F_x = 0тИСFxтАЛ=0 тАФ Sum of horizontal force components must be zero

тИСFy=0\sum F_y = 0тИСFyтАЛ=0 тАФ Sum of vertical force components must be zero

тИСMO=0\sum M_O = 0тИСMOтАЛ=0 тАФ Sum of moments about any point O must be zero

тЪЩя╕П Working Principle

For a system to be in static equilibrium, the vector sum of all forces must be zero, which resolves into two component equations (тИСFx=0\sum F_x = 0тИСFxтАЛ=0, тИСFy=0\sum F_y = 0тИСFyтАЛ=0), and the algebraic sum of moments about any point must be zero (тИСM=0\sum M = 0тИСM=0) ┬╖ These three equations allow for the solution of up to three unknown reaction forces or moments in a determinate planar structure.

ЁЯУМ Key Points
  • тЦ╕

    The three equations are sufficient to determine support reactions for statically determinate planar structures.

  • тЦ╕

    If the number of unknown reactions exceeds three, the structure is statically indeterminate.

  • тЦ╕

    InтВГD space, the fundamental equations of statics increase to six (three force equations and three moment equations).

тЬЕ Advantages
  • тЦ╕

    Provides a systematic method to analyze support reactions.

  • тЦ╕

    Formulates the basis for structural stability analysis.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Not directly sufficient for indeterminate structures without deformation compatibility conditions.

  • тЦ╕

    Assumes rigid body behavior which may be an approximation for flexible structures.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Calculation of reactions in beams and trusses.

  • тЦ╕

    Design of foundation and structural connections.

ЁЯУД Additional Information
  • тЦ╕

    The 3 equations are specific to 2D coplanar force systems.

  • тЦ╕

    Option B (3) is correct because it covers the two force summations and one moment summation required for planar balance.

ЁЯУК Diagram / Illustration
Equations of Static EquilibriumтИС FтВУ = 0 (Translational Equilibrium X)тИС F_y = 0 (Translational Equilibrium Y)тИС M_z = 0 (Rotational Equilibrium)
тЬЕ

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.

Core Concepts Used
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Static Equilibrium Free Body Diagram Determinate Structures
ЁЯТб EXAM TIP

Always verify if the structure is determinate by comparing the number of unknowns to the number of available equilibrium equations (333 in 2D; 666 in 3D).

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