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Which of the following is not a statically determinate beam?
Simply supported beam
Cantilever beam
Continuous beam
Overhanging beam
Continuous beam
A statically determinate structure is one where all reaction forces and internal member forces can be determined using only the equations of static equilibrium ┬╖ A continuous beam, having more than two supports, results in more unknown reaction components than available equilibrium equations, making it statically indeterminate.
A statically determinate structure is one where all reaction forces and internal member forces can be determined using only the equations of static equilibrium ┬╖ A continuous beam, having more than two supports, results in more unknown reaction components than available equilibrium equations, making it statically indeterminate.
DsтАЛ=rтИТ3 тАФ Static indeterminacy degree for planar beams
тИСFxтАЛ=0,тИСFyтАЛ=0,тИСMzтАЛ=0 тАФ Basic equations of static equilibrium
In a planar system, we have three fundamental equilibrium equations: тИСFxтАЛ=0, тИСFyтАЛ=0, and тИСM=0. For a structure with r reaction components, if r>3, the structure is statically indeterminate ┬╖ A continuous beam typically has four or more reaction components (at least three supports), requiring additional compatibility equations like the Theorem of Three Moments or Slope-Deflection method to solve.
A structure is determinate if the number of unknown reactions equals the number of independent equilibrium equations.
Simply supported, cantilever, and overhanging beams are basic statically determinate configurations.
Continuous beams are redundant structures because they have more supports than required for stability.
Degree of static indeterminacy (DsтАЛ) for a continuous beam over n spans is (n+1)тИТ3.
Determinate beams are independent of temperature changes or support settlements for stress calculations.
Easier to analyze manually without computational tools.
Continuous beams (indeterminate) are more structurally efficient and offer better load redistribution.
Failure in one component of a determinate structure leads to total collapse (no redundancy).
Simple residential floor beams.
Temporary bridge structures.
Structural analysis education.
Continuous beams require the Principle of Superposition or methods like Moment Distribution to solve.
Option A, B, and D are statically determinate because their reaction forces can be found using the three basic equilibrium equations.
C is correct тАФ Continuous beam is statically indeterminate because it possesses more reaction supports than the available equations of static equilibrium.
Always check the number of constraints (supports) versus the degrees of freedom; if you can't solve it with just three equilibrium equations, it's statically indeterminate!