Nelson Bustamante: Basic Concepts of Stability of Structure

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What is stability of concrete structures?

Stability of concrete structures is a crucial concept in structural engineering and has been defined in various ways by different authors and researchers. Generally, it refers to the ability of a structure to recover its equilibrium or resist sudden changes, dislodgment, or overthrow.

A stable structure should remain stable under any conceivable loading conditions, irrespective of the type or location of the load. If a structure cannot meet this criterion, it undergoes geometric deformation, resulting in the loss of its load-resisting capacity and leading to instability. Structural instability can cause catastrophic failures, which must be accounted for during the design phase.

Basic concepts of stability of structure
Fig.1:Basic concepts of stability of structure

Stability criteria

Establishing stability criteria is necessary to determine if a structure is in stable equilibrium under a given set of loads. The following points summarize the key stability conditions:

Stable Equilibrium:

If the structure returns to its original configuration upon releasing from a virtually displaced state, it is in stable equilibrium. Minor perturbations should not cause significant movements like a mechanism; rather, the structure vibrates around its equilibrium position.

Unstable Equilibrium

If the structure does not return to its original state after the release of virtual displacements, it is in unstable equilibrium. Small perturbations cause large movements, preventing the structure from returning to its equilibrium position.

Neutral Equilibrium

In this state, it’s unclear if the structure is in stable or unstable equilibrium. Small perturbations cause large movements, but the structure can be brought back to its original equilibrium position without requiring external work.

Stability concept

The concept of the stability of various forms of equilibrium of a compressed bar is explained by using the equilibrium of a ball as shown below:

Stable equilibrium

A ball displaced from its original equilibrium position returns to that position upon the removal of the disturbing force. The ball is in a state of stable equilibrium.

stable equilibrium
Fig.2:stable equilibrium

Unstable equilibrium

When a disturbing force displaces the ball, it continues moving downward without returning to its original position. This is an unstable equilibrium state.

stable equilibrium
Fig.3:stable equilibrium

Neutral equilibrium

If the ball is displaced, it neither returns to its original position nor continues to move away. Instead, it remains in the new position. There is no change in energy during displacement in a conservative force system.

neutral equilibrium
Fig.4:neutral equilibrium

Buckling vs. Stability 

Buckling, often confused with instability, is a phenomenon that occurs when structures under compressive loads deform:

  • Buckling: It is a sudden deformation that occurs when a structure under compression reaches a critical load (Pcr). After reaching this load, the structure buckles and changes to a deformed state.
  • Post-Buckling Stability: Post-buckling equilibrium can either be stable or unstable. After buckling, the structure typically experiences neutral or unstable equilibrium.
Phases of column buckling
Fig.5:Phases of column buckling

Types of instability 

Concrete structures subjected to compressive forces can undergo various forms of instability:

Bifurcation Buckling

The equilibrium path bifurcates when the load reaches a critical value, leading to sudden deformation.

Symmetric Bifurcation

  • If post-buckling paths are symmetric about the load axis:
    • Stable Symmetric Bifurcation: Load capacity increases after buckling.
    • Unstable Symmetric Bifurcation: Load capacity decreases after buckling.

Stable symmetric bifurcation
Fig.6:Stable symmetric bifurcation

Asymmetric Bifurcation

Post-buckling behavior is asymmetric about the load axis.

Asymmetric bifurcation
Fig.7:Asymmetric bifurcation

Instability failure 

  • Here, no bifurcation of the load-deformation path occurs. Instead:
    • Structure stiffness decreases due to large deformations and/or material inelasticity.
    • Load capacity is reached when stiffness becomes zero.
    • Neutral equilibrium occurs when stiffness is zero, while unstable equilibrium occurs when stiffness is negative.

Failure of Beam-Columns

Instability due to material and geometric nonlinearity
Fig.8:Instability due to material and geometric nonlinearity

Snap-Through Buckling

snap through buckling
Fig.9:snap through buckling

Shell Buckling failure – very sensitive to imperfections

shell buckling failure
Fig.10:shell buckling failure

Summary of Concepts

  • Bifurcation Buckling: Occurs in columns, beams, and symmetric frames under gravity loads.
    • Primary Path: Load-deformation path before buckling.
    • Secondary Path: Load-deformation path after buckling.
    • Critical Buckling Load (Pcr): The load at which the path bifurcates.
  • Elastic Instability: Seen in beam-columns and frames under gravity and lateral loads.
  • Inelastic Instability: Occurs in all members and the frame due to material inelasticity.

Stability analysis is essential in structural engineering to ensure that concrete structures can withstand various loading conditions without catastrophic failure. Understanding the criteria and types of instability, along with the difference between buckling and stability, helps in designing safer structures capable of maintaining equilibrium under different load scenarios.

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