CE 152 Chapter 1

26問 • 2年前

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the support reactions and internal forces can be determined from the equations of equilibrium (including equations of condition, if any)

Statically Determinate Structures

➢ have more support reactions and/or members than required for static stability ➢ the equilibrium equations alone are not sufficient for determining the reactions and internal forces, and must be supplemented by additional relationships based on the geometry of deformation of structures➢ have more support reactions and/or members than required for static stability ➢ the equilibrium equations alone are not sufficient for determining the reactions and internal forces, and must be supplemented by additional relationships based on the geometry of deformation of structures

Statically Indeterminate Structures

additional relationships needed in the analysis of indeterminate structures that ensure that continuity of the displacements is maintained throughout the structure and that the structure’s various parts fit together

Compatibility Conditions

Advantages Of Indeterminate Structure

smaller stresses, greater stiffness, redundanatics

statically indeterminate structures have the capacity for redistributing loads when certain structural portions become overstressed or collapse in cases of overloads due to earthquakes, tornadoes, impact, and other such events

Redundancies

support settlements do not cause any stresses in determinate structures; they may induce significant stresses in indeterminate structures

Stress Due To Support Settlements

these effects do not cause stresses in determinate structures but may induce significant stresses in indeterminate structures

Stress Due To Temperature Changes And Fabrication Errors

structure that maintains its shape and remains a rigid body when detached from the supports

Internally Stable (or rigid)

structure that can't maintain its shape and may undergo displacements under small disturbances when not supported externally

Internally Unstable

supported by exactly three reactions *examples of externally statically determinate plane structuressupported by exactly three reactions *examples of externally statically determinate plane structures

Statically Determinate Externally

supported by more than three reactions •the reactions can't be determined from the three equations of equilibrium

Statically Indeterminate Externally

excess reactions necessary for equilibrium

External Redundants

the number of external redundants

Degree Of External Indeterminacy

if a structure is supported by fewer than three support reactions the reactions are not sufficient to prevent all possible movements of the structure in its plane example of statically unstable externally plane structure

Statically Unstable Externally

• unstable due to improper arrangement of supports "by inspection"

Geometrically Unstable Externally

If the number of unknowns (m + r) is equal to the number of equilibrium equations (2j) - that is, m + r = 2j- all the unknowns can be determined by solving the equations of equilibrium, and the truss isIf the number of unknowns (m + r) is equal to the number of equilibrium equations (2j) - that is, m + r = 2j- all the unknowns can be determined by solving the equations of equilibrium, and the truss is

Statically Determinate

If there are more unknowns (m + r) than the available equilibrium equations (2j) - that is, m +r> 2j- all the unknowns cannot be determined by solving the available equations of equilibrium, the truss is calledIf there are more unknowns (m + r) than the available equilibrium equations (2j) - that is, m +r> 2j- all the unknowns cannot be determined by solving the available equations of equilibrium, the truss is called

Statically Indeterminate

If the number of unknowns (m + r) is less than the number of equations of joint equilibrium (2j) - that is, m + r < 2j - the truss is called

Statically Unstable

The excess members and reactions are called

Redundants

the number of excess members and reactions is referred to as the

Degree Of Static Indeterminacy

used for determinate and indeterminate structures

Fundamental Relationship

relate the forces acting on the structure (or its parts), ensuring that the entire structure as well as its parts remain in equilibrium

Equilibrium Equations

relate the displacements of the structure so that its various parts fit together

Compatibility Conditions

involve the material and cross-sectional properties (E, 1, and A) of the members, provide the necessary link between the forces and displacements of the structure

Member-Force Deformation Relations

• generally convenient for analyzing small structures with a few redundants (i.e., fewer excess members and/or reactions than required for static stability) • used to derive the member force-deformation relations needed to develop the displacement methods

Force Methods

more systematic, can be easily implemented on computers, and are preferred for the analysis of large and highly redundant structures

Displacement Methods

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Lance Margaux Sampayan · 50問 · 2年前

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