ACI 301 Specifications for Structural Concrete November 1 ...
CIEG 301: Structural Analysis
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Transcript of CIEG 301: Structural Analysis
CIEG 301:CIEG 301:Structural AnalysisStructural AnalysisLoads, conclusionLoads, conclusion
Teaching AssistantsTeaching Assistants Patrick CarsonPatrick [email protected]@udel.eduWednesday: 2-4pmWednesday: 2-4pm
Mike RakowskiMike [email protected]@udel.eduWednesday: 2-4pmWednesday: 2-4pm
Seismic LoadSeismic Load Due to the dynamic nature of the loads, Due to the dynamic nature of the loads,
determining the seismic load is complexdetermining the seismic load is complex E = f(Z,W,M,F,I,S) E = f(Z,W,M,F,I,S)
Z = location / seismic Zone W = Weight of the structure M = primary structural Material F = Framing and geometry of the structure I = Importance of the structure S = Soil properties
Seismicity MapSeismicity Map
Load Factors and Load Factors and Load CombinationsLoad Combinations
A load factor is:A load factor is: A “safety factor” used to conservatively represent
the uncertainty in load predictions Loads with more certainty generally have lower load
factors Load combinations account for various Load combinations account for various
combinations of load that may act combinations of load that may act simultaneously:simultaneously: Dead load + live load = yes Earthquake + wind = no
Building Design Load Building Design Load CombinationsCombinations
1.4D1.4D 1.2D + 1.6L + 0.5*max(L1.2D + 1.6L + 0.5*max(Lrr, S, or R), S, or R) 1.2D + 1.6*max(L1.2D + 1.6*max(Lrr, S, or R) + max(0.5L, 0.8W), S, or R) + max(0.5L, 0.8W) 1.2D + 1.6W + 0.5L + 0.5*max(L1.2D + 1.6W + 0.5L + 0.5*max(Lrr, S, or R), S, or R) 1.2D + 1.0E + 0.5L + 0.2S1.2D + 1.0E + 0.5L + 0.2S 0.9D 0.9D ++ 1.6W 1.6W 0.9D 0.9D ++ 1.0E 1.0E
Principle of SuperpositionPrinciple of Superposition(Section 2-2)(Section 2-2)
The total displacement or internal loading The total displacement or internal loading (stress) at a point in a structure subjected to (stress) at a point in a structure subjected to several external loadings can be determined by several external loadings can be determined by adding together the displacements or internal adding together the displacements or internal loadings (stresses) caused by each of the loadings (stresses) caused by each of the external loadings acting separatelyexternal loadings acting separately
This requires that there is a This requires that there is a linearlinear relationship relationship between load, stress, and displacementbetween load, stress, and displacement Hooke’s Law Small displacements
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CIEG 301:CIEG 301:Structural Structural AnalysisAnalysisDeterminancy and StabilityDeterminancy and Stability
Corresponding ReadingCorresponding Reading Chapter 2Chapter 2
Stability and Stability and DeterminancyDeterminancy
In order to be able to analyze a In order to be able to analyze a structure:structure:
1. It must be “stable”2. We must know its degree of determinancy
“Statically determinant” structures can be analyzed using statics
“Statically indeterminant” structures must be analyzed using other methods For statically indeterminant, we also need to know the
“degree of indeterminancy”
Review of SupportsReview of Supports RollerRoller
Displacement restrained in one direction Reaction force in one direction, perpendicular to the surface
PinPin Displacement restrained in all directions Reaction forces in two directions perpendicular to one another
Fixed SupportFixed Support Displacement and rotation restrained in all directions Reaction moment AND reaction forces in two directions
perpendicular to one another See Table 2-1See Table 2-1
FxFy Fy ’
Fx ’
Stable Structures?Stable Structures? Are the following structures stable?Are the following structures stable?
Criteria For Stable Structures:Criteria For Stable Structures:Single Rigid StructureSingle Rigid Structure
At least three support restraintsAt least three support restraints Equations of equilibrium can be satisfied Equations of equilibrium can be satisfied
for every memberfor every member Three support restraints that are not Three support restraints that are not
equivalent to a parallel or concurrent equivalent to a parallel or concurrent force systemforce system
Criteria For Stable Structures:Criteria For Stable Structures:Structures composed of Structures composed of Multiple Rigid bodiesMultiple Rigid bodies
Hinges can result in a Hinges can result in a structure being structure being composed of multiple composed of multiple rigid bodiesrigid bodies
Each force released by Each force released by a hinge, increases the a hinge, increases the number of equations of number of equations of equilibrium that must equilibrium that must be solvedbe solved
Stable structure?Stable structure?
Stability ConditionsStability Conditions Need to know the relationship between 2 quantities in Need to know the relationship between 2 quantities in
order to determine if a structure is stable order to determine if a structure is stable Number of reactions = r Number of Equations of Equilibrium (EOE)
EOE = 3n Where n = number of “parts” Hinges may subdivide structure into multiple parts
r < 3n r < 3n Structure is unstable Structure is unstable r r >> 3n 3n Structure is stable - provided none of the Structure is stable - provided none of the
restraints form a parallel or concurrent constraint restraints form a parallel or concurrent constraint systemsystem
Statical Determinacy Statical Determinacy We will begin the semester analyzing structures that are statically determinantWe will begin the semester analyzing structures that are statically determinant What does this mean? What does this mean?
The forces in the members can be determined using the equations of equilibrium
Equations of (2D) Equilbrium:Equations of (2D) Equilbrium: Fx = 0 Fx = 0 M = 0
For a 2D structure, the maximum number of unknowns for a statically For a 2D structure, the maximum number of unknowns for a statically determinate structure is:determinate structure is: 3n
n = number of “parts” in the structure Hinges subdivide the structure into multiple parts
r = 3n + C Statically determinant r > 3n + C Statically indeterminant Degree of indeterminancy = r – 3n
Two Requirements for Two Requirements for Using StaticsUsing Statics
1. Statically determinant1. Statically determinant Internal vs. External determinancy
2. Rigid 2. Rigid Stable Stable Do not change shape when loaded Displacements are small
Analyses are based on the original dimensions of the structure
Collapse is prevented
Stability and Stability and Indeterminancy: ConclusionIndeterminancy: Conclusion
Assuming no concurrent / parallel constraints, need to Assuming no concurrent / parallel constraints, need to know the relationship between 2 quantities in order to know the relationship between 2 quantities in order to determine if a structure is stable and determinant:determine if a structure is stable and determinant:
Number of reactions (r)Number of reactions (r) Number of Equations of Equilibrium (EOE)Number of Equations of Equilibrium (EOE)
EOE = 3n r < 3n r < 3n Structure is unstable Structure is unstable r = 3n r = 3n Structure is stable and determinant Structure is stable and determinant
can use statics to solve Unless forces form a parallel or concurrent system
r > 3n r > 3n Structure is stable and indeterminant Structure is stable and indeterminant Degree of indeterminancy is R – (3n)
Classifying Structures:Classifying Structures:ExamplesExamples
Solving for Forces:Solving for Forces:Review of StaticsReview of Statics
Idealizing structuresIdealizing structures Free body diagramsFree body diagrams Review of staticsReview of statics