CIEG 301:CIEG 301:Structural AnalysisStructural Analysis

Loads, conclusionLoads, conclusion

Teaching AssistantsTeaching Assistants

Patrick CarsonPatrick Carson

pdcarson@udel.edupdcarson@udel.edu

Wednesday: 2-4pmWednesday: 2-4pm

Mike RakowskiMike Rakowski

rak@udel.edurak@udel.edu

Wednesday: 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

8/31/20068/31/2006

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 We will begin the semester analyzing structures that are statically determinantdeterminant

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