Transcript ADVANCED STEEL DESIGN - Civil and Environmental

CIEG 301:
Structural Analysis
Loads, conclusion
Teaching Assistants
 Patrick Carson
[email protected]
Wednesday: 2-4pm
 Mike Rakowski
[email protected]
Wednesday: 2-4pm
Seismic Load
 Due to the dynamic nature of the loads,
determining the seismic load is complex
 E = f(Z,W,M,F,I,S)
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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 Map
Load Factors and
Load Combinations
 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
combinations of load that may act
simultaneously:
 Dead load + live load = yes
 Earthquake + wind = no
Building Design Load
Combinations
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1.4D
1.2D + 1.6L + 0.5*max(Lr, S, or R)
1.2D + 1.6*max(Lr, S, or R) + max(0.5L, 0.8W)
1.2D + 1.6W + 0.5L + 0.5*max(Lr, S, or R)
1.2D + 1.0E + 0.5L + 0.2S
0.9D + 1.6W
0.9D + 1.0E
Principle of Superposition
(Section 2-2)
 The total displacement or internal loading
(stress) at a point in a structure subjected to
several external loadings can be determined by
adding together the displacements or internal
loadings (stresses) caused by each of the
external loadings acting separately
 This requires that there is a linear relationship
between load, stress, and displacement
 Hooke’s Law
 Small displacements
CIEG 301:
Structural Analysis
Determinancy and Stability
8/31/2006
Corresponding Reading
 Chapter 2
Stability and
Determinancy
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In order to be able to analyze a
structure:
1. It must be “stable”
2. We must know its degree of determinancy
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“Statically determinant” structures can be
analyzed using statics
“Statically indeterminant” structures must be
analyzed using other methods
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For statically indeterminant, we also need to know the
“degree of indeterminancy”
Review of Supports
 Roller
 Displacement restrained in one direction
 Reaction force in one direction, perpendicular to the
surface
 Pin
 Displacement restrained in all directions
 Reaction forces in two directions perpendicular to one
another
Fy
F
F
Fx
x’
y’
 Fixed Support
 Displacement and rotation restrained in all directions
 Reaction moment AND reaction forces in two directions
perpendicular to one another
 See Table 2-1
Stable Structures?
 Are the following structures stable?
Criteria For Stable Structures:
Single Rigid Structure
 At least three support restraints
 Equations of equilibrium can be satisfied
for every member
 Three support restraints that are not
equivalent to a parallel or concurrent
force system
Criteria For Stable Structures:
Structures composed of
Multiple Rigid bodies
 Hinges can result in a
structure being
composed of multiple
rigid bodies
 Each force released by
a hinge, increases the
number of equations of
equilibrium that must
be solved
 Stable structure?
Stability Conditions
 Need to know the relationship between 2 quantities in
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  Structure is unstable
 r > 3n  Structure is stable - provided none of the
restraints form a parallel or concurrent constraint
system
Statical Determinacy
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We will begin the semester analyzing structures that are statically
determinant
What does this mean?
 The forces in the members can be determined using the equations of
equilibrium
Equations of (2D) Equilbrium:
 SFx = 0
 SFx = 0
 SM = 0
For a 2D structure, the maximum number of unknowns for a statically
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
Using Statics
 1. Statically determinant
 Internal vs. External determinancy
 2. Rigid  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 Indeterminancy:
Conclusion
 Assuming no concurrent / parallel constraints, need to
know the relationship between 2 quantities in order to
determine if a structure is stable and determinant:
 Number of reactions (r)
 Number of Equations of Equilibrium (EOE)
 EOE = 3n
 r < 3n  Structure is unstable
 r = 3n  Structure is stable and determinant
 can use statics to solve
 Unless forces form a parallel or concurrent system
 r > 3n  Structure is stable and indeterminant
 Degree of indeterminancy is R – (3n)
Classifying Structures:
Examples
Solving for Forces:
Review of Statics
 Idealizing structures
 Free body diagrams
 Review of statics