1. CIEG 301: Structural Analysis
Loads, conclusion

2. Teaching Assistants Patrick Carson pdcarson@udel.edu Wednesday: 2-4pm
Mike Rakowski
Wednesday: 2-4pm

3. Seismic Load
Due to the dynamic nature of the loads, determining the seismic load is complex
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

4. Seismicity Map

5. 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

6. Building Design Load Combinations
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

7. 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

8. CIEG 301: Structural Analysis
Determinancy and Stability
8/31/2006

9. Corresponding Reading
Chapter 2

10. Stability and Determinancy
In order to be able to analyze a structure:
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”

11. 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
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 Fx Fy
Fy ’
Fx ’

12. Stable Structures? Are the following structures stable?
First discuss what different support symbols mean.

13. 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

14. 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?

15. 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

16. Statical Determinacy
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
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

17. 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

18. 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)

19. Classifying Structures: Examples

20. Solving for Forces: Review of Statics
Idealizing structures
Free body diagrams
Review of statics