CIEG 301: Structural Analysis

1. CIEG 301:Structural Analysis Loads, conclusion

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

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 • 1.4D • 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

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

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. Fy Fx ’ Fy ’ Fx 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

12. Stable Structures? • Are the following structures stable?

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 • 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