1 / 20

CIEG 301: Structural Analysis

CIEG 301: Structural Analysis. Loads, conclusion. Patrick Carson pdcarson@udel.edu Wednesday: 2-4pm. Mike Rakowski rak@udel.edu Wednesday: 2-4pm. Teaching Assistants. Seismic Load. Due to the dynamic nature of the loads, determining the seismic load is complex E = f(Z,W,M,F,I,S)

huyen
Download Presentation

CIEG 301: Structural Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related