Structural analysis 1 civil engineering bachelor of technology

Static indeterminacy

1. Static Indeterminacy Presented by: Rimjhim Pratihar Roll No: 1580132400 3 Reg. No: 2415801201 42 Subject code-CE(PC)503 Subject: Structural Analysis-1 Department of Civil Engineering Mallabhum Institute of Technology

2. Introduction - Static indeterminacy refers to the degree to which the unknown reactions or internal forces exceed the available equilibrium equations. - Also called static redundancy. - Important in structural analysis and design.

3. Basic Concepts - Equilibrium Equations: - 2D: ΣFx = 0, ΣFy = 0, ΣM = 0 - 3D: 6 equilibrium equations - If the number of unknowns > number of equations, structure is statically indeterminate.

4. Degree of Static Indeterminacy (DSI) - DSI = Unknown reactions - Number of equilibrium equations - For internal and external indeterminacy: - DSI = (r + m) - 3j for planar trusses - DSI = r - 3 for beams and frames

5. Types of Indeterminacy - External Indeterminacy: More support reactions than needed. - Internal Indeterminacy: More members or connections than required for stability.

6. Examples - Simple beam with 3 supports: DSI = 1 - Continuous beam with 2 spans: DSI = 1 - Fixed beam: DSI = 2

7. Importance in Engineering - Redundant structures provide greater stability. - Distribution of loads across multiple paths. - Requires compatibility equations for analysis.

8. Calculation Procedure 1. Identify the type of structure (beam, frame, truss). 2. Count the number of unknown reactions. 3. Apply equilibrium equations. 4. Compute DSI.

9. Advantages and Challenges - Advantages: - Increased safety - Greater load-carrying capacity - Challenges: - Complex analysis - Requires advanced methods like flexibility or stiffness method

10. Conclusion - Static indeterminacy is key to understanding structural behavior. - Knowing DSI helps in choosing the right method of analysis. - Essential for safe and efficient structural design.

11. References - R.C. Hibbeler, "Structural Analysis" - S.S. Bhavikatti, "Structural Analysis Vol. I" - Lecture notes and university syllabus