displacement methods of analysis

Displacement Methods of Analysis

Detailed overview of Displacement Methods of Analysis.

Slope-Deflection Equations

Deflection is the displacement of a structural element under load. Common methods to calculate deflection:

1. Double Integration Method
2. Moment-Area Method
3. Conjugate Beam Method
4. Virtual Work Method

The fundamental equation for beam deflection is: $\frac{d^2y}{dx^2} = \frac{M(x)}{EI}$

Moment Distribution Method (Hardy Cross)

The Moment Distribution Method is an iterative procedure for analyzing indeterminate beams and frames. Key concepts:

• Stiffness Factor ($k$): $4EI/L$ for far end fixed.
• Distribution Factor ($DF$): $k / \sum k$.
• Carry-Over Factor ($COF$): Typically $0.5$.

Analysis of Frames with and without Sidesway

Explanation of Analysis of Frames with and without Sidesway. This section covers the fundamental principles and applications of Analysis of Frames with and without Sidesway in structural analysis.