influence lines for determinate structures

Influence Lines for Determinate Structures

Influence lines represent the variation of a reaction, shear, or moment at a specific point as a moving unit load traverses the structure. Useful for:

• Designing for moving loads (bridges).
• Determining maximum effects.

Muller-Breslau Principle: The influence line for a function is the scaled deflected shape of the structure when the function is removed and a unit displacement is introduced.

Moving Loads

Types of loads in structural engineering include:

• Dead Loads: Permanent loads such as the weight of the structure itself.
• Live Loads: Movable loads like people, furniture, and vehicles.
• Wind Loads: Forces exerted by wind, critical for tall structures.
• Earthquake Loads: Seismic forces resulting from ground motion.

The load combination is typically represented as: $U = 1.2D + 1.6L$

Influence Lines for Beams (Reactions, Shear, Moment)

Influence lines represent the variation of a reaction, shear, or moment at a specific point as a moving unit load traverses the structure. Useful for:

• Designing for moving loads (bridges).
• Determining maximum effects.

Muller-Breslau Principle: The influence line for a function is the scaled deflected shape of the structure when the function is removed and a unit displacement is introduced.

Influence Lines for Trusses

Analysis of trusses involves finding the axial forces in members.

• Method of Joints: Solving equilibrium at each joint.
• Method of Sections: Cutting the truss to solve for member forces using equilibrium of the section.

Equilibrium equations: $\sum F_x = 0, \quad \sum F_y = 0$

Absolute Maximum Shear and Moment

Explanation of Absolute Maximum Shear and Moment. This section covers the fundamental principles and applications of Absolute Maximum Shear and Moment in structural analysis.