6.2 Influence lines for beams and trusses

Influence lines are powerful tools for analyzing beams and trusses under moving loads. They show how forces, moments, and reactions change as loads move across structures. This concept is crucial for designing bridges, cranes, and other structures that experience dynamic loading.

For beams, influence lines help find critical load positions and maximum effects. In trusses, they reveal how member forces change with load position. Understanding influence lines is key to optimizing structural designs and ensuring safety under various loading conditions.

Beam Influence Lines

Types of Beams and Their Influence Lines

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  Moment diagrams for continuous beams - All this View original

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• Simply supported beam influence lines exhibit triangular shapes for reactions and bending moments
  • Maximum ordinate occurs at the point of interest
  • Slopes linearly to zero at supports
• Cantilever beam influence lines differ from simply supported beams due to fixed end
  • Reaction influence line at fixed support remains constant
  • Free end experiences larger deflections and moment values
• Continuous beam influence lines involve multiple spans
  • Require consideration of moment redistribution
  • Exhibit more complex patterns due to interaction between spans

Force and Moment Influence Lines

• Shear force influence line represents variation of shear at a specific point
  • Consists of straight line segments
  • Discontinuities occur at point loads or support locations
• Bending moment influence line illustrates changes in bending moment
  • Typically composed of curved segments (parabolic shapes)
  • Maximum ordinate corresponds to location of interest
• Reaction influence line shows how support reactions change
  • Linear for simple beams
  • Can be more complex for statically indeterminate structures

Applications and Analysis Techniques

• Müller-Breslau principle facilitates influence line construction
  • Involves applying a unit displacement at the point of interest
  • Resulting deformed shape represents the influence line
• Moving load analysis utilizes influence lines
  • Determines critical load positions for maximum effects
  • Aids in design of bridges and other structures subject to moving loads
• Influence lines help identify most unfavorable load positions
  • Essential for determining maximum positive and negative effects
  • Crucial in structural design and analysis processes

Truss Influence Lines

Truss Member Forces and Their Influence Lines

• Truss member forces depend on overall truss configuration
  • Top chord members typically experience compression
  • Bottom chord members usually under tension
  • Web members can be in tension or compression based on location and loading
• Axial force influence line represents variation of axial force in a specific member
  • Shows effect of a unit load moving across the truss
  • Helps identify critical load positions for maximum member forces

Constructing and Interpreting Truss Influence Lines

• Method of sections often used to determine member forces
  • Involves cutting the truss at the member of interest
  • Applies equilibrium equations to solve for member force
• Influence line construction for trusses follows similar principles as beams
  • Apply unit load at each joint and solve for member force
  • Plot resulting values to create the influence line
• Zero force members in trusses have flat influence lines
  • Indicates the member is not affected by the moving load
  • Important for identifying structurally efficient designs

Applications in Truss Analysis and Design

• Influence lines aid in determining maximum and minimum member forces
  • Critical for sizing truss members and connections
  • Helps in fatigue analysis of truss structures (bridges, cranes)
• Combination of load cases can be analyzed using superposition
  • Multiply influence line ordinates by actual loads
  • Sum effects to determine total member force
• Influence lines assist in optimizing truss designs
  • Identify members with low utilization
  • Guide decisions on member removal or size reduction for efficiency