User:Gaskins1/Influence line notes

My Influence Line Article

Hibbeler
Chapter 6: Influence lines for statically determinate structures Two Procedures: (1) tabulate values; (2) IL equations example 6.1; 6.3; 6.5

P. 221: Loadings: concentrated => "the value of the function can be found by multiplying the ordinate of the influence line at the position x by the magnitude of F" distributed => "the value of the function caused by a uniform distributed load is simply the area under the influence line for the function multiplied by the intensity of the uniform load"

[rewrite one of the previous examples with a distributed load?]

6-3 onward

IAState
" An influence line for a given function, such as a reaction, axial force, shear force, or bending moment, is a graph that shows the variation of that function at any given point on a structure due to the application of a unit load at any point on the structure.

''An influence line for a function differs from a shear, axial, or bending moment diagram. Influence lines can be generated by independently applying a unit load at several points on a structure and determining the value of the function due to this load, i.e. shear, axial, and moment at the desired location. The calculated values for each function are then plotted where the load was applied and then connected together to generate the influence line for the function.''" {introduction}

"There are two methods that can be used to plot an influence line for any function. In the first, the approach described above, is to write an equation for the function being determined, e.g., the equation for the shear, moment, or axial force induced at a point due to the application of a unit load at any other location on the structure. The second approach, which uses the Müller Breslau Principle, can be utilized to draw qualitative influence lines, which are directly proportional to the actual influence line."

Provides examples for:
 * Influence lines for a simple beam by developing the equations
 * Qualitative influence lines using the Müller Breslau Principle
 * Qualitative influence lines for a statically determinate continuous beam
 * Calculation of maximum and minimum shear force and moments on a statically determinate continuous beam
 * Qualitative influence lines and loading patterns for a multi-span indeterminate beam
 * Qualitative influence lines and loading patterns for an indeterminate frame

The Constructor
Overlaying multiple ILs on one diagram can demonstrate the relationship of reactions at supports.

shows examples

Online Freee Books
Module 7 Influence Lines
 * Lesson 37 Moving Load and Its Effects on Structural Members
 * Lesson 38 Influence Lines for Beams
 * Lesson 39 Influence Lines for Beams (Contd.)
 * Lesson 40 Influence Lines for Simple Trusses

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