Procedure for Developing Influence Line Diagram
Influence line
diagram
(ILD) can be developed by the following ways;
(a)
by independently applying a
unit load at several positions on the structure and determining the
structural response (reaction, shear, moment etc.) by applying the
principles of statics. Tabulate these values and then plot the graph of
load position(along x-axis) vs the structural response (along
y-axis).
(b)
write the equation for
structural response due to a unit load at a distance 'x' by applying
the principles of statics.
(c) Muller-Breslau Principle
which gives qualitative influence lines.
To explain the procedure of developing influence line we consider a beam of span L and apply a unit load at a distance x from the support A as shown in figure 1.
Influence line for Reaction
Calculating the reaction at
supports we get;
RB = x/L
(straight line equation)
RA = 1- x/L
(straight line equation)
The influence line diagrams for RB is plotted in figure 1(a) which shows that the value of RB is x/L when the unit load is at a distance x from A and it would be equal to 1 when the unit load will be at B.
Similarly the ILD for RA plotted in figure 1 (b) shows that the value of RA will be 1 when unit load is at A and it would be equal to 1-x/L when the unit load is at a distance x from support A.
Influence line for Shear Force at a section
FC = -RB
= - x/L ;when load is
between A and C
FC = RA
= 1- x/L ;when the
load is between C and B
Influence line for Bending Moment at a section
MC = RB
. (L-a) ;
when unit load is between A and C.
MC = RA
.(a) ; when
unit load is between C and B.
MC = a (L - a) / L ;when unit load is at C.
The ILD for MC plotted in figure 1(d) clearly indicates these values.
It is evident from the above equations and their plot that influence line diagram is a straight line in all the cases.
Please watch our following video lectures about moving load analysis
Video Lecture on Analysis of Moving Loads
This video lecture is about developing influence line diagram for shear force and bending moment to do analysis of structures in case of moving loads.
Video Lecture on Maximum Shear Force at a section due to a series of moving loads
This video lecture explains the trial and error procedure for determining the value of maximum shear force at a section due to a series of moving loads. It includes a solved example also.
Video Lecture on Maximum Bending Moment at a given section due to a series of moving loads
This video lecture is about determining maximum bending moment at a given section and the absolute maximum bending moment due to a series of moving loads on a simple beam
Applications of Influence Line Diagram
You can also use the following calculators for Moving Load Analysis
Calculator for Moving Load Analysis for Maximum B.M. at a section of simple beam
Calculator for Absolute Maximum B.M. due to moving loads for simple beam
Stress Transformation Calculator
Calculate Principal Stress, Maximum shear stress and the their planes
Calculator for Moving Load Analysis
To determine Absolute Max. B.M. due to moving loads.
Bending Moment Calculator
Calculate bending moment & shear force for simply supported beam
Moment of Inertia Calculator
Calculate moment of inertia of plane sections e.g. channel, angle, tee etc.
Reinforced Concrete Calculator
Calculate the strength of Reinforced concrete beam
Moment Distribution Calculator
Solving indeterminate beams
Deflection & Slope Calculator
Calculate deflection and slope of simply supported beam for many load cases
Fixed Beam Calculator
Calculation tool for beanding moment and shear force for Fixed Beam for many load cases
BM & SF Calculator for Cantilever
Calculate SF & BM for Cantilever
Deflection & Slope Calculator for Cantilever
For many load cases of Cantilever
Overhanging beam calculator
For SF & BM of many load cases of overhanging beam
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Test your knowledge on different topics of Civil Engineering
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