**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
at a support**

Calculating the reaction at
supports we get;

R_{B} = x/L
(straight line equation)

R_{A} = 1- x/L
(straight line equation)

The influence line diagrams for
R_{B}
is plotted in figure 1(a) which shows that the value of
R_{B} 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
R_{A } plotted
in figure 1 (b) shows that the value of
R_{A }
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**

F_{C} = -R_{B}
= - x/L ;when load is
between A and C

F_{C} = R_{A}
= 1- x/L ;when the
load is between C and B

_{C}
plotted in figure 1(c) clearly indicates the above values. Maximum
positive or negative shear force will occur at C when the load is
placed at C.

**
Influence line for Bending Moment at a section**

M_{C} = R_{B}
. (L-a) ;
when unit load is between A and C.

M_{C} = R_{A}
.(a) ; when
unit load is between C and B.

M_{C} = a (L - a) /
L
;when unit load is at C.

The ILD for
M_{C}
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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