**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.

**
Applications of Influence Line Diagram**

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