This document discusses influence lines for beams. Influence lines graphically show how a unit load moving across a structure affects structural responses like reactions, shears, moments, and deflections. The ordinates of an influence line diagram represent the magnitude and type of a structural response when a unit load is at that point. Influence lines are useful for analyzing the effects of moving loads on structures. They can be used to determine locations of loads that cause maximum structural responses, which can then be calculated. The document also provides properties of influence lines and discusses how to qualitatively and quantitatively draw them for beams.

1. INFLUENCE
LINE
For beams

2. INFLUENCE LINE FOR BEAMS
Influence line shows graphically how the of a unit
load across a structure influences some functions
such as reactions, shears, moments, forces and
deflections.
Influence line maybe defined as a diagram whose
ordinates show the magnitude and character of
some function of a structure as a unit load moves
across the structure. Each ordinate of the
diagram gives the value of the function when the
load is at that point.

3. Influence diagram is very useful for
moving loads. It is used to determine
where to place the loads to cause
maximum values of a function and then
compute those values
INFLUENCE LINE FOR BEAMS

4. PROPERTIES OF INFLUNCE
LINE
1. The value of a function due to a single
concentrated moving load equals the magnitude
of the load multiplied by the ordinate of the
influence diagram.
h
Influence Diagram

5. PROPERTIES OF INFLUNCE
LINE
2. The value of a function due to several
concentrated moving loads equals the algebraic
sum of the effects of each load described in
property 1
h1
Influence Diagram
h2
h3
P3P2P1

6. PROPERTIES OF INFLUNCE
LINE
3. The value of a function due to a uniformly
distributed load (w N/m) equals the product of w
and the area of the influence line under the
uniform load.
w
Influence Diagram
Area

7. SCOPE
Influence Line Diagram For
REACTION
SHEAR
MOMENT
STATICALLY DETERMINATE BEAMS

11. Drawing the INFLUENCE LINE Manually

13.  Qualitative influence lines – a diagram
showing the general slope of an influence line
without the numerical value of its ordinate.
 Quantitative influence lines – an influence
line with the numerical values of its ordinates
known

14. Reaction Influence Line = Push the beam
1 unit at the point/support where reaction
is studied. Then imagine how the beam
will respond in coordination with the other
supports within that beam.
Drawing the INFLUENCE LINE Qualitatively
Muller – Breslau’s Principle

15. 1
INFLUENCE LINE FOR
REACTION A

16. Draw the Influence line for reaction at B by the
same method earlier

22. PROBLEM SET

23. IMPORTANT NOTES
 IN TERMS OF UNIFORM LOADS, remember
that we have uniform live load and uniform
dead load.

24. Due to UNIFORM LIVE LOAD:
The value of a response function due to a uniformly
distributed live load over a potion of the structure
can be obtained by multiplying the uniform live load
by the area under corresponding portion of the
influence line.
The max positive value of a response function is
equal to the uniform live load multiplied by the area
over those portion of the structure where the
ordinates of the influence line are positive.
The max negative value. . . Opposite of the above
mentioned rule

25. VALUE OF REACTION AT B when UNIFORM LIVE LOAD IS
DISTRIBUTED ALL OVER THE SPANVALUE OF MAXIMUM POSTIVE REACTION. (Value of
maximum compressive reaction at column BG)
The maximum negative value of a response function
(Means – the maximum tensile reaction at column BG)

26. Due to UNIFORM DEAD LOAD:
To obtain the value of a response function due to a
uniform dead load, place the uniform dead load
through out the entire span

27. Due to Combined uniform dead load, uniform
live load and the live concentrated load:
Requires analysis

28.  The influence line for a given structure
function is drawn above. If the structure is
crossed by a distributed load of 30 kN/m with
a length of 6 m, determine the maximum
value of the function.
16 m
146.25
1

29. 12 m
4 m
 The influence line for a given structure
function is drawn above. If the structure is
crossed by a distributed load of 30 kN/m with
a length of 6 m, determine the maximum
value of the function.
-0.75
0.25
-101.25

30. 12 m 4 m