CC601: STRUCTURAL ANALYSIS 2
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CHAPTER 4:
INFLUENCE LINE OF DETERMINATE BEAM AND FRAMEWORK
Objective:
1. To Sketch diagram of influence line for reactions, shear force and moment for:
a. Simply supported beam
b. Simply supported beam with one end overhanging
c. Simply supported beam with both ends overhanging.
2. To calculate shear force and moment using influence line
3. To determine maximum shear force and moment
4. Calculate Absolute Maximum Moment (MMM)
4.1 INTRODUCTIONS:
Influence line is to:
 Analysis a structure due to moving load along the beam.
 Show the changes in reaction, shear stress, moment and displacement in certain point in
structure when applied a unit load.
 Determine the greatest position the greatest value of live load in beam.
4.2 DIFFERENCES BETWEEN INFLUENCE LINE DIAGRAM (ILD) AND BMD (BENDING
MOMENT DIAGRAM)
INFLUENCE LINE DIAGRAM
(ILD)
a) Static and Moving Load
b) Diagrams show only one point on the beam.
c) Calculations based on the virtual load.
d) Straight line only
e) Calculations do not refer to reactions of
beam.
f) Unit: m
a)
b)
c)
d)
e)
BENDING MOMENT DIAGRAM
(BMD)
Static load only.
Diagram shows the moment at all
points on the beam.
Calculations based on real loads.
Straight lines and curves.
Calculations based on the SFD.
f) Unit : kNm
CC601: STRUCTURAL ANALYSIS 2
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4.3 BASIC CONCEPT TO DRAW INFLUENCE LINE DIAGRAM (ILD)
1 unit
x
A
B
a
C
b
RAY = [L-x]/L 1-x/L
RCY=x/L
4.3.1 REACTION
ILD RAY
L/L
b/L
[+]
0
ILD RCY
L/L
a/L
0
[+]
4.3.2 SHEAR FORCE OF BEAM
ILD Vc
b/L
[+]
[-]
a/L
4.3.3 BENDING MOMENT OF BEAM
ILD Mc
0
[+]
ab/L
0
CC601: STRUCTURAL ANALYSIS 2
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EXAMPLE 1: SIMPLY SUPPORTED BEAM
Draw Influence Line Diagram for reaction at A and B, Shear force and bending moment
for the beam.
1 unit
x
A
C
B
7.5m
RAY
= [L-x]/L
=1-x/L
2.5m
10m
RBY=x/L
CC601: STRUCTURAL ANALYSIS 2
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EXAMPLE 2: SIMPLY SUPPORTED BEAM WITH ONE END OVERHANGGING
Draw Influence Line Diagram for reaction at A and B, Shear force and bending moment
for the beam.
1 unit
x
A
C
B
D
2m
RAY
5m
7m
3m
RBY
CC601: STRUCTURAL ANALYSIS 2
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EXAMPLE 3: SIMPLY SUPPORTED BEAM WITH BOTH END OVERHANGGING
Draw Influence Line Diagram for reaction at B and D, Shear force and bending moment
for the beam.
1 unit
x
A
B
C
D
E
5m
8m
RBY
3m
11m
6m
RDY
CC601: STRUCTURAL ANALYSIS 2
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4.4 TO DETERMINE REACTION, SHEAR FORCE AND BENDING MOMENT DUE TO
POINT LOAD AND UNIFORMLY DISTRIBUTION LOAD.
Basic Concept:
1. Due to Point load
2. Due to UDL
Rn, Vn, and Mc = ∑ PnYn where Pn
Yn
Rn, Vn, and Mc = ∑ Wn An where Wn
An
Pn kN
A
= Point load
= Odinit Y
= UDL load
= Area of section
B Wn Kn/m C
a
b
RA =[L-x]/L
RC=x/L
4.4.1 REACTION
ILD RAY
L/L
b/L
RA=+PnY1 + WnAn
= PnY1 + Wn [1/2 xbxY2]
[+]
0
Y1
Y2
ILD RCY
Y3=L/L
Y2=a/L
[+]
Rc= PnY1 + WnAn
= PnY1 + Wn [1/2{ Y2+Y3}xb]
0
Y1
4.4.2 SHEAR FORCE OF BEAM
Y2
ILD Vc
Y3
Y3=b/L
[+]
Vc= -PnY1 + WnAn
= -PnY1 + Wn [1/2 xbxY3]
[-]
Y1
Y2=a/L
4.4.3 BENDING MOMENT OF BEAM
ILD Mc
0
Y1
Y2
0
Mc=PnY1 + WnAn
= PnY1 + Wn[1/2 x Y2 x b]
CC601: STRUCTURAL ANALYSIS 2
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Determine Reaction at A, Shear Force, and Bending Moment for beam.
Example 1:
30kN
25kN/m
A
B
3m
Example 2
C
4m
D
5m
CC601: STRUCTURAL ANALYSIS 2
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ABSOLUTE MAXIMUM MOMENT (AMM)
Definition:
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
Example
Using the influence line diagram, determine Absolute Maximum Moment (AMM) for this simply supported
Beam if a series of point load moving from A to B.
10N 10N 20N
1m
1
20N
1m 2m
2
10N
3m
3
4
A
5
B
50m
SOLUTION:
10N 10N 20N
1m
1
1.
20N
1m 2m
2
10N 10N
3m
3
4
20N
4m
5
20N
2m
6
3m
7
8
Determine total load,
 Load, R
=
P1+P2+P3+…………..Pn
Rx
=
=
=
P2X1+ P3X2+ P4X3+ P5X4+…………………………… Pn+1Xn
=
=
=
____m
_________= ______m
_________= ______m
X
So,
a
b
c
b< c, x =
_______ (so, R locate between load __ & __ )
L/2 + b/2
10N
4m
20N
2m
6
20N
3m
7
8