Influence line for structure analysis in civil engineering

SNPIT & RC,
UMRAKH
Guided :- Vishal Patel
Subject:- Structural Analysis 2
Topic:- Influence Line For Determinant Beam
Mrunali Mehta 130490106064
Prepared by…

Analysis of Forces due to DEAD LOADS
DETERMINATE STRUCTURES
• Axial Force Elements - Trusses
• Compute element Forces
• Flexural Elements - Beams and Frames
• Shear and Moment Diagrams

LIVE LOADS
Common Structures
Bridges
Industrial Crane Rails
Conveyors
Floor Girders
any other structure where
loads move across its span

ANALYSIS OF FORCES DUE TO
LIVE LOADS
LIVE or MOVING LOADS
• Variable point of Application
• Temporary Loads
Shear Diagrams
P P
V1 V2
21 VV 

Definition of Influence Lines
INFLUENCE LINES
Variation of Reaction, Shear, Moment or Deflection
at a SPECIFIC POINT
due to a concentrated force moving on member

6
MOVING CONCENTRATED LOAD
Variation of Reactions RA and RB as functions of
load position
MA =0
(RB)(10) – (1)(x) = 0
RB = x/10
RA = 1-RB
= 1-x/10
x
1
A B
C
10 ft
3 ft
x
1
A B
C
RA=1-x/10 RB = x/10
x
A
C
RA=1-x/10 RB = x/10

7
RA occurs only at A; RB occurs only at B
Influence line
for RB
1-x/10
1
Influence
line for RA
x 10-x
x 10-x
x/10 1.0

8
Variation of Shear Force at C as a function of
load position
0 < x < 3 ft (unit load to the left of C)
Shear force at C is –ve, VC =-x/10
C
x 1.0
RA = 1-x/10 RB = x/10
3 ft
10 ft
A B
x/10
C

9
3 < x < 10 ft (unit load to the right of C)
Shear force at C is +ve = 1-x/10
Influence line for shear at C
C
x
3 ft
A
RA = 1-x/10 RB = x/10
B
C
1
1
-ve
+ve
0.3
0.7
RA = 1-x/10

INFLUENCE LINES FOR FLOOR GIRDERS :
Draw the Influence Lines for: (a) Shear in panel CD
of the girder; and (b) the moment at E.
11
A C D E
F
B
B´A´ D´C´ E´ F´
x
5 spaces @ 10´ each = 50 ft

12
A´ B´ C´ D´ E´ F´
x 1.0
0.2
0.4
0.4
0.2
2.0
4.0
6.0 8.0
I. L. for VCD
I. L. for ME
-ve
+ve
+ve

13
MAXIMUM SHEAR FORCE AND BENDING MOMENT
UNDER A SERIES OF CONCENTRATED LOADS
Taking moment about A,
RE  L = PR [L/2 - )]( xx 
)2/( xxL
L
P
R R
E 
a1 a2 a3
x
PR= resultant load
a1 a2 a3
x
PR= resultant load
C.L.
x
L/2
L
RE
A
B C D
E
P1
P2 P3 P4
P1 P2
P3 P4
RA

14
Taking moment about E,
2
2
02.,.
])2/()2/[(
)1)(2/()2/(0
0
)()()2/)(2/(
)()2/(
)2/(
)](2/[
22211
22211
x
x
xx
xxei
xLxxL
L
P
xL
L
P
xxL
L
P
dx
dM
aPaaPxLxxL
L
P
aPaaPxLRM
xxL
L
P
R
xxLPLR
R
RR
D
R
AD
R
A
RA










The centerline must divide the distance between the resultant of
all the loads in the moving series of loads and the load considered
under which maximum bending moment occurs.

Influence line for structure analysis in civil engineering

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Influence line for structure analysis in civil engineering