influence line for structure analysis in civil engineering
TRANSCRIPT
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SNPIT & RC,UMRAKH
Guided :- Vishal Patel
Subject:- Structural Analysis 2
Topic:- Influence Line For Determinant Beam
Mrunali Mehta 130490106064Prepared by…
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Analysis of Forces due to DEAD LOADSDETERMINATE STRUCTURES
• Axial Force Elements - Trusses• Compute element Forces
• Flexural Elements - Beams and Frames• Shear and Moment Diagrams
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LIVE LOADS
Common StructuresBridgesIndustrial Crane RailsConveyorsFloor Girdersany other structure where loads move across its span
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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
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Definition of Influence Lines
INFLUENCE LINESVariation of Reaction, Shear, Moment or Deflectionat a SPECIFIC POINTdue to a concentrated force moving on member
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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
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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
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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
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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
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Example-2
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INFLUENCE LINES FOR FLOOR GIRDERS :
Draw the Influence Lines for: (a) Shear in panel CD of the girder; and (b) the moment at E.
A C D E FB
B´A´ D´C´ E´ F´x
5 spaces @ 10´ each = 50 ft
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A´ B´ C´ D´ E´ F´
x 1.0
0.2 0.4
0.40.2
2.0 4.0 6.0 8.0
I. L. for VCD
I. L. for ME
-ve+ve
+ve
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MAXIMUM SHEAR FORCE AND BENDING MOMENT UNDER A SERIES OF CONCENTRATED LOADS
Taking moment about A,RE L = PR [L/2 - )]( xx
)2/( xxLLP
R RE
a1 a2 a3
xPR= resultant load
a1 a2 a3x
PR= resultant load
C.L.
xL/2L RE
AB C D
E
P1P2 P3 P4
P1 P2P3 P4
RA
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Taking moment about E,
2
202.,.
])2/()2/[(
)1)(2/()2/(0
0
)()()2/)(2/(
)()2/(
)2/(
)](2/[
22211
22211
xx
xxxxei
xLxxLLP
xLLPxxL
LP
dxdM
aPaaPxLxxLLP
aPaaPxLRM
xxLLPR
xxLPLR
R
RR
D
R
AD
RA
RA
The centerline must divide the distance between the resultant ofall the loads in the moving series of loads and the load consideredunder which maximum bending moment occurs.
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THANK YOU