Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev

Topic wise GATE Past Year Papers for Civil Engineering

Civil Engineering (CE) : Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev

The document Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Topic wise GATE Past Year Papers for Civil Engineering.
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Q.1 A long uniformly distributed load of 10 kN/m and a concentrated load of 60 kN are moving together on the beam ABCD shows in the figure (not drawn to scale). The relative positions of the two loads are not fixed. The maximum shear force (in kN, round off to the nearest integer) caused at the internal hinge B due to the two loads is______    [2019 : 2 Marks, Set-I I]
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Solution:

ILD for VB
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Max. shear Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
= 70KN
Note: The maximum shear force at hinge B may be +70 kN or -70 kN. So, student can challenge this questions.

Q.2 Consider the beam ABCD shown in the figure
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
For a moving concentrated load of 50 kN on the beam, the magnitude of the maximum bending moment (in kN-m) obtained at the support C will be equal to _________ .    [2017 : 2 Marks, Set-I]
Solution:

Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
ILD for BM at C
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Max. BM occurs at C, when 50 kN load is at B.
Max. BM at C = 50 x (-4) = -200 kNm

Q.3 A simply supported beam AB of span, L = 24 m is subjected to two wheel loads acting at a distance, d = 5 m apart as shown in the figure below. Each wheel transmits a load, P = 3 kN and may occupy any position along the beam. If the beam is an I-section having section modulus, S=16.2 cm3, the maximum bending stress (in GPa) due to the wheel loads is _________ .    [2015 : 2 Marks, Set-II]
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Solution:
 
Method-1 (By ILD)
C.G. of system = 2.5 m from any load
For maximum bending moment, system of load should be,
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev

Maximum BM will occur below load at C. Ordinate of ILD at C
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Ordinate of ILD at D
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Maximum BM = 5.935 x 3 + 3.695 x 3
= 28.89 kN-m
Maximum bending stress,
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Method-II  (By Statics)
Let the section at which absolute max. BM ocurs be at x distance from left support.
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Max. BM at section
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
For absolute max. BM,
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
⇒ x = 10.75 m
Absolute max BM
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Absolute max bending stress
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
AVOID MISTAK
(I)
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Max. bending stress
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
(II)
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Max. bending stress
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
This is the maximum bending stress at mid= span and not the absolute max. bending stress in the beam.

Q.4 In a beam of length L, four possible influence line diagrams for shear force at a section located at a distance of L/4  from the left end support (marked as P, Q, R and S) are shown below. The correct influence line diagram is    [2014 : 1 Mark, Set-I]
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
(a) P
(b) Q
(c) R
(d) S
Ans.
(A)
Solution:
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev

Q.5 Beam PQRS has internal hinges in spans in spans PQ and RS as shown. The beam may be subjected to a moving distributed vertical load of maximum intensity 4 kN/m of any length anywhere on the beam. The maximum absolute value of the shear force (in kN) that can occur due to this loading just to the right of support Q shall be   [2013 : 2 Marks]
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev 
(a) 30 kN
(b) 40 kN
(c) 45 kN
(d) 55 kN
Ans.
(C)
Solution:
Drawing the ILD of shear force just to right of Q by using Muller Breslau’s principle. A cut is made just to the right of Q, since cut is very close to support Q, therefore displacement of left portion is almost zero and that to the right portion will be 1.
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev
If moving distributed load is present over span PR then we get maximum shear force just to the right of Q.
Influence Line Diagram and Rolling Loads Civil Engineering (CE) Notes | EduRev 

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