Past Year Questions: Influence Line Diagram & Rolling Loads

# Past Year Questions: Influence Line Diagram & Rolling Loads | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) PDF Download

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]

Solution:

ILD for VB

Max. shear
= 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

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:

ILD for BM at C

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]

Solution:

Method-1 (By ILD)
C.G. of system = 2.5 m from any load
For maximum bending moment, system of load should be,

Maximum BM will occur below load at C. Ordinate of ILD at C

Ordinate of ILD at D

Maximum BM = 5.935 x 3 + 3.695 x 3
= 28.89 kN-m
Maximum bending stress,

Method-II  (By Statics)
Let the section at which absolute max. BM ocurs be at x distance from left support.

Max. BM at section

For absolute max. BM,

⇒ x = 10.75 m
Absolute max BM

Absolute max bending stress

AVOID MISTAK
(I)

Max. bending stress

(II)

Max. bending stress

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]

(a) P
(b) Q
(c) R
(d) S
Ans.
(A)
Solution:

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]

(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.

If moving distributed load is present over span PR then we get maximum shear force just to the right of Q.

The document Past Year Questions: Influence Line Diagram & Rolling Loads | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Topic wise GATE Past Year Papers for Civil Engineering.
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## FAQs on Past Year Questions: Influence Line Diagram & Rolling Loads - Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

 1. What is an influence line diagram in civil engineering?
Ans. An influence line diagram is a graphical representation used in civil engineering to determine the effect of a moving load on a structure, such as a beam or a bridge. It shows the variation of a specific response, such as shear force or bending moment, at different points along the structure as the load moves. The diagram helps engineers analyze and design structures to ensure their safety and efficiency.
 2. How is an influence line diagram constructed?
Ans. To construct an influence line diagram, one must consider the position of the moving load and the response being analyzed. The load is placed at different positions along the structure, and the corresponding effect on the response is determined. By plotting these effects at various positions, a line diagram is formed, representing the influence of the load on the response. The diagram can be further analyzed to determine the maximum and minimum values of the response and their locations.
 3. What are the applications of influence line diagrams in civil engineering?
Ans. Influence line diagrams have various applications in civil engineering. They are used to determine the maximum and minimum values of forces and moments in structures, such as beams and bridges, due to moving loads. This information is crucial for designing and assessing the structural integrity and safety of these elements. Influence line diagrams also aid in optimizing the design of structures, as they provide engineers with a visual representation of load effects, allowing for efficient load distribution and material usage.
 4. How are rolling loads considered in influence line diagrams?
Ans. Rolling loads, such as those caused by trains or vehicles, are considered in influence line diagrams by analyzing the effect of the load as it moves along the structure. The position of the load is systematically varied, and the resulting effect on the response, such as shear force or bending moment, is determined at each position. By plotting these effects, engineers can obtain the influence line diagram, which represents the response to rolling loads at different points along the structure.
 5. Can influence line diagrams be used for structures other than beams and bridges?
Ans. Yes, influence line diagrams can be used for structures other than beams and bridges. While they are most commonly used for these types of structures, the concept of influence lines can be applied to other elements as well, such as columns or trusses. The analysis and design principles behind influence line diagrams remain the same, with the diagram representing the effect of a moving load at different positions along the structure. However, the specific response being analyzed may differ depending on the type of structure.

## Topic wise GATE Past Year Papers for Civil Engineering

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