# Influence Line Diagram and Rolling Loads

 Question 1
A propped cantilever beam EF is subjected to a unit moving load as shown in the figure (not to scale). The sign convention for positive shear force at the left and right sides of any section is also shown.

The CORRECT qualitative nature of the influence line diagram for shear force at G is
 A B C D
GATE CE 2021 SET-1   Structural Analysis
Question 1 Explanation:

As per Muller Breslau principle ILD for stress function (shear $-V_{G}$) will be a combination of curves ($3^{\circ}$ curves).
 Question 2
Distributed load(s) of 50 kN/m may occupy any position(s) (either continuously or in patches) on the girder PQRST as shown in the figure
The maximum negative (hogging) bending moment (in kNm) that occurs at point R, is
 A 22.5 B 56.25 C 93.75 D 150
GATE CE 2020 SET-1   Structural Analysis
Question 2 Explanation:

ILD for BM at R:
To get maximum hogging BM at R, keep UDL over PQ and ST.
Max. -ve BM at R $=50\left [ -\frac{1}{2} \times 1.5 \times 0.6 \right ] +50 \left [ -\frac{1}{2} \times 1.5 \times 0.9 \right ]$
=56.25 kNm
 Question 3
A long uniformly distributed load of 10 kN/m and a concentrated load of 60 kN are moving together on the beam ABCD shown in the figure. 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 _____
 A 50 B 70 C 90 D 120
GATE CE 2019 SET-2   Structural Analysis
Question 3 Explanation:
ILD for $V_B$

Maximum shear $V_B=-\left [ \left ( \frac{1}{2}\times 2 \times 1 \times 10 \right )+(60 \times 1) \right ]=-70kN$
 Question 4
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 _____
 A 200 B 155 C 250 D 450
GATE CE 2017 SET-1   Structural Analysis
Question 4 Explanation:
$\text { B.M. at } C=50 \times 4=200 \mathrm{kNm}$

ILD for BM at C

 Question 5
A simply supported beam AB of span, L=24 m is subjected to two wheel loads acting at a distance, d=5m 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 $cm^{3}$, the maximum bending stress (in GPa) due to the wheel loads is ___________.
 A 1.78 B 1.24 C 2.21 D 0.81
GATE CE 2015 SET-2   Structural Analysis
Question 5 Explanation:
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
\begin{aligned} &=\frac{(12-1.25) \times(12+1.25)}{24} \\ &=5.935 \end{aligned}
Ordinate of LLD at D
\begin{aligned} &=\frac{5.935 \times 8.25}{13.25}=3.695 \\ \text { Maximum } \mathrm{BM} &=5.935 \times 3+3.695 \times 3 \\ &=28.89 \mathrm{kN}-\mathrm{m} \end{aligned}
Maximum bending stress,
\begin{aligned} \frac{M}{Z}&=\frac{28.89 \times 10^{3}}{16.2 \times 10^{-6} \times 10^{9}}\\ &=1.783 \mathrm{GPa} \end{aligned}
 Question 6
In a beam of length L, four possible influence line diagrams for shear force at a section located at a distance of $\frac{L}{4}$ from the left end support (marked as P, Q, R and S) are shown below. The correct influence line diagram is
 A P B Q C R D S
GATE CE 2014 SET-1   Structural Analysis
Question 6 Explanation:

ILD for SF at X-X
 Question 7
Beam PQRS has internal hinges in spans PQ and RS as shown. The beammay be subjected to a moving distributed vertical load of maximum intensity 4 kN/m of any length anywhere on the beam. The maximum absoulate value of the shear force that can occur due to this loading just to the right of support Q shall be:
 A 30 B 40 C 45 D 55
GATE CE 2013   Structural Analysis
Question 7 Explanation:
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 0, 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.

Vertical reaction at P and Q equal to 0
$\Sigma M_{0}=0$
\begin{aligned} \Rightarrow \quad 1 \times 4&=R_{R} \times 20 \\ \therefore \quad R_{A}&=0.25 \mathrm{kN} \\ V_{O \text { (Righit) }}&=0.25 \mathrm{kN}\\ \end{aligned}
Now, if moving distributed load is present over span P R then we get maximum shear force just to the right of Q .
$\Rightarrow \mathrm{SF}=\left[\left(\frac{1}{2} \times 0.25 \times 10\right)+\left(\frac{1}{2} \times 1 \times 20\right)\right] \times 4$
$\mathrm{SF}=45 \mathrm{kN}$
 Question 8
The span(s) to be loaded uniformly for maximum positive (upward) reaction at support P, as shown in the figure below, is (are)
 A PQ Only B PQ and QR C QR and RS D PQ and RS
GATE CE 2008   Structural Analysis
Question 8 Explanation:
With the help of Muller Breslau principle, we can 1 unit draw the ILD for reaction at P

The reaction is positive between P and Q and R and S respectively. Hence?the spans PQ and RS should be loaded uniformly for maximum positive reaction at P.
 Question 9
The influence line diagram (ILD) shown is for the member
 A PS B RS C PQ D QS
GATE CE 2007   Structural Analysis
Question 9 Explanation:

Note: Diagonal member subjected to reversal of stresses.
 Question 10
Consider the beam ABCD and the influence line as shown below. The influence line pertains to
 A reaction at A, $R_{A}$ B shear force at B, $V_{B}$ C shear force on the left of C, $V_{C}^{-}$ D shear force on the right of C, $V_{C}^{+}$
GATE CE 2006   Structural Analysis
Question 10 Explanation:

There are 10 questions to complete.