# Influence Line Diagram and Rolling Loads

 Question 1
Muller-Breslau principle is used in analysis of structures for
 A drawing an influence line diagram for any force response in the structure B writing the virtual work expression to get the equilibrium equation C superposing the load effects to get the total force response in the structure D relating the deflection between two points in a member with the curvature diagram inbetween
GATE CE 2023 SET-2   Structural Analysis
Question 1 Explanation:
Muller Breslass principle is used to draw influence line diagram for determinate and indeterminate structures. It states that influence line for any stress function may be obtained by removing the restraint offered by that function and introducing a directly related generalised unit displacement at that location in the direction of the stress function.
 Question 2
Consider a simply supported beam PQ as shown in the figure. A truck having 100 kN on the front axle and 200 kN on the rear axle, moves from left to right. The spacing between the axles is 3 m. The maximum bending moment at point R is ______ kNm. (in integer) A 124 B 180 C 147 D 582
GATE CE 2022 SET-1   Structural Analysis
Question 2 Explanation: $\frac{ab}{L}=\frac{1 \times 4}{5}=0.8m$
To get maximum BN at R
\begin{aligned} BM_{max}&=200 \times \frac{ab}{L}+100 \times y\\ \frac{ab/l}{b}&=\frac{y}{4-3}\Rightarrow \frac{0.8}{4}=\frac{y}{1}=0.2m\\ BM_{max}&=200 \times 0.8+100 \times 0.2=180kNm \end{aligned}

 Question 3
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 3 Explanation: As per Muller Breslau principle ILD for stress function (shear $-V_{G}$) will be a combination of curves ($3^{\circ}$ curves).
 Question 4
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 4 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 5
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 5 Explanation:
ILD for $V_B$ Maximum shear $V_B=-\left [ \left ( \frac{1}{2}\times 2 \times 1 \times 10 \right )+(60 \times 1) \right ]=-70kN$

There are 5 questions to complete.